*15141
mm-1050
>> Im trying to find a series where the sum of 
a subset of
that
>> is unique. Or in other words, I can find the numbers from
sum.
>>
>> An example would be f(n)=2^n, you add any number of
elements
>> in this set, youll get a number with all those bits set.
>> But Im looking for a series that does not grow
geometrically..
>I was looking for a series which consists of positive
integers
>which has this property.
> This has already been answered. Since the 2^n series is the
Ômost
efficient
> such series, all other series must grow faster.
Not true. See below.
>Is it helpful if the size of the subset is known?
>For example, the sum of random 10 elements of a series is
given,
>is it possible to get the individual elements(I mean is there
>such a series of positive integers other that 2^n and 
doesnt
>grow exponentially)?
> I believe this doesnt really change the outcome. All
size-10 subsets
must
> produce a unique sum implies (with handwave) that all
subsets must produce
a
> unique sum, so your sequence is going to grow exponentially.
I dont think I believe this. Its anyway not 
true that if
all size-2
subsets produce a unique sum then all subsets produce a
unique sum,
and its not clear to me why size-10 should differ from
size-2 in this
regard.
Theres a lot of literature on these problems. A good
starting place
is Guys Unsolved Problems in Number Theory. The 3rd edition
is out,
but I dont have it yet. In the 2nd edition, C9 concerns m,
the maximum
number of integers between 1 and n inclusive with all sums of
pairs
distinct. The conjecture is that m - sqrt n is bounded. C11
concerns
the requirement that sums of h terms all be distinct for some
given h.
C8 asks about the maximum number of positive integers not
exceeding
2^k with all subset sums distinct. Conway & Guy conjecture
its
k + 2 - notice that this is better than the k + 1 you get by
taking
powers of 2. An example that achieves k + 2 is given.
C5 says you can reconstruct a set of N numbers from the set
of sums of
pairs provided N is not a power of 2. Sums of size 3
determine the set
except perhaps when N = 27 or 486. Sums of larger size have
also been
considered.
--
Gerry Myerson (gerry@maths.mq.edi.ai) (i -> u for email)
===
Subject: Re: Finding unique sums.
> C8 asks about the maximum number of positive integers not
exceeding
> 2^k with all subset sums distinct. Conway & Guy conjecture
its
> k + 2 - notice that this is better than the k + 1 you get
by taking
> powers of 2. An example that achieves k + 2 is given.
I too was convinced that you couldnt do better than powers
of 2, and
Id be very interested to see that example. For those of us
who dont
have the book, is the example simple enough for you to
reproduce here?
(Im not asking you to type in ten pages of text!)
===
Subject: Re: Finding unique sums.
> C8 asks about the maximum number of positive integers not
exceeding
> 2^k with all subset sums distinct. Conway & Guy conjecture
its
> k + 2 - notice that this is better than the k + 1 you get
by taking
> powers of 2. An example that achieves k + 2 is given.
I too was convinced that you couldnt do better than powers
of 2, and
> Id be very interested to see that example. For those of 
us
who dont
> have the book, is the example simple enough for you to
reproduce here?
> (Im not asking you to type in ten pages of text!)
Here are some reviews from Math Reviews, you can probably
extract
the information you want (and more!) from them, especially if
TeX
doesnt bother you.
MR0917837 (89a:11019)
Lunnon, W. F.(4-WALC)
Integer sets with distinct subset-sums.
Math. Comp. 50 (1988), no. 181, 297--320.
11B13 (94A60)
The set of integers $p_i=2^{i-1}$, $i=1,2,cdots,n$, has the
interesting property that all of its distinct subsets have
distinct
sums. Let us call this property SSD. The question is whether
there are
sets $overline{p}={p_0=0<p_1=1<p_2cdots<p_n}$ such that
$p_n<2^{n-1}$ that have the SSD property. Denote by $[alpha]$
the
greatest integer not exceeding $alpha$. Take the sequence
$overline{v}={v_0=0<v_1=1<v_2<v_3cdots<v_ncdots}$ such that
$v_{n+1}=2v_n-v_{n-m}$ for $nge1$, where $m=[tfrac12 n+1]$
(this
sequence is called by the author the Atkinson-Negro-Santoro
sequence).
In the paper it is proved that the sequence
$overline{p}={p_i}$,
where $p_i=v_n-v_{n-i}$, $i=1,2,cdots,n$, has the SSD
property for all
$n$. Another sequence (the Conway-Guy sequence) $overline{u}=
{u_0=0<u_1=1<u_2<cdots}$ is defined by $u_{n+1}=2u_n-u_{n-m}$,
where
$m=[tfrac12+sqrt{2n}]$. It is conjectured that the set
$overline{p}={p_i}$, $p_i=u_n-u_{n-i}$, $i=1,2,cdots,n$, is
also SSD
for all $n$. The author investigates this conjecture. The
sequence
$overline{w}={w_0=0<w_1=1<w_2<cdots<w_n}$ is said to be SSDO
if all
distinct subsets of the same cardinality have distinct sums
(a weakening
of SSD). The author proves that, for some fixed $n$, if
$overline{u}$
is SSDO, then $p_i=u_n-u_{n-i}$ is SSD. It is not known
whether
$overline{u}$ is SSDO for all $n$. It is proved in the paper
that the
set ${u_0,u_1,cdots,u_{n-1},x}$ is not SSDO if $x<u_n$.
Starting from
this property, the author introduces the generalized
Conway-Guy sequence
as follows: Given $w_0<w_1<cdots<w_{n-1}$, let $w_n$ be equal
to the
smallest natural number which cannot be written in the form
$sum_{iin
I} w_i-sum_{jin J}w_j$, where $I,Jsubset(1,cdots,n-1)$, $Icap
J
=varnothing$ and $|I|-|J|=1$ $(|.87|$ means the cardinality of
the
set).
Setting $w_0=0$, this sequence is SSDO and is for $n<80$
identical to
$overline{u}$. The author defines other such sequences
$overline{w}$
where $w_0ne0$ and investigates whether these are SSDO for
all $n$.
The paper contains many other results about the above
question; among
other things some algorithms are proposed to verify the SSD
property.
One of the algorithms gives that $overline{u}$ is SSDO, and
hence
$overline{p}$ defined by it is SSD if $n<80$. In the paper two
interesting tables of concrete values can be found and
$lim_{nrightarrowinfty}z_n/2^{n-1}$ is also computed for
$overline{z}=overline{v}$, $overline{u}$ or $overline{w}$.
Reviewed by B.8ela Uhrin
Borwein, Peter(3-SFR-MS); Mossinghoff, Michael J.(1-UCLA)
Newman polynomials with prescribed vanishing and integer sets
with
distinct subset sums. (English. English summary)
11C08 (11B75 11Y55)
Let $d(m)$ be the minimal degree of a polynomial that has all
coefficients in ${0,1}$ and a zero of multiplicity $m$ at
$-1$. A
greedy solution can be defined as follows. Let $J_1=1$ and
$J_k$ be the
least odd integer greater than $J_1+dots+J_{k-1} (k>1)$. It
is easy to
see that the polynomial $g_m(x)=prod_{k=1}^m(1+z^{J_k})$ has
the
above-defined properties and that $$deg
g_m=frac43.872^m-frac32+frac{(-1)^m}6.$$ Therefore,
$$d(m)lefrac43.872^m-frac32+frac{(-1)^m}6.$$ The authors show
that the
equality holds if and only if $mle5$. In the general case,
they prove
that $$2^m+c_1mle d(m)le frac{103}{96}.872^m+c_2$$ and they
conjecture
that for any $epsilon>0$ the inequality $d(m)<(1+epsilon)2^m$
holds
for sufficiently large $m$. Also, they consider the related
problem of
finding a set of $m$ positive integers with distinct subset
sums and
minimal largest element and show that the well-known
Conway--Guy
sequence yields the optimal solution for $mle9$.
Reviewed by Sergeui V. Konyagin
MR1486396 (98k:11014)
Bohman, Tom(1-MIT)
A construction for sets of integers with distinct subset sums.
(English. English summary)
Electron. J. Combin. 5 (1998), Research Paper 3, 14 pp.
(electronic).
11B75 (05D10)
A finite set $S$ of positive integers has distinct subset sums
if the
$2sp{|S|}$ sums $sumsb{ain A}a$, where $Asubseteq S$, are
pairwise
distinct. For brevity, call sets with distinct subset sums
DSS-sets. The
paper investigates the following questions: How small can a
positive
integer $N$ be such that ${1,2,cdots,N}$ contains an
$n$-element
DSS-set?
For every $n$ let $f(n)$ be the smallest $N$ with this
property. In
different terms: $f(n) = min max_S N$, where the minimum is
taken over
all $n$-element DSS-sets. Obviously, $f(n)le 2sp {n-1}$ (take
$S={1,2,4,cdots,2sp{n-1}})$. Erd.9as conjectured that $f(n)gg
2sp n$
(the implicit constant is absolute). Together with Moser he
proved in
1955 a weaker inequality $f(n)ge 2sp n /(4sqrt n)$, which
remains, up
to the constant, the best known lower bound for $f(n)$.
In the opposite direction, J. H. Conway and R. K. Guy
ref[Notices
Amer. Math. Soc. 15 (1968), no. 2, 345, Abstract 654-32]
constructed
short DSS-sets, using a special sequence of integers they
discovered
(the Conway-Guy sequence). Their result implied an estimate
$f(n) le
0.23513.872sp n$ for $nge 40$. W. F. Lunnon ref[Math. Comp. 50
(1988),
no. 181, 297--320; MR0917837 (89a:11019)] suggested a similar
construction, which implied $f(n) le 0.22096 .872sp n$ for $nge
67$.
In his paper Bohman presents two parametric families of
infinite
sequences, which include, for small values of parameters, the
sequences
of Conway-Guy and Lunnon. Using his sequences, he finds many
new
examples of DSS-sets, and, in particular, obtains a new upper
estimate
$f(n) le 0.22002 .872sp n$ for sufficiently large $n$. 
Bohmans
construction is very subtle and interesting and is likely to
find
different applications in combinatorics, cryptography, and
related
fields.
Reviewed by Yuri Bilu
MR1464377 (98i:11012)
Maltby, Roy(3-CALG)
Bigger and better subset-sum-distinct sets. (English. English
summary)
Mathematika 44 (1997), no. 1, 56--60.
11B75
A set of natural numbers is called subset-sum-distinct (SSD)
if all
pairwise distinct subsets have unequal sums. If $A$ is any
SSD set,
define $alpha(A)=(max A)/2^{|A|-1}$, where $max A$ is the
biggest
element of $A$. Given an SSD set, it is shown how to
construct a bigger
SSD set whose $alpha$-ratio is smaller. This shows that
$inf{alpha(A)colon A$ is an SSD set}is not realised by any SSD
set.
(Erd.9as asked if the inf is positive.) The author also
points out that
one of the claims of W. F. Lunnon ref[Math. Comp. 50 (1988),
no. 181,
297--320; MR0917837 (89a:11019)] concerning SSD sets is false.
Reviewed by Ian Anderson
MR1363448 (97b:11027)
Bohman, Tom(1-RTG)
A sum packing problem of Erd.9as and the Conway-Guy sequence.
(English.
English summary)
Proc. Amer. Math. Soc. 124 (1996), no. 12, 3627--3636.
11B75
A set $A$ of positive integers has distinct subset sums if
the set
${sum_{xin X}xcolon Xsubseteq A}$ has $2^{|A|}$ distinct
elements.
J. H. Conway and R. K. Guy ref[Notices Amer. Math. Soc. 15
(1968),
345] defined a sequence, ${A_k}$, of sets of integers as
follows: (1)
let $u_0=0, u_1=1$, and, for $ngeq1, u_{n+1}=2u_n-u_{n-r}$,
where $r$
is the closest integer to $sqrt{2n}$; (2) for each $kgeq1$,
define
$A_k={u(k+1)-u(i)colon1leq ileq k}$. They conjectured that for
every $k, A_k$ has distinct subset sums, and they showed this
to be true
for $1leq kleq40$. W. F. Lunnon ref[Math. Comp. 50 (1988),
no. 181,
297--320; MR0917837 (89a:11019)] extended this to all
$kleq80$. In
this paper the author establishes the conjecture of Conway
and Guy for
all $k$. Define $f(n)=min{max_{sin S}scolon|S|=n$ and $S$ has
distinct subset sums}. The Conway-Guy sequence mentioned
above gives
rise to $2^{n-2}$ as an upper bound on $f(n)$. This bound was
improved
by Lunnon to $0.2246(2^n)$. In this paper, the author
presents a
modification of the Conway-Guy sequence, and states that this
leads to a
slight improvement over Lunnons bound, namely
$0.22002(2^n)$. The
author does not include a proof of this statement here, but
plans to
include it in a later paper.
Reviewed by Bruce Landman
--
Gerry Myerson (gerry@maths.mq.edi.ai) (i -> u for email)
===
Subject: Re: Finding unique sums.
matt a .8ecrit :
>> C8 asks about the maximum number of positive integers not
exceeding
>> 2^k with all subset sums distinct. Conway & Guy conjecture
its
>> k + 2 - notice that this is better than the k + 1 you get
by taking
>> powers of 2. An example that achieves k + 2 is given.
> I too was convinced that you couldnt do better than 
powers
of 2, and
> Id be very interested to see that example. For those of 
us
who dont
> have the book, is the example simple enough for you to
reproduce here?
> (Im not asking you to type in ten pages of text!)
Cest un forum en fran.8dais, respectez la charte !
--
Denis L.8eger
===
Subject: Re: Finding unique sums.
> matt a .8ecrit :
>> C8 asks about the maximum number of positive integers not
exceeding
>> 2^k with all subset sums distinct. Conway & Guy conjecture
its
>> k + 2 - notice that this is better than the k + 1 you get
by taking
>> powers of 2. An example that achieves k + 2 is given.
I too was convinced that you couldnt do better than powers
of 2, and
> Id be very interested to see that example. For those of 
us
who dont
> have the book, is the example simple enough for you to
reproduce here?
> (Im not asking you to type in ten pages of text!)
> Cest un forum en fran.8dais, respectez la charte !
Please accept my apologies. I didnt notice that this was
being posted
to a French-language group.
===
Subject: Re: Finding unique sums.
> Cest un forum en fran.8dais, respectez la charte !
> Please accept my apologies. I didnt notice that this was
being posted
> to a French-language group.
Dont worry Matt, some of us enjoy a little international
ßavour on
the French group :-) The bullies wont have their ways...
===
Subject: Re: Finding unique sums.
Vous avez aussi poste ce message a des forums anglais, donc
vous
navez pas respecte leurs chartes.
-ilan
> matt a .8ecrit :
>> C8 asks about the maximum number of positive integers not
exceeding
>> 2^k with all subset sums distinct. Conway & Guy conjecture
its
>> k + 2 - notice that this is better than the k + 1 you get
by taking
>> powers of 2. An example that achieves k + 2 is given.
I too was convinced that you couldnt do better than powers
of 2, and
> Id be very interested to see that example. For those of 
us
who dont
> have the book, is the example simple enough for you to
reproduce here?
> (Im not asking you to type in ten pages of text!)
> Cest un forum en fran.8dais, respectez la charte !
===
Subject: Re: Finding unique sums.
> How about the sequence
> 0.4142135623730950488016887242...
> 0.8284271247461900976033774484...
> 0.6568542494923801952067548968...
> 0.3137084989847603904135097936...
> 0.6274169979695207808270195873...
> 0.2548339959390415616540391747...
> 0.5096679918780831233080783494...
> ....
> (Puzzle - is the sequence dense in [0,1]? (The sequence is
2^(n + 1/2)
mod
> 1).)
Puzzle, or open problem?
Think of the sequence as the fractional part of 2^n sqrt2,
and youll
see it depends on the binary expansion of sqrt2. I dont
think enough
is known about the binary expansion of sqrt2 to answer the
question.
--
Gerry Myerson (gerry@maths.mq.edi.ai) (i -> u for email)
===
Subject: Re: Finding unique sums.
>> How about the sequence
>> 0.4142135623730950488016887242...
>> 0.8284271247461900976033774484...
>> 0.6568542494923801952067548968...
>> 0.3137084989847603904135097936...
>> 0.6274169979695207808270195873...
>> 0.2548339959390415616540391747...
>> 0.5096679918780831233080783494...
>> ....
>> (Puzzle - is the sequence dense in [0,1]? (The sequence is
2^(n + 1/2)
mod
>> 1).)
>Puzzle, or open problem?
>Think of the sequence as the fractional part of 2^n sqrt2,
and youll
>see it depends on the binary expansion of sqrt2. I dont
think enough
>is known about the binary expansion of sqrt2 to answer the
question.
Its equivalent to the question of whether every 
finite string
of 0s and
1s occurs in the binary expansion of sqrt(2). This is 
indeed
open
(although I would bet that the answer is yes).
Robert Israel israel@math.ubc.ca
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia Vancouver, BC, Canada
===
Subject: Re: Finding unique sums.
> How about the sequence
> 0.4142135623730950488016887242...
> 0.8284271247461900976033774484...
> 0.6568542494923801952067548968...
> 0.3137084989847603904135097936...
> 0.6274169979695207808270195873...
> 0.2548339959390415616540391747...
> 0.5096679918780831233080783494...
> ....
> (Puzzle - is the sequence dense in [0,1]? (The sequence is
2^(n + 1/2)
mod
> 1).)
> Puzzle, or open problem?
> Think of the sequence as the fractional part of 2^n sqrt2,
and youll
> see it depends on the binary expansion of sqrt2. I dont
think enough
> is known about the binary expansion of sqrt2 to answer the
question.
Well I dont know the answer myself, so I suppose I should
have said open
problem...
> --
> Gerry Myerson (gerry@maths.mq.edi.ai) (i -> u for email)
===
Subject: Courants Introduction to Calculus and Analysis I
solutions to
exercises
Im reading the R.Courant/F.John book Introduction to
Calculus and
Analysis I as a primer on real analysis. The preface (written
in
1965) alludes to a solutions pamphlet for the problem sets,
but I have
not been able to locate any solutions. As Im using this for
self-study, the solutions would be nice to have to check
against.
Does anyone have any information as to how I could obtain
solutions to
these problem sets?
Michael
===
Subject: Re: Courants Introduction to Calculus and Analysis
I solutions
to exercises
> Im reading the R.Courant/F.John book Introduction to
Calculus and
> Analysis I as a primer on real analysis. The preface
(written in
> 1965) alludes to a solutions pamphlet for the problem sets,
but I have
> not been able to locate any solutions. As Im using this 
for
> self-study, the solutions would be nice to have to check
against.
> Does anyone have any information as to how I could obtain
solutions to
> these problem sets?
> Michael
Most often, solutions manuals are only available to faculty.
David Ames
===
Subject: Re: Courants Introduction to Calculus and Analysis
I solutions
to exercises
posting-account=jcZk7AwAAADXpPEyHtVyWC264SxtppRB
I was speaking as a faculty member (and receiver of free
trial books,
esp. from
Freeman--do they still do that?).
Have you seen one for this book?
I never did, and I taught a math physics course.
Van
===
Subject: Re: Courants Introduction to Calculus and Analysis
I solutions
to exercises
posting-account=jcZk7AwAAADXpPEyHtVyWC264SxtppRB
I have this book, and have never seen a soln. book.
Certainly not on the net. As I recall, most his stuff
is examples worked out in the text.
Van
===
Subject: Re: When a genius commits murder (Hawking & Witten
composite on
Law
& Order CI)
> When a genius commits murder, how do you outsmart him?
9/8pm Sunday,
> November 21st
> http://www.nbc.com/Law_&_Order:_Criminal_Intent/index.html
> I just happened to catch this. Its a composite of Ed
Witten and Stephen
> Hawking as a murderer - motive to cover up the failure of
his theory.
> The actor is in Hawkings wheelchair with two wives - the
one accused of
> abusing him as in the recent Cambridge ßap (shes 
innocent
in the TV
> show) - I actually sat next to her and Hawking at GR 17 in
Dublin in the
> hotel as she was feeding him. The theory is more like Ed
Wittens i.e.
> 11 dimensions and the guy is an American not a Brit in the
TV story.
> Bizarre.
I didnt see it, but let me guess: in addition to being an
expert
on art, music, wine, diamonds, and just about everything else
(except
how to shave), that guy on L&O:CI turns out to know a lot
about
physics. Am I right?
-E
===
Subject: Re: When a genius commits murder (Hawking & Witten
composite on Law
& Order CI)
> When a genius commits murder, how do you outsmart him?
9/8pm Sunday,
> November 21st
> http://www.nbc.com/Law_&_Order:_Criminal_Intent/index.html
> I just happened to catch this. Its a composite of Ed
Witten and Stephen
> Hawking as a murderer - motive to cover up the failure of
his theory.
Of course the true answer is that if a genius in physics
commits
murder you outsmart him in any number of ways, because he
wont be a
genius at how to commit murder.
Its like the old joke about how to beat Bobby Fisher.
Answer: play
him at anything but chess.
SBH
===
Subject: Re: When a genius commits murder (Hawking & Witten
composite on Law
&
Order CI)
>When a genius commits murder, how do you outsmart him? 9/8pm
Sunday,
>November 21st
>http://www.nbc.com/Law_&_Order:_Criminal_Intent/index.html
>I just happened to catch this.
I watched the show. I decided that the hidden agenda was to
denigrate smart and productive people. The agenda wasnt all
that hidden because the actor was madeup to look like Hawking.
But the idiots couldnt get anything right...this actor was
able to talk through his mouth.
/BAH
Subtract a hundred and four for e-mail.
===
Subject: Elementary probability of the infinite for the
overworked
mathematicians
posting-account=Qiuj5AwAAACmGnmS12qcvqA9IXzD0s4L
You are one person tossing a coin.
I have infinite people, for every time you toss a coin, my
infinite
people all toss a coin aswell. A subset of my people have all
got the
same sequence as you, I never run out of people (infinite),
you can
toss your coin as long as you want, you NEVER form a new
sequence to
what an infinite set of people can make.
Whatever sequence you form must be a *possible outcome* of
tossing
coins, infinite trials at the possible always succeed.
With finite people, the length of the sequence where every
combination
is covered is finite, about log(#P).
With infinite people, the length of the sequence where every
combination is covered is without bound, INFINITE.
Infinite length sequences are all covered, the diagonal is a
Ôcheat
and in standard theory it does not provide any new
information to the
dataset.
Herc
===
Subject: Re: Deep Thoughts # 17: Liar Paradox is a Formal
Metamathematical
Theorem
>>You _really_ need to work on the irony detector. Truth
>>and provability are _different_ things - when you define
>>one to be the other you exhibit amazing ignorance of the
>>most basic issues.
>>************************
>>David C. Ullrich
>>We call a formula F(v1,. . .,vn) correct if for every
n-tuple (a1,.
.
>>.,an), the sentence F(a1,. . .,an) is true. We let N be the
>>first-order system whose axioms are all the correct formulas
(this
>>includes all logically valid formulas.) Thus, the provable
formulas
>>of N are nothing more than the axioms of N.
>>Recursion Theory for Metamathematics - Raymond M. Smullyan,
1993
> hes not defining provability to be the
> same as truth. (Hes setting up a _specific_ 
formal system in
> which the two coincide. Theres a big difference.)
That doesnt make any sense. How can you define 
provability (or
anything else) without being in a system? Smullyan is setting
up a
specific formal system and youre not? So what 
are you talking
about
if its not a formal system? How does that work?
> ************************
> David C. Ullrich
===
Subject: Re: Deep Thoughts # 17: Liar Paradox is a Formal
Metamathematical
Theorem
>>
>You _really_ need to work on the irony detector. Truth
>and provability are _different_ things - when you define
>one to be the other you exhibit amazing ignorance of the
>most basic issues.
************************
David C. Ullrich
>We call a formula F(v1,. . .,vn) correct if for every
n-tuple (a1,.
.
>.,an), the sentence F(a1,. . .,an) is true. We let N be the
>first-order system whose axioms are all the correct formulas
(this
>includes all logically valid formulas.) Thus, the provable
formulas
>of N are nothing more than the axioms of N.
Recursion Theory for Metamathematics - Raymond M. Smullyan,
1993
>> hes not defining provability to be the same 
as truth.
(Hes setting
>> up a _specific_ formal system in which the two coincide.
Theres a
>> big difference.)
> That doesnt make any sense.
It does. Really.
Given a language:
* Truth (defined in the model theory) is a semantic relation
that holds
between a sentence of the language and an interpretation of
the language.
* Provability (defined in the proof theory) is a syntactic
relation that
holds between a set of sentences in the language and a given
sentence of
the language.
It *follows* trivially from the definitions of N, truth, and
provability
that N |- A iff A is true in the standard model of the
language of
arithmetic iff A is an axiom of N. Thats a simple theorem.
It isnt a
definition of truth or provability.
Makes good sense.
HTH.
===
Subject: Re: what are the correct set theory axioms?
at 04:55 PM, jasontesh@yahoo.com (Jason Tesh) said:
>I checked out a SOL book thinking it would cover SO set
theory, but I
>couldnt find a statement of the axioms of SO 
set theory
anywhere in
>the book, so now Im still wondering what are the correct
set theory
>axioms?
There are none. Its like asking what is the correct way to
cook a
meal. There are several different set theories, e.g., GBN,
ZFC, and
several minor variations for the axioms of each. Some set
theories
are roughly equivalent to others, and some are more powerful
than
others. You use the one that best suits your purpose at the
time.
--
Shmuel (Seymour J.) Metz, SysProg and JOAT
<http://patriot.net/~shmuel>
Unsolicited bulk E-mail subject to legal action. I reserve the
right to publicly post or ridicule any abusive E-mail. Reply
to
domain Patriot dot net user shmuel+news to contact me. Do not
===
Subject: a<b<c<a+b
To show that 0<a,b,c, 1<n, and a^n + b^n = c^n --> a<b<c<a+b,
I need N, the set of natural numbers, positive integers, that
is, and
a way to write a,b,c,n in N. Whats an accepted notation in
ASCII for in
N
and not in N?
N = { 1, 2, 3, ...}
I tolerance everything and tolerate everyone.
I love: Dona, Jeff, Kim, Kimmie, Mom, Neelix, Tasha, and Teri,
alphabetically.
I drive: A double-step Thunderbolt with 657% range.
I fight terrorism by: Using less gasoline.
===
Subject: Re: a<b<c<a+b
>To show that 0<a,b,c, 1<n, and a^n + b^n = c^n --> a<b<c<a+b,
>I need N, the set of natural numbers, positive integers,
that is, and
>a way to write a,b,c,n in N. Whats an accepted notation in
ASCII for in
N
>and not in N?
in N and not in N, respectively.
>N = { 1, 2, 3, ...}
>I tolerance everything and tolerate everyone.
>I love: Dona, Jeff, Kim, Kimmie, Mom, Neelix, Tasha, and
Teri,
alphabetically.
>I drive: A double-step Thunderbolt with 657% range.
>I fight terrorism by: Using less gasoline.
************************
David C. Ullrich
===
Subject: Re: a<b<c<a+b
>>Whats an accepted notation in ASCII for in N
>>and not in N?
>in N and not in N, respectively.
Really? Theres no little sideways e or member of set
notation? Darn.
Ok, I like words. Well use words.
For a,b,c,n in N, the set of natural numbers {1,2,3...} with
a^n + b^n =
c^n,
we eliminate the trivial case a+b=c by adding 1<n.
That c=(a^n + b^n) ^ (1/n) is immediate, so if a=b, c is the
nth root of 2
times b, and is real, not in N, so a#b and without loss of
generality we
may
take a<b.
With a<b, and large n, b dominates the sum. c is the
Minkowski n-norm of a
and
b and as n approaches infinity, c approaches b, so a<b<c.
n need not be in N for the n-norm to compute a value for c.
For real n, as
n
increases, c decreases monotonically, and since 1 < n,
a<b<c<(a^1 + b^1) ^ (1/1) or
a<b<c<a+b.
I tolerance everything and tolerate everyone.
I love: Dona, Jeff, Kim, Kimmie, Mom, Neelix, Tasha, and Teri,
alphabetically.
I drive: A double-step Thunderbolt with 657% range.
I fight terrorism by: Using less gasoline.
===
Subject: Newbie question about percentiles
Hi group,
This is my first posting here, so please forgive me if it is
simple.
I am a programmer by profeesion and need to calculate
percentiles on a
certain dataset for a project.
What I remember (and found on the net) didnt cover one
important aspect.
If I have a list of values, eg:
1,2,5,7,8,8,9,10,10,10,11,13,15,18,18,19,20,22,25,30
That are 20 numbers.
If I work in steps of say 10%,
AND
I would like to answer questions like:
What percentile belongs to 10?
I hit a problem.
If all the numbers are different, thing are easy.
I can just use:
Percentile rank =
(Number of values less than my value * 100)/(TotalNumber of
values)
But how do I find the rank of Ômy 
10 if there are more 10s
in the set?
Any help would be greatly appriciated!
Erwin Moller
===
Subject: Re: Newbie question about percentiles
posting-account=Glvc4AwAAADzVCZ73XnxpzMhXir6xVzs
There are 7 values less than 10, so one reasonable assignment
is that
10 is the 7/20 = 35-th percentile.
There are 10 values less than 11, so the median (50-th
percentile) for
this data is reasonably assigned between 10 and 11.
http://mathworld.wolfram.com/Quantile.html
Theres an ambiguity in how you define the 
quantiles, and the
user thus has some freedom in their definition. Probably any
of those is reasonable, and you can just cite a reference for
the
appropriate definition.
Suppose we wanted to see where the 30-th, 40th and 50th
percentiles are. Lets look at a couple of the quantile
definitions
closest to qn):
x = 0.5+20q = 6.5, 8.5, or 10.5 for q = 0.3, 0.4, 0.5
For q=0.3, use the formula for q_a,b;c,d. Since c=d=0 for this
definition, we have cutoff = Y_[ßoor(x)] = Y_6 = 6th 
highest
value. Simiarly for q=0.4 the cutoff is Y_8 and for q=0.5 it
is Y_10.
Thus for that definition of quantile, the 30-th, 40-th and
50-th percentiles are 8, 10, and 10.
In comparison, look at Q7 (interpolation).
Now x = 1 + 19q = 6.7, 8.6, 10.5 for q = 0.3, 0.4 or 0.5.
Q = cutoff = Y_(ßoor(x)) + (Y_ceil(x) - Y_(ßoor(x)))*frac(x)
Q_30 = Y_6 + (Y_7 - Y_6)*0.7 = 8+(9-8)*0.7
= 8.7 for 30-th percentile
Q_40 = Y_8 + (Y_9 - Y_8)*0.6 = 10 + (10-10)*0.6
= 10 for 40-th percentile
Q_50 = Y_10 + (Y_11 -Y_10)*0.5 = 10 + (11-10)*0.5
= 10.5 for 50-th percentile or median
There are reasons for all of these, but I find this latter
measure a
little more intuitively reasonable.
- Randy
===
Subject: Re: Newbie question about percentiles
I was a little confused/surprises by the fact that many
methods exist for
calculation percentiles.
Naive as I am I expected that Ôwe had some 
clearcut
definition.
Erwin Moller
===
Subject: Re: NUMBER THEORETIC POLYNOMIAL QUESTION
> Do quartic polynomials exist which have all the following
properties
> (without regard to the size of their coefficients)?
> A: They have rational zeroes (they split over Z, the ring of
> integers),
> B: Critical points have rational coordinates (their
derivatives
> split over Z),
> C: Inßection points have rational coordinates (their second
> derivatives split over Z), and
> D: They have two distinct local minima (their derivatives
have
> three distinct zeroes), and the two points sharing a common
> tangent line have rational coordinates.
> My calculus students would have fun with these...easy to
graph, and
> to find the area of the region enclosed between the
polynomial and
> the tangent.
> Cubics having properties A,B, and C are not hard to
generate, but
> attempts to integrate these and adjust the constant have
not been
> successful. Likewise, it is not hard to find quartics Q
which split
> over Z and have property D; but so far roots of Q or Q
have come out
> irrational.
> I am sure Ramanujan would crack this peanut in a second...
This is closely related to a well-studied problem, see
--Bill Dubuque
===
Subject: Re: NUMBER THEORETIC POLYNOMIAL QUESTION
...
> This is closely related to a well-studied problem, see
of D(4) it gives:
x^2(x-1)(x-a)
with
a = ((9(2w+z-12)(w+z))/((z-w-18)(8w+z))
and (w,z) in E(Q),
E: z^2 = w(w-6)(w+18).
Now setting w = 9 and z = -27, I find that point on E and a =
-7/5.
Now the second derivative is 12.x^2 + 12/5.x - 14/5, and the
roots
of that quadratic are not rational. The roots of the first
derivative
are rational. (z = +27 gives a zero denominator in the
formula for a.)
Setting w = -12 and z = -36, I find a = 432/77, and in that
case the
first derivative does not have rational roots. (On the other
hand,
when z = +36, a = 0, and it fits, as per the formula for 
D(n).)
So either I am missing something, or the quoted formulas are
wrong.
I have no access to the original paper.
--
dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam,
nederland,
+31205924131
home: bovenover 215, 1025 jn amsterdam, nederland;
http://www.cwi.nl/~dik/
===
Subject: Re: How to determine f(x), given f(x)*f(-x) =
-exp(kx^2) ?
>> Hi all,
>> How to determine f(x), given f(x)*f(-x) = -exp(kx^2) ?
where x is a
>> complex variable.
>> Is there a method that I could use?
>> Nischal
>hi nischal,
>the equation does not determine f uniquely. if f is assumed
to even
>(i.e. f(x)=f(-x)), then f(x)=i exp(kx^2/2) is a solution.
>so, if no other condition is imposed on f, there seems to be
a variety
>of solutions for f.
>/j.
> A way to generalize is just adding any odd function g(x) so:
> f(x)=i exp(kx^2/2 + g(x))
> Alain.
Or, if one assumes that F is an odd function except at x = 0,
then
f(x) = sign(x) sqrt(e^(k x^2/2)), gives a solution except at
x = 0
===
Subject: Is this question fair for statistics class?
i got -20 from a test http://www.johncho.us/stat.jpg ,
because i put zero
correlation instead of curvilinear correlation, we did not
study
curvilinear correlations and such.
I think it is unfair to put it on the test. Nearly every
student got it
wrong.
Furthermore, every year that she has put it on the test
students have
gotten it wrong; that just tells me that she is not telling
students the
truth about things and rather going around the truth hoping
that students
find it.
she said she drops the lowest test, but it does not say that
on her syllbus
i cannot believe she did this
===
Subject: Re: Is this question fair for statistics class?
> i got -20 from a test http://www.johncho.us/stat.jpg ,
because i put zero
> correlation instead of curvilinear correlation, we did not
study
> curvilinear correlations and such.
> I think it is unfair to put it on the test. Nearly every
student got it
> wrong.
> Furthermore, every year that she has put it on the test
students have
> gotten it wrong; that just tells me that she is not telling
students the
> truth about things and rather going around the truth hoping
that students
> find it.
> she said she drops the lowest test, but it does not say
that on her
syllbus
> i cannot believe she did this
Although it may seem harsh, I do not think it was necessarily
unfair. The question did not ask, Is there a correlation? The
question asked, Is there a relationship? Your plot provided a
plausible conclusion that there was a relationship, but
clearly
it wasnt a linear one. In that case, the correlation
coefficient is not the right measure of association. Simply
put,
it was the wrong tool for the job as presented. An important
part of statistics is the selection of the right tool for the
job. Now, if the instructor did not spend class time on
discussing when correlations are and are not appropriate
measures
of assocation you may have a beef; I wasnt in the class and
so I
dont know. But if the instructor did discuss that (and she
certainly ought to have) then the question is actually a good
one
since it emphasizes the importance of intelligently looking at
the data rather than mechanically applying formulas.
--
Mark Thornquist
===
Subject: Bible Codes Resurrected?
Equidistant Letter Sequences in the Book of Genesis which
claimed to
find evidence for hidden codes in the Hebrew text of Genesis.
This
number of debates in the scientific community as to whether 
the
methodology was legitimate, then the implications would be
that
something supernatural is going on in the text of Genesis.
And if not,
debunked by a few enlightened scientists.
evidence that the methodology of the experiment described in
the 1994
1994 experiment was the fact that the experimenters did not
use all
possible Hebrew appellations of the names of the rabbis
listed in the
experiment and theoretically could have selected appellations
which
optimize the results of the experiment in favor of the claim
that
there are hidden codes in the Hebrew text of Genesis. In
fact, the
authors of the 1999 paper did just that by selecting different
appellations of the names of the same rabbis, forcing a proof
that
there are hidden codes in the novel, War and Peace. And thus,
the
verdict from the scientific community was that the methodology
in the
1994 experiment was ßawed and that there was no evidence for
a hidden
code phenomenon in Genesis.
there were hidden codes in Genesis; it only showed that the
original
1994 experiment methodology was ßawed. Furthermore, to their
discredit, the journal Statistical Science did not allow the
authors
finding, discovered by Robert Haralick a professor of Computer
Science
at CUNY, can be described as follows: When all of the
appellations
experiment when performed on Genesis favors the codes
phenomenon, and
the result of the experiment when performed on War and Peace
rejects a
codes phenomenon. This finding is a major challenge to the
authors of
possible appellations been used in the experiment, no codes
phenomenon
would have been detected in Genesis. In other words, even
though the
methodology of the 1994 experiment, their War and Peace
counterexample
would now be rendered irrelevant, assuming that Haralicks
findings
are technically correct.
You can download Haralicks paper here
http://www.torahcodes.net as
well as other papers in the section marked new. Note that I
am not
claiming that Haralicks findings are correct, 
but only that
his
claims should be taken seriously. I am interested to hear how
the
anti-codes crowd would intelligently dispute this finding.
Also, I recommend anyone who is skeptical about the general
codes
phenomenon and knows some basic Hebrew to go here:
http://www.meru.org/Lettermaps/B%27rePole.html
Then combine the picture on that site with the explanation:
When the
aleph-beis is counted in base 3 starting at zero, we get the
following
relationships: (beis,yud)=(001,100), (vav,taf)=(012,210),
(heh,mem)=(011,110), (lamed,reish)=(1,0,2)=(2,0,1). Notice
that every
letter in the picture (except for the first and last)
horizontally
pairs with itself or its mirror image. Whether or not you
think that
this is all a coincidence, youll have to agree that there 
is
a very
interesting pattern in the first verse of Genesis.
Craig
===
Subject: Re: Bible Codes Resurrected?
After thinking about Haralicks paper I have a few more
comments to
make.
The objectivity of the data used by Witztum et al (1994) has
been
seriously criticized for the reasons I specified in a previous
post to
this thread. If Haralick wanted to avoid the critcism that
his data is
biased, he should not be including this data in his
experiment at all.
In fact, Haralick had many choices about where he derived his
data
from:
1. The first list of rabbis, dates, and appellations found in
Witztum
et al (1994) [1].
2. The second list of rabbis, dates, and appellations in
Witztum et al
(1994) [1].
3. The list created by specialist Simcha Emanuel using the
rabbis from
Witztum et als first list but his own judgement 
for the dates
and
appellations [1].
4. The list created by Emanuel using a new list of rabbis
given by
McKay et al (1999) but still using his own judgement for the
dates and
appellations [1].
5. The list created by Emanuel using the rabbis from Witztum
et als
second list, but the rules and styles of the appellations and
dates
from Witztum et als first list [1].
6. The War and Peace list of rabbis and dates found by
Bar-Natan et al
(1999) [2].
This does not include the numerous other lists created from
the rabbis
cities experiment and its replications.
Clearly Haralick had many choices when selecting which lists
to use.
He could have used one or more of any of the above lists, or
he could
have created his own list. Lists 1 and 2 have been severely
criticized, and list 3, 5, and 6 are probably questionable.
List 4 or
a new list created properly would have been the two ideal
lists to
use.
Yet we find that Haralick is using list 2 and 3 (both of which
have
been severely critcized) combined with list 6. Why would
Haralick use
a list 1 and 2 as part of his data? Perhaps because he
realizes he has
no chance of achieving remarkable results unless he uses list
1 or 2.
Further, even if Haralick insists on using lists 1 and 2, why
did
Haralick choose 6 as his third list? This seems quite
arbitrary, as
Haralick could have used any of the four other lists or a new
list.
This certainly leaves much wiggle room as Barry Simon calls
it.
This only addresses some of the problems with the data. There
may be
similar problems with the improved protocol. For example, why
did
Haralick develop an improved protocol rather than the protocol
recommended to Witztum et al by Diaconis, or the protocol
actually
used in Witztum et al? This again leaves wiggle room.
> finding, discovered by Robert Haralick a professor of
Computer Science
> at CUNY, can be described as follows: When all of the
appellations
> experiment when performed on Genesis favors the codes
phenomenon, and
> the result of the experiment when performed on War and
Peace rejects a
> codes phenomenon. This finding is a major challenge to the
authors of
> possible appellations been used in the experiment, no codes
phenomenon
> would have been detected in Genesis. In other words, even
though the
> methodology of the 1994 experiment, their War and Peace
counterexample
> would now be rendered irrelevant, assuming that Haralicks
findings
> are technically correct.
[1] http://cs.anu.edu.au/~bdm/dilugim/StatSci/data.html
[2] http://cs.anu.edu.au/~bdm/dilugim/WNP/
===
Subject: Re: Bible Codes Resurrected?
> After thinking about Haralicks paper I have a few more
comments to
> make.
> The objectivity of the data used by Witztum et al (1994)
has been
> seriously criticized for the reasons I specified in a
previous post to
> this thread.
If Haralick wanted to avoid the critcism that his data is
> biased, he should not be including this data in his
experiment at all.
> In fact, Haralick had many choices about where he derived
his data
> from:
> 1. The first list of rabbis, dates, and appellations found
in Witztum
> et al (1994) [1].
> 2. The second list of rabbis, dates, and appellations in
Witztum et al
> (1994) [1].
> 3. The list created by specialist Simcha Emanuel using the
rabbis from
> Witztum et als first list but his own 
judgement for the
dates and
> appellations [1].
> 4. The list created by Emanuel using a new list of rabbis
given by
> McKay et al (1999) but still using his own judgement for
the dates and
> appellations [1].
> 5. The list created by Emanuel using the rabbis from
Witztum et als
> second list, but the rules and styles of the appellations
and dates
> from Witztum et als first list [1].
> 6. The War and Peace list of rabbis and dates found by
Bar-Natan et al
> (1999) [2].
> This does not include the numerous other lists created from
the rabbis
> cities experiment and its replications.
> Clearly Haralick had many choices when selecting which
lists to use.
> He could have used one or more of any of the above lists,
or he could
> have created his own list. Lists 1 and 2 have been severely
> criticized, and list 3, 5, and 6 are probably questionable.
List 4 or
> a new list created properly would have been the two ideal
lists to
> use.
> Yet we find that Haralick is using list 2 and 3 (both of
which have
> been severely critcized) combined with list 6. Why would
Haralick use
> a list 1 and 2 as part of his data? Perhaps because he
realizes he has
> no chance of achieving remarkable results unless he uses
list 1 or 2.
Or more likely he didnt have access to those lists, as he
said in his
paper that he knew of no other publicly released lists.
Remember that
McKay did not release these lists in his published paper,
only on his
website. I think it is asking a little to much to expect
Haralick, who
is a busy man, to have to surf the net in order to find out
about this
information. Furthermore, what if Haralick were to have
performed his
analysis with these lists and the experiment were successful?
Then
McKay could have easily taken the lists down from his website
and then
people might accuse Haralick of tuning his lists.
It sounds like you are moving the goalposts. In any case, if
these
other lists are reasonable, then there is no reason why
Haralick
should fear using them. But to accuse him of not having used
them
because he knows that they wont work is completely 
unfounded.
> Further, even if Haralick insists on using lists 1 and 2,
why did
> Haralick choose 6 as his third list? This seems quite
arbitrary, as
> Haralick could have used any of the four other lists or a
new list.
> This certainly leaves much wiggle room as Barry Simon calls
it.
See above.
> This only addresses some of the problems with the data.
There may be
> similar problems with the improved protocol. For example,
why did
> Haralick develop an improved protocol rather than the
protocol
> recommended to Witztum et al by Diaconis, or the protocol
actually
> used in Witztum et al? This again leaves wiggle room.
protocal. The new protocal addresses these problems and is
more
descriptive of the Torah Code hypothesis. And if you read
carefully
wiggle room involved with the selection of the new metric.
Craig
===
Subject: Re: Bible Codes Resurrected?
> After thinking about Haralicks paper I have a few more
comments to
> make.
The objectivity of the data used by Witztum et al (1994) has
been
> seriously criticized for the reasons I specified in a
previous post to
> this thread.
> If Haralick wanted to avoid the critcism that his data is
> biased, he should not be including this data in his
experiment at all.
> In fact, Haralick had many choices about where he derived
his data
> from:
1. The first list of rabbis, dates, and appellations found in
Witztum
> et al (1994) [1].
> 2. The second list of rabbis, dates, and appellations in
Witztum et al
> (1994) [1].
> 3. The list created by specialist Simcha Emanuel using the
rabbis from
> Witztum et als first list but his own 
judgement for the
dates and
> appellations [1].
> 4. The list created by Emanuel using a new list of rabbis
given by
> McKay et al (1999) but still using his own judgement for
the dates and
> appellations [1].
> 5. The list created by Emanuel using the rabbis from
Witztum et als
> second list, but the rules and styles of the appellations
and dates
> from Witztum et als first list [1].
> 6. The War and Peace list of rabbis and dates found by
Bar-Natan et al
> (1999) [2].
This does not include the numerous other lists created from
the rabbis
> cities experiment and its replications.
Clearly Haralick had many choices when selecting which lists
to use.
> He could have used one or more of any of the above lists,
or he could
> have created his own list. Lists 1 and 2 have been severely
> criticized, and list 3, 5, and 6 are probably questionable.
List 4 or
> a new list created properly would have been the two ideal
lists to
> use.
Yet we find that Haralick is using list 2 and 3 (both of which
have
> been severely critcized) combined with list 6. Why would
Haralick use
> a list 1 and 2 as part of his data? Perhaps because he
realizes he has
> no chance of achieving remarkable results unless he uses
list 1 or 2.
> Or more likely he didnt have access to those lists, as he
said in his
> paper that he knew of no other publicly released lists.
Remember that
> McKay did not release these lists in his published paper,
only on his
> website. I think it is asking a little to much to expect
Haralick, who
> is a busy man, to have to surf the net in order to find out
about this
> information. Furthermore, what if Haralick were to have
performed his
> analysis with these lists and the experiment were
successful? Then
> McKay could have easily taken the lists down from his
website and then
> people might accuse Haralick of tuning his lists.
> It sounds like you are moving the goalposts. In any case,
if these
> other lists are reasonable, then there is no reason why
Haralick
> should fear using them. But to accuse him of not having
used them
> because he knows that they wont work is completely
unfounded.
As a follow up, I notified Art Levitt, the author of the
website that
I pointed to, of your objection. He contacted Haralick and it
appears
that Haralick indeed was unaware of the other lists that you
mentioned.
He said, I will take a look to see if there are any additional
web site.
Craig
===
Subject: Re: Bible Codes Resurrected?
> Clearly Haralick had many choices when selecting which
lists to use.
> He could have used one or more of any of the above lists,
or he could
> have created his own list. Lists 1 and 2 have been severely
> criticized, and list 3, 5, and 6 are probably questionable.
List 4 or
> a new list created properly would have been the two ideal
lists to
> use.
> Yet we find that Haralick is using list 2 and 3 (both of
which have
> been severely critcized) combined with list 6. Why would
Haralick use
> a list 1 and 2 as part of his data? Perhaps because he
realizes he
has
> no chance of achieving remarkable results unless he uses
list 1 or 2.
Or more likely he didnt have access to those lists, as he
said in his
> paper that he knew of no other publicly released lists.
Remember that
> McKay did not release these lists in his published paper,
only on his
> website. I think it is asking a little to much to expect
Haralick, who
> is a busy man, to have to surf the net in order to find out
about this
> information. Furthermore, what if Haralick were to have
performed his
> analysis with these lists and the experiment were
successful? Then
> McKay could have easily taken the lists down from his
website
> and then people might accuse Haralick of tuning his lists.
It sounds like you are moving the goalposts. In any case, if
these
> other lists are reasonable, then there is no reason why
Haralick
> should fear using them. But to accuse him of not having
used them
> because he knows that they wont work is completely
unfounded.
> As a follow up, I notified Art Levitt, the author of the
website that
> I pointed to, of your objection. He contacted Haralick and
it appears
> that Haralick indeed was unaware of the other lists that you
> mentioned.
> He said, I will take a look to see if there are any
additional
> web site.
This is a good example of the quality of information that
gets around
on this subject.
Of course Haralick is aware of the other lists because they
are
described in my paper published in Statistical Science. He
also
http://cs.anu.edu.au/~bdm/dilugim/StatSci/emanuel_rep.html
So what you report is nonsense.
More interestingly, Haralick has even collected appellations
himself
that are not in the two lists he used. The idea that one can
take a
set of data which is the one whose objectivity is being tested
(WRRs data), combine it with some more data that was openly
cooked (War and Peace data), then suddenly have an objective
list, is breathtaking.
And thats only the start of the problems with this
appallingly bad
paper of Haralick.
Brendan McKay.
===
Subject: Re: Bible Codes Resurrected?
As a follow up, I notified Art Levitt, the author of the
website that
> I pointed to, of your objection. He contacted Haralick and
it appears
> that Haralick indeed was unaware of the other lists that you
> mentioned.
He said, I will take a look to see if there are any additional
> web site.
> This is a good example of the quality of information that
gets around
> on this subject.
> Of course Haralick is aware of the other lists because they
are
> described in my paper published in Statistical Science. He
also
> http://cs.anu.edu.au/~bdm/dilugim/StatSci/emanuel_rep.html
> So what you report is nonsense.
I directly quoted an email that Haralick cced me. It 
appears
to me
that he only made a mistake by forgetting about those extra
lists
he already used. I wouldnt infer from this that he
deliberately
ignored these lists because he knew that they would produce
bad
results - after all, what purpose would that serve him, as it
would
only be a matter of time when you or someone else would try
it out and
disprove him. And maybe they produce good results? I too
would like to
see him perform the experiment with the lists on your website.
> More interestingly, Haralick has even collected
appellations himself
> that are not in the two lists he used.
ones?
The idea that one can take a
> set of data which is the one whose objectivity is being
tested
> (WRRs data), combine it with some more data that was 
openly
> cooked (War and Peace data), then suddenly have an objective
> list, is breathtaking.
He never claimed that he had an objective list. However, the
fact that
the experiment with the combined lists worked on Genesis and
not War
and Peace is something that one would not expect if there
were no
codes effect in Genesis and is consistent with the Torah codes
hypothesis. In fact, it kind of reminds me of the Biblical
passage in
Exodus,
7:10 And Moses and Aaron went in unto Pharaoh, and they did
so, as
the Lord had commanded; and Aaron cast down his rod before
Pharaoh and
before his servants, and it became a serpent.
7:11 Then Pharaoh also called for the wise men and the
sorcerers; and
they also, the magicians of Egypt, did in like manner with
their
secret arts.
7:12 For they cast down every man his rod, and they became
serpents;
but Aarons rod swallowed up their rods.
- that is of course assuming that everything is as Haralick
describes.
> And thats only the start of the problems with this
appallingly bad
> paper of Haralick.
What are some other problems? I appreciate the work that you
have done
the subjectivity of the lists. If there are ßaws in the
Haralick
Craig
> Brendan McKay.
===
Subject: Re: Bible Codes Resurrected?
> As a follow up, I notified Art Levitt, the author of the
website that
> I pointed to, of your objection. He contacted Haralick and
it appears
> that Haralick indeed was unaware of the other lists that you
> mentioned.
> He said, I will take a look to see if there are any
additional
> web site.
This is a good example of the quality of information that
gets around
> on this subject.
Of course Haralick is aware of the other lists because they
are
> described in my paper published in Statistical Science. He
also
> http://cs.anu.edu.au/~bdm/dilugim/StatSci/emanuel_rep.html
> So what you report is nonsense.
> I directly quoted an email that Haralick cced me. It
appears to me
> that he only made a mistake by forgetting about those extra
lists
> he already used. I wouldnt infer from this that he
deliberately
> ignored these lists because he knew that they would produce
bad
> results - after all, what purpose would that serve him, as
it would
> only be a matter of time when you or someone else would try
it out and
> disprove him. And maybe they produce good results? I too
would like to
> see him perform the experiment with the lists on your
website.
They will only provide a few extra appellations. Anyway, note
that
I was responding to a specific claim and did not say that
Haralick
should have used or not used any particular data. Rather, the
whole
idea of his experiment is broken. A little on this below.
> More interestingly, Haralick has even collected
appellations himself
> that are not in the two lists he used.
> ones?
Other way around. Haralick knows lots of valid appellations
that are
not used in his experiment. These include appellations he has
collected
himself for his own (other) experiments. They also include
many that
everyone knows. For example, the original experiment used
appellations
of the form Rabbi Yakov, but not Rav Yakov. As you know, the
latter
is an extremely common expression; why is it not used? There
are many
more examples. Why is the much smaller and more irregular set
of
appellations that work in War and Peace the correct set of
additional
appellations? And why is it correct to only add appellations
when
(according to our hypothesis) a major problem with the
original data was
the selective inclusion of doubtful appellations? (There are
even two
that nobody ever found a single example of in the literature.)
> And thats only the start of the problems with this
appallingly bad
> paper of Haralick.
> What are some other problems? I appreciate the work that
you have done
> the subjectivity of the lists. If there are ßaws in the
Haralick
Ill summarise what Haralick did. There are two sets of data
and
a third constructed from them.
D1: data used by WRR for Genesis
D2: data used by BMMK (McKay & al.) for War and Peace
D3. the union of D1 and D2
Note that D1 and D2 have a very large overlap.
D1 works well in Genesis and very poorly in War and Peace.
D2 works well in War and Peace and fairly poorly in Genesis
The question is: how does D3 behave?
Using the analysis method of WRR, D3 works worse in Genesis
than D1 did, and worse in War and Peace than D2 did.
Somehow or other, Haralick found a different method of
analysis
for which D3 works about the same or slightly better in
Genesis
than D1 did, whereas D3 still works worse in War and Peace
than D2 did. (Actually he found 4 new methods of analysis,
some
of which behave this way and some of which do not.)
Haralick claims this proves something. I think it only proves
that
wishful thinking is strong medicine.
The fact is that the result is extremely sensitive to both
the data
and the method of analysis. Seemingly tiny changes (like
adding
or deleting a single word, or replacing a mathematical
expression
by another with the same properties) can make the result jump
up or down dramatically. Factors of 10 or more are nothing.
I know of tiny changes to the analysis method (far far more
minor
than the changes between WRR and Haralick) that make the
result for D2 in War and Peace 100 times better than the
result
for D1 in Genesis. What does this prove? Nothing. What does
it prove if Haralick can come up with a method showing some
other behaviour? Nothing.
Besides this, Haralick has not established a significance
level for
his results. How likely is it for his observations to occur
by chance?
He doesnt even ask the question. (I have reason to believe
that
they are not very unlikely.) And lets not get started on 
the
errors
in his new methods.
Brendan.
===
Subject: Re: Bible Codes Resurrected?
Then I suppose I was incorrect, but if this is Haralicks 
only
justification for neglecting to use these lists then this
certainly
not look good for Haralick or his experiment. The McKay et al
(1999)
paper uses two pages (pp. 24-25) to describe their independent
scientific experiments and then concludes with The data for
the above
three experiments can be found at McKays web site (1999b).
> As a follow up, I notified Art Levitt, the author of the
website that
> I pointed to, of your objection. He contacted Haralick and
it appears
> that Haralick indeed was unaware of the other lists that you
> mentioned.
> He said, I will take a look to see if there are any
additional
> web site.
> Craig
===
Subject: Re: Bible Codes Resurrected?
> Yet we find that Haralick is using list 2 and 3 (both of
which have
> been severely critcized) combined with list 6.
That should have been Yet we find that Haralick is using list
1 and 2
(both of which have been severely critcized) combined with
list 6.
===
Subject: Re: Bible Codes Resurrected?
I am aware that the Bible Code topic is a controversial
subject and
that as a result, there are people on both sides of the
issue, pro and
con, who hold very strong opinions that are based on emotions
and not
on reason. If you are one of those people, then I recommend
not
wasting your time responding to me as I will not answer. I
only posted
my original letter in order to inform the curious and/or to
receive
For example, I just read paper 3 here:
http://www.torahcodes.net/papers.html.
The paper is only four pages long and discusses a 29 letter
ELS
(equidistant letter sequence code) in the Torah found in
equidistant
letter sequence which translates into
I will name you ÔDestruction. Cursed is bin 
Laden and revenge
belongs to the Messiah.
encoded in (at least) a 29-letter ELS which contains the name
bin
Laden being found in the Torah are 1 in 83,000. Since this
particular
the capabilities of the codes author far exceed those of
human
beings.
The experiment which led to the odds 1 in 83,000 is described
fully in
described therein; I am curious as to other reactions.
Craig
===
Subject: Re: Bible Codes Resurrected?
> I am aware that the Bible Code topic is a controversial
subject and
> that as a result, there are people on both sides of the
issue, pro and
> con, who hold very strong opinions that are based on
emotions and not
> on reason. If you are one of those people, then I recommend
not
> wasting your time responding to me as I will not answer. I
only posted
> my original letter in order to inform the curious and/or to
receive
> For example, I just read paper 3 here:
> http://www.torahcodes.net/papers.html.
> The paper is only four pages long and discusses a 29 letter
ELS
> (equidistant letter sequence code) in the Torah found in
equidistant
> letter sequence which translates into
> I will name you ÔDestruction. Cursed is bin 
Laden and
revenge
> belongs to the Messiah.
The grammar of this phrase seems quite poor. I can hardly
translate
Hebrew, but I imagine the grammar is even worse before it is
translated. Since you can translate Hebrew perhaps you can
provide
your opinion.
The point is this: If God encoded phrases in the Torah, would
we
expect the grammar of the phrases to be this poor?
> encoded in (at least) a 29-letter ELS which contains the
name bin
> Laden being found in the Torah are 1 in 83,000. Since this
particular
> the capabilities of the codes author far exceed those of
human
> beings.
> The experiment which led to the odds 1 in 83,000 is
described fully in
> described therein; I am curious as to other reactions.
Perhaps you were not looking hard enough. Unless I am
misunderstanding
the details of the experiment, I see at least one major ßaw
that
makes it completely worthless. I will begin by brießy
summarizing the
procedure the authors used, based on my understanding.
1. An ELS was found by a Art Levitt in advance in the Torah
that they
translate to Destruction I will named you, Cursed [is] bin
Laden and
revenge [belongs] to the Messiah. The authors consider this
ELS to be
intelligible. (Huh?) The authors decide to test the
hypothesis that
this ELS is more intelligible than would be expected by
chance.
2. The authors generate numerous random phrases of 29
characters (the
length of the bin Laden ELS) or more and find 13,430 of these
ELSs in
their 614,400 control texts. They also manually find 8 phrases
that
are somewhat intelligible in these control texts. They
present these
ELSs to many subjects with the bin Laden ELS mixed in.
3. They present these ELSs to many control subjects with 
the
bin
Laden ELS mixed in. The subjects tended to consider the bin
Laden ELS
intelligible considerably more often (compared to the randomly
generated phrases -- not the manually found ones) than would
be
expected by chance. After some calculations they arrive at a
probability of 1.2e-05.
The problem with this experiment seems obvious to me. They are
measuring the intelligibility of an ELS found by a motivated
person in
a book the person was motivated to find an intelligible ELS
in. They
attempt to accomplish this by using human subjects to compare
it to
randomly generated phrases of the same length. Is it really
that
improbable that people would find the intelligible ELS more
intelligible than the randomly generated ones?
> Craig
===
Subject: Re: Bible Codes Resurrected?
> I am aware that the Bible Code topic is a controversial
subject and
> that as a result, there are people on both sides of the
issue, pro and
> con, who hold very strong opinions that are based on
emotions and not
> on reason. If you are one of those people, then I recommend
not
> wasting your time responding to me as I will not answer. I
only posted
> my original letter in order to inform the curious and/or to
receive
For example, I just read paper 3 here:
> http://www.torahcodes.net/papers.html.
> The paper is only four pages long and discusses a 29 letter
ELS
> (equidistant letter sequence code) in the Torah found in
equidistant
> letter sequence which translates into
I will name you ÔDestruction. Cursed is bin 
Laden and revenge
> belongs to the Messiah.
> The grammar of this phrase seems quite poor. I can hardly
translate
> Hebrew, but I imagine the grammar is even worse before it is
> translated. Since you can translate Hebrew perhaps you can
provide
> your opinion.
I agree that the first sentence is a little strange. However,
the
grammar in Hebrew is reasonable. The fact that the first
sentence is
strange was reßected in their experimental protocal, as this
sentence
did not get the highest marks as an intelligent sentence in
the group
of non-control sentences.
> The point is this: If God encoded phrases in the Torah,
would we
> expect the grammar of the phrases to be this poor?
This is not the issue. The issue is what are the odds of
sentence
being encoded in (at least) a 29-letter ELS which contains
the name
bin Laden being found in the Torah. Leave the theological
issues to
the theologians.
> encoded in (at least) a 29-letter ELS which contains the
name bin
> Laden being found in the Torah are 1 in 83,000. Since this
particular
> the capabilities of the codes author far exceed those of
human
> beings.
The experiment which led to the odds 1 in 83,000 is described
fully in
> described therein; I am curious as to other reactions.
> Perhaps you were not looking hard enough. Unless I am
misunderstanding
> the details of the experiment, I see at least one major ßaw
that
> makes it completely worthless. I will begin by brießy
summarizing the
> procedure the authors used, based on my understanding.
> 1. An ELS was found by a Art Levitt in advance in the Torah
that they
> translate to Destruction I will named you, Cursed [is] bin
Laden and
> revenge [belongs] to the Messiah. The authors consider this
ELS to be
> intelligible. (Huh?) The authors decide to test the
hypothesis that
> this ELS is more intelligible than would be expected by
chance.
> 2. The authors generate numerous random phrases of 29
characters (the
> length of the bin Laden ELS) or more and find 13,430 of
these ELSs in
> their 614,400 control texts. They also manually find 8
phrases that
> are somewhat intelligible in these control texts. They
present these
> ELSs to many subjects with the bin Laden ELS mixed in.
> 3. They present these ELSs to many control subjects with
the bin
> Laden ELS mixed in. The subjects tended to consider the bin
Laden ELS
> intelligible considerably more often (compared to the
randomly
> generated phrases -- not the manually found ones) than
would be
> expected by chance. After some calculations they arrive at a
> probability of 1.2e-05.
> The problem with this experiment seems obvious to me. They
are
> measuring the intelligibility of an ELS found by a
motivated person in
> a book the person was motivated to find an intelligible ELS
in. They
> attempt to accomplish this by using human subjects to
compare it to
> randomly generated phrases of the same length. Is it really
that
> improbable that people would find the intelligible ELS more
> intelligible than the randomly generated ones?
accomplish this by using human subjects to compare it to
randomly
generated phrases of the same length. is not at all
descriptive of
their experiment.
Craig
===
Subject: Re: Bible Codes Resurrected?
> The problem with this experiment seems obvious to me. They
are
> measuring the intelligibility of an ELS found by a
motivated person in
> a book the person was motivated to find an intelligible ELS
in. They
> attempt to accomplish this by using human subjects to
compare it to
> randomly generated phrases of the same length. Is it really
that
> improbable that people would find the intelligible ELS more
> intelligible than the randomly generated ones?
> accomplish this by using human subjects to compare it to
randomly
> generated phrases of the same length. is not at all
descriptive of
> their experiment.
Why is it not descriptive? Which part of that statement (or my
description in general) do you find to be incorrect? I do
think the
description in the paper supports that statement; for example:
Our method of significance estimation for an ELS phrase string
found
in a particular text is to compare its intelligibility to
that of a
large set of competitors. We do so by means of a large set of
human
reviewers who are asked to classify each string as to whether
it is
intelligible or not.
A string - from any of these [comparison] texts - is accepted
for
human review only if all of its words come from a lexicon of
the
language of interest [Hebrew].
To find ELS phrase strings in a comparison text, we
exhaustively
search all possible spacings of words, requiring only that
they form a
continuous ELS that includes the chosen anchor.
Certainly I could be incorrect, but if you wish to argue this
then
please do point out my error.
===
Subject: Re: Bible Codes Resurrected?
> The problem with this experiment seems obvious to me. They
are
> measuring the intelligibility of an ELS found by a
motivated person
in
> a book the person was motivated to find an intelligible ELS
in. They
> attempt to accomplish this by using human subjects to
compare it to
> randomly generated phrases of the same length. Is it really
that
> improbable that people would find the intelligible ELS more
> intelligible than the randomly generated ones?
accomplish this by using human subjects to compare it to
randomly
> generated phrases of the same length. is not at all
descriptive of
> their experiment.
> Why is it not descriptive? Which part of that statement (or
my
> description in general) do you find to be incorrect? I do
think the
> description in the paper supports that statement; for
example:
> Our method of significance estimation for an ELS phrase
string found
> in a particular text is to compare its intelligibility to
that of a
> large set of competitors. We do so by means of a large set
of human
> reviewers who are asked to classify each string as to
whether it is
> intelligible or not.
> A string - from any of these [comparison] texts - is
accepted for
> human review only if all of its words come from a lexicon
of the
> language of interest [Hebrew].
> To find ELS phrase strings in a comparison text, we
exhaustively
> search all possible spacings of words, requiring only that
they form a
> continuous ELS that includes the chosen anchor.
> Certainly I could be incorrect, but if you wish to argue
this then
> please do point out my error.
The part that says randomly generated phrases is not correct.
They
are phrases in virtual texts with specific characteristics.
===
Subject: Re: Bible Codes Resurrected?
> Equidistant Letter Sequences in the Book of Genesis which
claimed to
> find evidence for hidden codes in the Hebrew text of
Genesis. This
> number of debates in the scientific community as to whether
the
> methodology was legitimate, then the implications would be
that
> something supernatural is going on in the text of Genesis.
And if not,
> debunked by a few enlightened scientists.
> evidence that the methodology of the experiment described
in the 1994
> 1994 experiment was the fact that the experimenters did not
use all
> possible Hebrew appellations of the names of the rabbis
listed in the
> experiment and theoretically could have selected
appellations which
> optimize the results of the experiment in favor of the
claim that
> there are hidden codes in the Hebrew text of Genesis.
It is true that the choice of appellations is regarded by
McKay et al
(1999) to be the most serious problem with the data [1].
However,
nowhere in the paper is it argued that Witztum et al should
have used
have used all possible appellations.
> In fact, the
> authors of the 1999 paper did just that by selecting
different
> appellations of the names of the same rabbis, forcing a
proof that
> there are hidden codes in the novel, War and Peace.
This is certainly not the only evidence McKay et al (1999)
found to
support their argument that Witztum et al (1994) is ßawed.
Aside from
the demonstration by McKay et al that the phenomenon can be
replicated
in War and Peace, below is a brief summary of the evidence
presented
in McKay et al (1999) and in subsequent papers:
1. Witztum et al tended to choose options more favorable to
their
results when a choice was available [1]. The same was found in
numerous other experiments by Witztum et al [2], and the bias
is most
apparent in the 70 nations experiment [3].
2. The P2 value, a measurement used by Witztum et al., was
closer to
each other for the two lists of rabbis than what would be
expected by
chance. Having them close together makes it appear that the
results
are consistent. However, McKay et al. found that when
shufßing the
two lists of rabbis together and splitting them in half, the
results
were only equal around 1% of the time. The same study was
performed on
the rabbis in Gans cities experiment and found similar
results [1].
3. The several independent studies conducted by qualified
mathematicians using data directly from encyclopedias and from
independent experts have found no trace of the codes
[1][4][5][6].
> And thus, the
> verdict from the scientific community was that the
methodology in the
> 1994 experiment was ßawed and that there was no evidence
for a hidden
> code phenomenon in Genesis.
> there were hidden codes in Genesis; it only showed that the
original
> 1994 experiment methodology was ßawed.
Is there any evidence that could potentially be found that
would
refute the *possibility* that there are hidden codes in
Genesis? What
about hidden codes War and Peace?
> Furthermore, to their
> discredit, the journal Statistical Science did not allow
the authors
In fact, the editors of Statistical Science did invite Rips
to submit
a reply to McKay et als paper. However, the editors did not
agree to
allow Rips to bypass the peer-review process and have his
reply
published regardless of its quality [7].
This is nothing new. Witztum and others have posted numerous
rebuttals since McKay et al (1999) was published [8][9], and
McKay
has replied to many of them [1][2]. Unfortunately it seems
that many
of the researchers who have spent countless hours in the past
10 years
finding ßaw after ßaw in Torah Codes experiments are 
becoming
tired
of the subject [11].
> The major
> finding, discovered by Robert Haralick a professor of
Computer Science
> at CUNY, can be described as follows: When all of the
appellations
> experiment when performed on Genesis favors the codes
phenomenon, and
> the result of the experiment when performed on War and
Peace rejects a
> codes phenomenon. This finding is a major challenge to the
authors of
> possible appellations been used in the experiment, no codes
phenomenon
> would have been detected in Genesis. In other words, even
though the
> methodology of the 1994 experiment, their War and Peace
counterexample
> would now be rendered irrelevant, assuming that Haralicks
findings
> are technically correct.
Unfortunately I do not have the expertise to fully evaluate
Haralicks
paper. However, I think one sentence in their abstract is
certainly
worth commenting on:
We designed an improved protocol for the experiment using
statistically more powerful compactness measures and an ELS
Random
Placement control text population. [1]
If I had to guess, it is primarily this improved protocol
that is
behind the remarkable results of this experiment.
> You can download Haralicks paper here
http://www.torahcodes.net as
> well as other papers in the section marked new. Note that I
am not
> claiming that Haralicks findings are correct, 
but only that
his
> claims should be taken seriously. I am interested to hear
how the
> anti-codes crowd would intelligently dispute this finding.
Torah Codes claims have been taken seriously by its critics
for over
10 years. Like you I hope that someone qualified will
intelligently
dispute Haralicks paper. Unless it is published in
peer-reviewed
journal, however, I do not not expect a thorough analysis of
it.
> Also, I recommend anyone who is skeptical about the general
codes
> phenomenon and knows some basic Hebrew to go here:
> http://www.meru.org/Lettermaps/B%27rePole.html
> Then combine the picture on that site with the explanation:
When the
> aleph-beis is counted in base 3 starting at zero, we get
the following
> relationships: (beis,yud)=(001,100), (vav,taf)=(012,210),
> (heh,mem)=(011,110), (lamed,reish)=(1,0,2)=(2,0,1). Notice
that every
> letter in the picture (except for the first and last)
horizontally
> pairs with itself or its mirror image. Whether or not you
think that
> this is all a coincidence, youll have to agree that there
is a very
> interesting pattern in the first verse of Genesis.
Yes, it is quite amusing.
[1] http://cs.anu.edu.au/~bdm/dilugim/StatSci/
[2] http://cs.anu.edu.au/~bdm/dilugim/torah.html
[3] http://cs.anu.edu.au/~bdm/dilugim/Nations/
[4] http://cs.anu.edu.au/~bdm/dilugim/gans_exp.html
[5]
http://www.ratio.huji.ac.il/show-dp-abstract.asp?dpNumber=364
[6] http://www.wopr.com/biblecodes/Cities_Overview.htm
[7] http://cs.anu.edu.au/~bdm/dilugim/StatSci/gans_rep.html
[8] http://www.torahcodes.co.il/debate1.htm
[9]
http://www.aish.com/seminars/discovery/Codes/Primer/primer1.
htm
[10] http://www.torahcodes.net/hypoth.pdf
[11]
http://www.math.toronto.edu/~drorbn/Codes/NationsExtract.html
===
Subject: Re: Bible Codes Resurrected?
> It is true that the choice of appellations is regarded by
McKay et al
> (1999) to be the most serious problem with the data [1].
However,
> nowhere in the paper is it argued that Witztum et al should
have used
> have used all possible appellations.
Maybe not explicitly but it certainly was implied.
> In fact, the
> authors of the 1999 paper did just that by selecting
different
> appellations of the names of the same rabbis, forcing a
proof that
> there are hidden codes in the novel, War and Peace.
> This is certainly not the only evidence McKay et al (1999)
found to
> support their argument that Witztum et al (1994) is ßawed.
Aside from
> the demonstration by McKay et al that the phenomenon can be
replicated
> in War and Peace, below is a brief summary of the evidence
presented
> in McKay et al (1999) and in subsequent papers:
> 1. Witztum et al tended to choose options more favorable to
their
> results when a choice was available [1]. The same was found
in
> numerous other experiments by Witztum et al [2], and the
bias is most
> apparent in the 70 nations experiment [3].
This is basically the same argument as I described before.
> 2. The P2 value, a measurement used by Witztum et al., was
closer to
> each other for the two lists of rabbis than what would be
expected by
> chance. Having them close together makes it appear that the
results
> are consistent. However, McKay et al. found that when
shufßing the
> two lists of rabbis together and splitting them in half,
the results
> were only equal around 1% of the time. The same study was
performed on
> the rabbis in Gans cities experiment and found similar
results [1].
I talked in person with Gans about this a few years ago
because I had
questions about this. He said that when he did his cities
experiment,
he did not split the lists up as was done in the WRR paper.
In any
case, Haralicks paper renders this argument obsolete,
assuming that
it is correct.
> 3. The several independent studies conducted by qualified
> mathematicians using data directly from encyclopedias and
from
> independent experts have found no trace of the codes
[1][4][5][6].
Failure in other experiments does not negate the alleged
success of
this experiment.
> And thus, the
> verdict from the scientific community was that the
methodology in the
> 1994 experiment was ßawed and that there was no evidence
for a hidden
> code phenomenon in Genesis.
there were hidden codes in Genesis; it only showed that the
original
> 1994 experiment methodology was ßawed.
> Is there any evidence that could potentially be found that
would
> refute the *possibility* that there are hidden codes in
Genesis? What
> about hidden codes War and Peace?
That is pretty difficult to do. Sort of like trying to 
define
randomness. Its relatively easy to show that a sequence is
not random
by finding a pattern. However, showing that there is no
conceivable
pattern is much more difficult. So there is no real proof that
there
are no hidden codes in War and Peace although it is pretty
safe to
assume such.
> Furthermore, to their
> discredit, the journal Statistical Science did not allow
the authors
> In fact, the editors of Statistical Science did invite Rips
to submit
> a reply to McKay et als paper. However, the editors did
not agree to
> allow Rips to bypass the peer-review process and have his
reply
> published regardless of its quality [7].
That is unfortunate. However, at that point in time I doubt
Rips would
> This is nothing new. Witztum and others have posted numerous
> rebuttals since McKay et al (1999) was published [8][9],
and McKay
> has replied to many of them [1][2]. Unfortunately it seems
that many
> of the researchers who have spent countless hours in the
past 10 years
> finding ßaw after ßaw in Torah Codes experiments are
becoming tired
> of the subject [11].
I agree with you on this point. Witztums critiques come 
down
to why
his spellings are more legitimate than McKays monkey list.
This is
very weak since it is subject to so much subjectivity.
> The major
> finding, discovered by Robert Haralick a professor of
Computer Science
> at CUNY, can be described as follows: When all of the
appellations
> experiment when performed on Genesis favors the codes
phenomenon, and
> the result of the experiment when performed on War and
Peace rejects a
> codes phenomenon. This finding is a major challenge to the
authors of
> possible appellations been used in the experiment, no codes
phenomenon
> would have been detected in Genesis. In other words, even
though the
> methodology of the 1994 experiment, their War and Peace
counterexample
> would now be rendered irrelevant, assuming that Haralicks
findings
> are technically correct.
> Unfortunately I do not have the expertise to fully evaluate
Haralicks
> paper. However, I think one sentence in their abstract is
certainly
> worth commenting on:
> We designed an improved protocol for the experiment using
> statistically more powerful compactness measures and an ELS
Random
> Placement control text population. [1]
> If I had to guess, it is primarily this improved protocol
that is
> behind the remarkable results of this experiment.
The improved protocal is described fully in the paper and was
motivated at least partially by the critisms in McKays
paper. I just
read it yesterday and could not find obvious fault with the
reasoning.
> You can download Haralicks paper here
http://www.torahcodes.net as
> well as other papers in the section marked new. Note that I
am not
> claiming that Haralicks findings are correct, 
but only that
his
> claims should be taken seriously. I am interested to hear
how the
> anti-codes crowd would intelligently dispute this finding.
> Torah Codes claims have been taken seriously by its critics
for over
> 10 years. Like you I hope that someone qualified will
intelligently
> dispute Haralicks paper. Unless it is published in
peer-reviewed
> journal, however, I do not not expect a thorough analysis
of it.
I have a feeling that McKay and Simon will take Haralicks
claims
seriously and try to dispute them regardless of whether it is
published in a peer-reviewed journal or not. The fact that it
is up on
the internet and presents a serious challenge to their claims
by
someone as distinguished as Prof. Haralick (you can find his
resume
here:
http://prl.cs.gc.cuny.edu/web/LabWebsite/Haralick/main.htm) is
enough for them to intelligently try to dispute it. Up until
now,
McKay and Simon have been winning the codes debate.
> Also, I recommend anyone who is skeptical about the general
codes
> phenomenon and knows some basic Hebrew to go here:
> http://www.meru.org/Lettermaps/B%27rePole.html
Then combine the picture on that site with the explanation:
When the
> aleph-beis is counted in base 3 starting at zero, we get
the following
> relationships: (beis,yud)=(001,100), (vav,taf)=(012,210),
> (heh,mem)=(011,110), (lamed,reish)=(1,0,2)=(2,0,1). Notice
that every
> letter in the picture (except for the first and last)
horizontally
> pairs with itself or its mirror image. Whether or not you
think that
> this is all a coincidence, youll have to agree that there
is a very
> interesting pattern in the first verse of Genesis.
> Yes, it is quite amusing.
The reason I pointed it out was not to try to convince anyone
that
Genesis was written by God but to show that there are some
patterns in
the text which appear not to be by chance.
> [1] http://cs.anu.edu.au/~bdm/dilugim/StatSci/
> [2] http://cs.anu.edu.au/~bdm/dilugim/torah.html
> [3] http://cs.anu.edu.au/~bdm/dilugim/Nations/
> [4] http://cs.anu.edu.au/~bdm/dilugim/gans_exp.html
> [5]
http://www.ratio.huji.ac.il/show-dp-abstract.asp?dpNumber=364
> [6] http://www.wopr.com/biblecodes/Cities_Overview.htm
> [7] http://cs.anu.edu.au/~bdm/dilugim/StatSci/gans_rep.html
> [8] http://www.torahcodes.co.il/debate1.htm
> [9]
http://www.aish.com/seminars/discovery/Codes/Primer/primer1.
htm
> [10] http://www.torahcodes.net/hypoth.pdf
> [11]
http://www.math.toronto.edu/~drorbn/Codes/NationsExtract.html
===
Subject: Re: Bible Codes Resurrected?
> It is true that the choice of appellations is regarded by
McKay et al
> (1999) to be the most serious problem with the data [1].
However,
> nowhere in the paper is it argued that Witztum et al should
have used
> have used all possible appellations.
> Maybe not explicitly but it certainly was implied.
Perhaps the following sentences can be interpreted in that
way:
Since WRR used far less than half of the appellations by
which their
rabbis
were known, the issue of how the selection was made is
central to the
interpretation of their experiment ... This has led to the
widely held
misconception that the list was comprehensive or that the
selection was
rigorous and mechanical. Not so.
In any case, the paper does not at any time state that an
appropriate list
for an experiment attempting to provide evidence of Torah
Codes is a
combination of the two lists from Witztum et al (1994) and
the War and
Peace
list of Bar-Natan et al (1999). The reason this is
inappropriate is
because,
as McKay et al have shown, Witztum et als lists seem to be
tuned to
acheive
remarkable results in Genesis. Nobody has claimed that
combining the War
and
the effect.
> 1. Witztum et al tended to choose options more favorable to
their
> results when a choice was available [1]. The same was found
in
> numerous other experiments by Witztum et al [2], and the
bias is most
> apparent in the 70 nations experiment [3].
> This is basically the same argument as I described before.
No, this is a different argument. Please see the section of
the paper
titled
The study of variations (pages 14-20).
http://cs.anu.edu.au/~bdm/dilugim/StatSci/StatSci.pdf
> 2. The P2 value, a measurement used by Witztum et al., was
closer to
> each other for the two lists of rabbis than what would be
expected by
> chance. Having them close together makes it appear that the
results
> are consistent. However, McKay et al. found that when
shufßing the
> two lists of rabbis together and splitting them in half,
the results
> were only equal around 1% of the time. The same study was
performed on
> the rabbis in Gans cities experiment and found similar
results [1].
> I talked in person with Gans about this a few years ago
because I had
> questions about this. He said that when he did his cities
experiment,
> he did not split the lists up as was done in the WRR paper.
Yes, but Gans didnt compile the appellations and cities on
his own.
Rather,
he obtained the data from Zvi Inbal, a lecturer on the Torah
Codes and a
friend of Doron Witztum. (As far as I know Inbal has not made
any public
statement about the origins of the data.) The hypothesis
(which is not
explicitly stated) seems to be that Witztum compiled the
lists expecting
them to be used in two seperate experiments, adjusted them to
demonstrate
remarkable but consistent results (as he did with his
previous lists), and
gave them to Inbal to give to Gans. This hypothesis seems to
be the most
consistent with the data. Please see the section titled
Traces of naive
statistical expectation (pages 20-22) for more information.
> Is there any evidence that could potentially be found that
would
> refute the *possibility* that there are hidden codes in
Genesis? What
> about hidden codes War and Peace?
> That is pretty difficult to do. Sort of like trying to 
define
> randomness. Its relatively easy to show that a sequence 
is
not random
> by finding a pattern. However, showing that there is no
conceivable
> pattern is much more difficult. So there is no real proof
that there
> are no hidden codes in War and Peace although it is pretty
safe to
> assume such.
I agree. However, after considering the evidence for and
against the Torah
Codes, I also believe that it is pretty safe to assume that
there are no
codes in the Torah.
> I have a feeling that McKay and Simon will take Haralicks
claims
> seriously and try to dispute them regardless of whether it
is
> published in a peer-reviewed journal or not. The fact that
it is up on
> the internet and presents a serious challenge to their
claims by
> someone as distinguished as Prof. Haralick (you can find his
resume
> here:
http://prl.cs.gc.cuny.edu/web/LabWebsite/Haralick/main.htm) is
> enough for them to intelligently try to dispute it. Up
until now,
> McKay and Simon have been winning the codes debate.
Fortunately they will still be winning even if none of the
experts respond
to Haralicks paper, since the reliability of any experiment
using data
from
Witztum et als lists must automatically be questioned.
> Yes, it is quite amusing.
> The reason I pointed it out was not to try to convince
anyone that
> Genesis was written by God but to show that there are some
patterns in
> the text which appear not to be by chance.
Before it was demonstrated that hidden codes can be found in
any book,
Bible
Codes appeared to not exist by chance (and Im sure you 
would
agree that
*some* of the impressive looking codes exist by chance).
Before it was demonstrated that hidden patterns of 7 can be
found in any
book, Panins patterns in the Old Testament and New 
Testament
appeared to
not exist by chance:
http://cs.anu.edu.au/~bdm/dilugim/panin.html
It has not yet been demonstrated that similar patterns to the
pattern you
pointed out can be found in any book. However, when this
pattern becomes
the
subject of a bestseller or a paper in a peer-reviewed journal
I suspect
someone knowledgable will be motivated enough demonstrate
this.
http://www.polesoft.com/refer.html
===
Subject: Re: Bible Codes Resurrected?
> Yes, but Gans didnt compile the appellations and cities 
on
his own.
Rather,
> he obtained the data from Zvi Inbal, a lecturer on the
Torah Codes and a
> friend of Doron Witztum. (As far as I know Inbal has not
made any public
> statement about the origins of the data.)
Inbal and Witztum both say that Inbal compiled the date on
his own and
gave it to Gans.
Brendan.
===
Subject: Re: Bible Codes Resurrected?
> Fortunately they will still be winning even if none of the
experts
respond
> to Haralicks paper, since the reliability of any
experiment using data
from
> Witztum et als lists must automatically be questioned.
This contradicts what you said before. Before you suggested
that
Haralick use the appellations from all six lists that you
gave. But
the six lists that you gave include Witztums lists.
Craig
===
Subject: Re: Bible Codes Resurrected?
Fortunately they will still be winning even if none of the
experts
respond
> to Haralicks paper, since the reliability of any
experiment using data
from
> Witztum et als lists must automatically be questioned.
> This contradicts what you said before. Before you suggested
that
> Haralick use the appellations from all six lists that you
gave. But
> the six lists that you gave include Witztums lists.
When, in particular, did I say this?
This is what I have said on the subject:
The objectivity of the data used by Witztum et al (1994) has
been
seriously criticized for the reasons I specified in a previous
post to
this thread. If Haralick wanted to avoid the critcism that
his data is
biased, he should not be including this data in his
experiment at all.
In fact, Haralick had many choices about where he derived his
data
from ...
===
Subject: Re: Bible Codes Resurrected?
----- Original Message -----
===
Subject: Re: Bible Codes Resurrected?
> Yet we find that Haralick is using list 2 and 3 (both of
which have
> been severely critcized) combined with list 6. Why would
Haralick use
> a list 1 and 2 as part of his data? Perhaps because he
realizes he has
> no chance of achieving remarkable results unless he uses
list 1 or 2.
> Or more likely he didnt have access to those lists, as he
said in his
> paper that he knew of no other publicly released lists.
Remember that
> McKay did not release these lists in his published paper,
only on his
> website. I think it is asking a little to much to expect
Haralick, who
> is a busy man, to have to surf the net in order to find out
about this
> information.
If McKay had published the lists in the journal then it would
have been
quite time consuming to retype them one character at a time.
By publishing
the lists on the Internet McKay made them about as easy to
obtain as
possible. According to the biography you linked, Haralick is
a Computer
Science professor. Are you really arguing that a Computer
Science professor
who has spent numerous hours analyzing Torah Codes would not
be able to
find
such easily obtainable data?
Even if we assume that Haralick was unaware that the data was
publically
available or unable to locate it, could he not have send
McKay an e-mail
asking for the data?
I am certain Haralick was aware that this data existed, but
nevertheless
chose not to use it.
> Furthermore, what if Haralick were to have performed his
> analysis with these lists and the experiment were
successful? Then
> McKay could have easily taken the lists down from his
website and then
> people might accuse Haralick of tuning his lists.
Do you really believe that McKay is the only one who has this
data after it
has been publically available on his website for 4 years?
Do you realize that there are about 21 snapshots between
October 1999 and
any of these snapshots?
http://web.archive.org/web/*/http://cs.anu.edu.au/~bdm/
dilugim/StatSci/data.
html
> It sounds like you are moving the goalposts. In any case,
if these
> other lists are reasonable, then there is no reason why
Haralick
> should fear using them. But to accuse him of not having
used them
> because he knows that they wont work is completely
unfounded.
It is possible but I consider it very unlikely. Haralick
probably considers
these lists unreasonable for some reason or another, and will
probably cite
Witztums numerous objections to these lists.
http://www.torahcodes.co.il/emanuel/eman_hb.htm
http://www.torahcodes.co.il/emanuel/ema1_eng.htm
Responses are available to Witztums claims:
http://cs.anu.edu.au/~bdm/dilugim/StatSci/emanuel_rep.html
http://cs.anu.edu.au/~bdm/dilugim/StatSci/var_rep.html
> This only addresses some of the problems with the data.
There may be
> similar problems with the improved protocol. For example,
why did
> Haralick develop an improved protocol rather than the
protocol
> recommended to Witztum et al by Diaconis, or the protocol
actually
> used in Witztum et al? This again leaves wiggle room.
> protocal. The new protocal addresses these problems and is
more
> descriptive of the Torah Code hypothesis. And if you read
carefully
> wiggle room involved with the selection of the new metric.
Okay. I have no expertise in mathematics so right now I wont
make any
additional comments on the protocol, but I do hope that McKay
or someone
else with expertise takes the time to analyze it.
http://www.polesoft.com/refer.html
===
Subject: Re: Bible Codes Resurrected?
> ----- Original Message -----
===
> Subject: Re: Bible Codes Resurrected?
> Yet we find that Haralick is using list 2 and 3 (both of
which have
> been severely critcized) combined with list 6. Why would
Haralick use
> a list 1 and 2 as part of his data? Perhaps because he
realizes he
has
> no chance of achieving remarkable results unless he uses
list 1 or 2.
> Or more likely he didnt have access to those lists, as he
said in his
> paper that he knew of no other publicly released lists.
Remember that
> McKay did not release these lists in his published paper,
only on his
> website. I think it is asking a little to much to expect
Haralick, who
> is a busy man, to have to surf the net in order to find out
about this
> information.
> If McKay had published the lists in the journal then it
would have been
> quite time consuming to retype them one character at a
time. By
publishing
> the lists on the Internet McKay made them about as easy to
obtain as
> possible. According to the biography you linked, Haralick
is a Computer
> Science professor. Are you really arguing that a Computer
Science
professor
> who has spent numerous hours analyzing Torah Codes would
not be able to
find
> such easily obtainable data?
> Even if we assume that Haralick was unaware that the data
was publically
> available or unable to locate it, could he not have send
McKay an e-mail
> asking for the data?
> I am certain Haralick was aware that this data existed, but
nevertheless
> chose not to use it.
I think it is safe to say that we both have no idea why
Haralick did
not use the list on McKays website. The only way to know is
to ask
him. Regardless of what Haralick is thinking, I think his
experiment
on its own (assuming that it is as he described it and is
correct
technically) does give evidence that there is a codes
phenomenon in
the Torah. The results are consistent with what one would
expect if
there is a codes phenomenon and inconsistent with the null
hypothesis.
I eagerly await the response from the McKay and Simon team. I
agree
that they were successful in their attack of the WRR paper.
However,
given this new result, Im not certain they will be
successful. I hope
they will be successful if indeed there is a ßaw in
Haralicks work.
I saw that you helped McKay write his response to Gans
primer on
Codes. Perhaps you can make him aware of this new result of
Haralick,
if he is not already aware?
> Furthermore, what if Haralick were to have performed his
> analysis with these lists and the experiment were
successful? Then
> McKay could have easily taken the lists down from his
website and then
> people might accuse Haralick of tuning his lists.
> Do you really believe that McKay is the only one who has
this data after
it
> has been publically available on his website for 4 years?
> Do you realize that there are about 21 snapshots between
October 1999 and
> any of these snapshots?
I never knew this. Thats a good idea, as historians will go
through
this looking at the early days of the internet.
>
http://web.archive.org/web/*/http://cs.anu.edu.au/~bdm/
dilugim/StatSci/data.h
tml
> It sounds like you are moving the goalposts. In any case,
if these
> other lists are reasonable, then there is no reason why
Haralick
> should fear using them. But to accuse him of not having
used them
> because he knows that they wont work is completely
unfounded.
> It is possible but I consider it very unlikely. Haralick
probably
considers
> these lists unreasonable for some reason or another, and
will probably
cite
> Witztums numerous objections to these lists.
> http://www.torahcodes.co.il/emanuel/eman_hb.htm
> http://www.torahcodes.co.il/emanuel/ema1_eng.htm
> Responses are available to Witztums claims:
> http://cs.anu.edu.au/~bdm/dilugim/StatSci/emanuel_rep.html
> http://cs.anu.edu.au/~bdm/dilugim/StatSci/var_rep.html
I doubt that. Thats not Haralicks style.
> This only addresses some of the problems with the data.
There may be
> similar problems with the improved protocol. For example,
why did
> Haralick develop an improved protocol rather than the
protocol
> recommended to Witztum et al by Diaconis, or the protocol
actually
> used in Witztum et al? This again leaves wiggle room.
> protocal. The new protocal addresses these problems and is
more
> descriptive of the Torah Code hypothesis. And if you read
carefully
> wiggle room involved with the selection of the new metric.
> Okay. I have no expertise in mathematics so right now I
wont make any
> additional comments on the protocol, but I do hope that
McKay or someone
> else with expertise takes the time to analyze it.
> http://www.polesoft.com/refer.html
===
Subject: Re: Bible Codes Resurrected?
When you mix salt crystals and red or black crystals together
and
really shake them up in a glass container -- you do not end
up with an
evenly mixed pinkish or grayish mixture -- instead there are
striations of colour.
Similarly, for any sufficiently long text.
You will be able to do word wrap of various lengths and it
would be
very surprising if some words and/or phrases did not show up
at
least a few times.
--
Casey
===
Subject: Re: Bible Codes Resurrected?
> Then combine the picture on that site with the explanation:
When the
> aleph-beis is counted in base 3 starting at zero, we get
the following
> relationships: (beis,yud)=(001,100), (vav,taf)=(012,210),
> (heh,mem)=(011,110), (lamed,reish)=(1,0,2)=(2,0,1). Notice
that every
> letter in the picture (except for the first and last)
horizontally
> pairs with itself or its mirror image. Whether or not you
think that
> this is all a coincidence, youll have to agree that there
is a very
> interesting pattern in the first verse of Genesis.
Well, you sound like a perfect crackpot. I think you might
want to
think about your post once more.
Bible Codes? What are you talking about?
--
Eray Ozkural
===
Subject: Re: Bible Codes Resurrected?
>> Whether or not you think that
>> this is all a coincidence, youll have to agree that 
there
is a very
>> interesting pattern in the first verse of Genesis.
> Well, you sound like a perfect crackpot. I think you might
want to
> think about your post once more.
> Bible Codes? What are you talking about?
Since hes not putting forth a theory, but asking a 
question,
he hardly sounds like a crackpot. The responses to his
question have been only comments about how coincidences
happen.
The Bible Codes assertions are deeper than that. Everyone
acknowledges that coincidences happen. The assertion here
is that in Torah, the coincidences happen way too often
to be just random.
Specifically, it appears that the new paper shows that
the frequency of coincidences is much higher in the Torah
than in War and Peace.
So Craig asks whether this is a legitimate observation. No one
addresses this, but instead gives the pat rebuttal to the
1994 paper.
It makes me wonder if anyone read Craigs post.
Bart
===
Subject: Re: Bible Codes Resurrected?
>Specifically, it appears that the new paper shows that
>the frequency of coincidences is much higher in the Torah
>than in War and Peace.
> It may appear so; however, where does it say that?
> Since this is a math group -- is there a quantitative
comparison?
> How many letters in War and Peace? Torah?
> What Id be more interested in, is if there is a pattern 
in
the number
> of recognizable words/phrases for different letter
wrappings -- from
> 2, 3, 4, columns etc. up to 1/3 the length of the book.
> I wonder if the number of patterns follows a normal curve.
> Have other works been analyzed?
> Doby-Mick by Mervin Helville
http://www.crank.net/bible.html has lots of links to crank
sites based
on this idea, and also an anti crank site showing codes in
Moby
Dick:
http://cs.anu.edu.au/~bdm/dilugim/moby.html
Of course, I suspect that the Rev. Spooner could find many
many more.
> Jord Lim by Coseph Jonrad
> Letham by Shilliam Wakespeare
> The Flord of the Lies by Gilliam Wolding
Gill Bolding to her friends.
===
Subject: Re: Bible Codes Resurrected?
>Specifically, it appears that the new paper shows that
>the frequency of coincidences is much higher in the Torah
>than in War and Peace.
> It may appear so; however, where does it say that?
> Since this is a math group -- is there a quantitative
comparison?
> How many letters in War and Peace? Torah?
A brief introduction of the scientific Torah Codes dispute can
be
http://cs.anu.edu.au/~bdm/dilugim/Chance.pdf
The actual paper Craig referred to can be found at this URL:
http://www.torahcodes.net/hypoth.pdf
===
Subject: Re: Bible Codes Resurrected?
>>Specifically, it appears that the new paper shows that
>>the frequency of coincidences is much higher in the Torah
>>than in War and Peace.
> It may appear so; however, where does it say that?
> Since this is a math group -- is there a quantitative
comparison?
According to the OP, thats exactly the experiment performed
in the paper. I sure dont care one way or the other. My
point was that the responses to the OP were as if the OPs
question was much more shallow than it really was.
Bart
===
Subject: Re: Bible Codes Resurrected?
>Specifically, it appears that the new paper shows that
>the frequency of coincidences is much higher in the Torah
>than in War and Peace.
Thats hardly surprising, since the Torah allows you o 
fill in
any
vowels you like to create meaningful words, whereas with War
and
Peace the spelling is fixed for vowels and consonants.
--
Stan Brown, Oak Road Systems, Tompkins County, New York, USA
http://OakRoadSystems.com/
And if youre afraid of butter, which many people are nowa-
days, (long pause) you just put in cream. --Julia Child
===
Subject: Re: Bible Codes Resurrected?
>>Specifically, it appears that the new paper shows that
>>the frequency of coincidences is much higher in the Torah
>>than in War and Peace.
> Thats hardly surprising, since the Torah allows you o 
fill
in any
> vowels you like to create meaningful words, whereas with
War and
> Peace the spelling is fixed for vowels and consonants.
Recall that the original rebuttal paper DID find the high
frequency of coincidences in War and Peace. The OPs 
question
was, In this new investigation, supposedly done with more
statistical sense, the Torah beat War and Peace. Is
this significant?
Bart
===
Subject: Re: Bible Codes Resurrected?
> The Bible Codes assertions are deeper than that. Everyone
> acknowledges that coincidences happen. The assertion here
> is that in Torah, the coincidences happen way too often
> to be just random.
Rubbish.
> Specifically, it appears that the new paper shows that
> the frequency of coincidences is much higher in the Torah
> than in War and Peace.
Did you remove the vowels from the W&P text? Should have some
consequence
on
probability, me thinks.
(Hebrew is written without vowels)
===
Subject: Re: Bible Codes Resurrected?
===
>Subject: Re: Bible Codes Resurrected?
>Message-id: <58Pnd.30702$b%6.1484858@phobos.telenet-ops.be>
The Bible Codes assertions are deeper than that. Everyone
>> acknowledges that coincidences happen. The assertion here
>> is that in Torah, the coincidences happen way too often
>> to be just random.
>Rubbish.
>> Specifically, it appears that the new paper shows that
>> the frequency of coincidences is much higher in the Torah
>> than in War and Peace.
>Did you remove the vowels from the W&P text? Should have
some consequence
on
>probability, me thinks.
>(Hebrew is written without vowels)
Except when it isnt.
I just picked up a copy of the U.S. News and World Reports
bible codes and in Cracking the Bible Code it says:
<quote>
Some of the oldest Hebrew texts, in fact, omitted vowels
altogether, scholars say, while later writings used them
sporadically. Virtually all versions of the Hebrew Bible
known to us today employ a complex mixture of full and
defective spelling that is not even consistent for the same
words.
</quote>
Incidentally, I really liked the quote at the beginning of
this
Isiaiah 45:18-19
I am the Lord, and there is no other.
I did not speak in secret, in a land of darkness;
I did not say to the offspring of Jacob, Seek me in chaos.
I the Lord speak the truth, I declare what is right.
That passage seems most appropriate since it seems to
imply that God does not use secret codes. But it differs
from the KJV translation:
Isiaiah 45:18-19
I am the Lord, and there is none else.
I have not spoken in secret, in a dark place of the earth:;
I said not unto the seed of Jacob, Seek ye me in vain:
I the Lord speak righteousness, I declare things that are
right.
Seek me in chaos and Seek me in vain is _not_ a subtle
difference in translation. It completely changes the whole
passage.
--
Mensanator
Ace of Clubs
===
Subject: Re: Bible Codes Resurrected?
>> The Bible Codes assertions are deeper than that. Everyone
>> acknowledges that coincidences happen. The assertion here
>> is that in Torah, the coincidences happen way too often
>> to be just random.
>Rubbish.
Its not rubbish. I reported exactly correctly what
the Bible Codes folks are asserting.
> Did you remove the vowels from the W&P text?
ME? I didnt write the paper and Im not going 
to read
it either. All I did was to point out that the responders
didnt understand the OPs question.
Just like you didnt understand my post.
Bart
===
Subject: Re: Bible Codes Resurrected?
>Did you remove the vowels from the W&P text? Should have
some consequence
on
>probability, me thinks.
>(Hebrew is written without vowels)
IIRC this was done using a Hebrew translation of War and
Peace.
It would be silly to make this kind of comparison using texts
in
different languages. There still might be problems due to the
difference between biblical Hebrew and modern Hebrew.
Robert Israel israel@math.ubc.ca
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia Vancouver, BC, Canada
===
Subject: Re: Bible Codes Resurrected?
[Bible code stuff]
>Well, you sound like a perfect crackpot.
A _perfect_ crackpot? Surely that titles reserved for JSH!
:-)
--
Stan Brown, Oak Road Systems, Tompkins County, New York, USA
http://OakRoadSystems.com/
And if youre afraid of butter, which many people are nowa-
days, (long pause) you just put in cream. --Julia Child
===
Subject: Re: Bible Codes Resurrected?
>Equidistant Letter Sequences in the Book of Genesis which
claimed to
>find evidence for hidden codes in the Hebrew text of Genesis.
http://www.math.temple.edu/~paulos/bibcodes.html
--
Stan Brown, Oak Road Systems, Tompkins County, New York, USA
http://OakRoadSystems.com/
And if youre afraid of butter, which many people are nowa-
days, (long pause) you just put in cream. --Julia Child
===
Subject: Re: Bible Codes Resurrected?
>Equidistant Letter Sequences in the Book of Genesis which
claimed to
>find evidence for hidden codes in the Hebrew text of Genesis.
> http://www.math.temple.edu/~paulos/bibcodes.html
As do other mathematicians:
http://www.math.caltech.edu/code/petition.html
===
Subject: Re: Bible Codes Resurrected?
>> Uh-huh. John Allen Paulos disposed of that idea
>As do other mathematicians:
http://www.math.caltech.edu/code/petition.html
I was unaware of that page, but I have to confess Im a 
little
disappointed. They state that there are problems with the
1994 paper
but dont state what the problems are.
--
Stan Brown, Oak Road Systems, Tompkins County, New York, USA
http://OakRoadSystems.com/
And if youre afraid of butter, which many people are nowa-
days, (long pause) you just put in cream. --Julia Child
===
Subject: Re: Bible Codes Resurrected?
>> Uh-huh. John Allen Paulos disposed of that idea
>As do other mathematicians:
http://www.math.caltech.edu/code/petition.html
> I was unaware of that page, but I have to confess Im a
little
> disappointed. They state that there are problems with the
1994 paper
> but dont state what the problems are.
The problems can be found in the paper below:
http://cs.anu.edu.au/~bdm/dilugim/StatSci/
===
Subject: Re: Bible Codes Resurrected?
>>As do other mathematicians:
http://www.math.caltech.edu/code/petition.html
>> I was unaware of that page, but I have to confess Im a
little
>> disappointed. They state that there are problems with the
1994 paper
>> but dont state what the problems are.
>The problems can be found in the paper below:
>http://cs.anu.edu.au/~bdm/dilugim/StatSci/
educated!
--
Stan Brown, Oak Road Systems, Tompkins County, New York, USA
http://OakRoadSystems.com/
And if youre afraid of butter, which many people are nowa-
days, (long pause) you just put in cream. --Julia Child
===
Subject: Re: Bible Codes Resurrected?
funny; they did an ELS of Kaczynskis Manifesto,
getting b
mail o
m
b
s, or like that, and
readers are welcome to find Free Ted!
in it, as well.
>http://cs.anu.edu.au/~bdm/dilugim/StatSci/
--Harry Potter wants you, in Sudan!
http://larouchepub.com
===
Subject: Re: Bible Codes Resurrected?
posting-account=UtgH7gwAAACpBhTelVPOXNP7RAfbtQrK
<more bible code crap snipped>
Do you have any concept of how easy it is to find hidden words
in _any_ sufficiently large piece of text? To demonstrate how
silly
this is, I created
The Shakespeare Code
Start with a well known passage (Hamlets Soliloquy) and
remove
all spaces and punctuation. Now wrap the text in a spiral:
(this requires a monospaced font to view correctly)
yeltgnseptyltuovednoitaMmuslwaeskiir
inaursssootehtdnaehcatRaeseaelkierse
htnrutotfbhidotmehtdnEgnhnrtheadwpyv
usdnnhrhdeoemraekatoTroieoertdmntrmi
mttstaseewutsasgnilseheshchorssuaell
buhpatwraisoanbonsitrtnotatmawuehtle
lruunpretsasgdlhtsiterupdsyseathtnad
ynszdaoshhnlaaeenroahetpniaibletseee
tatzsTnpwddeirrqotehtfroetmhdeihrdbr
hwhlWigehtnenriutobtefoyeoatlhutenso
areEeetcaoapsonetobehufbwtefutqahant
nyNsanhttdtntwtstionwssdyrrfoesettog
kaatttetdiuoaShemindtounaidowvidohsn
ynthumphrermSofoutrageoaseodoohrogio
odieneraetaOeaoftroublesohtehlteturl
ulvwdrotaoLreandbyasleeptselwdhtyood
Now, all one has to do is play word search to find hidden
messages.
But only use diagonals so as not to pick up actual words from
the
quotation.
Ive capitalized three words:
NEWT TERM LOSS
which leads to the conclusion that Shakespeare predicted
Gingrichs
defeat in the 1998 Congressional election!
Spooky, eh?
===
Subject: Re: Bible Codes Resurrected?
I dont get how you wrapped the text
in a spiral, but thats a great spoof
of the whole BC sophistry. the question is, of course,
did you search for those terms via an increasing modulo,
or did you construct it in some other way?
> Start with a well known passage (Hamlets Soliloquy) and
remove
> all spaces and punctuation. Now wrap the text in a spiral:
> (this requires a monospaced font to view correctly)
> yeltgnseptyltuovednoitaMmuslwaeskiir
> inaursssootehtdnaehcatRaeseaelkierse
> htnrutotfbhidotmehtdnEgnhnrtheadwpyv
> usdnnhrhdeoemraekatoTroieoertdmntrmi
> mttstaseewutsasgnilseheshchorssuaell
> buhpatwraisoanbonsitrtnotatmawuehtle
> lruunpretsasgdlhtsiterupdsyseathtnad
> ynszdaoshhnlaaeenroahetpniaibletseee
> tatzsTnpwddeirrqotehtfroetmhdeihrdbr
> hwhlWigehtnenriutobtefoyeoatlhutenso
> areEeetcaoapsonetobehufbwtefutqahant
> nyNsanhttdtntwtstionwssdyrrfoesettog
> kaatttetdiuoaShemindtounaidowvidohsn
> ynthumphrermSofoutrageoaseodoohrogio
> odieneraetaOeaoftroublesohtehlteturl
> ulvwdrotaoLreandbyasleeptselwdhtyood
> Now, all one has to do is play word search to find hidden
messages.
> But only use diagonals so as not to pick up actual words
from the
> quotation.
> Ive capitalized three words:
> NEWT TERM LOSS
--Give Earth a Trickier Dick Cheeny -- out of office, after
gigayears!
http://tarpley.net/bush12.htm
http://www.benfranklinbooks.com/
http://members.tripod.com/~american_almanac
http://www.wlym.com/pdf/iclc/howthenation.pdf
http://www.rand.org/publications/randreview/issues/rr.12.00/
http://www.rwgrayprojects.com/synergetics/plates/figs/plate02.
html
===
Subject: Re: Bible Codes Resurrected?
===
>Subject: Re: Bible Codes Resurrected?
>I dont get how you wrapped the text
>in a spiral,
Are you familiar with Ulams Spiral, where integers are 
placed
in a spiral pattern?
765
814
923
Extending that out to a 100x100 grid, the primes seem to be
aligned in straight lines. For my spiral I used letters
instead of
numbers.
To be or not to be
becomes
Tobeornottobe
wrapped in a counter-clockwise spiral
nro
oTe
tob
tobe
>but thats a great spoof
>of the whole BC sophistry. the question is, of course,
>did you search for those terms via an increasing modulo,
>or did you construct it in some other way?
I didnt use any sort of modulo, I only looked at letter
patterns
that were in contiguous diagonal lines. When I first built the
spiral,
I had a program generate every possible word of 3, 4, 5, 6, 7
and 8
letters. I ended up with something like a half million words,
most
of which were garbage, of course. But I didnt have any way 
of
spell-checking the list to discard the chaff.
So I put the word list aside for 9 months until I got a Linux
system
and figured out how to write a shell script to process the
entire
list. I managed to sift out a couple thousand legitimate
words.
Then I simply looked through the list for something
interesting.
Curiously, it was during that 9 month delay that Gingrich lost
his re-election. Had I done the spell-check at the time I
created
the word list, the three words NEWT TERM LOSS would not
have struck me as being interesting. Its easy to predict 
the
past.
>> Start with a well known passage (Hamlets Soliloquy) and
remove
>> all spaces and punctuation. Now wrap the text in a spiral:
>> (this requires a monospaced font to view correctly)
>> yeltgnseptyltuovednoitaMmuslwaeskiir
>> inaursssootehtdnaehcatRaeseaelkierse
>> htnrutotfbhidotmehtdnEgnhnrtheadwpyv
>> usdnnhrhdeoemraekatoTroieoertdmntrmi
>> mttstaseewutsasgnilseheshchorssuaell
>> buhpatwraisoanbonsitrtnotatmawuehtle
>> lruunpretsasgdlhtsiterupdsyseathtnad
>> ynszdaoshhnlaaeenroahetpniaibletseee
>> tatzsTnpwddeirrqotehtfroetmhdeihrdbr
>> hwhlWigehtnenriutobtefoyeoatlhutenso
>> areEeetcaoapsonetobehufbwtefutqahant
>> nyNsanhttdtntwtstionwssdyrrfoesettog
>> kaatttetdiuoaShemindtounaidowvidohsn
>> ynthumphrermSofoutrageoaseodoohrogio
>> odieneraetaOeaoftroublesohtehlteturl
>> ulvwdrotaoLreandbyasleeptselwdhtyood
>> Now, all one has to do is play word search to find hidden
messages.
>> But only use diagonals so as not to pick up actual words
from the
>> quotation.
>> Ive capitalized three words:
>> NEWT TERM LOSS
>--Give Earth a Trickier Dick Cheeny -- out of office, after
gigayears!
>http://tarpley.net/bush12.htm
>http://www.benfranklinbooks.com/
>http://members.tripod.com/~american_almanac
>http://www.wlym.com/pdf/iclc/howthenation.pdf
>http://www.rand.org/publications/randreview/issues/rr.12.00/
>http://www.rwgrayprojects.com/synergetics/plates/figs/plate02
.html
--
Mensanator
Ace of Clubs
===
Subject: Re: Bible Codes Resurrected?
I see; I had seend Ulams spiral, before. its 
pretty obvious,
though, from the context
of skip codes, as used by scribes as a check
on their copying, that they just assembled a program,
into which was input what ever words were wished
to be found, and skipped throught the ring of text,
with an increasing modulus until the **** was found.
of course, all of it was ex post facto, except
for the one that the evil orthodox clowns had
Drosnin review, that Rabin would be assassinated.
> wrapped in a counter-clockwise spiral
> nro
> oTe
> tob
> tobe
> I didnt use any sort of modulo, I only looked at letter
patterns
> that were in contiguous diagonal lines. When I first built
the spiral,
> I had a program generate every possible word of 3, 4, 5, 6,
7 and 8
> letters. I ended up with something like a half million
words, most
> of which were garbage, of course. But I didnt have any 
way
of
> spell-checking the list to discard the chaff.
> the word list, the three words NEWT TERM LOSS would not
> have struck me as being interesting. Its easy to predict
the past.
--ils duces dEnron!
http://larouchepub.com
===
Subject: tessellations
by support1.mathforum.org (8.11.6/8.11.6/The Math Forum,
$Revision:
1.9 primary) id iAJL0VF16807;
A few years ago I worked with a math PhD who had a poster on
the wall called
the 13 semi-perfect tessellations or something along those
lines. An
example is Octagons and Squares.
Im trying to find out where I can buy this 
poster. Can anyone
help?
Its for an elementary school.
===
Subject: Re: tessellations
> A few years ago I worked with a math PhD who had a poster
on the wall
called the 13 semi-perfect tessellations or something along
those lines.
An example is Octagons and Squares.
> Im trying to find out where I can buy this 
poster. Can
anyone help?
> Its for an elementary school.
http://members.cox.net/tessellations/Posters.html
Something like this...?
Pawel Gladki
===
Subject: Re: NEAT PRODUCTS OF TRIG FUNCTIONS
by support1.mathforum.org (8.11.6/8.11.6/The Math Forum,
$Revision:
1.9 primary) id iAJL0Vj16794;
I can see now that this string should have been entitled Neat
but please do not stop now!
There are a couple I have not been able to verify, and I see
no
general method to my solution madness that suggests a
constructive
approach. I even wonder how some of these were generated or
discovered!
So, if you would let me know your solutions or methods I
would be
very grateful! Also, if anybody has others, why not post them
here?
Most of my verifications involve identities and minimal
polynomials
found for these (necessarily algebraic) values of trig
functions of
angles rationally commensurate with pi. Some are brief, while
others
are somewhat tedious; perhaps, unnecessarily so. I would love
to
exchange any notes or ideas on this genre of interesting and
>I am seeking examples of complicated combinations of trig
functions
>that have simple values (e. g., rational ones), even though
the
>functions themselves may not. One such example is the product
> P = cos(20)cos(40)cos(80)
>(where angles are measured in degrees), whose value equals
1/8. I
>would appreciate knowing about any similar relationships.
>You might be interested in a surprising direct calculation
of this
>value, which uses the fact that
> cos(60) = 1/2,
>and which is outlined below.
>The proof I had found in high school was done by multiplying
both
>sides by 8sin(20) and using the sine double angle identity
to obtain
> 8Psin(20) = sin(160),
>from which the result follows (since 20 and 160 are
supplementary).
>This admits generalizations (none so nice found) and
modifications,
>such as the more obfuscatory product of the same three
numbers:
> P = sin(10)sin(50)sin(70).
>My new one uses the identities
> cos(2A) = 2[cos(A)]^2 - 1
> cos(3A) = 4[cos(A)]^3 - 3[cos(A)]
> cos(4A) = 8[cos(A)]^4 - 8[Cos(A)]^2 + 1.
>We let
> u = cos(20).
>The second of these implies
> 4u^3 - 3u = 1/2,
>and our product becomes
> P = u[2u^2 - 1][8u^4 - 8u^2 + 1].
>Some rearrangement and serpendipitous recognitions lead to
the result:
> P = [2u^3 - u][8u^4 - 6u^2 - 2u^2 + 1]
> = (1/2)[4u^3 - 3u + u][2u(4u^3 - 3u)- 2u^2 + 1]
> = (1/2)[1/2 + u][u - 2u^2 + 1]
> = (1/4)[-4u^3 + 3u +1]
> = (1/4)[-1/2 + 1]
> = 1/8.
>Ta-DA!!!
>I note in passing that this is a clever variant of a purely
>mechanical technique which may be used to collapse any
polynomial in
> u = cos(20)
>to at worst a quadratic one. Here, the process terminates
with the
>constant 1/8.
===
Subject: Fourier Series and sum (-1)^p/(2p+1)^2
by support1.mathforum.org (8.11.6/8.11.6/The Math Forum,
$Revision:
1.9 primary) id iAJL0Wh16833;
Does someone know a function whose Fourier series can compute
the following
sum :
sum from p=0 to infinite of (-1)^p/(2p+1)^2 ?
===
Subject: Re: Fourier Series and sum (-1)^p/(2p+1)^2
> Does someone know a function whose Fourier series can
compute the
following
> sum :
> sum from p=0 to infinite of (-1)^p/(2p+1)^2 ?
I dont, but it might be of interest to know the above sum
equals the
integral of (arctan(x))/x over [0,1].
===
Subject: Re: Fourier Series and sum (-1)^p/(2p+1)^2
by support1.mathforum.org (8.11.6/8.11.6/The Math Forum,
$Revision:
1.9 primary) id iAJLF5q18673;
>Does someone know a function whose Fourier series can
compute the following
sum :
>sum from p=0 to infinite of (-1)^p/(2p+1)^2 ?
Try looking here.
http://mathworld.wolfram.com/CatalansConstant.html
Nick
===
Subject: Re: Fourier Series and sum (-1)^p/(2p+1)^2
by support1.mathforum.org (8.11.6/8.11.6/The Math Forum,
$Revision:
1.9 primary) id iAJLV9T20209;
OK.
===
Subject: Has the world gone mad?
Isnt it true that R (the real line) and R/{0} (the real 
line
with the
origin removed) *are not* isomorphic to each other (under the
usual
ordering of the real numbers)?
I ask because a certain very helpful Mr. Liou answered a
question of
by pointing me to a paper (by a certain Baumgartner) which
says that,
assuming the continuum hypothesis, all aleph-one-dense sets
of reals
could be isomorphic. I havent found a copy of the actual
paper, but
all references Ive found to it define an 
aleph-one-dense set
of reals
the obvious way, as a set that has aleph-one-many members in
any
interval of reals you care to name. Both R and R/{0} would
appear to
qualify, no? And if so, why does the following proof fail to
contradict Baumgartners statement trivially?
Let f : R/{0} -> R be a purported order-isomorphism. Call 
fs
image
on the negative reals N, and fs image on the positive reals
P. N
and P are then a partition of the reals into a left and a
right
subset. N has a least upper bound in R, and P has a greatest
lower
bound, and clearly they are the same. Call their shared bound
b. b
must be in N or in P. Assume without loss of generality that
b is in
N. Then its pre-image under f is some negative real number x.
But
then there is a negative real closer to the origin (x/2, for
example)
which has to be mapped to a point in N that is (because f
preserves
order) greater than b. There is no such point, so R/{0} and R
have no
isomorphism.
===
Subject: Re: Has the world gone mad?
|I havent found a copy of the actual paper, but
|all references Ive found to it define an 
aleph-one-dense set
of reals
|the obvious way, as a set that has
has _exactly_
| aleph-one-many members in any
|interval of reals you care to name. Both R and R/{0} would
appear to
|qualify, no?
Not unless the continuum hypothesis is true. Evidently the
Baumgartner statement, that all aleph-1-dense sets of reals
are order-isomorphic, contradict the continuum hypothesis.
This is a natural generalization of Cantors theorem that 
all
Keith Ramsay
===
Subject: Re: Has the world gone mad?
Keith is exactly right -- my misunderstanding was to assume
aleph-one dense meant having *at least* aleph-one-many points
in any
interval, when Baumgartner wants it to mean *exactly*
aleph-one-many
points. Apologies to anyone whose time was wasted on this;
Ill try
to post only substantive questions in the future.
On the other hand, someone was nice enough to mail me the
link the
Baumgartners paper, which I couldnt 
find myself.
http://matwbn.icm.edu.pl/ksiazki/fm/fm79/fm7911.pdf
Its amazing how much complicated structure might be hiding
in so
innocuous-sounding a thing as the real line. Theres a good
overview paper on different properties the real line might
have under
different set-theoretic hypotheses, by K. Kunen and F. Tall,
here:
http://www.math.toronto.edu/tall/publications/48.pdf
===
Subject: Re: Has the world gone mad?
> Isnt it true that R (the real line) and R/{0} (the real
line with the
> origin removed) *are not* isomorphic to each other (under
the usual
> ordering of the real numbers)?
They arent order-isomorphic: R has the least-upper-bound
property
but R{0} doesnt.
--
Robin Chapman, www.maths.ex.ac.uk/~rjc/rjc.html
Lacan, Jacques, 79, 91-92; mistakes his penis for a square
root, 88-9
Francis Wheen, _How Mumbo-Jumbo Conquered the World_
===
Subject: Re: Has the world gone mad?
<cnmti2$u7d$1@newsg3.svr.pol.co.uk Isnt it true that R (the
real line) and R/{0} (the real line with the
> origin removed) *are not* isomorphic to each other (under
the usual
> ordering of the real numbers)?
> They arent order-isomorphic: R has the least-upper-bound
property
> but R{0} doesnt.
Indeed. In contrast,
Q is order isomorphic to Q0.
Z is order isomorphic to Z0.
===
Subject: Re: Has the world gone mad?
> Isnt it true that R (the real line) and R/{0} (the real
line with
the
> origin removed) *are not* isomorphic to each other (under
the usual
> ordering of the real numbers)?
> They arent order-isomorphic: R has the least-upper-bound
property
> but R{0} doesnt.
> Indeed. In contrast,
> Q is order isomorphic to Q0.
> Z is order isomorphic to Z0.
The statement about Z is easily seen to be true. I doubt the
statement
about Q - assuming that the conventional order is being used
for both
Q and Q {0}.
--
Chris Henrich
The total lack of evidence is the surest sign that the
conspiracy is
working.
===
Subject: Re: Has the world gone mad?
>> Isnt it true that R (the real line) and R/{0} (the real
line with
>> the origin removed) *are not* isomorphic to each other
(under the
>> usual ordering of the real numbers)?
>> They arent order-isomorphic: R has the least-upper-bound
property
>> but R{0} doesnt.
>> Indeed. In contrast,
>> Q is order isomorphic to Q0.
>> Z is order isomorphic to Z0.
> The statement about Z is easily seen to be true. I doubt
the statement
> about Q - assuming that the conventional order is being
used for both
> Q and Q {0}.
Its true. All countably infinite totally 
ordered sets with no
maximum
and minimum and with a element strictly between any two given
distinct
elements are order-isomorphic.
--
Robin Chapman, www.maths.ex.ac.uk/~rjc/rjc.html
Lacan, Jacques, 79, 91-92; mistakes his penis for a square
root, 88-9
Francis Wheen, _How Mumbo-Jumbo Conquered the World_
===
Subject: Re: Has the world gone mad?
>> Q is order isomorphic to Q0.
>> Z is order isomorphic to Z0.
> The statement about Z is easily seen to be true. I doubt
the statement
> about Q - assuming that the conventional order is being
used for both
> Q and Q {0}.
> Its true. All countably infinite totally 
ordered sets with
no maximum
> and minimum and with a element strictly between any two
given distinct
> elements are order-isomorphic.
Its a bear, or at least a bob cat to prove.
List the elements and one by one order isomorphically fit them
into the
diatic rationals Z[1/2]. Then showing that the mapping is
surjective,
conclude the so described linear order is order isomorphic to
Z[1/2].
Thus as Q and Q0 both have the described property, theyre
both
order isomorphic to Z[1/2], hence to each other.
Now you see how removal of finite many elements from Q or Z,
produces
any order isomorphic set.
===
Subject: Re: Has the world gone mad?
> Q is order isomorphic to Q0.
> Z is order isomorphic to Z0.
>> The statement about Z is easily seen to be true. I doubt
the
statement
>> about Q - assuming that the conventional order is being
used for both
>> Q and Q {0}.
>> Its true. All countably infinite totally 
ordered sets with
no maximum
>> and minimum and with a element strictly between any two
given distinct
>> elements are order-isomorphic.
>Its a bear, or at least a bob cat to prove.
>List the elements and one by one order isomorphically fit
them into the
>diatic rationals Z[1/2]. Then showing that the mapping is
surjective,
>conclude the so described linear order is order isomorphic
to Z[1/2].
It is much easier than that to prove. Let A and B be the two
sets, and denote the orderings of them by <_A and <_B
respectively,
and the enumerations of them by q_A and q_B respectively.
Let A_j and B_j be the subsets chosen at time j, and let
f_j be the 1-1 order-preserving mapping from A_j into B_j.
A_0 and B_0 are the empty set, and as A_j and B_j will have
j elements, AA_j and BB_j will be divided into j+1 countable
subsets in their orderings <_A and <_B.
If j=2k, let a_j be the q_A first element of AA_j and
let b_j be the first element of BB_j in the corresponding
countable subset of BB_j. If j=2k+1, reverse the roles
of A and B. Let f_{j+1} = f_j u {<a_j, b_j>}.
It is now easy to prove by induction that the relevant
properties of A_j and B_j are preserved, and that all
of A and B are used.
--
This address is for information only. I do not claim that
these views
are those of the Statistics Department or of Purdue
University.
Herman Rubin, Department of Statistics, Purdue University
hrubin@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558
===
Subject: Re: Has the world gone mad?
>> Q is order isomorphic to Q0.
>> Z is order isomorphic to Z0.
> The statement about Z is easily seen to be true. I doubt the
statement
> about Q - assuming that the conventional order is being
used for
both
> Q and Q {0}.
> Its true. All countably infinite totally 
ordered sets with
no maximum
> and minimum and with a element strictly between any two
given distinct
> elements are order-isomorphic.
> Its a bear, or at least a bob cat to prove.
> List the elements and one by one order isomorphically fit
them into the
> diatic rationals Z[1/2]. Then showing that the mapping is
surjective,
> conclude the so described linear order is order isomorphic
to Z[1/2].
> Thus as Q and Q0 both have the described property, theyre
both
> order isomorphic to Z[1/2], hence to each other.
> Now you see how removal of finite many elements from Q or Z,
produces
> any order isomorphic set.
I think it is important to choose the next dyadic rational at
each step
with some care. If it is to be less than all previously chosen
numbers, or greater than all, it should be the integer with
the
smallest absolute value consitent with this requirement. If
it is to
be between two previously chosen numbers, it should be the
dyadic
rational with the smallest possible denominator.
Whats really a bear, and a bear with a toothache, is trying
to draw
the graph of that mapping.
--
Chris Henrich
God just doesnt fit inside a single religion.
===
Subject: Re: Has the world gone mad?
===
Subject: Re: Has the world gone mad?
>> Q is order isomorphic to Q0.
> Its true. All countably infinite totally 
ordered sets with
no
> maximum and minimum and with a element strictly between any
two
> given distinct elements are order-isomorphic.
>> Its a bear, or at least a bob cat to prove.
>> List the elements and one by one order isomorphically fit
them into
>> the diatic rationals Z[1/2]. Then showing that the mapping
is
>> surjective, conclude the so described linear order is order
>> isomorphic to Z[1/2].
>> Thus as Q and Q0 both have the described property, 
theyre
both
>> order isomorphic to Z[1/2], hence to each other.
> I think it is important to choose the next dyadic rational
at each
> step with some care. If it is to be less than all
previously chosen
> numbers, or greater than all, it should be the integer with
the
> smallest absolute value consitent with this requirement. If
it is
> to be between two previously chosen numbers, it should be
the dyadic
> rational with the smallest possible denominator.
For wherever theyre worth or not worth, 
heres my brief
outline notes or chronicals of the bob cat fight I had.
Do note the first part was showing any countable linear order
embeds in
the dyadic rationals. In particular, any countable ordinal
embedds in the
dyadic rationals. Ordermorphic is short for order isomorphic.
-- eta, order type rationals
countable linear order S ==> S embeds in dyadic rationals
bounded countable dense linear order S ==> S ordermorphic
Z[1/2] / [0,1]
unbounded countable dense linear order S ==> S ordermorphic
Z[1/2], Q
Add top, bottom to S as needed, remove afterwards
Let D = dyadic rationals = Z[1/2] / [0,1]
Enumerate S: s0 = bottom, s1 = top, s2, s3,...
Let f(s0) = 0, bn = max { si | i < n, si < sn }
f(s1) = 1, tn = min { si | i < n, sn < si }
f(sn) = (f(bn) + f(tn))/2 for n > 1
For all j,k, sj < sk ==> f(sj) < f(sk). (induction)
s0 = bottom < top = s1; f(s0) = 0 < 1 = f(s1). (case n = 2)
If for all j,k < n, sj < sk ==> f(sj) < f(sk) then
for all j,k < n+1, sj < sk ==> f(sj) < f(sk)
For i < n < n+1: f(sn) = (f(bn)+f(tn))/2 (case n = n+1)
some j,k < n with sj = bn < sn < tn = sk; f(bn) < f(tn)
f(bn) = 2f(bn)/2 < (f(bn)+f(tn))/2 = f(sn)
f(sn) = (f(bn)+f(tn))/2 < 2f(tn)/2 = f(tn)
if si < sn: si <= bn; f(si) <= f(bn) < f(sn)
if sn < si: tn <= si; f(sn) < f(tn) <= f(si)
f increasing injection into D
dense linear order S ==> f surjection. If f(S) /= D:
let m be smallest m for which n/2^m in Df(S)
some b,t with f(b) = (n-1)/2^m, f(t) = (n+1)/2^m
let n be smallest n with sn in (b,t); by construction:
f(sn) = (f(b) + f(t))/2 = n/2^m which cannot be
--
> Whats really a bear, and a bear with a toothache,
> is trying to draw the graph of that mapping.
Dont smell like a shaggy dog if youre out to 
out fox a bob
cat. ;-)
----
===
Subject: Re: Has the world gone mad?
days. My association with the Department is that of an
alumnus.
>Isnt it true that R (the real line) and R/{0} (the real
line with the
>origin removed) *are not* isomorphic to each other (under
the usual
>ordering of the real numbers)?
Order isomorphic?
>I ask because a certain very helpful Mr. Liou answered a
question of
>by pointing me to a paper (by a certain Baumgartner) which
says that,
>assuming the continuum hypothesis, all aleph-one-dense sets
of reals
>could be isomorphic. I havent found a copy of the actual
paper, but
>all references Ive found to it define an 
aleph-one-dense set
of reals
>the obvious way, as a set that has aleph-one-many members in
any
>interval of reals you care to name. Both R and R/{0} would
appear to
>qualify, no?
Dont you think that a precise knowledge of what Baumgartner
calls
aleph-one-dense and what Baumgartner calls isomorphic are
*incredibly* important in trying to figure this out?
> And if so, why does the following proof fail to
>contradict Baumgartners statement trivially?
Because we dont know what Baumgartners 
actual statement is,
because
we dont know what it is he calls aleph-one-dense or what it
is he
calls isomorphic? Note in particular the use of the
conditional
could in your paraphrase. What does two sets could be
isomorphic
mean, as opposed to are isomorphic?
--
Its not denial. Im just very selective 
about
what I accept as reality.
--- Calvin (Calvin and Hobbes)
Arturo Magidin
magidin@math.berkeley.edu
===
Subject: quaternions
what is the point of quaternions?
they are all the square root of -1. the only thing of
interest about
them is their relationships among each other... completely
arbitrary
to me.
===
Subject: Re: quaternions
at 02:00 PM, SharpNova@gmail.com (David Bandel) said:
>what is the point of quaternions?
Which point? The historical origins? The applications? The
place in
theory?
>they are all the square root of -1.
No. 1+I+j, for example, is not a square root of -1.
>the only thing of interest about them is their relationships
among
>each other
No, thats not the only thing of intereset, but if you
believe that
you know the answer then why are you asking?
>completely arbitrary to me.
I can live with that, but heres a free clue: if you want to
ask a
question, then dont presuppose that you know the answer.
More people
will be willing to help you if they believe that youre
willing to
listen.
--
Shmuel (Seymour J.) Metz, SysProg and JOAT
<http://patriot.net/~shmuel>
Unsolicited bulk E-mail subject to legal action. I reserve the
right to publicly post or ridicule any abusive E-mail. Reply
to
domain Patriot dot net user shmuel+news to contact me. Do not
===
Subject: Re: quaternions
> what is the point of quaternions?
> they are all the square root of -1. the only thing of
interest about
> them is their relationships among each other... completely
arbitrary
> to me.
There are more things in heaven and earth, Horatio, than are
dreamt of
in your philosophy.
===
Subject: Re: quaternions
>what is the point of quaternions?
>they are all the square root of -1. the only thing of
interest about
>them is their relationships among each other... completely
arbitrary
>to me.
There was a thread last year, quaternions-- whats the
point?, that
might be helpful. I saved the following therefrom:
>Did you try a Google search on quaternions? The fourth entry
I found was
>how to use them for representing rotations - including a
explanation of
one
>advantage quaternions have over other representations. If
you look at
>http://www.j3d.org/faq/manipulating.html#quaternions youll
get an idea of
>why quaternions are part of Java 3D.
===
Subject: Re: quaternions
>>what is the point of quaternions?
>>they are all the square root of -1. the only thing of
interest about
>>them is their relationships among each other... completely
arbitrary
>>to me.
...
> There was a thread last year, quaternions-- whats the
point?, that
> might be helpful. I saved the following therefrom:
>>Did you try a Google search on quaternions? The fourth
entry I found was
>>you how to use them for representing rotations - including
a explanation
>>of one
>>advantage quaternions have over other representations.
While the use of quaternions in representing rotations
is no doubt a valuable tool,
I wouldnt say it is the most important application.
The quaternions H form the only non-commutative division
algebra
(or skew-field) of finite dimension over the reals 
R.
As such they are likely to arise in any context
where R or the complex numbers C arise.
For example, every simple group representation of finite
degree over C
is associated to R, C or H,
with those associated to H corresponding to symplectic
structures.
This is a basic theme in the classification of simple Lie
groups.
--
Timothy Murphy
e-mail (<80k only): tim /at/ birdsnest.maths.tcd.ie
tel: +353-86-2336090, +353-1-2842366
s-mail: School of Mathematics, Trinity College, Dublin 2,
Ireland
===
Subject: Re: quaternions
>what is the point of quaternions?
>they are all the square root of -1. the only thing of
interest about
>them is their relationships among each other... completely
arbitrary
>to me.
What is the point of your question? Just a bunch of letters
in the
english alphabet... completely arbitrary to me.
G. Rodrigues
===
Subject: Re: quaternions
>what is the point of quaternions?
>they are all the square root of -1. the only thing of
interest about
>them is their relationships among each other... completely
arbitrary
>to me.
> What is the point of your question? Just a bunch of letters
in the
> english alphabet... completely arbitrary to me.
> G. Rodrigues
point of my question was that i didnt know much about
quaternions and
was curious what they are used for.. all i knew was the basic
relations. comments about algebras and rotations of spaces
lead me in
just the right directions to do the research i was looking to
do.
what was the point of your statement? just to look like an
idiot? it
seems as though both our points were well taken. yours by me
and mine
by everyone but you.
stuff that one up your stocking till christmas 2008 buddy :)
===
Subject: Re: quaternions
>>what is the point of quaternions?
>>they are all the square root of -1. the only thing of
interest about
>>them is their relationships among each other... completely
arbitrary
>>to me.
>> What is the point of your question? Just a bunch of
letters in the
>> english alphabet... completely arbitrary to me.
>> G. Rodrigues
>point of my question was that i didnt know much about
quaternions and
>was curious what they are used for.. all i knew was the basic
>relations. comments about algebras and rotations of spaces
lead me in
>just the right directions to do the research i was looking
to do.
>what was the point of your statement? just to look like an
idiot? it
>seems as though both our points were well taken. yours by me
and mine
>by everyone but you.
It is always sad when one has to point out the meaning of his
own
words, but the point of my irony was that you framed your
question in
a trollish manner and as such you deserved a trollish answer.
But probably its just me getting hyper-sensitive.
G. Rodrigues
===
Subject: Re: quaternions
>>
>>what is the point of quaternions?
>>they are all the square root of -1. the only thing of
interest about
>>them is their relationships among each other... completely
arbitrary
>>to me.
>>
>> What is the point of your question? Just a bunch of
letters in the
>> english alphabet... completely arbitrary to me.
>>
>> G. Rodrigues
>point of my question was that i didnt know much about
quaternions and
>was curious what they are used for.. all i knew was the basic
>relations. comments about algebras and rotations of spaces
lead me in
>just the right directions to do the research i was looking
to do.
>what was the point of your statement? just to look like an
idiot? it
>seems as though both our points were well taken. yours by me
and mine
>by everyone but you.
> It is always sad when one has to point out the meaning of
his own
> words, but the point of my irony was that you framed your
question in
> a trollish manner and as such you deserved a trollish
answer.
> But probably its just me getting hyper-sensitive.
> G. Rodrigues
i didnt need to point out the meaning of my words. i got
good answers
before i ever pointed out the meaning to you.
it is always sad when someone is such an old grouch that 
hes
set in
his obnoxious ways and cant find a way out of 
them (like
taking any
legitimate question to be a trolling) get a grip man.
besides, who
cares if you ARE hyper sensitive?
grouch around these groups for awhile longer and maybe 
youll
be able
to discern between trolls and nontrolls. judging from your
comments..
that would rate as a worthwhile expenditure of your time.. to
you.
===
Subject: Re: quaternions
days. My association with the Department is that of an
alumnus.
>what is the point of quaternions?
Just like complex numbers can be used to model the
rotations/contractions of the plane about the origin, the
quaternions
give the rotations and contractions of 3-dimensional space.
>they are all the square root of -1. the only thing of
interest about
>them is their relationships among each other... completely
arbitrary
>to me.
No; as Hamilton explained when he introduced them, the
relation
ij=-ji, (ij)^2=-1 has to do with their geometric
interpretation.
--
Its not denial. Im just very selective 
about
what I accept as reality.
--- Calvin (Calvin and Hobbes)
Arturo Magidin
magidin@math.berkeley.edu
===
Subject: Re: Proof of the Full Beal Conjecture
posting-account=i3V6Cw0AAADtbYn3XKL9H7v2PfvxgaVa
doh!
Old post on beal conjecture.
Sorry, but if anyone knows about the beal conjecture status
any news
would be helpful.
> Did you ever get any feed back on the Beal Conjecture thing?
> The beal conjecture website (www.bealconjecture.com) still
shows the
> prize money as available. I just wonder if you have heard
from Beal
> about his Conjecture. Has anyone solved the beal conjecture?
> Or has anyone disproved the beal conjecture.
> Is fermats last theorem and the Beal conjecture the same
thing?
> I have recently uploaded my proof of the Beal Conjecture.
It may
be
> downloaded from its listing under the 
Fermats Last Theorem
> category
> on the Open Directory Project.
> It is also available directly at-
geocities.com/kerrymerry2000.
===
Subject: Re: Proof of the Full Beal Conjecture
conjecture award is still not paid out.
If you didnt notice the date, I doubt you have much chance
of proving or
disproving the beal conjecture. Try something easier like the
lottery.
> doh!
> Old post on beal conjecture.
> Sorry, but if anyone knows about the beal conjecture status
any news
> would be helpful.
>> Did you ever get any feed back on the Beal Conjecture
thing?
>> The beal conjecture website (www.bealconjecture.com) still
shows the
>> prize money as available. I just wonder if you have heard
from Beal
>> about his Conjecture. Has anyone solved the beal
conjecture?
>> Or has anyone disproved the beal conjecture.
>> Is fermats last theorem and the Beal conjecture the same
thing?
>> I have recently uploaded my proof of the Beal Conjecture.
It may
> be
>> downloaded from its listing under the 
Fermats Last
Theorem
>> category
>> on the Open Directory Project.
>> It is also available directly at-
geocities.com/kerrymerry2000.
===
Subject: Re:
=?ISO-8859-1?Q?Automatic_generation_of_G=F6del_sentence?=
> |It sounds as though Emanuel has been reading
_Goedel,_Escher,_Bach_.
> |Hofstatders exposition of this point is at best
confusing; while
> |I cant put my hands on my copy to check what he actually
said, I
> |think its probably fair to say that Hofstatder just got
it wrong.
> My copy is not too deeply buried in boxes, but from what I
remember,
> he talks vaguely about our ability to Goedelize. This makes
it sound
> like it might be a question of generating Goedel sentences
for systems.
> But really hes talking about generating a sequence of
theories like
> PA, PA+con(PA), PA+con(PA+con(PA)),.... Call PA T, and call
> PA+con(PA) T2, and so on. This sequence can be extended to
> ordinal numbers given by suitable ordinal notations. The
union
> of T, T2, T3, T4,... can be axiomatized and we could call it
> T_omega where omega is the first infinite 
ordinal. (I think
> Hofstadter mentions this.) And we can keep going, letting
> T_{omega+1} be T_omega+con(T_omega) and so on.
> The problem with our ability to carry this on out is not
with our
> ability to generate con(T) for a theory T, but with our
ability to
> name ordinals (using ordinal notations). I think he just
fails to
> make this explicit.
> Keith Ramsay
> P.S. The original poster should be aware that the time has
not
> yet come to include ISO-8859 characters in subject lines.
For
> me this still displays the o as =F6. Patience, patience....
Well, Hofstadters exposition is a little dated, and as you
can tell
from the prizes it got, too literary for a mathematicians
liking.
Anyhow, there ought to be more interesting statements than
consistency
statements. There are a lot of undecidable statements for any
given
FAS. (And really I dont think the logical POV 
doesnt matter
as much
as many people think it does...)
--
Eray Ozkural
===
Subject: Re:
=?ISO-8859-1?Q?Automatic_generation_of_G=F6del_sentence?=
|Well, Hofstadters exposition is a little dated, and as you
can tell
|from the prizes it got, too literary for a mathematicians
liking.
I disagree. Not all mathematicians like literariness but some
do.
I also wouldnt call it highly literary, Pulitzer prize or 
no
Pulitzer
prize. Its not what I would choose as a textbook for 
teaching
Goedels theorem, but it is an entertaining popularization.
It came
out when I was at just the right age to appreciate it.
|Anyhow, there ought to be more interesting statements than
consistency
|statements.
There certainly should, but the diagonal argument is one of
the
easiest methods of proving independence, and it tends to
exhibit
similar-looking examples of independent statements.
Its also somewhat adaptable. Given a property of sentences
U(S)
definable in the system, it describes how to cook up a 
sentence
G such that G<->~U(G). So if you think that U(S) is sufficient
to guarantee the truth of S, then you think G is true, but you
dont think so because you think U(G) holds!
When philosophers of mathematics get started talking about
criteria for acceptance of axioms, I sometimes start to get
this
disturbing sense that they are on their way to providing a
notion
that could be arithmetized, and then turned into a conjecture:
the consequences of the axioms that satisfy their criteria for
axiom-acceptability should be true. But if it is so, it is not
possible to prove from axioms satisfying their criteria. The
criteria
for acceptability of axioms can include such uncomputable
things
as their consistency with other axioms, being simpler than any
other axioms having the same theorems and so on, having a lot
of consequences by some criterion of a lot, and this situation
still remains.
Keith Ramsay
===
Subject: Limits in topologies, limits of topologies
(categories anyone?)
Im sure I came across this somewhere on the net sometime,
but I cant
for the life of me find it (not that Im lazy, I 
have tried
(both to
find it on the internet, and to figure it out 
myself)). Or
perhaps
this is just an exercise in (my) ignorance. In any event,
heres a
question I would like to understand the answer to:
Simply put, is there any particularly nice way that anyone
knows of to
make (direct) limits in categories like limits in
analysis/topology?
Or more concretely, Im asking about the following:
You have the notion of the direct limit in categories, which
gives the
direct limit of topologies in the category of topologies. And
the
direct limit of topologies is very similar in definition to
the limit
of nets - but is there any way of building a category around a
particular topology so that the limit of a net *is* some
direct limit
in the category?
(in this sense either a topological clarification (linking
direct
limits of topologies to direct limits in topologies) or a
categorical
clarification (just giving a topology the appropriate
categorical
structure) would completely answer my question)
===
Subject: Triple Coincidence
With help from I.M. Davidson, Keith A. Lewis, Phil Carmody,
Daniel W.
Johnson,
Gerry Myerson, Brian Quincy Hutchings, Stan Liu, Saint Cad,
Jose Carlos
Santos, and Richard Miller, I have been exploring the triple
coincidence
associated with FLT in threads Perky People Prefer
Pseudorandom
Periodicity,
A fairly simple proposition, Counterexample to t((c^n - a^n)
mod b) |
phi(b), and On the Euler phi values of pairwise coprimer a,b,
and c.
The triple co-incidence derivable from a^n + b^n = c^n is
(a^n + b^n) == 0 mod c &
(c^n - a^n) == 0 mod b &
(c^n - b^n) == 0 mod a.
These three conditions are necessary but not sufficient for
a^n + b^n =
c^n.
I call
(a^n + b^n) mod c a dual additive exponential congruential
generator, and
(c^n - a^n) mod b a dual subtractive exponential congruential
generator,
and
(c^n - b^n) mod a the same.
Each generator has an associated congruential sequence
ordered by n and
these
sequences are purely periodic with period dividing the phi of
their
corresponding bases, c, b, and a. For all a, b, and c, and
n=0 the values
of
the three generators are 2, 0, and 0. At n = 1 the values are
(mod c)
unknown
(can be 2), (mod b) nonzero, and (mod a) nonzero. At n = 2
the values are
unknown (symbolically, so far).
What is of interest in searches is that the only time the
locations of the
individual coincidences are all three the same is when they
occur all at n =
2.
Larger values for the coincidence are associated with at
least one sequence
having a period that differs from the other two. This implies
that it might
be
possible to prove that for the triple coincidence to occur,
it must happen
either at 2 or at composite n. And we know from relatively
elementary
argument
that n is prime, or at least that if there is a solution for
composite n,
there
will be an associated solution for a prime n. 2 is the only
prime that
fits.
So I am looking for any knowledge any of you readers may
have, or references
to
knowledge of the periods of dual exponential congruential
sequences.
I thank you for your time. This is going to be all I have, I
think, until
after
we close our apartment deal. Its rather stressful. On the
other hand, its
pretty much in the bag now. On the other other hand, the
anticipation is
just
driving me up the wall. Closing is Wednesday, 24 Nov at 12:00.
I tolerance everything and tolerate everyone.
I love: Dona, Jeff, Kim, Kimmie, Mom, Neelix, Tasha, and Teri,
alphabetically.
I drive: A double-step Thunderbolt with 657% range.
I fight terrorism by: Using less gasoline.
===
Subject: Re: meta-proof that p is not np
Hi Torkel,
It sounds as if you have not read the referenced theorems in
Prof.
Caludes paper, which is only a click away from you. If you
would
please read that, we can discuss the relevance of the
referenced
theorem.
I have a complaint about your posting behavior. You ask a
question. I
give you an answer. You dont like the answer, or you do not
read it.
You rephrase exactly the same question and ask it. After you
do this
four times, people like me become demotivated, because this
looks like
an attempt to indoctrinate your ideas about indefinite things:
philosophical questions like What on earth is reasoning?.
Please
read and respond to my answers, if you are asking questions.
Otherwise, do not ask them.
Here _we_ give a specific answer to your query from the
viewpoint of
digital philosophy. If you dont like digital philosophy.
Fine. Then
say, I dont accept this, because I think X. But do explain
your
position as we do.
The question you have asked the second time is answered in
response to
your question once more. Please take the time to think about
it.
> Take any bit of Omega, there is no way to know _in general_
this
> single bit of information from something else, in the sense
of
> computing it from something, or more mathematically speaking
> proving it from some axioms (which are not distinct things,
of
> course).
> There is indeed no computational procedure which proves all
true
> statements of the form the n-th bit of Omega is i. The same
is true
> of any undecidable set of true statements - nothing special
about
> Omega here. What I am asking about is the claim that
statements
> of the form the n-th bit of Omega is i are true for no
reason
> and can only be postulated, not proved.
> That is, we are basing our argument on Chaitins version 
of
Godelian
> incompleteness. We say that no (finite) formal axiomatic
system can
> ever settle arbitrarily many bits of Omega.
> And how does this fact imply that the truth of a statement
of the
> form the n-th bit of Omega is i can only be postulated, not
arrived
> at by reasoning?
If COMPUTATIONAL=REASONING, then the answer is clear, Torkel.
Chaitin
implicitly assumes that MIND=COMPUTATION, but I doubt he is
aware of
his own assumption.
So, you are right in a sense. Hes making certain 
metaphysical
assumptions. And he does not make the effort to make these
clear. Its
not top-notch philosophy at all.
Now, here is the question to you. In your opinion, is the
mind a
discrete computation? Or is it something over and above
discrete
computation?
Let all the other discussion suspend until you answer this.
If you will answer, I will be more than glad to discuss this
matter
with you, a prominent scholar who is humble enough to write on
sci.math
Looking forward to hearing from you.
--
Eray Ozkural
miserable phd student
===
Subject: Re: meta-proof that p is not np
> You rephrase exactly the same question and ask it. After
you do this
> four times, people like me become demotivated,
Well done Torkel! I was wondering how to do that :-)
--
Robin Chapman, www.maths.ex.ac.uk/~rjc/rjc.html
Lacan, Jacques, 79, 91-92; mistakes his penis for a square
root, 88-9
Francis Wheen, _How Mumbo-Jumbo Conquered the World_
===
Subject: Re: meta-proof that p is not np
> I have a complaint about your posting behavior. You ask a
question. I
> give you an answer.
Nothing in your answer is anything to the point.
===
Subject: Re: meta-proof that p is not np
> I have a complaint about your posting behavior. You ask a
question. I
> give you an answer.
> Nothing in your answer is anything to the point.
Well, you seem to have reading comprehension problem.
I said. If mind is a computation, the philosophical
conclusions follow
easily.
Do you agree that mind is a computation or not?
Please answer this simple question.
--
Eray
===
Subject: Ozkural solves mind-body problem was Re: meta-proof
that p is not
np
> I said. If mind is a computation, the philosophical
conclusions follow
> easily.
> Do you agree that mind is a computation or not?
Ônuff said!
--
Robin Chapman, www.maths.ex.ac.uk/~rjc/rjc.html
Lacan, Jacques, 79, 91-92; mistakes his penis for a square
root, 88-9
Francis Wheen, _How Mumbo-Jumbo Conquered the World_
===
Subject: Re: Ozkural solves mind-body problem was Re:
meta-proof that p is
not np
> I said. If mind is a computation, the philosophical
conclusions follow
> easily.
Do you agree that mind is a computation or not?
> Ônuff said!
You better attribute that to Stan Lee - you copyright
violator!
===
Subject: Re: Ozkural solves mind-body problem was Re:
meta-proof that p is
not np
> I said. If mind is a computation, the philosophical
conclusions follow
> easily.
Do you agree that mind is a computation or not?
Well, I am not even the last to suggest that the mind may be a
computation.
However, in the above quote, I am not asserting that the
computational
view of the mind is correct. (Although I think so) Again, you
are
misrepresenting my quotes. Try to read my sentences more
carefully.
The claim is this: Chaitin seems to be implicitly
presupposing the
correctness of computationalism. On such a premise, the other
philosophical claims about no reason trivially follow. Torkel
might
not be able to see that.
So, here is a challenge for Torkel. If the mind is a
computation, then
no reason has a very precise mental meaning, and indeed Omega
is not
amenable to any reason in such a possible world. You have to
accept
its bits as brute facts about the world if youre 
unfortunate
enough
to occupy such a world. Regardless of whether our world is
like that,
do you agree with this answer?
--
Eray Ozkural
===
Subject: Re: Ozkural solves mind-body problem was Re:
meta-proof that p is
not np
>> Eray are there integers with an infinite number of digits?
Ozkural
>> I said. If mind is a computation, the philosophical
conclusions follow
>> easily.
>>
>> Do you agree that mind is a computation or not?
> Well, I am not even the last to suggest that the mind may
be a
> computation.
> However, in the above quote, I am not asserting that the
computational
> view of the mind is correct. (Although I think so) Again,
you are
> misrepresenting my quotes. Try to read my sentences more
carefully.
What would be the point in that? Is there any reason
to read your sentences at all?
--
Robin Chapman, www.maths.ex.ac.uk/~rjc/rjc.html
Lacan, Jacques, 79, 91-92; mistakes his penis for a square
root, 88-9
Francis Wheen, _How Mumbo-Jumbo Conquered the World_
===
Subject: Re: meta-proof that p is not np
> I said. If mind is a computation, the philosophical
conclusions
> follow easily.
Nothing in what you have said is anything to the point.
===
Subject: Re: meta-proof that p is not np
> I said. If mind is a computation, the philosophical
conclusions
> follow easily.
> Nothing in what you have said is anything to the point.
You seem to have a reading problem.
1. If mind is computation, then reasoning too is mere
computation
2. Hence any truth that cannot be ascertained by mere
computation,
as is the case with the problem of determining an arbitrary
number of
bits of Omega, is impenetrable to reason.
3. Hence, we say they are true for no reason. There is no
deeper
reason to why they are what they are. The individual bits are
brute
facts of the world, which must be accepted without reasoning.
Cannot you understand such a simple argument? Here is the
complete
answer to your question, and you cannot understand it.
True for no reason if reason is computation.
Chaitin seems to assume this. You probably do not agree with
it,
because you sound like some sort of vitalist, or religious
person.
You probably believe mind is not computational, but has some
kind of
logical existence distinct from the physical. I wouldnt be
surprised
if you believed in such a silly thing. Prove me wrong.
--
Eray
===
Subject: Re: meta-proof that p is not np
> 1. If mind is computation, then reasoning too is mere
computation
> 2. Hence any truth that cannot be ascertained by mere
computation,
> as is the case with the problem of determining an arbitrary
number of
> bits of Omega, is impenetrable to reason.
Whats supposed to be special about Omega in this argument?
===
Subject: Re: meta-proof that p is not np
> Do you agree that mind is a computation or not?
What is a mind? People have been slicing a dicing other
people for
10,000 years and no one has ever found a mind in a body he
didnt own.
There are brains, glands and other gooey and s
Please answer this simple question.
Bob Kolker
===
Subject: Re: meta-proof that p is not np
Do you agree that mind is a computation or not?
> What is a mind? People have been slicing a dicing other
people for
> 10,000 years and no one has ever found a mind in a body he
didnt own.
That may be because minds are not things to be found in a
body you do
not own.
Or perhaps because we dont have the proper technology to 
find
minds.
I dont know the answer. You are basically asking the 
problem
of other
minds. Are you familiar with philosophy of mind? This is a
question
with no definite answer. There are *answers*, none of which is
conclusive.
But the best answer seems to be computational, for what its
worth.
Its easy to work out one. To see another mind, you would
have to
become part of the same computation, which only occurs to a
small
extent using language. So the answer of computationalism is
that you
do *see* other minds every day, only in a very limited
fashion due to
architectural limits. You see them through computation, not
by opening
up their brains and looking at them!
There are some versions of computationalism, the most famous
is
Putnams machine functionalism which he abandoned later to
retreat
into some ancient myst. (claiming that we need a theory of
direct
perception, yes...) (Note that I dont favor 
Putnams brand of
computationalism. His theories do not seem physically
plausible)
> There are brains, glands and other gooey and s
Nobody claimed that there are no brains.
But claiming that there are NO MINDS is quite naive. Consider
the
problem of qualia. You can try to get rid of qualia by
denying that it
exists. But that is seen as a poor way of argumentation.
(Worse if you
say minds do not exist. That is actually the claim of David
Longleys brand of radical behaviorism. Beware!)
Because its similar to this imaginery tale. There is an
obvious
phenomenon called light. Suppose that we didnt have a good
theory
of light, we couldnt really explain how all the rainbows,
refractions, etc. occured, but these things, however magical
looking,
occured, it is certain that there is a physical phenomenon.
Now,
philosophers in this world of poor science may try this
route: light
does not exist. How realistic is that?
The challenge of contemporary philosophy of mind is the
challenge of
explaining the mind-body problem and other fundamental issues
(like
the problem of qualia) satisfactorily well from the point of
view of
physicalism. These things exist, and they are physical (like
light),
what is their nature? Is there a universal theory of mind,
etc.? (Or
for instance, is mind always a particular type of thing, like
the
minds realized by biological brains, etc.)
We cannot really accept any form of substance dualism, and
that is
definitely not what Im suggesting. However, you 
just *cant*
turn
your back to the harsh reality of subjective experience. We
cant yet
explain what it is, but we think it is worth explaining. We
might even
lack the necessary conceptual framework entirely. My
suggestion is
that we should try an alternative metaphysics, lets forget
Platonism.
I think if we can explain computation, we can explain
subjective
experience, too. But I dont think we can explain 
computation
well
enough. A basic problem is this. There is something to being
you. But
most philosophers think there is nothing to being a glass.
Why this
difference?
Ive worked on the above problems of subjective experience
and qualia,
and I think I have come to an interesting answer through
modern theory
of computation and information theory that does not seem to
be limited
to narrow content. A more metaphysical version of this theory
is
called Multism, and you can find its synopsis on
comp.ai.philosophy
and elsewhere. (There is also the Multism of Plamen Petrov,
which is
similar but not the same) It seems substance monism inherent
in my
Multism theory and mechanical irreducibility can easily
answer what
qualia is. In particular, there is digital multism, which
tries to
give more specific answers under the digital postulate. It
goes like
this, there is an irreducible essence to the computation that
occurs
in your brain. This irreducible essence defines the extent of
your
subjective experience, and with every bit you take out of
this essence
you would become less you, until when we reduced your essence
to
nothing, there would be nothing left to being you. This is
quite
physicalist, as you can imagine. However, it says the
*quality* of a
mental state is best explained by the information theoretic
properties
of the computation. And it suggests that the solution should
be
somewhere between radical reductionism (basically any idea
that wants
to reduce us to nothing) and radical nonreductionism (Quine).
I have not yet made my mind about supporting multiple
realizability,
but I think at one level, we will have to accept a form of
multiple
realizability. Obviously, I can transfer one idea from this
bubble of
subjective experience to another by tapping on keys. So,
thats quite
remarkable. It means ideas can be multiply realized. Why not
for
greater constructs like complete mental states then? Maybe,
subjective
experience changes, but other properties remain the same,
which is
sufficient for multiple realizability (So here again, I think
we need
to make some compromises to arrive at a solution)
--
Eray Ozkural
===
Subject: Fermat 420
Fermats Last Theorem
Ben Ito
11-19-04
I will show that Fermats n=4 and Wiles 
proofs are invalid
then prove
Fermats last theorem.
l. Introduction
Fermats last theorem states that
A^n + B^n = C^n, (equ 1)
when n>2 does not form integer solutions of A, B and C.
2. Fermats n=4 Proof
Fermats n=4 proof is described. Fermat uses the integer
solution
equations of n=2,
A = 2uv, B = u^2 - v^2, and C = u^2 + v^2 (equ 2),
to derive,
A^2 = 2uv, B^2 = u^2 - v^2, and C = u^2 + v^2 (equ 3a,b,c),
(Shanks, p.141). Equations 3a,b,c are used to prove that n=4
does not
form integer solutions. Fermats proof is only proving
equations
3a,b,c do not form integer solutions. Equations 3a,b,c are
derived
from n=2 integer solution equations (equ 2a,b,c); therefore,
Fermats
proof violates logic.
3. Wiles Proof
Wiles proof of FLT uses Fermats elliptic 
curve. The
elliptic curve
equation is derived using the integer solution equations of
n=2
(Osserman, p.21),
a = (m^2 - n^2), b = 2mn, c = (m^2 + n^2). (equ 3)
The elliptic curve is only valid for n=2; therefore, Wiles
proof of
FLT is invalid since Wiles proof is using 
Fermats elliptic
curve.
4. Proof of FLT.
I will prove Fermats last equation using the pattern formed
by the
solutions formed by n=1 and n=2. Using n=1 in equation 1,
X + Y = Z (equ 4)
All integers of equation 4 form solutions. An integer
solution set
occurs at (1,2,3).
The integer solutions of n=2 are described with the following
equations,
X = 2uv, Y = u^2 - v^2 and Z = u^2 + v^2 (equ 5)
Not all integers form integer solutions for n=2. An integer
solution
set occurs at (3,4,5).
The n=1 and n=2 solutions show a pattern where solutions are
formed
when a solution set is forms close to the origin, n=1 -->
(1,2,3)
and n=2 --> (3,4,5).
In addition, when n=1, the strength of the solution set
formation is
maximum since all integers form solutions. When n=2, not all
integers form solutions; therefore, the strength of the
solution
formation is weakening. When n=3, the solution set is
weakening as n
increases and the solution set is not formed close to the
origin;
consequently, the integer sequence ends at n = 3. Therefore,
only n=1
and n=2 form integer solutions.
5. Conclusion
Fermats n=4 proof uses equations derived from the integer
solutions
equation of n=2 to prove that n=4 does not form integers;
therefore,
Fermats n=4 proof violates logic.
Fermats elliptic curves are derived using the integer
solution
equations of n=2; therefore, an elliptic curve can not be
used to
prove FLT when n>2.
I will prove FLT by showing a pattern forms from the n=1 and
n=2
solution sets which indicates that only n=1 and n=2 form
integer
solution sets.
6. References
Robert Osserman. Fermats Last Theorem (a supplement to the
video).
MSRI. 1994
Daniel Shanks. Solved and Unsolved Problems in Number Theory.
Chelsea
Pub. 1985.
*-----------------------*
www.GroupSrv.com
*-----------------------*
===
Subject: (probably stupid) question on Fermat decidability
I was reading Simon Singhs book on Fermats 
last theorem,
and got a
big confused by one passage - he mentions the possibility
that the
theorem was undecidable (although obviously it turned out not
to be).
What confused me was this: The theorem couldnt be false but
undecidable, since falsehood implies the existance of a
definite
counter-example. So if its undecidable then it must be 
true,
which
contradicts it being undecidable. So you get a contradiction,
therefore it cannot be undecidable.
Would anyone care to point out where Im going wrong here?
===
Subject: Re: (probably stupid) question on Fermat decidability
. So if its undecidable then it must be true, which
> contradicts it being undecidable. So you get a
contradiction,
> therefore it cannot be undecidable.
> Would anyone care to point out where Im going wrong here?
The word undecidable is a translation of unentscheidbare,
thus the
undecidability must be Goedels undecidability that is, 
formal
undemonstrability
within a system of axioms. A counterexample is not a formal
demosntration.
If Goldbachs conjecture is shown undecidable within 
accepted
arthmetic, a counterexample will not take off its 
Goedels
undecidability.
===
Subject: Re: (probably stupid) question on Fermat decidability
> . So if its undecidable then it must be true, which
>> contradicts it being undecidable. So you get a
contradiction,
>> therefore it cannot be undecidable.
>> Would anyone care to point out where Im going wrong 
here?
> The word undecidable is a translation of unentscheidbare,
thus the
> undecidability must be Goedels undecidability that is,
formal
> undemonstrability
> within a system of axioms. A counterexample is not a formal
> demosntration.
Huh?
A counter example is most definitely a formal demonstration
that something
is false.
If somebody shows me that
15^235 + 126^235 = 127^235
That establishes that FLT is untrue.
Nothing informal about that.
> If Goldbachs conjecture is shown undecidable within
accepted
> arthmetic, a counterexample will not take off its 
Goedels
> undecidability.
Oh yes it will.
If you can find a counter example, it is 
definitely decidable
(in the
negative, as it turns out).
And if you have shown that it is undecidable within accepted
arithmetic,
and you can use accepted arithmetic to show it is false, then
you proved
accepted arithmetic is inconsistent, at which point most of
mathematics
as
we know it disaapears in a puff of smoke ...
===
Subject: Re: (probably stupid) question on Fermat decidability
In sci.math, Peter Webb
<41a17fea$0$20521$afc38c87@news.optusnet.com.au>:
>> . So if its undecidable then it must be true, which
> contradicts it being undecidable. So you get a
contradiction,
> therefore it cannot be undecidable.
> Would anyone care to point out where Im going wrong here?
>> The word undecidable is a translation of unentscheidbare,
thus the
>> undecidability must be Goedels undecidability that is,
formal
>> undemonstrability
>> within a system of axioms. A counterexample is not a formal
>> demosntration.
> Huh?
> A counter example is most definitely a formal demonstration
that something
> is false.
> If somebody shows me that
> 15^235 + 126^235 = 127^235
> That establishes that FLT is untrue.
Sorry, cant oblige.
15^235 + 126^235 - 127^235 =
-2090269352984120073921722601405239849756
98701156813977808530086497347643268855835153351409895379215712
70545556
96047113642907266161896490603848988223386752695909209616202863
73126245
79003191791437569316475219065598456749706850464082308913917438
62001266
14584142281680681711860394371540275476446763248337752289071905
08149387
62305958339298913102809397702883908437833507352734231665434920
08228388
76298259266359220806875535614140466167947509312461332307198356
85424633
75358215282629964552579522143894992
:-)
[rest snipped]
--
#191, ewill3@earthlink.net
Its still legal to go .sigless.
===
Subject: Re: (probably stupid) question on Fermat decidability
===
Subject: Re: (probably stupid) question on Fermat decidability
>The theorem couldnt be false but
>undecidable, since falsehood implies the existance of a
definite
>counter-example.
Yes, it couldnt be false but undecidable. In logic, but
means and. The
theorem
could be false, undecidable *or* true. It is true.
I tolerance everything and tolerate everyone.
I love: Dona, Jeff, Kim, Kimmie, Mom, Neelix, Tasha, and Teri,
alphabetically.
I drive: A double-step Thunderbolt with 657% range.
I fight terrorism by: Using less gasoline.
===
Subject: Re: (probably stupid) question on Fermat decidability
> Yes, it couldnt be false but undecidable.
What do you mean by undecidable?
===
Subject: Re: (probably stupid) question on Fermat decidability
> Yes, it couldnt be false but undecidable.
> What do you mean by undecidable?
Undecidable means there cannot exist a formal proof of a
theorems
true/false status. How to prove undecidability is beyond me.
But I
know you cant, in general, prove a negative, that is, that
nobody had
proven FLT until Wiles et al proved it certainly did not
establish the
undecidability of FLT. That no proof of something exists
isnt proof
no proof can exist. Exhaustive search of possible proofs is
as futile
as exhaustive search of quadruples n,a,b,c, looking for a
counterexample to FLT. You never run out.
Wiles proof reached beyond the axioms of number theory,
didnt it?
Number theory is what Goedel (spelling?) undecidability is
about,
isnt it? Anybody?
Doug
===
Subject: Re: (probably stupid) question on Fermat decidability
> How to prove undecidability is beyond me.
The consensus seems to be that you cant (in this case at
least); if
you did prove FLT to be unprovable then youd generate a
contradiction
(because that would in turn prove it true).
Is this generally true of all theorems?
===
Subject: Re: (probably stupid) question on Fermat decidability
days. My association with the Department is that of an
alumnus.
>> How to prove undecidability is beyond me.
>The consensus seems to be that you cant (in this case at
least); if
>you did prove FLT to be unprovable then youd generate a
contradiction
>(because that would in turn prove it true).
You are mistaken. There would be no contradiction. If
something like,
say, Goldbachs Conjecture (a better example than FLT since
FLT is
know proven) were shown to be formally undecidable in, say,
Peano
Arithmetic, this would not generate any contradiction, but it
would be
possible to state that Goldbachs Conjecture will 
necessarily
be true
in the standard model (because a counterexample would be
verifiable).
>Is this generally true of all theorems?
The same conclusion (undecidable in the system -> true in the
standard model) holds for statements of the specific kind like
FLT or
Goldbach, where if they were false, then there would be a
verifiable
counterexample.
--
Its not denial. Im just very selective 
about
what I accept as reality.
--- Calvin (Calvin and Hobbes)
Arturo Magidin
magidin@math.berkeley.edu
===
Subject: Re: (probably stupid) question on Fermat decidability
> The same conclusion (undecidable in the system -> true in
the
> standard model) holds for statements of the specific kind
like FLT or
> Goldbach, where if they were false, then there would be a
verifiable
> counterexample.
No!!
Either one of A or ~A, where A is a formally undecidable
statement
within a model, can be added as an axiom to that model to
form a new
and larger model which remains consistent. If, for example, A
is the
Goldbach conjecture, then adding ~A to the model for
arithmetic as it
is generally understood does not lead to a contradiction. All
it says
is that a counterexample can not be found by any finite number
of
steps within the model which omits the axiom.
Lets see if a simpler example would help.
Within the natural numbers, consider the statement there is
no natural
number x such that x*x=2. Lets pretend for the sake of
illustration
that it is formally undecidable and then add it as an axiom
that there
exists an x such that x*x=2. A completely consistent theory
is the
result. The new theory includes the theory of natural numbers
as a
sub-theory (and all true derivable theorems within that model
would
remain derivable in the larger model), but there is still no
*natural*
number x such that x*x=2 which can be found by any finite
number of
deductions from the Peano axioms.
Its a subtle point, perhaps, but a formal system and an
interpretation of a formal system are very different things.
In the
example given, one can no longer interpret a variable x as a
natural
number but is forced to interpret it as an irrational number,
which
contains the interpretation as a natural number as merely a
special
case.
Also as the example shows, adding underivable statements as
axioms can
lead to interesting mathematics.
Paul
--
Hanging on in quiet desperation is the English way.
The time is gone, the song is over.
Thought Id something more to say.
===
Subject: Re: (probably stupid) question on Fermat decidability
>> The same conclusion (undecidable in the system -> true in
the
>> standard model) holds for statements of the specific kind
like FLT or
>> Goldbach, where if they were false, then there would be a
verifiable
>> counterexample.
>No!!
>Either one of A or ~A, where A is a formally undecidable
statement
>within a model, can be added as an axiom to that model to
form a new
>and larger model which remains consistent.
Yes.
> If, for example, A is the
>Goldbach conjecture, then adding ~A to the model for
arithmetic as it
>is generally understood does not lead to a contradiction.
You did notice the point where I said standard model? The
model we
would get by adjoining ~A would contain non-standard integers.
>All it says
>is that a counterexample can not be found by any finite
number of
>steps within the model which omits the axiom.
You did notice I explicitly said standard model, right? IF
Goldbachs conjecture were undecidable in Peano Arithmetic,
then the
fact you mention (that a counterexample cannot be found by
any finite
number of steps within the model which omits the axioms) would
establish that, in the ->standard model<-, Goldbachs
conjecture would
be true. When we adjoing the negation to obtain a larger
axiom system,
the standard model is no longer a model for this enriched
system.
The rest of what you said seemed right to me. Yes, I am aware
that if
you have a formally undecidable proposition relative to an
axiom
system, you may add either the sentence or its negation to
the axiom
system and obtain a new consistent system.
[.rest deleted.]
--
Its not denial. Im just very selective 
about
what I accept as reality.
--- Calvin (Calvin and Hobbes)
Arturo Magidin
magidin@math.berkeley.edu
===
Subject: Re: (probably stupid) question on Fermat decidability
> Undecidable means there cannot exist a formal proof of a
theorems
> true/false status.
There is no such concept in logic.
===
Subject: Re: (probably stupid) question on Fermat decidability
: I was reading Simon Singhs book on Fermats 
last theorem,
and got a
: big confused by one passage - he mentions the possibility
that the
: theorem was undecidable (although obviously it turned out
not to be).
: What confused me was this: The theorem couldnt be false 
but
: undecidable, since falsehood implies the existance of a
definite
: counter-example. So if its undecidable then it must be
true, which
: contradicts it being undecidable. So you get a
contradiction,
: therefore it cannot be undecidable.
: Would anyone care to point out where Im going wrong here?
There is a difference between truth in an absolute system, and
decidability (synonymous with provability in this context)
in a first-order axiom system. See an old post of mine
http://www.math.niu.edu/~rusin/known-math/97/goedel
for a more detailed discussion. Usually decidability refers
to a first-order axiom system, where as truth in the 
Ôabsolute
natural numbers is defined by a second-order set of axioms. So
a given statement could be true in the natural numbres
(provable
by second-order axioms that define the natural numbers) but 
not
decidable (provable by the first-order axioms we are working
with).
Ted
===
Subject: Re: (probably stupid) question on Fermat decidability
>I was reading Simon Singhs book on Fermats 
last theorem,
and got a
>big confused by one passage - he mentions the possibility
that the
>theorem was undecidable (although obviously it turned out
not to be).
>What confused me was this: The theorem couldnt be false 
but
>undecidable, since falsehood implies the existance of a
definite
>counter-example. So if its undecidable then it must be
true, which
>contradicts it being undecidable. So you get a contradiction,
>therefore it cannot be undecidable.
>Would anyone care to point out where Im going wrong here?
If you could prove that FLT was undecidable, that would prove
it true,
which
would actually be a contradiction. But saying it might be
undecideable and
proving that it definitely is are 2 different things.
Finding a counterexample would have proven it false. But not
finding a
counterexample doesnt prove it non-false unless you have
checked all
possibilities, which for FLT are infinite.
--Keith Lewis klewis {at} mitre.org
The above may not (yet) represent the opinions of my employer.
===
Subject: Re: (probably stupid) question on Fermat decidability
days. My association with the Department is that of an
alumnus.
>>I was reading Simon Singhs book on Fermats 
last theorem,
and got a
>>big confused by one passage - he mentions the possibility
that the
>>theorem was undecidable (although obviously it turned out
not to be).
>>What confused me was this: The theorem couldnt be false 
but
>>undecidable, since falsehood implies the existance of a
definite
>>counter-example. So if its undecidable then it must be
true, which
>>contradicts it being undecidable. So you get a
contradiction,
>>therefore it cannot be undecidable.
>>Would anyone care to point out where Im going wrong here?
>If you could prove that FLT was undecidable, that would
prove it true,
which
>would actually be a contradiction.
No. Because undecidable should really be formally
undecidable; the
proof that it is true (in the standard model based on the
fact that it
is formally undecidable) is not formalizable within the
model, so
there is no contradiction.
--
Its not denial. Im just very selective 
about
what I accept as reality.
--- Calvin (Calvin and Hobbes)
Arturo Magidin
magidin@math.berkeley.edu
===
Subject: Re: (probably stupid) question on Fermat decidability
> If you could prove that FLT was undecidable,
What do you mean by undecidable?
===
Subject: Re: (probably stupid) question on Fermat decidability
> I was reading Simon Singhs book on Fermats 
last theorem,
and got a
> big confused by one passage - he mentions the possibility
that the
> theorem was undecidable (although obviously it turned out
not to be).
> What confused me was this: The theorem couldnt be false 
but
> undecidable, since falsehood implies the existance of a
definite
> counter-example. So if its undecidable then it must be
true, which
> contradicts it being undecidable. So you get a
contradiction,
> therefore it cannot be undecidable.
In what way does that contradict it being undecidable?
> Would anyone care to point out where Im going wrong here?
The Goedel sentence is an example of a statement that is true
but
unproveable (hence undecidable) within the system under
consideration.
--
Dave Seaman
Judge Yohns mistakes revealed in Mumia Abu-Jamal ruling.
<http://www.commoncouragepress.com/index.cfm?action=book&
bookid=228>
===
Subject: Re: Is this question fair for statistics class?
by support1.mathforum.org (8.11.6/8.11.6/The Math Forum,
$Revision:
1.9 primary) id iAJNXxR30254;
You pose an interesting question and raise others implicitly.
Regarding the one you pose, it is of course unfair to ask a
question
requiring knowledge not given or pointed to in class or
homework
assignments; but is that indeed what happened? I sure see a
difference between no correlation and curvilinear correlation;
and given that choice and the data points shown I must agree
with
your instructors evaluation of your response - totally
incorrect.
I find some correlation so strongly evident that I probably
would
have queried the instructor before saying the data were so
chaotic
that no correlation existed. Look, think; maybe ask if unsure.
What did the instructor say about the deduction after the
test was
returned to you? Did you consult her in a private office
visit, in a
confrontational manner in class, or not at all? I would surely
suggest diplomacy as a first response rather than the somewhat
emotional outburst revealed in your post.
Why are you so concerned that she offers advantages not on the
syllabus? I would see such surprises (dropping lowest score)
as
pleasant developments rather than opportunities to criticize
the
syllabus! If she said it in class, she couldnt be lying -
not with
all those witnesses!
Finally, if you KNEW she has done the same thing in years
past, why
hadnt THE WORD gotten out? You can bet that where I went to
college, everyones answer would be tailored in advance to 
be
exactly
what she wanted to see, down to the last semicolon!!
These comments are offered, not to stand up for another
college math
teacher, but rather to suggest that cooling off and learning
what you
can (statistics and otherwise) from the experience will serve
you
well in the long run. I simply do not know both sides of the
story,
but sense that nurturing your displeasure will only escalate a
conßict best forgotten.
>i got -20 from a test <a
href=http://www.johncho.us/stat.jpg>http://www.johncho.us/
stat.jpg</a> ,
because i put zero
>correlation instead of curvilinear correlation, we did not
study
>curvilinear correlations and such.
>I think it is unfair to put it on the test. Nearly every
student got it
>wrong.
>Furthermore, every year that she has put it on the test
students have
>gotten it wrong; that just tells me that she is not telling
students the
>truth about things and rather going around the truth hoping
that students
>find it.
>she said she drops the lowest test, but it does not say that
on her
syllbus
>i cannot believe she did this
===
Subject: Re: Why Do Americans Call It Math?
by support1.mathforum.org (8.11.6/8.11.6/The Math Forum,
$Revision:
1.9 primary) id iAJNY0e30265;
><preHow do you pronounce schedule?
>If an American pronouce it like British people,
>do you think hes snobbish?
></pre> If an American pronounced schedule like the BritÇs 
he
would be speaking correct English! If a Brit pronounced it
like an American
he would be considered uneducated.
===
Subject: Re: Why Do Americans Call It Math?
at 11:34 PM, jm.drew@ntlworld.com (John Drew) said:
>If an American pronounced schedule like the Brit s he would
be
>speaking correct English! If a Brit pronounced it like an
American he
>would be considered uneducated.
I find the statement ironic, considering the context. I might
consider
you uneducated for not knowing that Usenet is an ASCII medium
and that
header indicates an appropriate character set and encoding,
e.g.,
Presumably you meant to write Brits.
--
Shmuel (Seymour J.) Metz, SysProg and JOAT
<http://patriot.net/~shmuel>
Unsolicited bulk E-mail subject to legal action. I reserve the
right to publicly post or ridicule any abusive E-mail. Reply
to
domain Patriot dot net user shmuel+news to contact me. Do not
===
Subject: Re: Why Do Americans Call It Math?
I used to say Maths, as a Brit, I still do sometimes in the
UK, but I gave
putting the s on the end makes it awkward to lisp out. Math
avoids the
horrible triple consonant Ôths
Math or Mathematics is easier to say... one has to bow to
simplicity
Richard Miller
><preHow do you pronounce schedule?
>If an American pronouce it like British people,
>do you think hes snobbish?
></pre> If an American pronounced schedule like the BritÇs
he would be
speaking correct English! If a Brit pronounced it like an
American he would
be considered uneducated.
===
Subject: Re: Why Do Americans Call It Math?
>><pre>How do you pronounce schedule?
>>If an American pronouce it like British people,
>>do you think hes snobbish?
>></pre> If an American pronounced schedule like the 
BritÇs
he would be speaking correct English! If a Brit pronounced it
like an
American he would be considered uneducated.
There is a story of how Dorothy Parker was at a party, and an
American there who had just returned from London was talking
airily about his experience, dropping names and Brittishisms,
including go on and on about the tube schedule, pronouncing
the
second word as the British do. Ms. Parker found this
unbearably
pretentious, and finally leaned over to him and said in a loud
whisper, I think youre full of skit.
--
Mark Thornquist
===
Subject: Schwartzneleaticus Paradox
The Schwartzneleaticus Paradox presented 
here of course
constitutes a
proof by reduction to the absurd that SR is nonsense, but SR
undoubtedly
has
a way of Ôcooking the books to convince 
themselves the
absurd is a fact of
nature.
It is named in part for Melvin Schwarts because of something
really stupid
he said in his excellent (as far as I can tell) book,
Principles of
Electrodynamics, available from those horrible promulgators of
historical
foundations, Dover Publications.
In the book he argued that there could be no contraction
transverse to the
line of movement because if identical twins collided upright
at high speed
John could see Jims head plow into his belly, and Jim could
see Johns
head
plow into his belly.
The argument was fine as is but ignored the obvious, which
perhaps I posted
here sometime or other: let two identical boxers pass each
other at high
velocity, Ôeast and 
Ôwest, both with their heads to the
Ôeast and feet
to
the Ôwest and each facing a direction that 
would allow them
to throw a
straight punch at the other when their feet are coincident.
John would see
his fist pass over Jims head and 
Jims fist plow into his
belly, but Jim
would see his fist pass over Johns head and 
Johns fist plow
into his
belly.
Schwartz was absolutely correct that his gedanken experiment
disproved
transverse contraction, and the obvious extention has proved
parallel
contraction absurd.
There is a way to remove the necessity of punch throwing in
the paradox
(reduction to the absurd of SR).
Let identical twins approach each other at high speed, gamma
= 2.1 or so,
each with their heads in the Ôeast and feet in 
the Ôwest
along the
direction of movement, and both tilted somewhat to the
Ônorth side of the
direction of movement. Let their feet collide. John feels
Jims head crash
into his testicles and Jim feels Johns head crash into his
testicles.
Ouch! Not just for John and Jim but for SR, which is thus
shown to be
nonsense and proved invalid by reduction to the absurd.
SR is consistent?
You betcha! Consistent idioocy!
eleaticus
===
Subject: Re: Schwartzneleaticus Paradox
> The Schwartzneleaticus Paradox presented 
here of course
constitutes a
> proof by reduction to the absurd that SR is nonsense, but
SR undoubtedly
has
> a way of Ôcooking the books to convince 
themselves the
absurd is a fact
of
> nature.
> It is named in part for Melvin Schwarts because of
something really
stupid
> he said in his excellent (as far as I can tell) book,
Principles of
> Electrodynamics, available from those horrible promulgators
of
historical
> foundations, Dover Publications.
> In the book he argued that there could be no contraction
transverse to
the
> line of movement because if identical twins collided
upright at high
speed
> John could see Jims head plow into his belly, and Jim
could see Johns
head
> plow into his belly.
> The argument was fine as is but ignored the obvious, which
perhaps I
posted
> here sometime or other: let two identical boxers pass each
other at high
> velocity, Ôeast and 
Ôwest, both with their heads to the
Ôeast and feet
to
> the Ôwest and each facing a direction that 
would allow
them to throw a
> straight punch at the other when their feet are coincident.
John would
see
> his fist pass over Jims head and 
Jims fist plow into his
belly, but Jim
> would see his fist pass over Johns head and 
Johns fist plow
into his
> belly.
> Schwartz was absolutely correct that his gedanken
experiment disproved
> transverse contraction, and the obvious extention has
proved parallel
> contraction absurd.
> There is a way to remove the necessity of punch throwing in
the paradox
> (reduction to the absurd of SR).
> Let identical twins approach each other at high speed,
gamma = 2.1 or so,
> each with their heads in the Ôeast and feet 
in the Ôwest
along the
> direction of movement, and both tilted somewhat to the
Ônorth side of
the
> direction of movement. Let their feet collide. John feels
Jims head
crash
> into his testicles and Jim feels Johns head crash into 
his
testicles.
> Ouch! Not just for John and Jim but for SR, which is thus
shown to be
> nonsense and proved invalid by reduction to the absurd.
> SR is consistent?
Yes, it is consistent.
Your example assumes that simultaneity is absolute; which is
inconsistent with SR. You have assumed your conclusion, which
is
falacious.
One other thing that is consistent is your intense stupidity.
ROS has
been pointed out to you many times before, but your pathetic
little
mind is incapable of learning.
Paul Cardinale
===
Subject: Re: Schwartzneleaticus Paradox
SR is consistent?
> Yes, it is consistent.
> Your example assumes that simultaneity is absolute; which is
> inconsistent with SR. You have assumed your conclusion,
which is
> falacious.
Why go so far out of your way to prove your corrupt cretinism?
Non-absolute simultaneity has no utility when discussing
human sized
objects
in impact. If you think it does, then make it ant sized
objects.
What a cretin you are!
eleaticus
> One other thing that is consistent is your intense
stupidity. ROS has
> been pointed out to you many times before, but your
pathetic little
> mind is incapable of learning.
> Paul Cardinale
===
Subject: Re: Schwartzneleaticus Paradox
>> SR is consistent?
>> Yes, it is consistent.
>> Your example assumes that simultaneity is absolute; which
is
>> inconsistent with SR. You have assumed your conclusion,
which is
>> falacious.
>Why go so far out of your way to prove your corrupt
cretinism?
>Non-absolute simultaneity has no utility when discussing
human sized
objects
>in impact. If you think it does, then make it ant sized
objects.
>What a cretin you are!
Non-absolute simultaniety applies to any object, however
small, provided
the impact is sufficiently rapid that the time scale is
comparable to
the time it takes for light to travel along the object.
John Savard
http://home.ecn.ab.ca/~jsavard/index.html
===
Subject: Re: Schwartzneleaticus Paradox
SR is consistent?
> Yes, it is consistent.
> Your example assumes that simultaneity is absolute; which is
> inconsistent with SR. You have assumed your conclusion,
which is
> falacious.
> Why go so far out of your way to prove your corrupt
cretinism?
> Non-absolute simultaneity has no utility when discussing
human sized
objects
> in impact. If you think it does, then make it ant sized
objects.
> What a cretin you are!
Jeezzuss! Non absolute simultaneity doesnt have to have
utility
to explain SR for any size objects. Can you even define 
utility
in the context that you introduced the term into this
discussion.
SR predicts non absolute simultaneity and predicts how to
relate
measurements made in different frames of reference using
relativity
of simultaneity.
If you think that you can disprove this, then show us an
experiment
that does so. And dont just claim that it 
hasnt been done
at some
particular scale.
John Anderson
===
Subject: Viewpoint and Schwartzneleaticus 
Paradox
> Non-absolute simultaneity has no utility when discussing
human sized
objects
> in impact. If you think it does, then make it ant sized
objects.
> What a cretin you are!
> Jeezzuss! Non absolute simultaneity doesnt have to have
utility
> to explain SR for any size objects. Can you even define
utility
> in the context that you introduced the term into this
discussion.
> SR predicts non absolute simultaneity and predicts how to
relate
> measurements made in different frames of reference using
relativity
> of simultaneity.
Both are hoizontal Ôheight
.0000000000000000000000000000000000000866
approx.
A feet start at time t=t=0 by convention and 
at x=-.866
approx,
x=--1.732
approx.
A feet start at time t=t=0 by convention and at x=0.
Their relative velocity is .866c approx and gamma = 2..
Their feet become adjacent at t=1, at which time the A head
is at
.0000000000000000000000000000000000000866 , the lower abdomen
of A, gamma
being 2.
So far there is unmistakable simultaneity, being strictly
from viewpoint A.
location zero and the A head is at
.0000000000000000000000000000000000000433, the location of
the A belly.
That being from an unmistakable simultaneity viewpoint, being
strictly from
viewpoint A.
Hence, boxer A fist misses the A head but he 
sees the A fist
plow into
his belly.
And hence, boxer A fist misses the A head but 
he sees the A
first plow
into
his belly.
QED
If you are half my height, our feet are adjacent, and our
heads extend in
the same direction, your head is just above my crotch, no
matter what time
it is. And SR says that is the situation in the given setup
at my time
t=1.
If I am half your height, our feet are adjacent, and our
heads extend in
the
same direction, my head is just at the lower parta of your
belly no matter
what time it is. And SR says that is the situation in the
given setup at
your time t=1.
Wait a minute!
That is direct application of SR.
But dont you know that SR is so ed up that the direct
application of
its basic equations is tacitly outlawed by the SR-cult?
You are not allowed to use those basic equations directly.
To do so shows them to be complete nonsense, invalid by
reduction to the
absurd, as above.
So, lets play the True Believer SR-cult cretin game and
pretend SR isnt
crap, and that the non-simulataneity isnt the most vomitous
version of the
crap.
No, lets dont. Why practice their idiocy?
The given resolution being absolutely irrefutable given
SR-contraction, any
further SR-idiocy that says otherwise is proof by reduction
to the absurd
that SR is crap.
Whats the problem, over and above the basic problem that SR
is crap?
Screwed up viewpoint.
We know that the contraction result of x=gx-gvt is not the
moving system
viewpoint, it is supposedly what A will see, not what A 
will
see for
itself. A does not see himself contracted according to
SR-dogma. Too bad,
because if he saw himself as contracted the .866 distance
would be 1.732
for
him and at v=.866 the feet would become adjacent at t=2, 
the
same figure
the SR-idiot A would calculate for t.
We also know that A doesnt see A as 
contracted: let a rail
run from
adjacent to the A feet to adjacent to the A feet, to mark
the distance
with
something physical. The rail would be only .433 long and at
v=.866 it would
be at time t=.5 that the feet were adjacent, not the 
t=2
the SR-idiot A
calculated using SR, not the t=1 an actual A 
would see it
taking.
We know that the dilation result of (the corrupt)
t=gt-gxt/cc is not the
moving system viewpoint, it is supposdedly what A will see,
not what A
will
see for itself. A does not see himself slowed down. No 
Ôtoo
bad here
because there is no way the (mis)info can be used. With
t=d/v, what in
hell would it mean to say time has slowed? Nothing! No
consequence.
That is, not just x and t but also x and t 
are stationary
system
viewpoints, one pair sane, and the other pair pure psychotic
idiocy.
In our setup, the moving system also see that it takes t=1
elapsed time
unit
to become feet-adjacent. The moving system sees at that time
that - given
contraction - the A head is at the A belly.
Period. The idiocy of the BEER (Basic Equations of 
Einsteins
Relativity)
has nothing to do with the moving system measures, it is
nonsense, crap,
and
... well, SR.
eleaticus
===
Subject: Re: Schwartzneleaticus Paradox
> The Schwartzneleaticus Paradox presented 
here of course
constitutes a
> proof by reduction to the absurd that SR is nonsense,
[snip crap]
eleaticus, Oren Webster, is a despised and stooopid troll,
http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/
Crimes.html
Several crimes against logic and science Ha ha ha!
Originally trolled across sci.physics sci.physics.relativity
alt.physics sci.math sci.answers alt.answers news.answers
Psychotic ineducable boring troll Eleaticus,
Were there to be internal inconsistencies in SR (meaning
inconsistencies of a purely mathematical logical nature) that
would
automatically lead to contradictions in number theory,
itself, and
arithmetic, since the mathematics of Minkowski geometry is
equiconsistent with the theory of real numbers and with
arithmetic.
Eleaticus explicitly demonstrates that he is completely
ignorant of
multivariable calculus. He has no concept of the Chain Rule in
multivariable calculus. Consider his Galilean Transformation
goo and
dribble:
t = t,
x = x - vt,
y = y,
z = z.
His refusal to accept that t must be introduced as a 
separate
variable springs from a massive emprical stupidity re space
and time
are described as a four-dimensional manifold, with four
coordinates
instead of a time evolution of a three-dimensional manifold,
and that
the change of coordinate system should be a change of four
coordinates, and not a time-dependent change of three
coordinates.
This is particularly vital when it comes to fields over space
and time
(electric and magnetic fields for example).
The transformation law for the differential operators under
the
Galilean transformation is given by:
d/dt = d/dt + v d/dx,
d/dx = d/dx,
d/dy = d/dy,
d/dz = d/dz.
This shows the necessity of introducing a new variable t,
since
partial differentiation with respect to t (constant 
x, y,
z) is a
different operation to partial differentiation with respect
to t
(constant x, y, z). The above transformation law is
determined by the
Chain Rule:
d/dt = dt/dt d/dt + dx/dt 
d/dx + dy/dt d/dy + dz/dt d/dz,
d/dx = dt/dx d/dt + dx/dx 
d/dx + dy/dx d/dy + dz/dx d/dz,
d/dy = dt/dy d/dt + dx/dy 
d/dx + dy/dy d/dy + dz/dy d/dz,
d/dz = dt/dz d/dt + dx/dz 
d/dx + dy/dz d/dy + dz/dz d/dz.
The presence of the term involving d/dx in the expression for
d/dt is
indicative of the fact that x depends on t 
(x, y, z,
being held
constant), as can be seen from the fact that the coefficient
of d/dx
in the expression for d/dt is dx/dt. Because 
of the now
demonstrated fact that Eleaticus has no formal education in
multivariable calculus, he has managed, somehow, to get it
into his
head that the presence of the term involving d/dx in the
expression
for d/dt is indicative of t depending on x 
(t, y, z, being
held
constant). Because of his stupidty Eleaticus cannot get the
correct
transformation law for the differential operators under the
Galilean
Transformation, and he cannot determine the invariance or
otherwise of
Maxwells Equations under the Galilean Transformation. The
first
advice to Eleaticus is to learn multivariable calculus.
Eleaticus should not pretend that he can understand how to
determine
invariance or otherwise of Maxwells Equations under the
Galilean
Transformation, or under the Lorentz Transformation, until he
understands the multivariable calculus which underlies such
considerations. Eleaticus is a loud idiot.
The homogeneous Maxwell equations are invariant under the
Galilean
Transformation, with transformation laws:
E_x = E_x,
E_y = E_y - v B_z,
E_z = E_z + v B_y,
B_x = B_x,
B_y = B_y,
B_z = B_z.
The derivation of these transformation laws was determined
using the
transformation laws for the differential operators given
above. These
transformation laws have the additional advantage that they
determine
the correct transformation for the force law, thus providing
further
evidence in favour of the transformation law for the
differential
operators, as above.
The inhomogeneous Maxwell equations are also invariant under
the
Galilean transformation, with transformation laws:
E_x = E_x,
E_y = E_y,
E_z = E_z,
B_x = B_x,
B_y = B_y + v/c^2 E_z,
B_z = B_z - v/c^2 E_y,
rho = rho,
J_x = J_x - v rho,
J_y = J_y,
J_z = J_z.
Note the the transformation laws for the charge density and
current
density are as they should be under the Galilean
transformation.
Homogeneous equations are invariant under the Galilean
Transformation,
and inhomogeneous equations are invariant under the Galilean
Transformation, but Maxwells Equations as a whole are NOT
invariant
under the Galilean Transformation, since the transformation
laws
required for the EM field for the two cases are inconsistent
with each
other. The transformation law for the EM field which makes the
homogeneous equations invariant will not also make the
inhomogeneous
equations invariant. The transformation law for the EM field
which
makes the inhomogeneous equations invariant will not also
make the
homogeneous equations invariant.
On the other hand, all of Maxwells equations are invariant
under the
Lorentz Transformation, with transformation laws:
E_x = E_x,
E_y = gamma (E_y - v B_z),
E_z = gamma (E_z + v B_y),
B_x = B_x,
B_y = gamma (B_y + v/c^2 E_z),
B_z = gamma (B_z - v/c^2 E_y),
rho = gamma (rho - v/c^2 J_x),
J_x = gamma (J_x - v rho),
J_y = J_y,
J_z = J_z,
where gamma = 1/sqrt(1 - v^2/c^2).
Idiot Oren Webster sees himself this way,
http://www.mazepath.com/uncleal/effete6.jpg
The entire remainder of the planet sees him this way,
http://www.mazepath.com/uncleal/effete3.png
<http://www.albinoblacksheep.com/ßash/youare.swf>
http://www.mazepath.com/uncleal/sunshine.jpg
http://www.apa.org/journals/psp/psp7761121.html
http://insti.physics.sunysb.edu/~siegel/quack.html
<http://www.firehead.org/~jessh/film/kubrick/
Kubrick-Psycho.html>
<http://www.naturalchild.com/elliott_barker/prisons.html>
Hey, stooopid troll Eleaticus - Do you want EVIDENCE? Each of
the 24
GPS satellites carries either four cesium atomic clocks or
three
rubidum atomic clocks in orbit, with full relativistic
corrections
being applied.
<http://math.ucr.edu/home/baez/RelWWW/tests.html>
Mathematics of gravitation
<http://wugrav.wustl.edu/people/CMW/update98.pdf>
<http://www.astro.northwestern.edu/AspenW04/Papers/lorimer1.
pdf>
Equivalence Principle testing
http://arXiv.org/abs/hep-th/0111236
Geometric structure of reality
http://arxiv.org/abs/gr-qc/0103044
http://arXiv.org/abs/hep-th/0307140
GR structure, especially Part 4/p. 7
http://arXiv.org/abs/gr-qc/0311039
<http://www.weburbia.demon.co.uk/physics/experiments.html>
Experimental constraints on General Relativity
<http://tycho.usno.navy.mil/ptti/ptti2002/paper20.pdf>
http://www.eftaylor.com/pub/projecta.pdf
<http://www.public.asu.edu/~rjjacob/Lecture16.pdf>
Relativity in the GPS system
http://arXiv.org/abs/gr-qc/9909014
falling light
<http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/
airtim.html>
Hafele-Keating Experiment
http://www.hawaii.edu/suremath/SRtwinParadox.html
<http://physics.syr.edu/courses/modules/LIGHTCONE/twins.html>
Twin Paradox
http://arXiv.org/abs/astro-ph/0401086
http://arxiv.org/abs/astro-ph/0312071
Deeply relativistic neutron star binaries
http://arxiv.org/abs/hep-th/0405160
Black hole evaporation
No aether
http://fsweb.berry.edu/academic/mans/clane/
No Lorentz violation
http://arXiv.org/abs/gr-qc/0409089
Spin-2 gravitons have problems (so does the proposal)
<http://www.npl.washington.edu/eotwash/pdf/prl83-3585.pdf>
http://arXiv.org/abs/gr-qc/0301024
Nordtvedt Effect
NIM A 355 537 (1995)
Physics Letters B 328 103 (1994)
Physical Review Letters 64 1697 (1990)
Physical Review Letters 39 1051 (1977)
Physical Review 135 B1071 (1964)
Physics Letters 12 260 (1964)
Europhysics Letters 56(2) 170-174 (2001)
General Relativity and Gravitation 34(9) 1371 (2002)
http://fourmilab.to/etexts/einstein/specrel/specrel.pdf
<http://www.geocities.com/physics_world/sr/ae_1905_error.htm>
<http://www.physics.gatech.edu/people/faculty/finkelstein/
relativity.pdf>
http://users.powernet.co.uk/bearsoft/Paper6.pdf
http://users.powernet.co.uk/bearsoft/LPHrel.html
Longitudinal and transverse mass
http://www.navcen.uscg.gov/pubs/gps/gpsuser/gpsuser.pdf
http://www.navcen.uscg.gov/pubs/gps/sigspec/default.htm
http://www.navcen.uscg.gov/pubs/gps/icd200/default.htm
http://www.trimble.com/gps/index.html
http://sirius.chinalake.navy.mil/satpred/
http://www.phys.lsu.edu/mog/mog9/node9.html
http://egtphysics.net/GPS/RelGPS.htm
http://www.schriever.af.mil/gps/Current/current.oa1
http://edu-observatory.org/gps/gps_books.html
<http://www-astronomy.mps.ohio-state.edu/~pogge/Ast162/Unit5/
gps.html>
--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/qz.pdf
===
Subject: Uncle assAl: Troll House Kookie
> eleaticus, Oren Webster, is a despised and stooopid troll,
> Psychotic ineducable boring troll Eleaticus,
You can buy your very own Uncle assAl (yuck!) at the bakery.
Just ask for a TrollHouse Kookie.
eleaticus
===
Subject: Re: Uncle assAl: Troll House Kookie
> eleaticus, Oren Webster, is a despised and stooopid troll,
> Psychotic ineducable boring troll Eleaticus,
> You can buy your very own Uncle assAl (yuck!) at the bakery.
> Just ask for a TrollHouse Kookie.
> eleaticus
I have added an appropriate little cartoon to that page:
http://users.pandora.be/vdmoortel/dirk/Physics/Fumbles/
Crimes.html
Hey Oren Coward Webster, how come you dont reply to
?
Dirk Vdm
===
Subject: Fermat 420
Optica!
Ben Ito
10-19-04
I will prove that the wave theory of light is invalid then
prove that
1. Introduction
which conßicts with Maxwells EM plane wave structure of
light. The
wave theory of light is justified with Huygens principle,
Fresnels
T&R equations, Maxwells structure of light, 
Plancks
blackbox,
Einsteins quanta, quantum mechanics, and QED. I will prove
that the
the wave effects of light.
2. Huygens Principle
Huygens principle describes wave theories propagation, and
aperture
diffraction mechanisms of light. According to Huygens
principle the
energy of the source is re-create at interval of a
wavelength, away
from the source, which violate the law of conservation of
energy.
3. Fresnels T&R Equations
Fresnels T&R equations are derived using non-propagating
plane
waves. A propagating plane wave forms an average field effect
of
zero, at the glass surface; therefore, Fresnels derivation
of the
T&R equations uses non-propagating plane waves conßicts with
the
experimental propagation of light.
4. Maxwells Structure of Light
Maxwells structure of light is derived from 
Maxwells (radio
wave)
equations. A continuous and dispersive field structure of an 
EM
spherical wave is approximated with Maxwells plane wave.
Therefore,
conßicts with the photoelectric effect experiment.
5. Plancks Blackbox Emission Derivation
Plancks blackbox emission derivation (1900) uses the
standing waves
of Maxwells structure of light (Eisberg, p. 15). However,
light
cannot physically form standing waves since the propagation
of the
plane wave cannot maintain the standing waves nodes at both
surfaces. Standing waves are used to derive Plancks 
discrete
energy
equation.
6. Einsteins Quanta
Einsteins photoelectric quanta equation derivation (1905)
uses the
work-dependent entropy equation (Nye, p. 470). However, the
volume of
Einstein system is constant; therefore, the change in entropy
of
Einsteins system is zero. Einstein derives the energy 
quanta
equation using entropy equation.
7. Quantum Mechanics and QED
Maxwells plane wave structure of light. However, a plane
wave has an
aperture, to the intensity areas of the diffraction pattern
and does
when the light contact the aperture edge does not aperture
diffraction
effect occur.
9. Conclusion
Huygens principle describes a wave structure. A wave
structure is
then used by Fresnel to derive the T&R equations. Maxwells
equations are used to derive an EM plane wave structure of
light;
which conßict with the experimental results of the
photoelectric
effect of light.
Wave theory uses Plancks blackbox emission derivation,
quantum
structure; however, all these derivations use Maxwells
structure of
Einsteins photoelectric quanta equation derivation (1905)
uses a gas
however, Einsteins gas molecule analogy is inappropriate.
The wave
theory of light is a defense of Huygens principle.
the intensity areas of the diffraction pattern, and does not
allow
10. Books
Robert Eisberg and Robert Resnick. Quantum Physics of Atoms,
1974.
Dietrich Marcuse. Engineering Quantum Electrodynamics.
Harcourt,
Brace & World, Inc. 1970.
Mary Jo Nye. The Question of the Atom. Tomash. 1984.
*-----------------------*
www.GroupSrv.com
*-----------------------*
===
Subject: Finding unique sums.
Im trying to find a series where the sum of a 
subset of that
is unique. Or in other words, I can find the numbers from sum.
An example would be f(n)=2^n, you add any number of elements
in this set, youll get a number with all those bits set.
But Im looking for a series that does not grow
geometrically..
Pradeep
===
Subject: Re: Finding unique sums.
> Im trying to find a series where the sum of a 
subset of that
> is unique. Or in other words, I can find the numbers from
sum.
> An example would be f(n)=2^n, you add any number of elements
> in this set, youll get a number with all those bits set.
> But Im looking for a series that does not grow
geometrically..
> Pradeep
Something a bit different (not better) from the other answers
given...
How about the sequence
0.4142135623730950488016887242...
0.8284271247461900976033774484...
0.6568542494923801952067548968...
0.3137084989847603904135097936...
0.6274169979695207808270195873...
0.2548339959390415616540391747...
0.5096679918780831233080783494...
....
(Puzzle - is the sequence dense in [0,1]? (The sequence is
2^(n + 1/2) mod
1).)
Mike.
===
Subject: Re: Finding unique sums.
> Im trying to find a series where the sum of a 
subset of that
> is unique. Or in other words, I can find the numbers from
sum.
> An example would be f(n)=2^n, you add any number of elements
> in this set, youll get a number with all those bits set.
> But Im looking for a series that does not grow
geometrically..
I was looking for a series which consists of positive integers
which has this property.
Is it helpful if the size of the subset is known?
For example, the sum of random 10 elements of a series is
given,
is it possible to get the individual elements(I mean is there
such a series of positive integers other that 2^n and 
doesnt
grow exponentially)?
===
Subject: Re: Finding unique sums.
>> Im trying to find a series where the sum of 
a subset of
that
>> is unique. Or in other words, I can find the numbers from
sum.
>> An example would be f(n)=2^n, you add any number of
elements
>> in this set, youll get a number with all those bits set.
>> But Im looking for a series that does not grow
geometrically..
>I was looking for a series which consists of positive
integers
>which has this property.
This has already been answered. Since the 2^n series is the
Ômost
efficient
such series, all other series must grow faster.
>Is it helpful if the size of the subset is known?
>For example, the sum of random 10 elements of a series is
given,
>is it possible to get the individual elements(I mean is there
>such a series of positive integers other that 2^n and 
doesnt
>grow exponentially)?
I believe this doesnt really change the outcome. All 
size-10
subsets must
produce a unique sum implies (with handwave) that all subsets
must produce
a
unique sum, so your sequence is going to grow exponentially.
You can probably do away with the handwave above, by showing
that assuming
the
existence of two size-N+1 subsets with identical sum but no
size-N subsets
leasds to a contradiction.
--
Patrick Hamlyn posting from Perth, Western Australia
Windsurfing capital of the Southern Hemisphere
Moderator: polyforms group (polyforms-subscribe@egroups.com)
===
Subject: Re: Finding unique sums.
>> Im trying to find a series where the sum of 
a subset of
that
>> is unique. Or in other words, I can find the numbers from
sum.
>> An example would be f(n)=2^n, you add any number of
elements
>> in this set, youll get a number with all those bits set.
>> But Im looking for a series that does not grow
geometrically..
>I was looking for a series which consists of positive
integers
>which has this property.
>Is it helpful if the size of the subset is known?
>For example, the sum of random 10 elements of a series is
given,
>is it possible to get the individual elements(I mean is there
>such a series of positive integers other that 2^n and 
doesnt
>grow exponentially)?
Knowing the number of elements as well as their sum adds some
possibilities.
For example, f(n)=1000000+2^(n-1).
But the core problem is that for every number you add, the
number of
possible subsets doubles. In order for each combination of
numbers to
produce a sum different from all other combinations, there
need to be 2^N
possible sums, where N is the number of values which might be
part of the
sum.
Is this for a magic trick?
--Keith Lewis klewis {at} mitre.org
The above may not (yet) represent the opinions of my employer.
===
Subject: Re: Finding unique sums.
> Im trying to find a series where the sum of a 
subset of that
> is unique. Or in other words, I can find the numbers from
sum.
> An example would be f(n)=2^n, you add any number of elements
> in this set, youll get a number with all those bits set.
> But Im looking for a series that does not grow
geometrically..
What about f(n) = 1/2^n (or 1/a^n, where a >= 2)? Does that
count?
-- Christopher Heckman
===
Subject: Re: Finding unique sums. - Super-increasing
sequences and knapsack
problems
A super-increasing sequence is a sequence of integers >= 1 in
which each
element is larger than the sum of all the preceding elements.
Starting
with 1 and aiming at the slowest growing rate you get 1, 2,
4, 8, ... .
This is the only super-increasing sequence that allows any
integer >= 1
to be represented as the sum of some of its elements. No
proof given
here; must be not too difficult.
Because of the super-increasing property these
representations are unique.
One could ask: given a sheath (one-dimensional knapsack) of
integer
length N >= 1; given a set S of rods of integer lengths,
their total
length being >= N; determine what subsets of S exactly fit
into the
sheath, if any such subsets exist.
This problem is known as the knapsack problem. In general it
is an
NP-hard problem, reason why it plays an important role in
cryptography.
If the lengths of the rods in S form a super-increasing
sequence, then
the knapsack problem can be solved at once; for cryptographic
applications you need sequences that are much slower
increasing than
2^n. The farther below 2^n, the better.
The 2^n sequence is at the borderline between (A)
representing all
integers but not uniquely, and (B) representing not all
integers, but
uniquely if possible.
Literature: Denning: Cryptography and Data Security.
Addison-Wesley,
1982. ISBN 0-201-10150-5
>> Im trying to find a series where the sum of 
a subset of
that
>> is unique. Or in other words, I can find the numbers from
sum.
>> An example would be f(n)=2^n, you add any number of
elements
>> in this set, youll get a number with all those bits set.
>> But Im looking for a series that does not grow
geometrically..
>>
>What about f(n) = 1/2^n (or 1/a^n, where a >= 2)? Does that
count?
> -- Christopher Heckman
===
Subject: Re: Finding unique sums.
> Im trying to find a series where the sum of a 
subset of that
> is unique. Or in other words, I can find the numbers from
sum.
> An example would be f(n)=2^n, you add any number of elements
> in this set, youll get a number with all those bits set.
> But Im looking for a series that does not grow
geometrically..
> Pradeep
How about ANY series of positive numbers where each term is
greater
than the sum of all those preceding it? Would that work?
(Still grows
fast, but not necessarily geometrically.)
===
Subject: Re: Finding unique sums.
>> Im trying to find a series where the sum of 
a subset of
that is unique.
Or
>> in other words, I can find the numbers from sum.
>> An example would be f(n)=2^n, you add any number of
elements in this
set,
>> youll get a number with all those bits set. But 
Im
looking for a
series
>> that does not grow geometrically..
> How about ANY series of positive numbers where each term is
greater than
the
> sum of all those preceding it? Would that work? (Still
grows fast, but
not
> necessarily geometrically.)
Actually, that is geometric. Say the first term is a_0. Then
the second
term
is a_1 > a_0, the third term is a_2 > a_1 + a_0 > 2a_0, the
fourth is a_3 >
a_2
+ a_1 + a_0 > 2a_0 + a_0 + a_0 = 4a_0, etc. Apply induction
if you wish;
the
answer is a sequence bounded below by a constant multiple of
a geometric
sequence.
--
Ryan Reich
ryanr@uchicago.edu
===
Subject: Re: Finding unique sums.
>
>>
>> Im trying to find a series where the sum of 
a subset of
that is
unique. Or
>> in other words, I can find the numbers from sum.
>>
>> An example would be f(n)=2^n, you add any number of
elements in this
set,
>> youll get a number with all those bits set. But 
Im
looking for a
series
>> that does not grow geometrically..
>
How about ANY series of positive numbers where each term is
greater than
the
> sum of all those preceding it? Would that work? (Still
grows fast,
but not
> necessarily geometrically.)
> Actually, that is geometric. Say the first term is a_0. Then
the second
term
> is a_1 > a_0, the third term is a_2 > a_1 + a_0 > 2a_0, the
fourth is a_3
> a_2
> + a_1 + a_0 > 2a_0 + a_0 + a_0 = 4a_0, etc. Apply induction
if you wish;
the
> answer is a sequence bounded below by a constant multiple
of a geometric
sequence.
Oh ... I understood grow geometrically to mean than
a[i+1]/a[i] was
constant. Is that not right?
===
Subject: Re: Finding unique sums.
> How about ANY series of positive numbers where each term is
greater
than the
> sum of all those preceding it? Would that work? (Still
grows fast,
but not
> necessarily geometrically.)
Actually, that is geometric. Say the first term is a_0. Then
the
second term
> is a_1 > a_0, the third term is a_2 > a_1 + a_0 > 2a_0, the
fourth is
a_3 > a_2
> + a_1 + a_0 > 2a_0 + a_0 + a_0 = 4a_0, etc. Apply induction
if you
wish; the
> answer is a sequence bounded below by a constant multiple
of a geometric
sequence.
> Oh ... I understood grow geometrically to mean than
a[i+1]/a[i] was
> constant. Is that not right?
Youre right.
Ryan appears to think that n!, 2^2^n and 2^n! grow
geometrically. This is
either a gross abuse of terminology, or just plain wrong.
Phil
--
... one Marine noticed one of the prisoners was still
breathing. A Marine
can be heard saying on the pool footage provided to Reuters
Television:
Hes ing faking hes dead. He faking 
hes ing dead.
The Marine then raises his riße and fires into the 
mans head.
The pictures are too graphic for us to broadcast, Sites said.
===
Subject: Re: Finding unique sums.
>
>> How about ANY series of positive numbers where each term
is greater
>> than the sum of all those preceding it? Would that work?
(Still grows
>> fast, but not necessarily geometrically.)
Actually, that is geometric. Say the first term is a_0. Then
the
second
> term is a_1 > a_0, the third term is a_2 > a_1 + a_0 >
2a_0, the fourth
> is a_3 > a_2 + a_1 + a_0 > 2a_0 + a_0 + a_0 = 4a_0, etc.
Apply
induction
> if you wish; the answer is a sequence bounded below by a
constant
> multiple of a geometric sequence.
>> Oh ... I understood grow geometrically to mean than
a[i+1]/a[i] was
>> constant. Is that not right?
> Youre right.
> Ryan appears to think that n!, 2^2^n and 2^n! grow
geometrically. This is
> either a gross abuse of terminology, or just plain wrong.
> Phil
Well, if you are trying to avoid geometric growth it is
reasonable for me
to
expect you to be trying to avoid greater-than-geometric
growth as well. I
was
thinking of this from an efficiency perspective. The original
question
seemed
to me to desire such an answer, which is impossible, of
course.
Totally off-topic for the thread, but pertinent to the
terminology: has
anyone
else read Orson Scott Cards Memory of Earth series (I think
its
called) and
winced at the Overminds description of its memory layout? 
It
says
something
like This made my memory grow geometrically, but that is not
enough; it
needed
to be exponential.
--
Ryan Reich
ryanr@uchicago.edu
===
Subject: Re: Finding unique sums.
> Im trying to find a series where the sum of a 
subset of that
> is unique. Or in other words, I can find the numbers from
sum.
> An example would be f(n)=2^n, you add any number of elements
> in this set, youll get a number with all those bits set.
> But Im looking for a series that does not grow
geometrically..
How about sqrt{p_n} where p_n is the n-th prime?
--
Robin Chapman, www.maths.ex.ac.uk/~rjc/rjc.html
Lacan, Jacques, 79, 91-92; mistakes his penis for a square
root, 88-9
Francis Wheen, _How Mumbo-Jumbo Conquered the World_
===
Subject: Re: Finding unique sums.
> Im trying to find a series where the sum of a 
subset of that
> is unique. Or in other words, I can find the numbers from
sum.
> An example would be f(n)=2^n, you add any number of elements
> in this set, youll get a number with all those bits set.
> But Im looking for a series that does not grow
geometrically..
The series f(n)=2^n grows exponentially. And it is clearly
the most
efficient
series with your desired property, since all sums can be made
with the
minimum
of terms.
Any other such series would therefore be less efficiently
Ôpacked, and
would
grow at a greater rate.
Allowing negative numbers would be one way to 
Ôbreak this
argument.
--
Patrick Hamlyn posting from Perth, Western Australia
Windsurfing capital of the Southern Hemisphere
Moderator: polyforms group (polyforms-subscribe@egroups.com)
===
Subject: Re: Finding unique sums.
> Im trying to find a series where the sum of a 
subset of that
> is unique. Or in other words, I can find the numbers from
sum.
> An example would be f(n)=2^n, you add any number of elements
> in this set, youll get a number with all those bits set.
> But Im looking for a series that does not grow
geometrically..
2^n should be the smallest such series, at least if you are
dealing with
non-negative integers.
===
Subject: Re: Finding unique sums.
<419e97d2$1_1@news.unc.edu> Im trying to find a 
series where
the sum of a subset of that
>> is unique. Or in other words, I can find the numbers from
sum.
>> An example would be f(n)=2^n, you add any number of
elements
>> in this set, youll get a number with all those bits set.
>> But Im looking for a series that does not grow
geometrically..
>2^n should be the smallest such series, at least if you are
dealing with
>non-negative integers.
If you remove that restriction, you could go the opposite
way, f(n)=2^(-n).
Then youd have a fraction between 0 and 1. In fact, x^(+-n)
will work for
any x >= 2.
--Keith Lewis klewis {at} mitre.org
The above may not (yet) represent the opinions of my employer.
===
Subject: Computability: Recovering Delta_0 from Sigma_1?
> This question is necessarily vague, but is there a known
way to
> Ôrecover the set of all -primitive- recursive 
relations
(Delta_0)
> from the set of recursively enumerable relations (Sigma_1)?
Going up
> the arithmetical hierarchy is easy, going down not so.
> Note: I use the convention that Delta_0 is the set of
primitive
> recursive relations, not the set of computable relations. In
> particular Delta_0 is not equal to Delta_1. Either way, the
resulting
> hierarchies are the same everywhere except of course at
Delta_0. I
> posted a thread asking about this choice a while back, see
Primitive
> recursive vs recursive at the base of the arithmetical
hierarchy.
> Rex Butler
Speaking of, are there any other non-trivial
characterizations of the
set of primitive recursive relations?
Rex Butler
===
Subject: Re: strong induction
But isnt that redundant, since I already have proven it as 
a
base case??
Radu Vlad
> Say you have a sequence {x_n} defined by:
> x_1 = -3
> x_2 = 23
> x_3 = -45
> x_n = 7x_(n-2) - 6x_(n-3) for n>=4
> Prove that:
> x_n = 2(-3)^n + 2^n + 1 for all positive integers n (*)
> If you prove that the base cases n = 1,2,3 are true, then
> you have to assume that the formula (*) is true in the
following
conditions,
> if n=r, for all 1<=r<= k for some k>=3 (n, k are positive
integers)
> My question is why is it you have to assume its true for
k>=3 and not
just
> for k>3,
> since you already have proven its true for k=3.
> Is it not sufficient to assume the formula is true for 
k>3???
> ...and what if - in the course of the proof - you have to
> use the assumption that your statement holds for k=3...?
> Pawel Gladki
===
Subject: Re: strong induction
days. My association with the Department is that of an
alumnus.
[.reformartted to remove the top-posting.]
>> Say you have a sequence {x_n} defined by:
>> x_1 = -3
>> x_2 = 23
>> x_3 = -45
>> x_n = 7x_(n-2) - 6x_(n-3) for n>=4
>> Prove that:
>> x_n = 2(-3)^n + 2^n + 1 for all positive integers n (*)
>> If you prove that the base cases n = 1,2,3 are true, then
>> you have to assume that the formula (*) is true in the
following
>conditions,
>> if n=r, for all 1<=r<= k for some k>=3 (n, k are positive
>integers)
>> My question is why is it you have to assume its true for
k>=3 and not
>just
>> for k>3,
>> since you already have proven its true for k=3.
>> Is it not sufficient to assume the formula is true for
k>3???
>> ...and what if - in the course of the proof - you have to
>> use the assumption that your statement holds for k=3...?
>But isnt that redundant, since I already have proven it as
a base case??
When doing strong induction, you dont have base cases, you
have
special cases. That is, cases where the general argument does
not
apply.
Part of the confusion people seem to have between regular and
strong
induction comes from confusing these two. In strong
induction, I think
the pedagogically better way of doing the proof would be to
do the
general argument FIRST, and then do any necessary special
cases
second (if any are needed); while in regular induction we do
the base
case first and the inductive step second.
In this case, you have two choices: you can either assume it
is true
for k>=3; or else assume it is true for k>3 AND use the fact
that it
is also true for k=3. They both amount to the same (since you
have
established k=3 as a special case), and it is easier to do
the single
assumption in the former.
--
Its not denial. Im just very selective 
about
what I accept as reality.
--- Calvin (Calvin and Hobbes)
Arturo Magidin
magidin@math.berkeley.edu
===
Subject: Re: Help me for an idea about the equation below? THx
> A*r+B*(r)^2+C*r=D
> Differential equation above has bothered me for a long
time. I need
> help.
> I think I need the process of dealing with the equation.
Can someone
> do me a favor? I would rather appreciate.
(Another respondent overlooked the square at the first
derivative and
treated the equation as linear.)
Let me guess: it is a model of motion of a mass-spring system
at high
speeds when the friction is proportional to the square of
velocity.
Warning: At a certain stage, we will run into a
non-elementary integration
problem; the old-school terminology considers it still
solvable in
quadratures, that is, leaving the integration problem
unfinished and
relying on the theoretical existence of the solution.
The traditional procedure is: Observe that the independent
variable (say
t) is not showing, so at the first stage we seek a relation
between r
and r.
(I just gave my engineering students a test where one of the
equations was
of this type, although not as difficult.)
Set v = r; then by Chain Rule,
r = dv/dt = (dv/dr) * (dr/dt) = v * 
(dv/dr).
Into your equation:
A * v * dv/dr + B * v^2 + C*r - D = 0
or
(A * v) * dv + (B * v^2 + C*r - D) * dr = 0
becomes a first order ODE. It is not exact but has an
integrating factor
m = exp(2*B*r/A)
and you are on your own. You obtain an ODE relating r and r
(and a first
integration constant); here the mess starts.
===
Subject: Re: Help me for an idea about the equation below? THx
>A*r+B*(r)^2+C*r=D
>Differential equation above has bothered me for a long time.
I need
>help.
>I think I need the process of dealing with the equation. Can
someone
>do me a favor? I would rather appreciate.
Learning how to do this is a significant portion of 3rd
semester calculus,
which you should take if youre really interested in this
kind of math.
Now for the abbreviated version. Differential equations
usually wind up as
an exponential added to a polynomial. In this case, by
inspection, the
polynomial is D/C, which has first and second derivatives
equal to 0.
The exponential part is of the form
r = e^(ax)
r = ae^(ax)
r = a^2 * e^(ax)
A*r+B*(r)^2+C*r=0
(A*a^2 + B*a + C)*e^(ax) = 0
Since e^(ax) is never 0, this becomes a quadratic equation in
a. Youll
usually get two roots, sometimes complex, call them a_1 and
a_2. Since
either of them will work, add exponentials for both of them
to your
polynomial, multiplied by constants. Then you have:
r(x) = D/C + c_1 * e^(a_1 * x) + c_2 * e^(a_2 * x)
To find c_1 and c_2, you need to apply boundary conditions. 
For
example,
if you know r(0)=10 and r(1)=5 you can substitute into the
above equation
twice and solve. But you didnt mention having any boundary
conditions, so
the answer contains two unconstrained constants.
--Keith Lewis klewis {at} mitre.org
The above may not (yet) represent the opinions of my employer.
===
Subject: Re: Find a suitable cylinder to fit on helix
I thought about this some more and decided one could indeed
finish
the computation more or less automatically, without having to
look
at the graph of a function of 2 variables to find the minimum.
> I have a bunch of point in 3D with known (x,y,z)
coordiantes.
> They form a 3-D helix structure in space.
> I choose to minimize (ahem) the sum of the squares of the
differences
> between the square of the nominal radius of the cylinder
and the squares
> of the distances between the points and the central axis.
(phew!)
[Summary: Let E be this sum. For a fixed plane we can easily
find the best
cylinder with central axis perpendicular to that plane, and
compute this
best E in terms of nine parameters r_i, each computed from the
coordinates of the projections of the points to the plane.]
> where D = (-r3*r2^2-r5*r1^2+r3*r5*r0-r4^2*r0+2*r2*r4*r1).
> Using these values in the expansion of E, I get the minimum
value of E
=
>
(-r5*r6^2*r0-r0*r8*r4^2+2*r3^2*r2*r7+2*r5^2*r1*r6+r5^2*r4^2+2
*r3*r5*r4^2
>
-2*r2*r4*r6*r5-2*r1*r4*r7*r5+2*r3*r5*r1*r6-2*r3*r2*r6*r4-2*r1
*r4*r3*r7
>
-r3^3*r5-2*r3^2*r5^2+r4^2*r3^2-r3*r5^3+2*r3*r2*r7*r5-r5*r8*r1
^2-r3*r7^2*r0
>
-r3*r8*r2^2+r7^2*r1^2+r6^2*r2^2-2*r1*r2*r7*r6+2*r8*r2*r4*r1+2
*r0*r4*r7*r6
> +r3*r5*r8*r0) / D
[We still have to choose the optimal plane. Pick an
orthonormal basis
{u,v}
and compute the r_i from them. Heres where it gets 
messy...]
> This isnt too bad a calculation. Almost every plane
includes a unit
> vector which also lies in the xy plane, necessarily of the
form
> u = ( 2*a/(1+a^2), (1-a^2)/(1+a^2), 0 )
> for some a, and then the other unit vector perpendicular to
it must
> be of the form
> v = ( (1-b^2)*(1-a^2)/(1+b^2)/(1+a^2),
> -2*a*(1-b^2)/(1+b^2)/(1+a^2), -2*b/(1+b^2) )
> for some b. The coordinates (x,y) of the projected
> points p are the dot products ( u.p, v.p ), so that the r_i
> computed above will be fairly simple rational functions of
a and b.
> In principle, this amounts to just algebra: you need to
solve the
> equations dE/da = dE/db = 0, essentially a pair of
polynomials in
> a and b, which you can do with resultants or something. But
I have
> to say --- and this is hard for me as a person who loves
complicated
> algebraic problems -- that this is just too hard!
I couldnt resist. Its actually a fun 
challenge to carry
this out; one
could even do it fairly mechanically. Heres a summary of 
the
steps I used.
> Lets try this with some random points on a random 
cylinder:
> [.6638582964, -.1489534114, -.7999397803]
etc. But I want to work with exact arithmetic, so I prefer to
scale
these to integers. On the other hand, there are practical
reasons I
want the integers to be small (see below), so I will round
these off;
for example, the first point will now be [66,-15,-80].
> We must compute e.g. r1 = sum x_i = sum (u.x_i) ; I get
this is now (-3838*a+1840*(1-a^2))/(1+a^2)
> and similar expressions for the other r_i.
> Substitute all of them into the prior expression for E and
you get,
E becomes a ratio of two integral polynomials in a and b, each
of total degree 24. The coefficients have up to 25 digits.
Then the vanishing of the derivatives dE/da, dE/db is
equivalent
to a pair of integral polynomials in a and b, of total degree
47.
Actually there are some powers of (1+a^2) and (1+b^2) which
can
be factored out, so the degrees and the sizes of the
coefficients are
somewhat lower.
Now, I think it is still true that it is not productive to
try to
eliminate b (say) from these two equations to get one
polynomial
equation to solve in a alone. I have some terrific software 
for
this sort of thing, and it gets nowhere after a night of
number crunching.
Ah, but I have some more tricks up my sleeve!
It is fairly easy to carry out the elimination over a FINITE
field.
For all the primes p I tested, Magma was able to eliminate b
from the pair of polyomials over the Galois field GF(p),
taking just a
couple of minutes for 100-digit primes p. In every case, the
result of
the elimination was a monic polynomial of degree 132 with
coefficients
in GF(p). (As I will explain in a moment, I could have
arranged the
degree to be much lower.)
Now, if the elimination were carried out over the rationals,
we would
also end up with a single polynomial, which we could assume
to be
monic by dividing by the lead coefficient. This polynomial
could be
reduced to the corresponding polynomial over GF(p) for every
prime p
except the few which divide the denominator of a coefficient
of the
rational polynomial.
In order to determine the rational polynomial, we use the
Chinese Remainder
Theorem to find an integral polynomial which has the right
reduction to
each of the mod-p polynomials found. This can be done in
seconds, even
when the primes are a hundred digits long. The resulting
integer polynomial
has the property that each of its coefficients is congruent,
modulo
each of the primes p which I used, to the actual rational
coefficient
which we seek. In other words, we have found a large
composite modulus N
and an integer M < N with the property that M = z/x mod N for
some
(hopefully small) integers x and z.
This is equivalent to the Diophantine equation M x + N y - 1
z = 0,
where M,N (and -1 !) are known and x,y,z are sought. There
certainly
exist solutions; indeed, the set of all solutions is the
integer lattice
spanned by [ 1,0,M ] and [ 0,1,N ]. But we expect the right
[x,y,z] to be some linear combination of these which is a
much smaller
vector in the Euclidean sense.
(Just how small do I expect [x,y,z] to be? Thats not clear,
although
since M and N will be of comparable size, so should x and y
be.
So however large x and z are, we can reapply the previous
construction
to enough primes p, or to sufficiently large p, so that M and 
N
are much larger than x,y,z; indeed [x,y,z] is likely to be the
unique (up to sign) smallest vector in this lattice, as long
as M and N
are large enough. Taking what I hoped was a safe guess, I
used 100
hundred-digit primes p, so that N had about 10,000 digits,
and M
was about as large. As long as x,y,z had only a few hundred
digits each,
the vector [x,y,z] would be very much smaller than any other
vector
in the lattice, except its own negative of course.)
This circle of ideas would be useless if there were no way to
FIND the
smallest vector in a lattice, but in fact there is a
now-well-known
algorithm called LLL which does just that. (Actually it is
only
guaranteed to produce a pretty small vector, though not
necessarily the
very smallest, but it succeeds pretty well!) Magma can find
the small
vector almost instantly, and as it happens, finds a vector
[x,y,z]
whose entries have less than 400 digits each -- puny numbers!
Applying this idea to each of the 133 coefficients in the
monic integral
polynomial, we obtain a monic rational polynomial whose
coefficients
are all small, and which still has the property that the
rational
polynomial reduces mod p to exactly the elimination
polynomial we
already found for each of these 100 large primes p. Having
never
won a lottery, we assume this cannot be dumb luck, and so we
believe
we have found the degree-132 polynomial in a which results
from
eliminating b from the pair of equations dE/da = dE/db = 0.
Total time spent: about 1 hour.
(Note that if I had retained more accuracy in the coordinates
of my
ten points, I would have correspondingly large integer values
for the
r_i, thus giving the polynomial equations dE/da = dE/db = 0
corresponding large integer equations. We thus expect the
resultant
of these two, w.r.t. b, to have larger integer coefficients
too;
x and z, above, will be larger, and thus the vector [x,y,z]
will
not stand out as the smallest vector in the lattice unles N
and M
are even larger. So I would have needed more than 100
hundred-digit
primes to come to a conclusion if I had retained more
accuracy in
my points.)
As further evidence that this is the right resultant
polynomial, we
observe that it has some special properties. It turns out to
be a product
(1+a^2)^15 * F1^3 * F2 where F1 has degree 12 and no real
roots,
and F2 has degree 66. In retrospect I could have tried
factoring
the mod-p polynomials first; had I noticed that there were
always a
few factors of high multiplicity, I might have
Chinese-Remaindered
my way back to the rational functions F1 and F2 separately,
thus
having only half as many coefficients -- smaller ones, no
doubt -- to
compute. Moreover, F1 and F2 are essentially unchanged under
the substitution a -> -1/a, which we know is appropriate (that
substitution corresponds to replacing the unit vector u with
its
antipode.)
Our conclusion, then, is that there is a finite list of values
of a
which can be a coordinate of a critical point for the
function E .
We find these among the real roots of F2, of which there are
ten:
0.04571164912, 0.2712828681, 0.2840536847, 0.4273887096,
0.7257134347
and the negatives of the reciprocals of these. Sure enough,
for each
of these there seem to be values of b making both
dE/da=dE/db=0;
again its just a matter of finding the roots of 
a polynomial.
In
each case there are two values of b which will serve, which
are negative
reciprocals of each other, i.e. the critical points of E come
in
sets of four ( (t,u), (t,-1/u), (-1/t,-u), and (-1/t,1/u) ).
Representatives of the five sets are (a,b) =
(0.0457116491, 3.1381940425)
(0.2712828681, 0.3949015917)
(0.2840536847, 0.4246190643)
(0.4273887096, 0.5146083351)
(0.7257134347, 0.3186546105)
Once the general neighborhood of a critical point is known,
one may use
Maple to hunt for a solution to dE/da = dE/db = 0 nearby .
> On the other hand, now that E is just a function of two
variables
> a and b, its easy to look at its graph e.g. with Maple.
> I find, for example,
> that there is a local minimum where a = 0.27, b=0.43 and E
= 0.92.
> However, the really interesting minima occur where
> a = 0.42742, b=-3.11419
The actual location of the minimum has shifted around a bit
since I
have worked with a coarse rounding of the coordinates of the
ten points,
but this is fairly consistent with my present calculations;
the
difference is that now I dont have to look for the critical
points,
and I know I have a complete list of them.
So I guess its a fairly reasonable project to locate the
cylinder
which minimizes E without resorting to looking at a graph to
locate
the minima.
dave
===
Subject: Re: subseries of harmonic series converges iff ...
>I recall reading a theorem once that says
> For a subset S of Z+ , the following are equivalent:
> * Sum_{s in S} 1/s < infty
> * Something else.
>Does anyone know what that something else is?
I was hoping someone else would give the correct answer but I
was
under the impression theres a correct Something else of the
form,
* { x^s, s in S } is a basis for C[0,1]
(the set of continuous functions on the interval). Or
something like that.
Its probably on my website but I cant 
figure out how to
search for it!
Erdos conjectured
* {Something else} => {Sum_{s in S} 1/s < infty}
(and offered a large prize for a proof). In this case
Something else =
There is an upper bound on the length of the arithmetic
progressions in
S.
Golly, that sounds bad. The usual statement is the
contrapositive of this.
dave
If you cant lead it to water or can make it drink, then 
its
not a
horse.
===
Subject: Re: subseries of harmonic series converges iff ...
>I recall reading a theorem once that says
> For a subset S of Z+ , the following are equivalent:
> * Sum_{s in S} 1/s < infty
> * Something else.
>Does anyone know what that something else is?
> I was hoping someone else would give the correct answer but
I was
> under the impression theres a correct Something else of
the form,
> * { x^s, s in S } is a basis for C[0,1]
> (the set of continuous functions on the interval). Or
something like
that.
This is the Muntz-Szasz theorem: If 0 < p1 < p2 < p3 < ...,
then the span
of {1, x^p1, x^p2, ...} is dense in C[0,1] iff 1/p1 + 1/p2 +
... = oo.
(There is a nice proof of this in Rudins Real and Complex
Analysis.)
===
Subject: Re: subseries of harmonic series converges iff ...
in part:
>I recall reading a theorem once that says
> For a subset S of Z+ , the following are equivalent:
> * Sum_{s in S} 1/s < infty
> * Something else.
Does anyone know what that something else is?
I was hoping someone else would give the correct answer but I
was
> under the impression theres a correct Something else of
the form,
> * { x^s, s in S } is a basis for C[0,1]
> (the set of continuous functions on the interval). Or
something like
that.
> This is the Muntz-Szasz theorem: If 0 < p1 < p2 < p3 < ...,
then the span
> of {1, x^p1, x^p2, ...} is dense in C[0,1] iff 1/p1 + 1/p2
+ ... = oo.
> (There is a nice proof of this in Rudins Real and Complex
Analysis.)
Michael Hamm
msh210@math.wustl.edu Standard disclaimers:
http://math.wustl.edu/~msh210/ ... legal.html
===
Subject: Re: suggested free LaTex for windows
> I am looking for a Latex editor for windows, which free
ones are good out
there.
> thank you.
The combination of MiKTeX and TeXnicCentre is nice (if by
windows you
mean Microsoft Windows).
===
Subject: Re: suggested free LaTex for windows
> I am looking for a Latex editor for windows, which free
ones are good out
there.
> thank you.
I personally like to use plain old emacs, which is available
for
any common editor you might use under Linux/Unix will have a
Windows
port. (At least in the case of emacs you can even find
versions that
run on PDAs, which is pretty cool :) .)
Lasse
---
===
Subject: Re: suggested free LaTex for windows
> I am looking for a Latex editor for windows, which free
ones are good
out there.
thank you.
> I personally like to use plain old emacs, which is
available for
> any common editor you might use under Linux/Unix will have
a Windows
> port. (At least in the case of emacs you can even find
versions that
> run on PDAs, which is pretty cool :) .)
> Lasse
> ---
yes, I use emacs under windows. Just like under unix/linux, it
Ôunderstands .tex files. 
Ive found it fairly sufficient for
basic
editing. There is add-on tex mode with lots of bells and
whistles, but
I didnt bother to install it. Ive found it 
having the same
editor
for unix and windows is a Good Thing(TM). Like I use
emacs/win to edit
tex files at home, and emacs/Unix at school.
===
Subject: Re: suggested free LaTex for windows
> yes, I use emacs under windows. Just like under unix/linux,
it
> Ôunderstands .tex files. 
Ive found it fairly sufficient for
basic
> editing. There is add-on tex mode with lots of bells and
whistles, but
> I didnt bother to install it.
Its name is AucTeX and I think that its a great add-on.
Jose Carlos Santos
===
Subject: Dynamic domain ?
Im back once again, bloodied, but sincere. I have come to
the conclusion
that what I am doing is probably just stupidity, but I have
resolved that
if
I am to engage myself in stupidity, then I might as well
excell in it. So,
I
have refined my idiocy yet again, and here it is -
---------------------------------
Example-----------------
Given two physical objects in the physical universe, O1 and
O2.
Let O1 be a block of steel.
Let O2 be a given quantity of heat energy.
O1 and O2 are both unique physical objects.
Now, combine O1 and O2 somehow to get O3, a warmer piece of
steel.
O1 and O2 no longer exist, and a brand new object O3 has come
into
existence.
O3 is unique.
End of example-----------------
Discussion:
It seems interesting that the property of uniqueness is
preserved under
the operation of combining the steel and the heat.
The strange thing is that if you consider the operation of
combining
as a sort of operator, and if you consider your domain as all
physical
objects, then you have a domain which is not fixed. It is
difficult maybe
impossible to even define it formally.
The question:
I cant think of a single instance in math where you have an
operator
which performs upon a domain where your domain is so loose.
The domain is
dynamic ? New elements come into existence, and other
elements cease to
exist ? It just seems crazy. Ridiculous.
Does anyone know of anything in mathematics where your domain
is so
changeable ? And the operator seems to control existence of
elements in the
domain ?
It seems the exact opposite of any math Ive ever seen.
Ordinarily, you
define your domain, you have an operator(s), and this will
yield groups,
rings, fields, etc. But, this thing is crazy. The operator is
controlling
existence of elements within the domain. I dont know of any
operators in
math which can effect existence in the domain like this. It
seems very
odd.
Any feedback ?
===
Subject: Re: Dynamic domain ?
> Given two physical objects in the physical universe, O1 and
O2.
> Let O1 be a block of steel.
> Let O2 be a given quantity of heat energy.
O2 isnt an object.
> O1 and O2 are both unique physical objects.
> Now, combine O1 and O2 somehow to get O3, a warmer piece of
steel.
> O1 and O2 no longer exist, and a brand new object O3 has
come into
> existence.
A block of warm steel is a block of steel is a block of cold
steel.
> O3 is unique.
It is? After a while it cools and becomes O1. What happened
to O2?
> End of example
I hope so.
> Discussion:
> It seems interesting that
> The strange thing is
> The question:
> Any feedback ?
Real farm feedback.
Farmer feeds cows.
Farmers wife feeds chickens.
Farmers daughter milks cows and gathers eggs.
===
Subject: Re: Dynamic domain ?
> Any feedback ?
> Real farm feedback.
> Farmer feeds cows.
> Farmers wife feeds chickens.
> Farmers daughter milks cows and gathers eggs.
I could run with that, but ......
So, lets say you have an operator F, and a domain D. As
elements of D are
fed into F they cease to exist in D, and a completely new
element for D is
the result.
I would have to say, this is a very strange F.
I dont think that Ive ever seen such a thing as a function
which does this
to its own domain. Ever heard of anything like this ?
===
Subject: Re: Dynamic domain ?
<ZPHnd.643575$8_6.4842@attbi_s04 Any feedback ?
Real farm feedback.
> Farmer feeds cows.
> Farmers wife feeds chickens.
> Farmers daughter milks cows and gathers eggs.
> I could run with that, but ......
dont run with the farmers daughter.
> So, lets say you have an operator F, and a domain D. As
elements of D are
> fed into F they cease to exist in D, and a completely new
element for D
is
> the result.
> I would have to say, this is a very strange F.
> I dont think that Ive ever seen such a thing as a 
function
which does
this
> to its own domain. Ever heard of anything like this ?
Live person is fed to death operator, ceases to exist.
Now you new object, a dead body.
US democracy is fed to Bushs operator, ceases to exist.
Now you new object, a fascist state.
===
Subject: Re: Dynamic domain ?
> Any feedback ?
Real farm feedback.
> Farmer feeds cows.
> Farmers wife feeds chickens.
> Farmers daughter milks cows and gathers eggs.
> I could run with that, but ......
> dont run with the farmers daughter.
> So, lets say you have an operator F, and a domain D. As
elements of D
are
> fed into F they cease to exist in D, and a completely new
element for D
is
> the result.
> I would have to say, this is a very strange F.
> I dont think that Ive ever seen such a thing as a 
function
which does
this
> to its own domain. Ever heard of anything like this ?
> Live person is fed to death operator, ceases to exist.
> Now you new object, a dead body.
> US democracy is fed to Bushs operator, ceases to exist.
> Now you new object, a fascist state.
Humor and math go very well together.
Bushs war is killing people one at a time. It is 
arithmetic.
Al Queda uses 1 assasin to kill hundreds. The killing is
geometric.
If I had to choose, I would choose no war at all. I love
bears, and I love
sharks. But if one was trying to eat me I would certainly try
to kill it.
War should always be the very last resort, but there is one
option which
might be even worse, and that would be surrendering yourself
knowing that
you will be killed without mercy.
I dont have the answers to this problem. In fact, I once
thought that I
knew
the answer to such a problem and the judge disagreed. They
put me in the
timecube (see www.timecube.com ) for a while, and now I
generally try to
avoid solving such problems because every possible solution
is always
wrong.
Now Im just an illogical cubiq, and my math skills are
isomorphic to the
empty set.
I am still wondering about operators which modify their own
domains -
Lefty
TIMETRAVELLER
and CUBIQ
===
Subject: Re: Dynamic domain ?
<vGJnd.122186$R05.68217@attbi_s53 Feedback.
> Farmer feeds cows.
> Farmers wife feeds chickens.
> Farmers daughter milks cows and gathers eggs.
> Bushs war is killing people one at a time. It is
arithmetic.
> Al Queda uses 1 assassin to kill hundreds. The killing is
geometric.
> If I had to choose, I would choose no war at all. I love
bears, and I
love
> sharks. But if one was trying to eat me I would certainly
try to kill it.
> War should always be the very last resort, but there is one
option which
> might be even worse, and that would be surrendering
yourself knowing that
> you will be killed without mercy.
> I dont have the answers to this problem. In fact, I once
thought that I
knew
> the answer to such a problem and the judge disagreed. They
put me in the
> timecube (see www.timecube.com ) for a while, and now I
generally try to
> avoid solving such problems because every possible solution
is always
wrong.
What problem? You stated none. You also didnt
http://www.timecube.com
so your reference not highlighting, wouldnt open.
> Now Im just an illogical cubiq, and my math skills are
isomorphic to the
> empty set.
I suggest you look sci.logic, thread logic is obsolete.
In fact, sci.logic is a more appropriate location for your
Ôobjective posts as also 
alt.math.recreational.
> I am still wondering about operators which modify their own
domains -
Yes, tyrants. Bush for example, modifies his democratic domain
into
a theo-fascist domain.
===
Subject: Re: Dynamic domain ?
> Now Im just an illogical cubiq, and my math skills are
isomorphic to
the
> empty set.
> I suggest you look sci.logic, thread logic is obsolete.
> In fact, sci.logic is a more appropriate location for your
> Ôobjective posts as also 
alt.math.recreational.
They threw me out. Im a usenet refugee.
> I am still wondering about operators which modify their own
domains -
> Yes, tyrants. Bush for example, modifies his democratic
domain into
> a theo-fascist domain.
Well, I suppose that if birth and death are operators on
living
systems,
then youd have a sort of _analogy_ of what 
Im talking
about. Because,
both
birth and death modify the domain upon which they operate.
They are like
functions which create and also destroy elements in the
domain.
I dont think that there are any mathematical instruments
which do this. I
think that its very wierd, and Im trying to 
think of
something more
formal - but like I said - my math talents have converged to
zero.
Consider this algorithm -
-----------------------------
10 ÔStart with a finite set of numbers S
20 Select x1 at random from S
30 x2 = (x1)^2
40 Let x1 be deleted from S
50 Let x2 be joined to S
60 Select x3 at random from S
70 x4 = (x3)^(1/2)
80 Let x3 be deleted from S
90 Let x4 be joined to S
100 Goto 20
-------------------------------
Now, it might be equivalent to some type of recursive
function, but whats
the symbol for select at random ?
Whats the symbol for delete from S ?
Whats the symbol for join x1 to S ?
I have never seen union and intersection operators used in a
difference
equation, or on the ßy. In fact, I dont think that any 
first
order
logical operators have ever been used dynamically - as one
would
construct
coupled differential equations, or other recursive relations.
I have never
seen this. Have you ?
Stephen Hawkings secretary wont put me through to him
anymore. She just
dumps me in his voicemail. I have to ask someone -
===
Subject: Re: Dynamic domain ?
> Consider this algorithm -
> -----------------------------
> 10 ÔStart with a finite set of numbers S
> 20 Select x1 at random from S
> 30 x2 = (x1)^2
> 40 Let x1 be deleted from S
> 50 Let x2 be joined to S
> 60 Select x3 at random from S
> 70 x4 = (x3)^(1/2)
> 80 Let x3 be deleted from S
> 90 Let x4 be joined to S
> 100 Goto 20
> -------------------------------
> Now, it might be equivalent to some type of recursive
function, but
whats
> the symbol for select at random ?
> Whats the symbol for delete from S ?
> Whats the symbol for join x1 to S ?
> I have never seen union and intersection operators used in
a difference
> equation, or on the ßy. In fact, I dont think that any 
first
order
> logical operators have ever been used dynamically - as one
would
construct
> coupled differential equations, or other recursive
relations. I have
never
> seen this. Have you ?
OK - I said stupid things again.
First, you can have infinite unions and infinite 
intersections.
This is
well
known.
Secondly, in the algorithm above, you can let S be a subset
of R or
something, and instead of deleting from S you can simple say
not
contained in S. It probably equivalent.
I dont think its neccesary to have a function which 
modifies
R itself, if
you can just select subsets of R and you get the equivalent
result.
Back to square one - maybe -
===
Subject: Re: Dynamic domain ?
<S03od.438129$D%.267066@attbi_s51 Now Im just an illogical
cubiq, and my math skills are isomorphic to
> the
> empty set.
I suggest you look sci.logic, thread logic is obsolete.
> In fact, sci.logic is a more appropriate location for your
> Ôobjective posts as also 
alt.math.recreational.
> They threw me out. Im a usenet refugee.
Awe come on, I dont believe you. If they threw you out at
sci.logic, you
would have been fried at sci.math. Tell you what, put next
your post in
sci.logic instead of sci.math, perhaps upon timecube. Then
well
know. We may even get more cross chatter there than what
weve been
getting here.
===
Subject: Re: Dynamic domain ?
> Im back once again, bloodied, but sincere. I have come to
the conclusion
> that what I am doing is probably just stupidity, but I have
resolved that
if
> I am to engage myself in stupidity, then I might as well
excell in it. So,
I
> have refined my idiocy yet again, and here it is -
> ---------------------------------
> Example-----------------
> Given two physical objects in the physical universe, O1 and
O2.
> Let O1 be a block of steel.
> Let O2 be a given quantity of heat energy.
> O1 and O2 are both unique physical objects.
You lost me there. Couldnt the same quantity of heat energy
exist in
many different places? If I take two pieces of steel and heat
them both
energy? I think youre fooling yourself with semantic games.
===
Subject: Re: Dynamic domain ?
> Im back once again, bloodied, but sincere. I have come to
the
conclusion
> that what I am doing is probably just stupidity, but I have
resolved
that if
> I am to engage myself in stupidity, then I might as well
excell in it.
So, I
> have refined my idiocy yet again, and here it is -
> ---------------------------------
> Example-----------------
> Given two physical objects in the physical universe, O1 and
O2.
> Let O1 be a block of steel.
> Let O2 be a given quantity of heat energy.
> O1 and O2 are both unique physical objects.
> You lost me there. Couldnt the same quantity of heat
energy exist in
> many different places? If I take two pieces of steel and
heat them both
> energy? I think youre fooling yourself with semantic 
games.
Very likely yes - I am probably just going up against a brick
wall. But
just
for the sake of argument -
Whatever heat is made of, if you have a certain quantity of
it in a
certain place it is unique. That is, no other quantity of
heat is identical
to it. You might be able to have two separate samples with
nearly identical
quantities of heat, but the samples are in two different
locations. They
are
unique. Same with the chunk of steel.
The actual objects in the example are arbitrary, I just used
them to
illustrate that the domain consists of real objects and not
abstract ones.
I was trying to use the idea that All physical objects are
unique.
If
that were true, then maybe you can build on it. Thats what
Im trying to
do.
There was a thread about it a few weeks ago.
I will probably chase my tail until Ive proved the whole
thing futile, and
my folly will serve as an example for others to avoid. : )
===
Subject: Re: Dynamic domain ?
> Im back once again, bloodied, but sincere. I have come to
the
> conclusion
> that what I am doing is probably just stupidity, but I have
resolved
> that if
> I am to engage myself in stupidity, then I might as well
excell in
it.
> So, I
> have refined my idiocy yet again, and here it is -
> ---------------------------------
> Example-----------------
> Given two physical objects in the physical universe, O1 and
O2.
Let O1 be a block of steel.
> Let O2 be a given quantity of heat energy.
O1 and O2 are both unique physical objects.
> You lost me there. Couldnt the same quantity of heat
energy exist in
> many different places? If I take two pieces of steel and
heat them both
> energy? I think youre fooling yourself with semantic 
games.
> Very likely yes - I am probably just going up against a
brick wall. But
just
> for the sake of argument -
> Whatever heat is made of, if you have a certain quantity of
it in a
> certain place it is unique. That is, no other quantity of
heat is
identical
> to it. You might be able to have two separate samples with
nearly
identical
> quantities of heat, but the samples are in two different
locations. They
are
> unique. Same with the chunk of steel.
> The actual objects in the example are arbitrary, I just
used them to
> illustrate that the domain consists of real objects and not
abstract
ones.
> I was trying to use the idea that All physical objects are
unique.
If
> that were true, then maybe you can build on it. Thats what
Im trying to
do.
> There was a thread about it a few weeks ago.
> I will probably chase my tail until Ive proved the whole
thing futile,
and
> my folly will serve as an example for others to avoid. : )
I believe I can identify the source of the confusion.
Quantity of heat
is not a thing that has existence in the universe. Its an
abstraction.
Something that exists only in the world of thought. (Of
course thought
itself, being a byproduct of measurable electrical activity
in the
brain, has physical existence. But then we have to ask whether
consciousness has physical existence, and wed have to move 
to
alt.amateur.metaphysics.)
Anyway what you really have is a piece of steel, on the one
hand, and a
couple zillion little molecules (the molecule is the
traditional level
of discourse for discussions of heat -- rather than atoms or
quarks or
strings or whatever). Each of those individual molecules is
unique, and
is moving around with a certain amount of energy. The energy
dissipated
from the collisions as the molecules bounce around against
each other,
is what we call heat. But the amount of heat, as a specific
thing, is
an ABSTRACTION. It is a thought, like a set or truth or
justice
or
even the number 5. Abstractions dont follow the same rule 
of
uniqueness as physical objects do. There are many many
individual
marbles in the world, but there is only one abstract concept
marble
that applies to each of the individual physical marbles.
===
Subject: Re: Dynamic domain ?
Im back once again, bloodied, but sincere. I have come to 
the
> conclusion
> that what I am doing is probably just stupidity, but I have
resolved
> that if
> I am to engage myself in stupidity, then I might as well
excell in
it.
> So, I
> have refined my idiocy yet again, and here it is -
> ---------------------------------
> Example-----------------
> Given two physical objects in the physical universe, O1 and
O2.
Let O1 be a block of steel.
> Let O2 be a given quantity of heat energy.
O1 and O2 are both unique physical objects.
You lost me there. Couldnt the same quantity of heat energy
exist in
> many different places? If I take two pieces of steel and
heat them
both
> energy? I think youre fooling yourself with semantic 
games.
> Very likely yes - I am probably just going up against a
brick wall. But
just
> for the sake of argument -
> Whatever heat is made of, if you have a certain quantity of
it in a
> certain place it is unique. That is, no other quantity of
heat is
identical
> to it. You might be able to have two separate samples with
nearly
identical
> quantities of heat, but the samples are in two different
locations.
They
are
> unique. Same with the chunk of steel.
> The actual objects in the example are arbitrary, I just
used them
to
> illustrate that the domain consists of real objects and not
abstract
ones.
> I was trying to use the idea that All physical objects are
unique.
If
> that were true, then maybe you can build on it. Thats what
Im trying
to
do.
> There was a thread about it a few weeks ago.
> I will probably chase my tail until Ive proved the whole
thing futile,
and
> my folly will serve as an example for others to avoid. : )
> I believe I can identify the source of the confusion.
Quantity of
heat
> is not a thing that has existence in the universe. Its an
abstraction.
> Something that exists only in the world of thought. (Of
course thought
> itself, being a byproduct of measurable electrical activity
in the
> brain, has physical existence. But then we have to ask
whether
> consciousness has physical existence, and wed have to 
move
to
> alt.amateur.metaphysics.)
> Anyway what you really have is a piece of steel, on the one
hand, and a
> couple zillion little molecules (the molecule is the
traditional level
> of discourse for discussions of heat -- rather than atoms
or quarks or
> strings or whatever). Each of those individual molecules is
unique, and
> is moving around with a certain amount of energy. The
energy dissipated
> from the collisions as the molecules bounce around against
each other,
> is what we call heat. But the amount of heat, as a specific
thing, is
> an ABSTRACTION. It is a thought, like a set or truth or
justice or
> even the number 5. Abstractions dont follow the same rule
of
> uniqueness as physical objects do. There are many many
individual
> marbles in the world, but there is only one abstract
concept marble
> that applies to each of the individual physical marbles.
Agreed - but lets simplify it a little.
Let O1 be a blob of white clay. O1 is unique.
Let O2 be a blob of black clay. O1 is unique.
Now, smash them and mush them together.
You have O3, a blob of gray clay, and O3 is also unique.
Further, O1 and O2 no longer exist. And, you have an O3 which
did not exist
previously. The operation of mushing together is unaffected,
but the
domain has changed.
You could probably extend this to the rest to all physical
objects, but
just
trying to keep it simple for the mean time.
I dont know of any mathematical operators which will do this
- actually
modifying the domain that they are defined for. Seems like
some 1st rate
lunacy, certainly more interesting than your run-of -the-mill,
garden-variety nonsense.
===
Subject: Re: Dynamic domain ?
Im back once again, bloodied, but sincere. I have come to 
the
> conclusion
> that what I am doing is probably just stupidity, but I have
resolved
> that if
> I am to engage myself in stupidity, then I might as well
excell
in
> it.
> So, I
> have refined my idiocy yet again, and here it is -
> ---------------------------------
> Example-----------------
> Given two physical objects in the physical universe, O1 and
O2.
Let O1 be a block of steel.
> Let O2 be a given quantity of heat energy.
O1 and O2 are both unique physical objects.
You lost me there. Couldnt the same quantity of heat energy
exist
in
> many different places? If I take two pieces of steel and
heat them
> both
> energy? I think youre fooling yourself with semantic 
games.
> Very likely yes - I am probably just going up against a
brick wall.
But
> just
> for the sake of argument -
Whatever heat is made of, if you have a certain quantity of
it in
a
> certain place it is unique. That is, no other quantity of
heat is
> identical
> to it. You might be able to have two separate samples with
nearly
> identical
> quantities of heat, but the samples are in two different
locations.
They
> are
> unique. Same with the chunk of steel.
> The actual objects in the example are arbitrary, I just
used them
to
> illustrate that the domain consists of real objects and not
abstract
> ones.
I was trying to use the idea that All physical objects are
unique.
> If
> that were true, then maybe you can build on it. Thats what
Im trying
to
> do.
> There was a thread about it a few weeks ago.
> I will probably chase my tail until Ive proved the whole
thing
futile,
> and
> my folly will serve as an example for others to avoid. : )
> I believe I can identify the source of the confusion.
Quantity of
heat
> is not a thing that has existence in the universe. Its an
abstraction.
> Something that exists only in the world of thought. (Of
course thought
> itself, being a byproduct of measurable electrical activity
in the
> brain, has physical existence. But then we have to ask
whether
> consciousness has physical existence, and wed have to 
move
to
> alt.amateur.metaphysics.)
> Anyway what you really have is a piece of steel, on the one
hand, and a
> couple zillion little molecules (the molecule is the
traditional level
> of discourse for discussions of heat -- rather than atoms
or quarks or
> strings or whatever). Each of those individual molecules is
unique, and
> is moving around with a certain amount of energy. The
energy dissipated
> from the collisions as the molecules bounce around against
each other,
> is what we call heat. But the amount of heat, as a specific
thing,
is
> an ABSTRACTION. It is a thought, like a set or truth or
justice or
> even the number 5. Abstractions dont follow the same rule
of
> uniqueness as physical objects do. There are many many
individual
> marbles in the world, but there is only one abstract
concept marble
> that applies to each of the individual physical marbles.
> Agreed - but lets simplify it a little.
> Let O1 be a blob of white clay. O1 is unique.
> Let O2 be a blob of black clay. O1 is unique.
> Now, smash them and mush them together.
> You have O3, a blob of gray clay, and O3 is also unique.
> Further, O1 and O2 no longer exist. And, you have an O3
which did not
exist
> previously. The operation of mushing together is
unaffected, but the
> domain has changed.
Ok, thats much clearer.
> You could probably extend this to the rest to all physical
objects, but
just
> trying to keep it simple for the mean time.
> I dont know of any mathematical operators which will do
this - actually
> modifying the domain that they are defined for. Seems like
some 1st rate
> lunacy, certainly more interesting than your run-of
-the-mill,
> garden-variety nonsense.
I dont know, this reminds me a little of what happens when
you take 3
and combine it with 5 to get 8. Whered the 5 and the 3 go?
They are
both present in the 8. In fact 8 = 5+3 after youve put 5 
and
3
together, just as claylump 03 is made up of claylumps 01 and
02. If you
took 03 and took away all the atoms that used to be part of
01, youd be
left with 02.
===
Subject: Cantor Normal Form
by support1.mathforum.org (8.11.6/8.11.6/The Math Forum,
$Revision:
1.9 primary) id iAK471W20421;
Hi guys,
What is the Cantor Normal Form of ordinals? Why is it that
the Cantor Normal
form of w + w^2 + w^3 + w^4 + 2 = w^4 + 2?
And what would be the CAntor Normal Form of
(w+3)^5 + (w^2+17).(w+8) + w^12 ?
===
Subject: Re: Cantor Normal Form
>Why is it that the Cantor Normal form of w + w^2 + w^3 + w^4
+ 2 = w^4 +
2?
This one is so simple that even I can answer it.
Why is the Cantor Normal Form of 1 + w equal to w, while the
Cantor
Normal Form of w + 1 equal to w + 1?
This is because an ordinal refers to the structure of an
ordered set.
The set {A, 1, 2, 3, 4,...} has the same structure as the set
{1, 2, 3,
4, 5,...}; just re-name A as 1, 1 as 2, 2 as 3, and so on.
So, in
general, appending a small ordinal to a big ordinal on the
left doesnt
change the structure.
But the set {1, 2, 3, 4,... A} has a different structure; you
keep
counting forever, and you never get to A; A is after the
infinite
counting process.
John Savard
http://home.ecn.ab.ca/~jsavard/index.html
===
Subject: Re: Cantor Normal Form
> What is the Cantor Normal Form of ordinals? Why is it that
the Cantor
> Normal form of w + w^2 + w^3 + w^4 + 2 = w^4 + 2?
> And what would be the CAntor Normal Form of
> (w+3)^5 + (w^2+17).(w+8) + w^12 ?
w^12 because all the other exponents after expanding the
expressions
are less than 12.
===
Subject: Re: Cantor Normal Form
> Hi guys,
> What is the Cantor Normal Form of ordinals? Why is it that
the Cantor
> Normal form of w + w^2 + w^3 + w^4 + 2 = w^4 + 2?
Ôcos w + w^2 = w^2 =/= w^2 + w etc.
A simpler example: 1 + w is the order type of a singleton
followed
by a simple infinite sequence, that is it looks like
*, *, *, .....
so its a simple infinite sequence: 1 + w = w.
But w + 1 is the order type of a simple infinite seuqence
followed
by a singleton: so
*, *, *, .... *
Not the same as w :-)
--
Robin Chapman, www.maths.ex.ac.uk/~rjc/rjc.html
Lacan, Jacques, 79, 91-92; mistakes his penis for a square
root, 88-9
Francis Wheen, _How Mumbo-Jumbo Conquered the World_
===
Subject: Re: Cantor Normal Form
>> Hi guys,
>> What is the Cantor Normal Form of ordinals? Why is it that
the Cantor
>> Normal form of w + w^2 + w^3 + w^4 + 2 = w^4 + 2?
> Ôcos w + w^2 = w^2 =/= w^2 + w etc.
> A simpler example: 1 + w is the order type of a singleton
followed
> by a simple infinite sequence, that is it looks like
> *, *, *, .....
> so its a simple infinite sequence: 1 + w = 
w.
> But w + 1 is the order type of a simple infinite seuqence
followed
> by a singleton: so
> *, *, *, .... *
> Not the same as w :-)
Concrete models clarify this:
1 + w = w
e.g. {0} / N = N
but w + 1 != w
e.g. N /{oo} != N
Note esp. N /{oo} contains an infinite elt oo > n
with no immediate predecessor, but N has no such elt.
--Bill Dubuque
===
Subject: Difference between FT & LT
Hi there, Fourier transform convert the time domain function
into
frequency domain and so the Laplace transform. Then who do
they
differ? Fourier transform work at complex frequency and that
of
Laplace transform works at s plane, also they have different
limits of
integration, is this all how they differs? I need some
intuitive
understanding, how they actually work.
Any help is appreciated
===
Subject: Turing Machines and Physical Computation
Hi Stephen,
I would have expected a thoughtful reply.
> I have had such a discussion with an extremely intelligent
and
> experienced mathematician. He told me that PCs are not
Turing
> Machines, because they have an infinite tape. I think he did
not
> know anything about descriptive complexity. This infinite
portion of
> the tape consists entirely of blank symbols, and therefore
has
> descriptive complexity O(1), which is easily realized by a
physical
> system. When I told him about Ullmans 
indefinite growing
argument, he
> objected But when the universe is filled up, it cannot grow
any more!
> Then, it is not infinite, to which I responded Yes, but
there is
> *nothing* that is larger than the universe. To assume the
contrary
> would be theology, which I despise.
> Turing Machines are idealized which means they are not
physically
realized.
What a nice assertion.
A TM is just the specification of a very low level machine
code,
thats all there is to it. Its just another 
model of
computation, and
not an extremely telling or useful one. Thinking about Turing
Machines which have not been realized yet does not mean that
these
things cannot be implemented. Besides, a bounded size FSA
simulator,
too, is a Turing Machine... You people overlook this simple
point, I
wonder why.
Also, I suggest you to get the most recent edition of
Cinderella book
and have a look at what Ullman thinks about this subject.
(Thats
another argument!) IIRC, in that edition, the authors argue
persuasively that we should think of PCs as TMs rather than
DFAs. I
find that a subtle point.
Now, I recall that you made this strange argument about Turing
Machines being able to do things that real computers cannot,
because
they have an infinite tape. What an observation.
> TMs are not meant to have physical constraints applied to
them.
Another assertion.
Ignoring physical plausibility directly opposes physicalism.
When we
start talking about immaterial things, we are not making
scientific
statements, we are making metaphysical ones, and that is not
a good
sign if the metaphysical statements depict worlds that are not
physically similar to our own. It is a matter of degree,
which we can
observe.
The question is: how far from reality? The further you talk,
the less
real your statements are, not just as real!
> That mixes categories.
No.
> Sometimes the question is asked, how many sentences can be
> generated in some natural (say English) language? There are
finitely many
> words in the language, but the standard answer is that
there are
countably
> infinite number of sentences, due to appending etc.
That is potential infinity, a plausible concept, considering
time for
instance. Current theory of physics *seems* to suggest that
time is
going to continue forever. The idea of potential infinity is
then, at
least in the temporal sense, not too far from our world.
However...
> These kind of questions ask what is the potential in
theory, not what is
> practically possible. Observations like: a person can only
articulated
> finitely
> many sentences in a lifetime, or any sentence has to be
uttered before
> somebody dies or a machine wears out, or that how many
sentences
> potentially exist is related to how many people generate
sentences over
> the lifetime of humanity in the universe are not relevant,
because that
is
> not the question being asked. Every process within the
universe is finite
> due to heat death of the universe, so that makes all such
questions
trivial,
> if one interprets them to mean or apply to a physical
reality.
Thats a quite amazing thought, because it rejects that some
facts
about our universe can be simple. That some answer is trivial
does
not necessarily mean it is wrong. If we are talking about our
universe, yes, if universe is going to expand, and
accelerating in
expansion, then, at some time T no efficient causal
interaction will
remain, which will disable large computations. Sad for the
universe.
But what else can we say? Then, those never-ending
computations arent
quite possible. If thats so, its not 
sensible to talk about
things
that cannot ever be constructed in our world. Then, lets
talk of
finite quantities only. Lets see how big 
computations behave,
without
pretending that there is no bound to their time/space use.
At this point, I should remind you the famous Levin quote.
Levin was
Kolmogorovs student, so he probably has a better idea of
this issue
than you have.
> A Turing
> Machine or potential sentence of a language (there is no
pre-existing
> specification that the sentence has to be of 
finite length)
is not of this
> world.
Of which world is it then? (^_^) And you are saying this
Platonist
talk is not theology! You have just murdered physicalism.
> The set of natural numbers is countably infinite and is has
some use
> theoretically. Would you claim infinite sets have no use
because they
It has some use theoretically. An immortal being is nice in
theory, as
well, but we dont know if it will work out well for us. But
that is a
sorry analogy. We can do better. God has some use
theoretically, we
can use it to resolve our ethical problems. But we dont 
know
if it
exists. Its just an idea. As you can see, 
its pointless to
say that
the set of natural numbers exist except as an idea. And that
is what
you are affirming in the first sentence. The 
second is
nonsense. I say
nothing about their theoretical use, they make good mental
exercise,
and they help us construct simpler theories in exchange for
loss of
physicality. (Again, when it becomes less physical, it does
not
automatically gain some positive ontological status, if you
are also a
physicalist!)
That something has some use theoretically does not grant
attaching the
word exists to it, from a philosophical point of view. And
giving it
a privilege might betray philosophical consistency.
> And the original description of a Turing Machine. It is
common to call
> this tape Ôinfinite though some 
prefer finitely unbounded.
The latter camp has the precise terminology.
> There is no
> physical time constraint applied to when the calculation
has to be
> completed.
If you mean *any* computation. But a Turing Machine is a
*particular*
computer. Not just *any* computer. Lets pay attention to 
our
language.
> So there are calculations that a physical PC the size of
> a galaxy could not complete before the universe ran out of
power to
> energize the computer. A Turing Machine can of course
complete
> such a calculation (because the calculation does not need
to be infinite,
> just finitely larger/longer in time that can be accomplished
by any
> physical device during the existence of the physical
universe) because
> the constraint of physical time is not applied to idealized
situations.
Wittgenstein once said Turings theory was of human
computers. Which
was quite true if we take the original paper literally,
without
abstracting computer. (And that is what such people were
called at
the time, who made calculations)
You are also making a significant conceptual error. We have a
theory
T, only a small portion of which has models in the real
world. But no
experiments contradict our theory (such as computers
existing,that
cannot be explained by T). I think this is a perfectly
legitimate
situation in science. And you are twisting the whole
physicalist
argument upside-down by saying that, since the theory
predicts (by way
of *generalization*) Ôthere would be machines which can grow
absolutely with no end, if and only if our universe had an
infinite
space; *then* you conclude that this theory must not be a
physical
theory. What a bad use of language!
Instead you should have paid attention to basic rules of
grammar and
linguistic analysis. What the theory predicts is a
*counterfactual*,
it is not too different from saying that If my mother had a
beard,
she would have a lot of hair on her chin. This is quite
possibly
*false* for most of our mothers. And for our world, the theory
*predicts* that there will be no machines which can grow
absolutely
with no end, since our universe does not have an infinite
space. It is
regrettable to think of the theory as independent from
physical
statements, if we accept that it is a theory of *machines*.
Anyway, the point remains that Turings theory is a theory 
of
actual
machines, if not merely humans. Wittgenstein has a point! And
then it
is nonsense to argue that:
> A Turing Machine can of course complete such a calculation
.... because
the
> constraint of physical time is not applied to idealized
situations.
But that is a terrible metaphysics you have there! Idealized
situations do not exist. By situation we mean a complex
aggregate of
physical events, nothing more. (Again, if we are to call
ourselves
physicalists. And Cartesian Dualists, can leave the hall
silently!)
> Keeping those categories seperate, the idealized and the
physical,
> is definitional. The answer to theoretical questions is
trivial and
obvious
> if you mix these categories. Mathematicians invented
infinity without
> the requirement that it be physically realized because it
was useful.
> Pure mathematics invents formal mathematical systems with no
> requirement that this formal system represent any physical
event or
> process.
This is quite a muddled reasoning, especially this bit:
> Pure mathematics invents formal mathematical systems with no
> requirement that this formal system represent any physical
event or
> process.
There is no requirement of representation, so you think.
There is the
requirement of representation of *ideas* in your head, and if
your
ideas are *physical*, then it follows that the *exact
opposite* of
your statement holds!
> Yes, but there is
> *nothing* that is larger than the universe. To assume the
contrary
> would be theology, which I despise.
> When you say *nothing* you mean no physical something.
Platonist semantics. *shudder*
When you utter nothing, you do not refer to anything that
exists.
You do not refer to something that does not exist! (That is
generally
seen as a wrong account of designating the reference of
expressions
with counter-factuals in philosophy of language.)
That would be a very confused understanding of the word
nothing.
Lets do some ordinary philosophy of language to draw a 
better
picture.
Here are some easy semantics questions. Formalize the
semantics of the
following sentences, excluding questions using common
knowledge
representation techniques in First Order Logic: (I am
explicitly
asking for truth-referential semantics, of course. Usual
Tarskis
World stuff, if you are familiar with formal semantics)
- What do you want?
- I want nothing.
- What are you going to do tomorrow?
- I am going to do nothing.
There is nothing in the box.
* An example of an analytically false statement (for nonempty
interpretation domains)
Everything is nothing. (Hint: the solution is like the liar
paradox)
> Mathematical
> objects need not be physical.
A Turing Machine is not just a mathematical object! [*]
Lets repeat our basic argument again.
1. Not all Turing Machines require finite bounded space.
2. Therefore some Turing Machines run in finite bounded space.
3. Many PCs do just that.
4. Then, PCs are physical functioning models of Turing
Machines. (But
most of them are also simple DFAs, or formal axiomatic
systems, or
whatever general theory they fit. The theory which has the 
most
*explanatory* power will be preferred according to the
question we are
trying to answer.)
Could this argument be any simpler?
> When you made this comparison, infinity and theology/God, to
the size
> of the physical universe, you crossed over from debating
potential vs.
> actual infinities to declaring abstract thinking is just
theology in
another
> guise.
That is exactly what Poincare implied in his famous remark. I
will bet
on Poincare, and not on your championing of one school of
mathematics.
(I am not the only person who made the comparison!)
ever discuss foundational issues with those who cannot
question the
assumptions of their favorite school of thought?
What I explained to a slightly confused mathematician who
believed
himself to be a constructivist was that a sane analysis in
philosophy
of computation suggests that Turing Machines should be
thought of
physical devices, if we are to remain physicalists. You do not
challenge any of the arguments. Instead, you assert things,
like
saying that Turing Machines are not of this world. Show us
that
world, or is it the fairy-land of mathematics?
[snip some philosophy]
Amused,
--
Eray Ozkural
[*] And you might as well say, our language expressions do
not need
to refer to physically plausible things. Then, you should
perhaps
think of defending that we freely talk of God in scientific
discourse.
But that is not permissible in scientific talk. Maybe it is
good for
mythology, which is not our business.
===
Subject: Re: Turing Machines and Physical Computation
Ah, modern symbolic logic, even translated to English, is so
much
clearer and less prone to false word arguments than ancient
platonic
logic language. Its a joy for me to translate from your
platonic
language to modern:
> - What do you want?
> - I want nothing.
It is not true that there exists X such that I want X.
> - What are you going to do tomorrow?
> - I am going to do nothing.
It is not true that there exists X such that I am going to do
X tomorrow.
> There is nothing in the box.
It is not true that there exists X such that X is in the box.
> Everything is nothing.
It is not true that there exists X.
-or-
For all X, it is not true that there exists Y such that Y is
in X.
===
Subject: Re: Turing Machines and Physical Computation
>> I have had such a discussion with an extremely intelligent
and
>> experienced mathematician. He told me that PCs are not
Turing
>> Machines, because they have an infinite tape. I think he
did not
>> know anything about descriptive complexity. This infinite
portion of
>> the tape consists entirely of blank symbols, and therefore
has
>> descriptive complexity O(1), which is easily realized by a
physical
>> system. When I told him about Ullmans 
indefinite growing
argument, he
>> objected But when the universe is filled up, it cannot grow
any
more!
>> Then, it is not infinite, to which I responded Yes, but
there is
>> *nothing* that is larger than the universe. To assume the
contrary
>> would be theology, which I despise.
It is true that a Turing Machine is not infinitely complex to
describe.
But it also remains true that a PC is not capable of
performing a
computation which requires an infinite amount of intermediate
results,
or even a large finite amount of intermediate results which is
larger
than the capacity of its storage devices.
Mathematics deals with the infinite, and the arbitrarily large
finite,
and, thus, computations requiring more intermediate storage
than the
whole Universe could supply are real and meaningful in
mathematics; to
exclude them would only make things more complicated, not
simpler. (And
we do not even know exactly how big the Universe is.)
John Savard
http://home.ecn.ab.ca/~jsavard/index.html
===
Subject: Re: Turing Machines and Physical Computation
>> Turing Machines are idealized which means they are not
physically
realized.
So are tigers, Buicks, the letter q, ... any noun, much less
any
natural kind. I guess nothing exists but ideas. Of course,
that
means ideas are of no use in dealing with actual objects.
This is
Modern Cartesianism - in its worst form, as I often defend
Descartes
of many of the sins attributed to him.
As soon as you assume into the problem a divide between ideas
and the
physically realized, you are assured of never finding a
solution to
major problems.
>> And the original description of a Turing Machine. It is
common to call
>> this tape Ôinfinite though some 
prefer finitely unbounded.
...
>> So there are calculations that a physical PC the size of
>> a galaxy could not complete before the universe ran out of
power to
>> energize the computer.
The question is why a physical computer can do anything at
all, and
what the limits are of any particular class of physical
computers.
Im sure there is a limit to the size that you can build
balls of
string in this universe, before they collapse of their own
mass into
black holes. That does not mean that somewhat smaller - and
in fact,
rather large! -- balls of string cannot be built or studied.
--
Bottom line: if you see even the tiniest trace of idealism in
a theory
about computation, expunge it or discard the entire theory,
because
you are certainly wasting your time dealing with it.
J.
===
Subject: Re: Turing Machines and Physical Computation
http://mygate.mailgate.org/mynews/comp/comp.theory/
61bad26451853979aa12696535
2b4240.48257%40mygate.mailgate.org
> Hi Stephen,
> I would have expected a thoughtful reply.
Perhaps if you had avoided wandering off in
the weeds again you would have received one?
The reactions you receive from others are the
reactions _you_ _provoke_ by _your_ behavior.
This is a constant of the universe.
Failing to understand that permanent reality has a
technical name: autism.
> I have had such a discussion with an extremely intelligent
and
> experienced mathematician. He told me that PCs are not
Turing
> Machines, because they
Turing Machines, not PCs.
> have an infinite tape.
> I think he did not know anything about
> descriptive complexity.
And I think this is merely another example of you
failing to pay attention in class.
> This infinite portion of the tape consists
> entirely of blank symbols, and therefore has
> descriptive complexity O(1),
Ummm, no, that doesnt even make sense, since the
infinite portion of the tape does not have a known
starting position. There are Turing Machine programs
which will overwrite any mark you place on the tape
and say, from here on out, I can describe this with
O(1) complexity, so that refuge is unavailable to
you as a way to limit the complexity of describing
the tape as a whole.
> which is easily realized by a physical system.
Again, you snoozed when you should have been taking
notes. Not being realizable in any physical system
is one well known attribute of Turing Machines.
> When I told him about Ullmans indefinite
> growing argument, he objected But when the
> universe is filled up, it cannot grow any more!
> Then, it is not infinite, to which I responded
> Yes, but there is *nothing* that is larger than
> the universe. To assume the contrary would be
> theology, which I despise.
The problem being that it is precisely what _you_
are doing, trying to limit abstract devices to the
bounds appropriate to mere physical reality, that is
theology.
You cannot both limit the construct you are
discussing to the bounds of the physical universe,
and pretend that you are still discussing Turing
Machines, which specifically have no such
limitations.
You can call your construct an Eray Machine if you
choose, but much like the Olcott Machines
previously proposed here, your devices will be toys,
of no intellectual interest whatever, where Alan
Turings invention is one of the most powerful
constructs ever produced by the human mind, and
finds constant new applications.
>> Turing Machines are idealized which means they
>> are not physically realized.
> What a nice assertion.
That is not an assertion, that is a definition.
Perhaps alertness during your classes would have
taught you the difference?
> A TM is just the specification of a very low level
> machine code, thats all there is to it.
Well, no. Perhaps, rather than filling Usenet with
endless more reams of pointless blather, you could
go find out _on your own_ what a Turing machine is,
and what that implies, rather than conducting
another bulldog defense of your chosen battlefield
of intensely applied ignorance here in this venue,
and spare the rest of us the misery of wading
through your endless time wasting eructions?
> Its just another model of computation, and not an
> extremely telling or useful one.
My, you have a lot of opinions grounded in utter
ignorance. That one alone should have prevented your
ever receiving a PhD in the computer desmesne.
> Thinking about Turing Machines which have not been
> realized yet does not mean that these things
> cannot be implemented.
Your these things is a reference without a
referent.
> Besides, a bounded size FSA simulator, too, is a
> Turing Machine...
You have two concepts too muddled to be easily
separated, like siamese twins. Perhaps you could
borrow some class notes from someone who bothered to
pay attention in school?
> You people overlook this simple point, I wonder
> why.
Perhaps because we people set enough value on our
education to be mentally present in class as well as
physically there?
> Now, I recall that you made this strange argument
> about Turing Machines being able to do things that
> real computers cannot, because they have an
> infinite tape. What an observation.
Again, you bemusedly give your mere ignorance-based
_opinion_ the same stature as the received wisdom of
the computer science theory community. That may
amuse you, but it makes you clearly and publically
the idiot you are so determined to be, also.
>> TMs are not meant to have physical constraints
>> applied to them.
> Another assertion.
Again you confuse opinion with definition. That is
no more an assertion than is gravity works.
> Ignoring physical plausibility directly opposes
> physicalism.
So what? When you go wandering off into the weeds
where your abberant philosophy lives, you leave
Turing Machines, and computer theory, far behind.
Turing Machines are under precisely _no_ obligation
to be physically realizable. They teach this point
in school, Eray, where were you at the time?
> When we start talking about immaterial things, we
> are not making scientific statements, we are
> making metaphysical ones, and that is not a good
> sign if the metaphysical statements depict worlds
> that are not physically similar to our own.
Im pretty sure at this point you have stepped well
past the bounds of sane thinking. You are trying to
limit science to physical science, and that
limitation only exists in your own mind.
> It is a matter of degree, which we can observe.
That statement is a meaningless noise.
> The question is: how far from reality? The further
> you talk, the less real your statements are, not
> just as real!
Again, you are expressing some degree of insanity,
no degree of intelligence or attention to your
education, here.
I refuse to waste more time on your inane drivel.
This should be clues enough you need to go back and
_learn_ that which you have inappropriately already
claimed credit to have learned with your accepting a
PhD.
xanthian, disgusted.
--
===
Subject: Re: Turing Machines and Physical Computation
>Turing Machines are under precisely _no_ obligation
>to be physically realizable. They teach this point
>in school, Eray, where were you at the time?
I dont know where Eray was, but from the moment I 
first heard
this
sort of stuff, I wondered about it. Many false fact are
taught in
school, though their falsity may not be overturned until
years or
centuries later. Dont just appeal to authority here.
Technically,
sure, one can study Turing Machine functions that cannot be
physically
realized. But that does not make Turing Machine theory
inapplicable
to machines that can be realized.
>Im pretty sure at this point you have stepped well
>past the bounds of sane thinking. You are trying to
>limit science to physical science, and that
>limitation only exists in your own mind.
Would you like to give an example of non-physical science?
J.
===
Subject: Re: Turing Machines and Physical Computation
>Turing Machines are under precisely _no_ obligation
>to be physically realizable. They teach this point
>in school, Eray, where were you at the time?
> I dont know where Eray was, but from the moment I 
first
heard this
> sort of stuff, I wondered about it. Many false fact are
taught in
> school, though their falsity may not be overturned until
years or
> centuries later. Dont just appeal to authority here.
Technically,
> sure, one can study Turing Machine functions that cannot be
physically
> realized. But that does not make Turing Machine theory
inapplicable
> to machines that can be realized.
Well, our instructors were careful enough to teach us the
Cinderella
book which says no such stupid thing. It talks about abstract
machines, but it takes pains to make it awfully clear that
this is
indeed the theory of real-world computers. Abstract does not
mean
non-physical, and Im grateful that the authors are clever
persons.
I wonder, can these so-called hobbyists of theory like Harris
and
Dolan provide for me a reference from a respected theory of
computing
textbook that claims Turing machines are inapplicable to
machines that
can be realized? I would be quite surprised with that. For a
reasonable computer scientist, the Turing Machine is just
another kind
of automata, and its mechanism is firmly rooted in the
physical world.
There is no ontological difference between a PDA and a TM. It
is no
magic construction. When we see the transition graph of a TM,
etc. we
immediately know that this is just another computer. And it
is one
among many models of c.e. computation. Only these self-branded
sci.math philosophers seem to insist on this naive idealist
talk.
And in our textbooks, it is clearly written: the ID of a TM
is finite
at all times. This is a physical machine specification.
I wonder. Will these people also say that Lambda calculus
depicts
non-physical processes? That the mundane task of substituting
and
rewriting is in fact a non-physical thing? I wonder that very
much.
Because *if* the TM is equivalent to evaluation of Lambda
calculus
expressions, then that should be the case. This is I believe a
sufficient refutation of years of Harriss posts 
full of
misconceptions about the subject.
You see, all that is happening is that the theory programs on
these
peoples brains, which seems short of a stack, crashes the
moment
they see the word infinity somewhere.
There are surely skyhook workers who would imagine
hypercomputation
and other physically impossible classes of machines, but
lets see, we
dont really deal with that in any reasonable curriculum.
Computer
Science is first and foremost the science of complex physical
events.
Computer Science does not deal with what an angel could have
done in
heaven, assuming he could process an infinite amount of
information in
a finite time. That *is* theology. And it 
doesnt work.
We like things that work.
>Im pretty sure at this point you have stepped well
>past the bounds of sane thinking. You are trying to
>limit science to physical science, and that
>limitation only exists in your own mind.
> Would you like to give an example of non-physical science?
Lester uttered geometry, logic, math as examples.
However, he may be neglecting that these disciplines too are
based on
our sensory experience. That is their true foundation.
(However, it
may not be precise to call these sciences in their present
state.)
On the other hand, these are seen more analytic than the
purely
empirical branches of inquiry, naturally. That is not to say
that they
should be indulging in useless metaphysics, though. There are
surely
measures for the utility of their statements.
For mathematics, we can know where to draw the line. For
instance,
there is no need to talk about actually infinite fractal
objects.
Nobody can observe such a thing in the world. What we can
indeed
observe is the unbounded nature of computation, a far more
natural
thing than the continuum, which has never existed, and never
will.
Of course, if one shows a physical phenomenon that makes it
_necessary_ to invoke these absurd objects to explain them,
then they
are useful, and that would actually be a physical proof of the
continuum, that there are indeed such infinite objects that
are a part
of our world! No such thing has been done.
To propose a theory which is based on nomologically
impossible axioms
is most definitely in the realm of theology or bad
metaphysics. Modern
philosophy has no dealing with the non-physical, and it need
not
either.
I am actually expecting a brilliant reply by some of the least
sophisticated philosophers I have ever had the opportunity to
meet,
who are available on sci.math. Lets see these philosophers
assert
that Turing Machines are nonphysical entities.
--
Eray Ozkural
===
Subject: Re: Turing Machines and Physical Computation
[. . .]
>>Im pretty sure at this point you have stepped well
>>past the bounds of sane thinking. You are trying to
>>limit science to physical science, and that
>>limitation only exists in your own mind.
>Would you like to give an example of non-physical science?
Oh, geometry, math, logic.
===
Subject: Re: Turing Machines and Physical Computation
Mr. Dolan, I dont deal with those in your intelligence
class. Youd
be wrong to think I will actually waste time with reading
your posts.
Yes, you fare better David Longley, but this is a discussion
between
me and Stephen, who is a very good reader, thinker, a
philosopher, and
a generally smart person, unlike you.
I value Stephens ideas very much in general.
I dont value your ideas, because I think you are an 
arrogant
and
stupid man. Dont try to abuse me.
--
Eray
===
Subject: Re: Turing Machines and Physical Computation
<ogGFp6BAYAnBFwB6@longley.demon.co.uk>
<419c4735$0$44080$5fc3050@dreader2.news.tiscali.nl>
<Jpfd7EJk2LnBFw1T@longley.demon.co.uk>
<419cd7d4$0$44068$5fc3050@dreader2.news.tiscali.nl>
<4zrnd.46389$QJ3.16198@newssvr21.news.prodigy.com>
<61bad26451853979aa126965352b4240.48257@mygate.mailgate.orgMr
. Dolan, I dont deal with those in your intelligence class.
Youd
>be wrong to think I will actually waste time with reading
your posts.
>Yes, you fare better David Longley, but this is a discussion
between
>me and Stephen, who is a very good reader, thinker, a
philosopher, and
>a generally smart person, unlike you.
be better off reading a good novel. In fact, thats all that
much of
this sort of philosophy is. Its fiction for the 
thinking man
and
you need to wise up to that.
>I value Stephens ideas very much in general.
For all the wrong reasons. Its the same disorder that
Michaels is a
victim of as is Harris himself.
>I dont value your ideas, because I think you are an
arrogant and
>stupid man. Dont try to abuse me.
But thats because you are ignorant and naive. In time, with
any luck,
but mainly through the inßuence of your environment, 
youll
grow out of
it. The sooner the better... (remember I said that ;-)
--
David Longley
http://www.longley.demon.co.uk
===
Subject: Re: Turing Machines and Physical Computation
> Hi Stephen,
> I would have expected a thoughtful reply.
I gave you a factual reply. It doesnt take all that much
thought
because Ive already learned the definitions and 
been over
this before,
sometimes in your position, having misconceptions.
>> I have had such a discussion with an extremely intelligent
and
>> experienced mathematician. He told me that PCs are not
Turing
>> Machines, because they have an infinite tape. I think he
did not
>> know anything about descriptive complexity. This infinite
portion of
>> the tape consists entirely of blank symbols, and therefore
has
>> descriptive complexity O(1), which is easily realized by a
physical
>> system. When I told him about Ullmans 
indefinite growing
argument, he
>> objected But when the universe is filled up, it cannot grow
any
more!
>> Then, it is not infinite, to which I responded Yes, but
there is
>> *nothing* that is larger than the universe. To assume the
contrary
>> would be theology, which I despise.
>> Turing Machines are idealized which means they are not
physically
>> realized.
> What a nice assertion.
It is a fact. I dont know how you missed this. A TM can be
simulated,
parts of its description realized, on a physical computer.
But not the
part that allows unbounded resources. The physical resources
of the
universe could be converted to physical memory for a computer
and
eventually would not suffice to match the resources of a
Turing Machine.
A TM is a theoretical machine that can compute some number X,
which
could not be contained if the physical universe down to
sub-atomic
A TM can compute X because it is an abstract theoretical
process not
a physical machine. There are no physical constraints applied
to TMs
while all PCs or physical computers operate under physical
constraints.
TMs are logical, theoretical entities, not machines as in a
physical
device.
TMs have the same potential to solve computing problems as do
the still theoretical quantum computers. I think the
descriptional term
is Ôcomputational power which does not mean 
speed of
computation.
A TM has the same level of computational power as a series or
conceived as working in parallel with other TMs. Time is a
physical
constraint. They talk about differences in computational
power when
they compare a TM to a Super-TM. That is because a Super-Tm
is idealized, or theoretically specified to use the real
numbers which
of course are infinite. Therefore there theoretical
calculations will
reach a new plateau of computational resolution. As you may
know,
physical computers use truncated, approximated representations
of numbers which are finite. This difference in computational
resolution
does not exist between TMs in series or parallel, or quantum
computers.
Real world physical computers can overlap TMs if the problems
they
calculate have a practically realized boundary. For instance
a PC
can calculate two billion digits of Pi and a TM in theory can
calculate
two billion digits of Pi. A Tm run by simulation on a PC can
calculate
two billion digits of Pi. But the simulation runs out of gas,
is not
isomorphic
to TM potential when problems involving huge huge huge memory
space
are required. All physical memory will be eventually
expended, there is
no endless adding to physical memory, and this is a
well-known point.
I realize that one of the causes of contention between us is
that you think
TMs are physically realized as devices rather than logical
thought
experiments.
TMs were used to develop the definition of an algorithm, which
is sort of
circular. But that logical mathematical representation is not
perfectly
physically realized on a real world physical computer.
Im going to provide
> A TM is just the specification of a very low level machine
code,
> thats all there is to it. Its just another 
model of
computation, and
> not an extremely telling or useful one.
> Thinking about Turing
> Machines which have not been realized yet does not mean
that these
> things cannot be implemented. Besides, a bounded size FSA
simulator,
> too, is a Turing Machine... You people overlook this simple
point, I
> wonder why.
> Also, I suggest you to get the most recent edition of
Cinderella book
> and have a look at what Ullman thinks about this subject.
(Thats
> another argument!) IIRC, in that edition, the authors argue
> persuasively that we should think of PCs as TMs rather than
DFAs. I
> find that a subtle point.
> Now, I recall that you made this strange argument about
Turing
> Machines being able to do things that real computers
cannot, because
> they have an infinite tape. What an observation.
>> TMs are not meant to have physical constraints applied to
them.
> Another assertion.
> Ignoring physical plausibility directly opposes
physicalism. When we
> start talking about immaterial things, we are not making
scientific
> statements, we are making metaphysical ones, and that is
not a good
> sign if the metaphysical statements depict worlds that are
not
> physically similar to our own. It is a matter of degree,
which we can
> observe.
> The question is: how far from reality? The further you
talk, the less
> real your statements are, not just as real!
>> That mixes categories.
> No.
>> Sometimes the question is asked, how many sentences can be
>> generated in some natural (say English) language? There
are finitely
many
>> words in the language, but the standard answer is that
there are
>> countably
>> infinite number of sentences, due to appending etc.
> That is potential infinity, a plausible concept, considering
time for
> instance. Current theory of physics *seems* to suggest that
time is
> going to continue forever. The idea of potential infinity is
then, at
> least in the temporal sense, not too far from our world.
However...
>> These kind of questions ask what is the potential in
theory, not what is
>> practically possible. Observations like: a person can only
articulated
>> finitely
>> many sentences in a lifetime, or any sentence has to be
uttered before
>> somebody dies or a machine wears out, or that how many
sentences
>> potentially exist is related to how many people generate
sentences over
>> the lifetime of humanity in the universe are not relevant,
because that
>> is
>> not the question being asked. Every process within the
universe is
finite
>> due to heat death of the universe, so that makes all such
questions
>> trivial,
>> if one interprets them to mean or apply to a physical
reality.
> Thats a quite amazing thought, because it rejects that
some facts
> about our universe can be simple. That some answer is
trivial does
> not necessarily mean it is wrong. If we are talking about
our
> universe, yes, if universe is going to expand, and
accelerating in
> expansion, then, at some time T no efficient causal
interaction will
> remain, which will disable large computations. Sad for the
universe.
> But what else can we say? Then, those never-ending
computations arent
> quite possible. If thats so, its not 
sensible to talk
about things
> that cannot ever be constructed in our world. Then, lets
talk of
> finite quantities only. Lets see how big 
computations
behave, without
> pretending that there is no bound to their time/space use.
> At this point, I should remind you the famous Levin quote.
Levin was
> Kolmogorovs student, so he probably has a better idea of
this issue
> than you have.
>> A Turing
>> Machine or potential sentence of a language (there is no
pre-existing
>> specification that the sentence has to be of 
finite length)
is not of
>> this
>> world.
> Of which world is it then? (^_^) And you are saying this
Platonist
> talk is not theology! You have just murdered physicalism.
>> The set of natural numbers is countably infinite and is has
some use
>> theoretically. Would you claim infinite sets have no use
because they
>> universe?
> It has some use theoretically. An immortal being is nice in
theory, as
> well, but we dont know if it will work out well for us.
But that is a
> sorry analogy. We can do better. God has some use
theoretically, we
> can use it to resolve our ethical problems. But we dont
know if it
> exists. Its just an idea. As you can see, 
its pointless
to say that
> the set of natural numbers exist except as an idea. And
that is what
> you are affirming in the first sentence. The 
second is
nonsense. I say
> nothing about their theoretical use, they make good mental
exercise,
> and they help us construct simpler theories in exchange for
loss of
> physicality. (Again, when it becomes less physical, it does
not
> automatically gain some positive ontological status, if you
are also a
> physicalist!)
> That something has some use theoretically does not grant
attaching the
> word exists to it, from a philosophical point of view. And
giving it
> a privilege might betray philosophical consistency.
>> And the original description of a Turing Machine. It is
common to call
>> this tape Ôinfinite though some 
prefer finitely unbounded.
> The latter camp has the precise terminology.
>> There is no
>> physical time constraint applied to when the calculation
has to be
>> completed.
> If you mean *any* computation. But a Turing Machine is a
*particular*
> computer. Not just *any* computer. Lets pay attention to
our
> language.
>> So there are calculations that a physical PC the size of
>> a galaxy could not complete before the universe ran out of
power to
>> energize the computer. A Turing Machine can of course
complete
>> such a calculation (because the calculation does not need
to be
infinite,
>> just finitely larger/longer in time that can be
accomplished by any
>> physical device during the existence of the physical
universe) because
>> the constraint of physical time is not applied to
idealized situations.
> Wittgenstein once said Turings theory was of human
computers. Which
> was quite true if we take the original paper literally,
without
> abstracting computer. (And that is what such people were
called at
> the time, who made calculations)
> You are also making a significant conceptual error. We have
a theory
> T, only a small portion of which has models in the real
world. But no
> experiments contradict our theory (such as computers
existing,that
> cannot be explained by T). I think this is a perfectly
legitimate
> situation in science. And you are twisting the whole
physicalist
> argument upside-down by saying that, since the theory
predicts (by way
> of *generalization*) Ôthere would be machines which can grow
> absolutely with no end, if and only if our universe had an
infinite
> space; *then* you conclude that this theory must not be a
physical
> theory. What a bad use of language!
> Instead you should have paid attention to basic rules of
grammar and
> linguistic analysis. What the theory predicts is a
*counterfactual*,
> it is not too different from saying that If my mother had a
beard,
> she would have a lot of hair on her chin. This is quite
possibly
> *false* for most of our mothers. And for our world, the
theory
> *predicts* that there will be no machines which can grow
absolutely
> with no end, since our universe does not have an infinite
space. It is
> regrettable to think of the theory as independent from
physical
> statements, if we accept that it is a theory of *machines*.
> Anyway, the point remains that Turings theory is a theory
of actual
> machines, if not merely humans. Wittgenstein has a point!
And then it
> is nonsense to argue that:
>> A Turing Machine can of course complete such a calculation
.... because
>> the
>> constraint of physical time is not applied to idealized
situations.
> But that is a terrible metaphysics you have there! Idealized
> situations do not exist. By situation we mean a complex
aggregate of
> physical events, nothing more. (Again, if we are to call
ourselves
> physicalists. And Cartesian Dualists, can leave the hall
silently!)
>> Keeping those categories seperate, the idealized and the
physical,
>> is definitional. The answer to theoretical questions is
trivial and
>> obvious
>> if you mix these categories. Mathematicians invented
infinity without
>> the requirement that it be physically realized because it
was useful.
>> Pure mathematics invents formal mathematical systems with
no
>> requirement that this formal system represent any physical
event or
>> process.
> This is quite a muddled reasoning, especially this bit:
>> Pure mathematics invents formal mathematical systems with
no
>> requirement that this formal system represent any physical
event or
>> process.
> There is no requirement of representation, so you think.
There is the
> requirement of representation of *ideas* in your head, and
if your
> ideas are *physical*, then it follows that the *exact
opposite* of
> your statement holds!
>> Yes, but there is
>> *nothing* that is larger than the universe. To assume the
contrary
>> would be theology, which I despise.
>> When you say *nothing* you mean no physical something.
> Platonist semantics. *shudder*
> When you utter nothing, you do not refer to anything that
exists.
> You do not refer to something that does not exist! (That is
generally
> seen as a wrong account of designating the reference of
expressions
> with counter-factuals in philosophy of language.)
> That would be a very confused understanding of the word
nothing.
> Lets do some ordinary philosophy of language to draw a
better
> picture.
> Here are some easy semantics questions. Formalize the
semantics of the
> following sentences, excluding questions using common
knowledge
> representation techniques in First Order Logic: (I am
explicitly
> asking for truth-referential semantics, of course. Usual
Tarskis
> World stuff, if you are familiar with formal semantics)
> - What do you want?
> - I want nothing.
> - What are you going to do tomorrow?
> - I am going to do nothing.
> There is nothing in the box.
> * An example of an analytically false statement (for
nonempty
> interpretation domains)
> Everything is nothing. (Hint: the solution is like the liar
paradox)
>> Mathematical
>> objects need not be physical.
> A Turing Machine is not just a mathematical object! [*]
> Lets repeat our basic argument again.
> 1. Not all Turing Machines require finite bounded space.
You mean that not all Turing Machines will need finite
_unbounded_
space to solve a certain class of (less complex) problems.
> 2. Therefore some Turing Machines run in finite bounded
space.
Yes, they can, though you didnt arrive at this quite
correctly.
> 3. Many PCs do just that.
I think PCs must only do that much. Basically agree.
> 4. Then, PCs are physical functioning models of Turing
Machines. (But
> most of them are also simple DFAs, or formal axiomatic
systems, or
I described this as overlapping in the class of problems they
can both
compute.
And they both use an algorithmic procedure. It is high level
programming
languages which are considered Ôcomplex enough 
to exhibit or
fall under
the scope of Godels Inc. Theorem.
> whatever general theory they fit. The theory which has the
most
> *explanatory* power will be preferred according to the
question we are
> trying to answer.)
Im not sure what you mean by this. The explanation 
Ive
presented covers
the cases in which TMs can compute more complex problems than
PCs
because PCs require physical resources, are physical. That
TMs have
no limitations due to physical resources is a matter of
definition, not
debate.
The explanation Ive presented covers the cases in which the
resolution
of complex computation problems overlaps, TMs and PCs enjoy
the
same functionality as to producing some answer within
restricted
boundaries.
> Could this argument be any simpler?
At this point, it misses saying how your TM/PC argument has a
bearing on
Cantors potential/actual infinity and his 
transfinite relative
actual
infinity
which is quite different than the historical theological
absolute actual
infinity.
Infinity and a PC are eliminated by physical reality and a TM
and infinity
are included by definition, Turings description 
of a
hypothetical machine.
Machine means works by rote, in a routine manner, as in
mechanical,
not some type of physical device. Because it inspired a
physical device
has no bearing on this, that I can see. TMs and PCs have a
basic
difference.
> The PC does not have to actually run an arbitrarily growing
software.
> It suffices that it has this property *in principle*. This
is so not
> because of some deeper running assumption, but rather
because of the
> fact that many Turing machines run in bounded space.
Not in principle, the PC has a finite restriction on physical
resources.
The PC cannot compute a large class of intractable problems
that a
TM can compute in principle. Sure they overlap for most
practical
purposes. But the idea of a potential infinity changing into
an actual
infinity is just another change in logical abstraction. It is
not physical
in any sense. Thus discussing this in terms of how PCs which
are
physical are like some TMs, isnt in the same category as
potential
and actual infinities which are entirely abstract. TMs which
are abstract
entities which do not have physical requirements is the
correct level of
focus for the potential/actual infinity abstraction which also
does not
have
a physical implication. It is the TM which has unbounded
resources in
principle, not the PC. Adding to a PC will reach a limit.
Infinity has no
limit.
>> When you made this comparison, infinity and theology/God,
to the size
>> of the physical universe, you crossed over from debating
potential vs.
>> actual infinities to declaring abstract thinking is just
theology in
>> another
>> guise.
> That is exactly what Poincare implied in his famous remark.
I will bet
> on Poincare, and not on your championing of one school of
mathematics.
> (I am not the only person who made the comparison!)
...Full Turing machine power cannot be _necessary_ for mental
states.
There
is no evidence at all that cats and dogs, which clearly have
mental states,
or even human beings (when unaided by external memories),
have the power
of a Turing machine. E.g. we quickly get into trouble if we
have to parse a
deeply nested sentence, whereas this would not bother a
Turing machine,
or even many computers of lesser power. Even when we use
external
memory aids analagous to the Turing Machines tape, to help
us with
calculations or reasoning, we can still make mistakes of many
kinds, that
no functioning Turing machine would.
When this happens we are still awake, thinking, seeing,
feeling etc.
Behavior thats unlike a Turing machine does not indicate a
lack of mind.
So it is not sheer computational power that is required for
mentality. If
computational abilities enter into mentality at all, it must
have something
to do with the partiuclar kinds of computations and the
partiuclar kinds
of mental capabilities, and it is quite possible that many of
these require
something less than Turing power, and at the same time
something more,
which Ill try to characterize below.
...
Weve seen that theres vagueness in the 
causal requirements
for an
algorithm alleged to generate intelligence. Theres another
kind of
vagueness
concerning a process produced by one algorithm (e.g. the UAI)
and a
process involving many different algorithms. Penrose
apparently interprets
an algorithm as a rule or set of rules specifying permitted
sequences of
changes of state of some structure. Such rules may be
expressed in many
different syntactic forms, including the use of recursion,
sub-routines,
and
other concepts found in high level programming languages.
This is
somewhat vague, but all attempts to make the notion more
precise have
so far produced formulations that can be proved to be
mathematically
equivalent to what can be specified in a Turing machine.
Moreover, it is possible to prove that any function computed
by a
collection of Turing machines running (synchronously) in
parallel can be
modelled by a single Turing machine, by showing how the
collection
can be modelled on a single machine, e.g. by interleaving
their operations.
So, from a mathematical point of view, the concept of an
algorithm is not
things are very different.
The fact that any function computed by a collection of Turing
machines
(synchronously) in parallel can also be computed by a single
Turing
machine,
leaves open the question whether there are any other
important properties,
besides the function computed, that may be different in
parallel and serial
implementations. Speed differences are relatively
uninteresting: they can
be
overcome in principle by speeding up the machine used for the
serial
implementation, though there may be physical limits to this.
Other differences between parallel and serial implementations
are deeper.
Consider the control requirements for a collection of
co-existing
interacting sub-systems. It is sometimes possible to produce
the required
interactions on a single time-shared processor, by providing
a collection of
concurrent virtual machines, but virtual parallel processes
on a single
machine sometimes have slightly different causal powers from
processes
implemented on a collection of machines, even when they do
compute the
same input/output function.
http://www.cs.bham.ac.uk/~sra/People/Stu/Sloman/#TheEmperors
The Emperors Real Mind by Aaron Sloman
Lengthy review/discussion of Penrose (The Emperors New
Mind). This review
appeared in the journal Artificial Intelligence Vol 56 Nos 2-3
August 1992,
pages 355-396
Compressed Postscript
17. How can we think about infinite sets?
There remains the question whether we have a non-logical,
non-formal, way
of
specifying an infinite series? It may be that we do have ways
of
representing
information that cannot be modelled with full precision on
Turing machines
or equivalent computational systems. Various authors (e.g.
Sloaman [20],
Funt [4] have suggested that there are methods of
representing and
manipulating information using pictures, maps, models and
other formalisms
that are distinct from Fregean or applicative formalisms to
which
the
limit theorems of logic and computer science apply. Is there
some way of
representing the notion of the infinite set of integers that
is different
from the
use of a formal system of the kind considered by Godel? Could
we use a
physical mechanism for generating numerals, i.e.
representations of
numbers, indefinitely? Is it possible that there is some way
of perceiving
properties of
such a concrete numeral-generating mechanism that is
different from a formal
derivation or a digital computation? Some mathematicians seem
to think that
the mental operation of adding 1 is the basis of the grasp of
the whole
infinite series of natural numbers. Could this be based on
something like
perception of some kind of iterative mechanism and its
properties? Perhaps
such formalisms and mechanisms would have to play a role in
the thought
processes of a robot mathematician with human capabilities.
Until it is demonstrated that we do have some way of
completely specifying
exactly which infinite set we are talking about as a model of
F then it is
not the case that we can claim to have seen that G(F) is
true: for it will
actually be false in some models of F and we have no basis
for saying that
our grasp of the intended model rules this out. At present it
is
totally
unclear what such a method of determining the intended model
could be
like, except that Godels theorem shows that no axiom system
or
algorithmic method suffices, as Penrose correctly points out.
18. Mathematical Platonism
Penrose makes much of mathematical Platonism, claiming that
certain
mathematical entities, such as the natural number series and
the Mandlebrot
set, exist independently of us, and that we can somehow
discover truths
about them. His Platonism has exasperated some critics who
regard it as a
metaphysical or mystical nonsense. For Penrose, however, it
plays a crucial
role in explaining how we discover facts like the truth of
G(F). He thinks
that we have some kind of direct contact with these entities,
which enables
us to grasp statements about them. Some Platonists (e.g.
Plato?) claim that
if mathematical entities exist in a special non-physical
realm then the
discovery of mathematical truths must employ special
spiritual mechanisms
that enable such entities to be explored. This would pose a
real threat to
the long term aims of AI as a discipline committed to the use
of mechanisms
wholly embedded in the physical world. However, Penrose does
not
construe Platonism in this extreme anti-physicalist form. In
particular, he
does not believe that the brains of mathematicians depend on
anything that
is in principle beyond the reach of physics. All he is
claiming is that
mathematical truths and concepts exist independently of
mathematicians,
and they are discovered not invented. This, I believe,
deprives Platonism
of any content, and certainly leaves it as no threat to AI.
Despite the effort Penrose puts into his defence of
mathematical Platonism,
and the strong counter-claims of others that it is a
mystical, or
anti-scientific doctrine, such disagreements are really empty.
It makes not
a whit of difference to anything whether the Mandlebrot set,
or the natural
natural number series, does or does not exist prior to our
discovering
them.
The dispute, like so many in philosophy, depends on the
mistaken assumption
that there is a clearly defined concept (in this case
existence of
mathematical
objects) that can be used to formulate a question with a
definite answer.
We
all know what it means to say that a unicorn (defined as a
horse with a
single
horn) exists, and we know how to investigate whether that is
true or false.
Quite different procedures are involved in checking the
equally
intelligible
question whether there exists a prime number beteween two
given integers N1
and N2. But there is no reason to assume that any clear
content is
expressed
by the question whether all the integers do or do not
Ôreally exist, 
or
exist
independently of whether we study them or not. For example,
this cannot
make any difference to the design requirements for
mathematical
intelligence.
The practice of mathematics, the process of explorationa and
conjecture,
the
nature of proof, the devastating effect of counter-exampless,
would all be
the same no matter whether entities exist in advance of
discovery or not.
Intuitionists have argued that because mathematical objects
have no
independent existence certain methods of proof, e.g. those
using
~ ~p --> p
are not valid. But other mathematicians have happily gone on
ignoring this
stricture without any disastrous consequences. Mathematics is
a subject in
which different classes of things can be studied and
different methods of
reasoning can be explored. Once a method is well specified we
can then find
out what can and what cannot be done with it. Arguing that
one is right and
another wrong because certain things do or do not exist is
pointless when
the relevant notion of existence in question is so
ill-defined. I conclude
that
the question whether Platonism is true is just one of those
essentially
empty
philosophical questions that have an aura of profundity, like
Where
exactly
is the Universe? or How fast does time really ßow? An
intelligent
machine, like many intelligent human beings, may be tempted
to misconstrue
such questions as having significance, but they provide no
basis for
doubting
the possibility of intelligent machines. ....
There is, however, a real problem here, which can be put in
much more
straightforward language by stating that many mathematicians
and others
claim to think about and communicate about types of abstract
objects that
cannot easily be specified by giving examples, and which need
some kind
of indirect identification. One of the oldest examples is the
infinite set
of
natural numbers, or even the infinite set of numerals denoting
them. We can
easily present examples of increasingly large subsets, but
never the whole
thing. Immanual Kant [8] claimed many years ago that such
infinite
totalities
can only be grasped via rules that generate them, and this is
widely
believed.
But, as Ive explained above, if the rules are 
specified in
something like
a
formal syste, Godels incompleteness theorem shows that 
there
is a problem
about whether the intended set can be specified completely.
Unless
there
is some important undiscovered mechanism for such thinking,
all those
mathematicians are fooling themselves, not about the
particular theorems
they prove, but about the nature of their understanding. If
so that
suggests
that artificial intelligences may fall into the same trap. If
every method
of
specifying infinite sets is equivalent to the use fo a formal
axiom system,
then
Godels theorem, far from proving the impossibility of
artificial
intelligence,
is a pointer to some limitations of intelligence in general.
> ever discuss foundational issues with those who cannot
question the
> assumptions of their favorite school of thought?
I dont have a side especially. I think it is poorly 
defined
philosophical
issue
which has lasted this long just because of lack of
definitions. I think
infinities
are used in quantum theory calculations. I dont think
whether the
infinities
are actual or potential changes the outcome of a calculation.
> What I explained to a slightly confused mathematician who
believed
> himself to be a constructivist was that a sane analysis in
philosophy
> of computation suggests that Turing Machines should be
thought of
> physical devices, if we are to remain physicalists.
This is rather bizarre. To remain a physicalist think of a PC
as physical
because it is. Do you think physicalists should not have
abstract thoughts?
TMs are abstract devices, conceptions. Because TMs share some
functional
properties with the output of PCs does not confer
non-physical abstract
properties that are used in the definition of a TM.
>You do not
> challenge any of the arguments. Instead, you assert things,
like
> saying that Turing Machines are not of this world. Show us
that
> world, or is it the fairy-land of mathematics?
I challenged your arguments by presenting definitions which 
you
call assertions. I said there are abstract ideas. A Turing
machine
is an abstract idea. Do you deny there are abstract ideas??
Do you deny that there are ideas??
Are ideas physical so that you can capture one, put it in a
jar?
Our brain processes provide our ideas. That does not mean
that the content of the idea is physically real. What is
imagined,
such as counterfactuals or unicorns does not need to
physically
exist (the product of our abstract thinking) just because
there
is an underlying physical process in the brain creating
thought.
Do you find thought experiments useless because the object
of the thought experiment does not physically exist?
> [snip some philosophy]
> Amused,
Well, they say ignorance is bliss. Have you ever done a Google
search and seen the definitions of a Turing Machine?
http://en.wikipedia.org/wiki/Turing_machine
The Turing machine is an abstract model of computer execution
and storage
introduced in 1936 by Alan Turing to give a mathematically
precise
definition
of algorithm or Ômechanical procedure. As such 
it is still
widely used in
theoretical computer science, especially in complexity theory
and the
theory
of computation. The thesis that states that Turing machines
indeed capture
the informal notion of effective or mechanical method in
logic and
mathematics
is known as the Church-Turing thesis.
A theoretical model of a computing device, devised by Alan
Turing.
www.rsasecurity.com/rsalabs/faq/B.html
A form of universal computer, assumed to take its
instructions from an
infinite paper punched tape and output results to the same
medium before
stopping upon completion of the program. [SH: This infinite
medium is
never
presumed to have actual physical existence. Turings machine
was a
thought
experiment that used an imaginary condition. I doubt that
because there is
no physical actually infinitely long tape that this has
anything to do
with Cantors discussion of potential and actual 
infinities in
set theory.
Cantor is not saying abstract infinities potential or acutal
are real world.
I dont think the ideas are connected except in your mind.]
www.calresco.org/glossary.htm
A hypothetical computing device, invented by Alan Turing in
1936, used to
study the nature of algorithms and computation. [SH:
**hypothetical**]
cs.uhh.hawaii.edu/cs/courses/cs100/glossary.htm
a hypothetical computer with an infinitely long memory tape
www.cogsci.princeton.edu/cgi-bin/webwn
Alan Turings definition of a Turing machine was 
not intended
as a blueprint
for how one would actually build practical computing
machinery.
SH: In the real world this would practically be too slow. In
another
respect, it is not possible to build a Turing machine because
Turing gave
the TM a potentially infinitely long tape. No PC has access to
infinite
memory because the resources of the universe are not
potentially infinite,
they are finite. Because memory can be added to a PC so that
it can solve a
great many of the problems that a TM is capable of solving
does not make
them fully equivalent in computational power.
Remember, that does not mean speed of calculation. Yes, there
are a great
many similarities between a TM and a PC. But the precise
similarity between
a potentially infinitely long tape of a TM and the physical
memory of a PC
does not exist. And that is by far the most important link,
if you try to
compare Cantors usage of infinity with TM 
infinity. PCs dont
have an
anything infinite nor unbounded finiteness.
The universe is a bounded physical memory resource.
1 idea : a transcendent entity that is a real pattern of
which existing
things are imperfect representations b : a standard of
perfection : IDEAL
3 abstract : dealing with a subject in its abstract aspects :
THEORETICAL
3 : theoretical: existing only in theory : HYPOTHETICAL <gave
as an example
a theoretical situation>
2 : hypothetical/hypothesis a tentative assumption made in
order to draw out
and test its logical or empirical consequences
> --
> Eray Ozkural
> [*] And you might as well say, our language expressions do
not need
> to refer to physically plausible things. Then, you should
perhaps
> think of defending that we freely talk of God in scientific
discourse.
> But that is not permissible in scientific talk. Maybe it is
good for
> mythology, which is not our business.
Who is talking about God?? You are claiming that actual
infinities,
which have no physical implication, are theological
constructs.
You are using the idea as theologians used it, not Cantor.
Again, Cantor and or Godel belief in mathematical platonism
is not necessary to establish the existence of set theory or
incompleteness.
Just because Cantor was a Platonist does not mean his usage
creation of set theory and actual infinities requires a belief
in
mathematical platonism! There are millions of mathematicians
who are not Platonists that accept godelian incompleteness
and set theory using Ôcompleted 
infinity. You write like you
think platonism is a necessary requirement to understanding
set theory.
>You do not
> challenge any of the arguments. Instead, you assert things,
like
> saying that Turing Machines are not of this world. Show us
that
> world, or is it the fairy-land of mathematics?
SH: Of course I assert this because it is a fact. You lose
credibility when
you so emphatically announce misunderstanding something this
basic.
Your arguments dont make sense when your basic premise is
wrong.
PCs are not like TMs in precisely the area which has
application to
Cantor and infinities. TMs have an infinite 
property and PCs
dont.
Adding the universes memory to a PC just moves its capacity
up,
but it is still finite, not any type infinity 
under discussion
in this
thread.
Cantor does his abstraction on a potential infinitiy --->
actual infinity.
PCs have a universe with finite resources, not potentially
infinite, and
using all the universe as a memory source does not
become/achieve infinity.
I cant see how bringing finite TMs into this 
issue, just
because they
are practical is useful at all. The issue being discussed is
not
practical/physical
but theoretical, hypothetical and abstract; an idea not a
physical thing.
I suppose I should edit this and shorten it. But Im not
willing to spend
any more time on this. Andrew Hodges took a bit too much
poetic license.
Stephen
===
Subject: Re: Turing Machines and Physical Computation
<cyberguard1048-usenet@yahoo.com> quoted, in part:
>Unless there
>is some important undiscovered mechanism for such thinking,
all those
>mathematicians are fooling themselves, not about the
particular theorems
>they prove, but about the nature of their understanding. If
so that
suggests
>that artificial intelligences may fall into the same trap. If
every method
>specifying infinite sets is equivalent to the use fo a formal
axiom system,
>then
>Godels theorem, far from proving the impossibility of
artificial
>intelligence,
>is a pointer to some limitations of intelligence in general.
Although there are many true theorems that any given
mathematician may
never prove, the reasons are generally due to limitations of
powers and
knowledge.
Since there are many things that will need to be discovered
before
artificial intelligences equivalent to human intelligence can
be
constructed, I see no reason to fear that a limitation on
formal systems
is also a limitation on minds - natural or artificial.
John Savard
http://home.ecn.ab.ca/~jsavard/index.html
===
Subject: Re: Turing Machines and Physical Computation
> Hi Stephen,
> I would have expected a thoughtful reply.
> I gave you a factual reply. It doesnt take all that much
thought
> because Ive already learned the definitions 
and been over
this before,
> sometimes in your position, having misconceptions.
You are missing the entire point that computation is meant to
be a
physical process. That is all there is to computation. It is
a theory
of computing machines. And it describes a large number of
them. Lets
get down to your particular objections to my detailed
analysis.
An analysis of your first response shall suffice.
>> I have had such a discussion with an extremely intelligent
and
>> experienced mathematician. He told me that PCs are not
Turing
>> Machines, because they have an infinite tape. I think he
did not
>> know anything about descriptive complexity. This infinite
portion of
>> the tape consists entirely of blank symbols, and therefore
has
>> descriptive complexity O(1), which is easily realized by a
physical
>> system. When I told him about Ullmans 
indefinite growing
argument,
he
>> objected But when the universe is filled up, it cannot grow
any
more!
>> Then, it is not infinite, to which I responded Yes, but
there is
>> *nothing* that is larger than the universe. To assume the
contrary
>> would be theology, which I despise.
>> Turing Machines are idealized which means they are not
physically
>> realized.
> What a nice assertion.
> It is a fact.
I dont think you understand your presupposition that runs
underneath
your fact.
You are presupposing that
(Ideal -> Immaterial)
If a concept is idealized, it does not describe any part of
physical reality.
This is a quite bad presupposition.
I urge you to reveal from whom you gathered such a
misconception. (Or
otherwise, make some ordinary philosophy of language, to
disprove that
the above stated principle is inherent in your answer. Either
way,
your argument cannot be maintained as I try to show below.)
> I dont know how you missed this. A TM can be simulated,
> parts of its description realized, on a physical computer.
> But not the part that allows unbounded resources.
Really.
> The physical resources of the
> universe could be converted to physical memory for a
computer and
> eventually would not suffice to match the resources of a
Turing Machine.
What a trivial observation.
You mean, the theory contains *descriptions* of machines that
cannot
be constructed.
That is all there is to what you are saying, and it makes
perfect
sense for many *general* theories.
> A TM is a theoretical machine that can compute some number
X, which
> could not be contained if the physical universe down to
sub-atomic
Stephen, about this issue you are completely misguided.
A physicalist philosophy of computation restricts discrete
computation
to computation of finite entities. Some process that 
*actually*
outputs an infinite string is NO COMPUTATION. That is why
computability in the limit has this strange notion of a
sequence of
bounded computations which seems to escape your reason. (Yes,
I think
there is a metaphysical reason for insisting on such a
definition, and
its a correct one!)
I dont think you truly understand my basic arguments.
You are still claiming, in spite of many explanations I have
made to
you over the course of the last couple of years, that a A
Turing
Machine can calculate Pi, but a PC cannot.
Why do you still assert such a blatantly wrong statement? You
may have
thought you *found* something, but I will have to disagree.
Your PC can calculate Pi, exactly in the same quality the
theory of
computation predicts. And that is all that we can ever say
about the
computability of Pi.
Since the number Pi, by definition is not something that can
physically exist (for all we know about quantum theory...),
only
approximations to this metaphysical idea can be mechanized.
And Turing
Machine makes this notion of mechanization explicit, thats
all.
Turing Machine is only one of several equivalent
specifications of
computation. Infinite space, as a construction component,
occurs in
none of the other models, hence it should be understood, even
by those
who have difficulty in abstracting from Turing Machine to any
computer, that the infinite tape part of 
Turings description
entails NO NECESSARY CONDITION for computing machinery in
general.
Recall, dear Stephen, that Turing was exclusively concerned
with
Computing MACHINERY. Machinery has a very specific meaning, it
means
physical, mechanical devices.
If your presupposition held, then Machinery would mean
something else,
like angels, or deities.
Turing knew exactly what Machinery meant, but this most
elementary
concept in philosophy of computation is alien to you, and
unfortunately I suspect to many others on these forums.
The only relief I take is that Ullman et al. agree with me,
in that
they believe PCs are indeed Turing Machines. And this is no
surprise.
Any sensible computer scientist would know that. Only
mathematicians
and philosophers would claim otherwise.
But every couple of months, a naive mathematician will show
up (not
you) and try to purport an imaginery dichotomy between
physical
computation and Turing computation. That is unfortunate, very
unfortunate indeed, because in my opinion it shows a
systematic mental
error. It is the shadow of Cartesian Dualism which bothers me,
Stephen, and I am certain that you do not appreciate how
tight the
coupling is. In general, I call this issue the
software/hardware
dichotomy, and I believe I showed it to be equivalent to
substance
dualism. It is just a naive application of Platos theory
(which Plato
himself would probably not approve of) to modern terms. I
will dub
this more specific, and in my opinion more catastrophic case,
the
physical/Turing computation dichotomy. It is unfortunate,
because it
presupposes that two kinds of machines exist: material and
immaterial.
However, a closer physicalist analysis as mine rigorously
reveals that
it is nonsense to talk of immaterial machines, otherwise we
would
bring all the demons of the medieval ages together with these
immaterial machines. Immaterial machine is an oxymoron,
because
there is NO IMMATERIAL PLANE. I believe I am making it very
clear what
is at stake.
In contemporary philosophical circles, there seem to be some
people
who hold the idea of these uncomputable things akin to the
idea of
God, or that we have such a theory is in fact an implicit
ontological
argument for the existence of God. [*] That would be *just*
as silly
as saying that the existence of the Bible is a proof of the
existence
of God. As an opponent of God, I do not allow such ideas to
slip in.
If you do not want to discuss your assumptions in more
detail, we can
stop discussing. Ive made my position clear. We can draw 
the
borders
clearly and tell the audience where the ideas diverge. That
much is
sufficient for me.
Cordially,
--
Eray Ozkural
[*] I dont know what Chaitin really thinks, but I would be
delighted
if he made an explanation. I believe he would agree with me,
because
he is a sensible computer scientist.
PS: I dont think your argument from dimensionality
strengthens the
validity of your Ideal -> Immaterial assumption. That is no
such
thing. Similar arguments were advanced by neo-physicalists,
but I
dont think dimensionality makes a great difference. We can
safely
abstract away from the actual dimensionality of our universe,
WHICH WE
DO NOT KNOW.
===
Subject: Re: Turing Machines and Physical Computation
>You are missing the entire point that computation is meant
to be a
>physical process. That is all there is to computation. It is
a theory
>of computing machines. And it describes a large number of
them. Lets
>get down to your particular objections to my detailed
analysis.
>But every couple of months, a naive mathematician will show
up (not
>you) and try to purport an imaginery dichotomy between
physical
>computation and Turing computation. That is unfortunate, very
>unfortunate indeed, because in my opinion it shows a
systematic mental
>error.
Although a theory of physical computing machines is possible,
we do not
have such a theory as yet.
The Turing Machine, as A. M. Turing specified it, cannot
calculate pi,
but it can calculate any finite number of digits of pi, such 
as
(10^(10^(10^(10^(10^1000))))) digits of pi, even though no
physically-realizable computer could calculate that many
digits of pi.
Turing _did_ specify the Turing machine that way, so it is a
fact that
he made the same systematic mental error you refer to. Why
did he do
such a thing?
Because it made it possible for him to derive results from
his theory in
a reasonable amount of time. Determining what the limits of
computation
in the physical universe are, and what can be done within
those limits,
is a very complicated problem. Assuming infinite memory
capacity is a
simplifying assumption that makes for a theory much easier to
derive and
work with.
What is the use of such a theory, a theory that doesnt 
refer
to the
real world? If certain things cannot be done with even an
infinite
memory, then they cannot be done with a finite memory. And
many things
that can be computed dont need an infinite 
amount of memory,
or even an
absurdly large finite one. So the Turing machine is an
*approximation*
to a real computing machine.
lines made with real pencils and the pinpricks made by the
point of a
real compass, mathematicians have always approximated the
real world by
abstractions which are not physically realizable. This makes
the
symbolic manipulations in mathematics simpler - and thus
makes them
realizable instead of impractical. Giving this up would mean
giving up
mathematics, because taking into account the limitations of
the real
world in every case would make many fields far too complicated
to
investigate.
John Savard
http://home.ecn.ab.ca/~jsavard/index.html
===
Subject: Re: Turing Machines and Physical Computation
>lines made with real pencils and the pinpricks made by the
point of a
>real compass, mathematicians have always approximated the
real world by
>abstractions which are not physically realizable.
Well, I dont know about that. Whose theory is this? I
thought most
mathematicians who expressed an opinion were generally some
sort of
Platonists, believing that effective mathematics is
discovered, not
invented, and that it is the real world which approximates
the ideal.
In any case, I would disagree with it, in the name of a
nominalist,
instrumentalist theory that focuses on the agent doing the
computing,
and not on the approximations of reality to a model, or
vice-versa, as
the case may be.
Its a violent rearrangement of fundamentals for most 
people,
but try
it sometime!
J.
===
Subject: Re: Turing Machines and Physical Computation
>>lines made with real pencils and the pinpricks made by the
point of a
>>real compass, mathematicians have always approximated the
real world by
>>abstractions which are not physically realizable.
>Well, I dont know about that. Whose theory is this? I
thought most
>mathematicians who expressed an opinion were generally some
sort of
>Platonists, believing that effective mathematics is
discovered, not
>invented, and that it is the real world which approximates
the ideal.
Both real and ideal worlds are discovered and invented.
Neither is the
other; they approximate each other. Its my theory.
>In any case, I would disagree with it, in the name of a
nominalist,
>instrumentalist theory that focuses on the agent doing the
computing,
>and not on the approximations of reality to a model, or
vice-versa, as
>the case may be.
>Its a violent rearrangement of fundamentals for most
people, but try
>it sometime!
===
Subject: Re: Turing Machines and Physical Computation
>>lines made with real pencils and the pinpricks made by the
point of a
>>real compass, mathematicians have always approximated the
real world by
>>abstractions which are not physically realizable.
> Well, I dont know about that. Whose theory is this? I
thought most
> mathematicians who expressed an opinion were generally some
sort of
> Platonists, believing that effective mathematics is
discovered, not
> invented, and that it is the real world which approximates
the ideal.
> In any case, I would disagree with it, in the name of a
nominalist,
> instrumentalist theory that focuses on the agent doing the
computing,
> and not on the approximations of reality to a model, or
vice-versa, as
> the case may be.
Well, I can see how it is possible to see how nominalism has
a bearing
on this. Im going to append a quote by Anders Weinstein.
Mostly, people do not endorse mathematical platonism which
means
mathematics pre-exists and is discovered in another realm by
the
mathematician. But a conventional view, that mathematics is
invented
still describes mathematical objects, such as i, the square
root of -1, or
the infinity of dimensionless points on a number line as
abstract ideas not
concrete physical things. The definitions are not tied into
Platonism (P)
so that one can make an analogy to abstract mythical realms
due to P.
> Its a violent rearrangement of fundamentals for most
people, but try
> it sometime!
> J.
They teach you in school that a number line is composed of a
series of dimensionless points, neither of which has physical
existence.
All physical things have dimension. A point you make with a
pencil is not
a point that corresponds to a mathematical point on a number
line
because the point created by a pencil has dimension. But I
can see how
nominalism could point to a pencil point as a physical
expression of point,
rather than a mathematical concept.
I dont think nominalism can help in this tape discussion.
Turing did in
fact
use an abstract approach in his paper which does not have a
foothold in
the physical world. There is no physical correlate to his
endless tape.
(He states that the TM can compute Pi which is an infinite
limit.)
Turing says one can substitute a _one-dimensional_ tape that
can have
symbols printed on it from an infinite ink supply. There are
aspects of
this logical computing machine that can be physically
represented, but
not the tape. Nor is there any mention of any time
constraint. The reason
the TM is described as hypothetical or an abstraction is
because that
is how Turing presents it. I dont see evidence of his
adopting a
philosophy,
such as nominalism, anywhere in the 1936 paper. I dont see
how stating
that he could have done this and that it might have been
legitimate denial
of abstraction presents any evidence that he did do this or
that he thought
this way. I think he tried to make his paper tangibly clear.
And his paper
seems
much more intuitively understandable than Godels to many
people. The
idea of building a physical computer came later after working
on Enigma.
Once upon a time, some philosophers like Nelson Goodman
explored a
program they called nominalism. They wanted to analyze away
*all*
putative reference to abstract entities. This included
propositions,
but also such things as patterns or words (as types) or
letters (as
types). They did this by offering to paraphrase them away via
reference
to concrete exemplars and use of equivalence relations.
reference to some abstract object, they would try to analyze
it as:
John made some inscription which is a replica of (or
cotypical with)
this one followed by reference to another concrete
inscription.
So they hoped to trade in abstract *objects*, although they
still
employed a variety of equivalence relations.
There are various technical objections to this, e.g. it
cannot obviously
handle reference to expressions, the name of God, perhaps,
that are never
actually inscribed. (You can talk about unactualized possible
inscriptions,
but they are also taboo for the nominalist).
jumped ship, and accepted abstract objects as irreducible in
science.
So for Quine, there is no real problem about propositions due
to
their abstractness -- just define them as equivalence classes
of
synonymous expressions. The problem is in the similarity
relation.
But others think there is some advantage. They think at least
that
it helps avoid a mythology of abstract objects, independent
of the human
world. Rather, we should recognize that a meaning is
something always
expressed in *signs*, which have a foothold in the concrete,
spatio-temporal
world.
===
Subject: Re: Turing Machines and Physical Computation
>But others think there is some advantage. They think at
least that
>it helps avoid a mythology of abstract objects, independent
of the human
>world. Rather, we should recognize that a meaning is
something always
>expressed in *signs*, which have a foothold in the concrete,
spatio-temporal
>world.
Not to give a primer on nominalism itself, of which there are
endless
varieties, and the kind I prefer is pretty far off to one
side, but
the point is that in talking about AI, one possible approach,
and the
only one Im interested in, focuses on how it is an agent 
can
have
anything remotely like intelligence. With the focus on the
agent, one
classically gets into questions of epistemology rather than
ontology,
language rather than physics. Nominalism(s) are about the
effective
use of signs and symbols with the least possible commitments
to facts
about the world. It blends naturally with the methodological
solipsism which is characteristic of any discussions of
computation.
J.
===
Subject: Re: Turing Machines and Physical Computation
<419c4735$0$44080$5fc3050@dreader2.news.tiscali.nl>
<Jpfd7EJk2LnBFw1T@longley.demon.co.uk>
<419cd7d4$0$44068$5fc3050@dreader2.news.tiscali.nl>
<4zrnd.46389$QJ3.16198@newssvr21.news.prodigy.com>
<ddEnd.23771$6q2.22891@newssvr14.news.prodigy.com>
<41a0f0ff.2213961@news.ecn.ab.ca>
<7a68q0tortpkm6dlj983kgg4kvlpgrbapa@4ax.com>
<YZYod.49079$QJ3.6811@newssvr21.news.prodigy.comlines made
with real pencils and the pinpricks made by the point of a
>real compass, mathematicians have always approximated the
real world by
>abstractions which are not physically realizable.
>> Well, I dont know about that. Whose theory is this? I
thought most
>> mathematicians who expressed an opinion were generally
some sort of
>> Platonists, believing that effective mathematics is
discovered, not
>> invented, and that it is the real world which approximates
the ideal.
>> In any case, I would disagree with it, in the name of a
nominalist,
>> instrumentalist theory that focuses on the agent doing the
computing,
>> and not on the approximations of reality to a model, or
vice-versa, as
>> the case may be.
>Well, I can see how it is possible to see how nominalism has
a bearing
>on this. Im going to append a quote by Anders Weinstein.
>Mostly, people do not endorse mathematical platonism which
means
>mathematics pre-exists and is discovered in another realm by
the
>mathematician. But a conventional view, that mathematics is
invented
>still describes mathematical objects, such as i, the square
root of -1, or
>the infinity of dimensionless points on a number line as
abstract ideas
not
>concrete physical things. The definitions are not tied into
Platonism (P)
>so that one can make an analogy to abstract mythical realms
due to P.
>> Its a violent rearrangement of fundamentals for most
people, but try
>> it sometime!
>> J.
>They teach you in school that a number line is composed of a
>series of dimensionless points, neither of which has
physical existence.
>All physical things have dimension. A point you make with a
pencil is not
>a point that corresponds to a mathematical point on a number
line
>because the point created by a pencil has dimension. But I
can see how
>nominalism could point to a pencil point as a physical
expression of
point,
>rather than a mathematical concept.
>I dont think nominalism can help in this tape discussion.
Turing did in
>fact
>use an abstract approach in his paper which does not have a
foothold in
>the physical world. There is no physical correlate to his
endless tape.
>(He states that the TM can compute Pi which is an infinite
limit.)
>Turing says one can substitute a _one-dimensional_ tape that
can have
>symbols printed on it from an infinite ink supply. There are
aspects of
>this logical computing machine that can be physically
represented, but
>not the tape. Nor is there any mention of any time
constraint. The reason
>the TM is described as hypothetical or an abstraction is
because that
>is how Turing presents it. I dont see evidence of his
adopting a
>philosophy,
>such as nominalism, anywhere in the 1936 paper. I dont see
how stating
>that he could have done this and that it might have been
legitimate denial
>of abstraction presents any evidence that he did do this or
that he
thought
>this way. I think he tried to make his paper tangibly clear.
And his paper
>seems
>much more intuitively understandable than Godels to many
people. The
>idea of building a physical computer came later after
working on Enigma.
>Once upon a time, some philosophers like Nelson Goodman
explored a
>program they called nominalism. They wanted to analyze away
*all*
>putative reference to abstract entities. This included
propositions,
>but also such things as patterns or words (as types) or
letters (as
>types). They did this by offering to paraphrase them away
via reference
>to concrete exemplars and use of equivalence relations.
>reference to some abstract object, they would try to analyze
it as:
>John made some inscription which is a replica of (or
cotypical with)
>this one followed by reference to another concrete
inscription.
>So they hoped to trade in abstract *objects*, although they
still
>employed a variety of equivalence relations.
>There are various technical objections to this, e.g. it
cannot obviously
>handle reference to expressions, the name of God, perhaps,
that are never
>actually inscribed. (You can talk about unactualized possible
inscriptions,
>but they are also taboo for the nominalist).
>jumped ship, and accepted abstract objects as irreducible in
science.
>So for Quine, there is no real problem about propositions
due to
>their abstractness -- just define them as equivalence classes
of
>synonymous expressions. The problem is in the similarity
relation.
>But others think there is some advantage. They think at
least that
>it helps avoid a mythology of abstract objects, independent
of the human
>world. Rather, we should recognize that a meaning is
something always
>expressed in *signs*, which have a foothold in the concrete,
spatio-temporal
>world.
misleading and requires one to understand the modus vivendi
and
pragmatic nature of the double standard or anomalous monism.
Quines
extensionlism renders much of the above talk of nominalism
redundant
metaphysics. But to understand that, *you* would have to show
a little
more respect for what you have been criticised for and an
even greater
willingness to listen instead of presume.
--
David Longley
===
Subject: Re: Platonism
>>I thought most
>>mathematicians who expressed an opinion were generally some
sort of
>>Platonists, believing that effective mathematics is
discovered, not
>>invented, and that it is the real world which approximates
the ideal.
...
> Mostly, people do not endorse mathematical platonism which
means
> mathematics pre-exists and is discovered in another realm
by the
> mathematician.
I disagree ... sort of. People is a bit too broad. I was
under the
impression that mathematicians are naively platonistic, in
that,
without giving too much thought to it, they consider all the
things
they work with as real as anything a mechanical engineer
works with.
But for those mathematician who care about philosophy, they
are split
between those who think that platonism is totally
discredited, and
those who accept a weak form of it (realism or naturalism).
--
Mitch Harris
(remove q to reply)
===
Subject: Re: Platonism
> .... I was under the
> impression that mathematicians are naively platonistic, in
that,
> without giving too much thought to it, they consider all
the things
> they work with as real as anything a mechanical engineer
works with.
> But for those mathematician who care about philosophy, they
are split
> between those who think that platonism is totally
discredited, and
> those who accept a weak form of it (realism or naturalism).
===
> Subject: Re: What is a function?
> ....
> .... Still, does thinking of an ordered pair as of a
> typographically ordered string of symbols suffice? Is that
what
> real mathies do, I mean, really, is that all there is to
it? No,
> I shouldnt think so.
> As Im sure you know, the strings of symbols are used in
the syntax
of
> formal theories. However, you seem to be more interested in
> mathematical intuition or even philosophy, when you ask Is
that
what
> real mathies do, I mean, really ....
> .... having thought about it quite a lot over the years, I
believe
that
> the day-to-day intuitive thinking of most mathematicians is
different.
> We very much tend to be relative Platonists. Let me explain
that.
> First, heres my view of the question whether mathematics 
is
discovered
> or invented. In principle, a mathematical theory can be set
up on
any
> consistent axiomatic basis (although in practice, long
historical
> developments of ideas lead to the most fruitful sets of
axioms).
But
> _after_ that, mathematicians have the job of exploring the
> consequences: proving theorems and finding interesting
examples
(models
> of the theory). So after _inventing_ an axiomatic system,
we must
> _discover_ its consequences. For example, after inventing
the
axioms
> of group theory, we are left with the endless and
fascinating job of
> discovering all about groups.
> Working within such an established theory certainly _feels_
Platonic.
> Consequences of the axioms seem to be out there waiting to
be
> discovered, and we often struggle to find them.
> In that context, my answer to your question would be that my
intuition
> of ordered pairs involves two mental objects which seem
real in some
> way, and I know which is first and which is second. But
handling
them
> depends heavily on writing down pairs of symbols, because
the
> _language_ of mathematics is primarily written and not
spoken (an
> important point not often mentioned). My mind needs to feed
on the
> written symbols, certainly if they are to be manipulated
much....
> Ken Pledger.
===
Subject: Re: Platonism
>>I thought most
>>mathematicians who expressed an opinion were generally some
sort of
>>Platonists, believing that effective mathematics is
discovered, not
>>invented, and that it is the real world which approximates
the ideal.
> ...
> Mostly, people do not endorse mathematical platonism which
means
> mathematics pre-exists and is discovered in another realm
by the
> mathematician.
> I disagree ... sort of. People is a bit too broad. I was
under the
> impression that mathematicians are naively platonistic, in
that,
> without giving too much thought to it, they consider all
the things
> they work with as real as anything a mechanical engineer
works with.
> But for those mathematician who care about philosophy, they
are split
> between those who think that platonism is totally
discredited, and
> those who accept a weak form of it (realism or naturalism).
I agree. However, as evidenced by this newsgroup most
mathematicians
are naive platonists. They dont understand the distinction
between
the reality of a table and mathematical ideas.
Godel claimed that there was no distinction. Godel was not
naive.
Actually, some of his arguments are quite strong. But he was
wrong
about that, in my opinion, and I also think you cant argue
for
mathematical platonism without also arguing against a
mechanical mind,
or arguing for the existence of a mathematical god.
--
Eray Ozkural
===
Subject: Re: Platonism
>>I was under the impression that
(in general)
>> mathematicians are naively platonistic, in that,
>>without giving too much thought to it, they consider all
the things
>>they work with as real as anything a mechanical engineer
works with.
>>But for those mathematician who care about philosophy, they
are split
>>between those who think that platonism is totally
discredited, and
>>those who accept a weak form of it (realism or naturalism).
> I agree. However, as evidenced by this newsgroup most
mathematicians
> are naive platonists.
How does the anecdote go? On weekdays Im a platonist, but 
on
the
weekend Im a formalist ?
> They dont understand the distinction between
> the reality of a table and mathematical ideas.
That is a bit strong. understand? maybe they dont -care-. 
or
maybe
it is more important to them the similarities.
> Godel claimed that there was no distinction. Godel was not
naive.
> Actually, some of his arguments are quite strong. But he
was wrong
> about that, in my opinion, and I also think you cant 
argue
for
> mathematical platonism without also arguing against a
mechanical mind,
> or arguing for the existence of a mathematical god.
I dont see the against a mechanical mind connection.
As to a god, maybe Einsteins Spinozas God.
--
Mitch Harris
(remove q to reply)
===
Subject: Re: Platonism
> Godel claimed that there was no distinction. Godel was not
naive.
> Actually, some of his arguments are quite strong. But he
was wrong
> about that, in my opinion, and I also think you cant 
argue
for
> mathematical platonism without also arguing against a
mechanical mind,
> or arguing for the existence of a mathematical god.
> I dont see the against a mechanical mind connection.
> As to a god, maybe Einsteins Spinozas 
God.
The mathematical God could indeed be the One and the Infinite
God in
Spinozaa metaphysics. (And similar stuff is also in
Leibniz), and
since Spinoza is considered a neo-Platonist, I could accept
this
remark, accept that I do not know what neo-Platonist really
means.
It does not seem too far from Godels ideas. In 
Godels
world, there
would be a realm of mathematical objects even if our universe
happened
to be finite (he has separate arguments for that) No reason
why I
should not call that a part of God, but its probably
different from
Spinozas God, I presume, although there is also some
similarity, I
think Godel was careful enough to allow for Spinozas 
monism.
Interesting relations that deserve more reßection. In
particular,
Godel allows for the possibility that the mind is mechanical,
but in
that case something awful happens that upsets the
materialists.
--
Eray Ozkural
===
Subject: Re: Platonism
>>I was under the impression that
> (in general)
>> mathematicians are naively platonistic, in that,
>>without giving too much thought to it, they consider all
the things
>>they work with as real as anything a mechanical engineer
works with.
>>But for those mathematician who care about philosophy, they
are split
>>between those who think that platonism is totally
discredited, and
>>those who accept a weak form of it (realism or naturalism).
I agree. However, as evidenced by this newsgroup most
mathematicians
> are naive platonists.
> How does the anecdote go? On weekdays Im a platonist, but
on the
> weekend Im a formalist ?
Yes, I think Ive heard this quote often. Maybe it serves to
illustrate that most mathematicians dont even care about
these
incompatible positions.
> They dont understand the distinction between
> the reality of a table and mathematical ideas.
> That is a bit strong. understand? maybe they dont -care-.
or maybe
> it is more important to them the similarities.
Most mathematicians dont care, and many of which do not 
care
probably
do not have enough motivation to know either. The ones who
care
probably understand much better than the rest. :) Maybe, they
wouldnt
subscribe to any position, but they would know what each
prominent
position actually means philosophically.
> Godel claimed that there was no distinction. Godel was not
naive.
> Actually, some of his arguments are quite strong. But he
was wrong
> about that, in my opinion, and I also think you cant 
argue
for
> mathematical platonism without also arguing against a
mechanical mind,
> or arguing for the existence of a mathematical god.
> I dont see the against a mechanical mind connection.
This is an almost direct paraphrasing of Godels disjunctive
proposition! I have added nearly nothing to it, except for
the word
god. We can talk about it further. I think Godel was the only
philosophically rigorous mathematical Platonist. Except him,
its just
a lot of handwaving and make-belief. He was intelligent
enough to
present a detailed and quite strong argument that
mathematical objects
have an independent existence, just like your keyboard.
> As to a god, maybe Einsteins Spinozas 
God.
Maybe. I dont know if Einstein was a Platonist. Was 
Spinozas
pantheism a kind of Platonism? I dont know, 
Ill have to
read Spinoza
directly to answer that.
--
Eray Ozkural
===
Subject: Re: Platonism
iD8DBQFBp6zwvmGe70vHPUMRAhFBAJ9V6kt8hWW87JD/
OCL7V3KFlv6URwCgyvXO
u6Jcc7ig3oCVCpIjU7b01oE=
=xg8+
>> How does the anecdote go? On weekdays Im a platonist, 
but
on the
>> weekend Im a formalist ?
>Yes, I think Ive heard this quote often. Maybe it serves 
to
>illustrate that most mathematicians dont even care about
these
>incompatible positions.
They are not at all incompatible.
===
Subject: Re: Platonism
iD8DBQFBpilFvmGe70vHPUMRAldOAKDBB6bTbyamr8N5Pe8u91dmm4dA5ACfRp
sY
64nvtwl8dF351RKbSYs3YrY=
=2wm+
>I agree. However, as evidenced by this newsgroup most
mathematicians
>are naive platonists. They dont understand the distinction
between
>the reality of a table and mathematical ideas.
Nonsense! Of course mathematicians understand the distinction.
===
Subject: Re: Platonism
>I agree. However, as evidenced by this newsgroup most
mathematicians
>are naive platonists. They dont understand the distinction
between
>the reality of a table and mathematical ideas.
> Nonsense! Of course mathematicians understand the
distinction.
Well, I dont think most of them have even an inkling.
Otherwise, they
would stop suggesting that PCs are not models of Turing
Machines, or
that real numbers exist or other silly Platonism.
In particular, they should acknowledge that consistency alone
is no
indication of reality. That is the issue. I can come up with a
completely consistent, and a completely fabricated story,
like the
Bible. But that is a fairy tale. It is not real. Likewise,
mathematicians can come up with consistent and un-real
stories. Most
mathematicians do not appreciate that whatever idea they can
think
about is not automatically real.
In my opinion, most mathematicians think that real numbers
existed
before humanity. That is seen by their naive reliance on the
strict
truth of their assumptions about real numbers, and by the
fact that
they think it is clear what is real! They seem to think that
real
numbers have an independent existence than us! (Or sets or
whatever)
Then, it should follow, that mythology also has an independent
existence, because, it is conceivable that a future tribe of
monkeys
could discover the same naive mythology!
Neither do they understand that the immediate reality of
mathematical
ideas consist only and only in their becoming part of their
subjective
experience, and as shadows of their ideas in their written
and spoken
work, exactly in the same fashion as works of theology
immediately
persists such. Unless their reality is confirmed by empirical
trials
that extend beyond such an inadequate use, no mathematical
idea is
real. (Just like no dream is real)
I can fantasize all that I want in other terms than
mathematics. That
is best seen in metaphysics. I can define terms, and some
rules, and
then describe a world built in these terms and rules. That
does not
mean that the world in question exists. Speech alone does not
create a
strong reality. I suggest that exists has always a physical
meaning. (Neither do the complexity or difficulty of our
fantasies
make them mathematical! But that is another issue)
If on the other hand, we are saying that mathematics is not
concerned
with this world, but with wildly different possible worlds,
e.g. it is
the same thing as metaphysics, then I dont believe that. I
dont
believe thats necessary. And I also think computation sets
the limits
to real mathematics. I admit that the views of this paragraph
are
controversial views, and I dont expect you to buy them. But
the
previous paragraphs are quite ordinary philosophy of
mathematics. (And
not some extremely naive logical positivist view)
I suggest lets stop using those notorious skyhooks.
In particular, I am making the following important claim, and
I think
you should think about it. Please tell me your opinion about
it,
because this is the principle (or one of principles) from
which I
derive the whole analysis.
(Principle of ontological homogeneity)
Mathematical statements have no ontological privilege. That
is, when
we are talking about existence, mathematical statements are
absolutely no different than statements in any other language
or
framework. Using the word exists differently for arts,
sciences,
philosophy and mathematics, would be irresponsible, it would
only show
that we have no idea what exists means.
The principle has no proof, thats what I think. It is
equally dubious
to say that integers exist, by the way. (So, Im not blindly
following Kronecker or Chaitin) You have to give a
philosophical
explanation of why you think that is the case. Because *no
mathematical explanation* can be ontologically adequate on
its own, it
seems that mathematics is merely symbol pushing when it comes
to
explaining these matters. Once you explain what you mean by
the
existence of integers, however, you can refer to this
explanation and
construct more complex ontological statements. (None of which
can
include God, naturally)
That is in fact what we should do, and I think its been 
done
fairly
well for integers, but not well at all for real numbers...
(And that
is where I could agree with Kronecker)
God is just an idea. It is not real.
--
Eray Ozkural
===
Subject: Re: Platonism
>I agree. However, as evidenced by this newsgroup most
mathematicians
>are naive platonists. They dont understand the distinction
between
>the reality of a table and mathematical ideas.
>>Nonsense! Of course mathematicians understand the
distinction.
> Well, I dont think most of them have even an inkling.
Otherwise, they
> would stop suggesting that PCs are not models of Turing
Machines, or
> that real numbers exist or other silly Platonism.
> In particular, they should acknowledge that consistency
alone is no
> indication of reality. That is the issue. I can come up
with a
> completely consistent, and a completely fabricated story,
like the
> Bible. But that is a fairy tale. It is not real. Likewise,
> mathematicians can come up with consistent and un-real
stories. Most
> mathematicians do not appreciate that whatever idea they
can think
> about is not automatically real.
This is a follow up to my previous posting on this matter. The
semantics of language works such that if we refer to a thing
it must
exist in our interpretation (world or model). But if we want
to
restrain our interpretive world to be a bit more realistic
(for some
interpretation of realistic) we can choose a more restrictive
criteria.
As we do this we will be consigning references outside the
chosen
scope of the additional criteria to the nonsense heap. I
would like to
consider several kinds of interpretations (worlds or models)
according
to reasonable criteria for existence in those worlds ...
working from
one extreme to the other ...
fictional worlds
no - physical - things located in time/space
no - effective - procedures exist for identification
no - objective - can be verified by multiple agents
mental worlds
yes - physical - things located in time/space
no - effective - procedures exist for identification
no - objective - can be verified by multiple agents
mathematical worlds
no - physical - things located in time/space
yes - effective - procedures exist for identification
yes - objective - can be verified by multiple agents
physical worlds
yes - physical - things located in time/space
yes - effective - procedures exist for identification
yes - objective - can be verified by multiple agents
Note that in all the worlds considered here, if things are
effective
they are also objective. Perhaps those are the same criteria,
perhaps
not; if not then we should be able to describe those worlds
distinct
from the ones i mentioned.
Also note that in all cases we are talking about *things* in
whatever
kind of world of which we speak. We are not talking of the
marks which
stand for those things in some other world. For example the
marks which
comprise a work of fiction are not usually allowed to exist in
the world
created by the interpretation of those marks.
Constructive comments and critique gladly accepted.
patty
===
Subject: Re: Platonism
>(Principle of ontological homogeneity)
>Mathematical statements have no ontological privilege. That
is, when
>we are talking about existence, mathematical statements are
>absolutely no different than statements in any other
language or
>framework.
You will have to be more careful at phrasing the
question/principle.
Any physical collection of marks lacks privilege, doesnt
even have
a meaning, much less any ontological commitments, until and
unless it
is properly interpreted.
On the other extreme, once it has been interpreted and its
meaning and
extensions evaluated, if it turns out to have pragmatic
value, that
is, if it turns out to be true, then perhaps it can be
granted some
additional label, which might be privilege, compared to not
quite
identical statements which do not evaluate truly.
So, does this all support your principle, or not?
J.
===
Subject: Re: Platonism
>(Principle of ontological homogeneity)
>Mathematical statements have no ontological privilege. That
is, when
>we are talking about existence, mathematical statements are
>absolutely no different than statements in any other
language or
>framework.
> You will have to be more careful at phrasing the
question/principle.
> Any physical collection of marks lacks privilege, doesnt
even have
> a meaning, much less any ontological commitments, until and
unless it
> is properly interpreted.
> On the other extreme, once it has been interpreted and its
meaning and
> extensions evaluated, if it turns out to have pragmatic
value, that
> is, if it turns out to be true, then perhaps it can be
granted some
> additional label, which might be privilege, compared to not
quite
> identical statements which do not evaluate truly.
> So, does this all support your principle, or not?
I think it kind of undermines my principle if accepted. But
Im not
sure if existence, which is in my opinion always a physical
matter,
could change its meaning in any context of interpretation. In
particular, Im not sure if it has anything to do with
relativity of
truth. Surely, a chair either exists or not, whatever
interpretation
we have of the chair.
Now, if theologists could produce rhetoric as fast as Neil,
they would
say, well when we say God exists, we use it in another sense
than
you say a table exists, and we dont expect you to 
understand
this
sense because you are ignorant about theology. Only after you
admit
that this sense of existence should be accepted in its own
right, will
we decide to call you educated in matters of faith. (You
know, those
theologists would probably be burnt at the stake.)
Well, I will have to insist that exists word must have a very
very
definite meaning. Otherwise, it is nonsense. If I am allowed 
to
distort the meaning of exists every now and then, I will be
able to
talk of God and angels as if they existed, and that will be
heresy for
me: I am a physicalist.
--
Eray Ozkural
===
Subject: Re: Platonism
>Well, I will have to insist that exists word must have a
very very
>definite meaning.
Go ahead and insist, then, it wont hurt anything.
:)
> Otherwise, it is nonsense. If I am allowed to
>distort the meaning of exists every now and then, I will be
able to
>talk of God and angels as if they existed, and that will be
heresy for
>me: I am a physicalist.
Well, me too, I think, but my physicalism relates only to the
sub-domains of philosophy that I care about, those of
cognition and
language and computation. As far as cognitive agencies go,
they may
assume that things exist and make the appropriate ontological
commitments, and then we can get on with the internal matters
that we
need to deal with, about how agencies do what they do, in a
material
world.
But the question here was whether mathematical statements have
privilege, and I was just pointing out two very different
ways of
interpreting the question. If you feel a need to insist there
is only
one way of understanding the question, well, I suppose youd
have
company, as when Russell asserted that false statements have
no
meaning. But for me, that unsoundly combines several domains
of
philosophy.
J.
===
Subject: Re: Platonism
>(Principle of ontological homogeneity)
>Mathematical statements have no ontological privilege. That
is, when
>we are talking about existence, mathematical statements are
>absolutely no different than statements in any other
language or
>framework.
>>You will have to be more careful at phrasing the
question/principle.
>>Any physical collection of marks lacks privilege, doesnt
even have
>>a meaning, much less any ontological commitments, until and
unless it
>>is properly interpreted.
>>On the other extreme, once it has been interpreted and its
meaning and
>>extensions evaluated, if it turns out to have pragmatic
value, that
>>is, if it turns out to be true, then perhaps it can be
granted some
>>additional label, which might be privilege, compared to not
quite
>>identical statements which do not evaluate truly.
>>So, does this all support your principle, or not?
> I think it kind of undermines my principle if accepted. But
Im not
> sure if existence, which is in my opinion always a physical
matter,
> could change its meaning in any context of interpretation.
In
> particular, Im not sure if it has anything to do with
relativity of
> truth. Surely, a chair either exists or not, whatever
interpretation
> we have of the chair.
Well if we define existence as that which we can assign
timespace
coordinates (however approximate), then most of the
abstractions that
engineers use to make our world go suddenly have no
ontological status.
However if we define existence at that for which an effective,
objective
procedure can be performed, then we can allow these useful
objects into
our ontology.
> Now, if theologists could produce rhetoric as fast as Neil,
they would
> say, well when we say God exists, we use it in another
sense than
> you say a table exists, and we dont expect you to
understand this
> sense because you are ignorant about theology.
... which does not meet my (new?) definition of existence
unless you can
write an effective procedure for theological matters that can
be
performed with the same result by any arbitrary individual.
> Only after you admit
> that this sense of existence should be accepted in its own
right, will
> we decide to call you educated in matters of faith. (You
know, those
> theologists would probably be burnt at the stake.)
> Well, I will have to insist that exists word must have a
very very
> definite meaning. Otherwise, it is nonsense. If I am allowed
to
> distort the meaning of exists every now and then, I will be
able to
> talk of God and angels as if they existed, and that will be
heresy for
> me: I am a physicalist.
Well i suppose it is your choice, but for you most of math,
logic,
semantics, economics, and ethics wont be making any sense.
patty
===
Subject: Re: Platonism
-----BEGIN PGP SIGNED MESSAGE-----
Hash: SHA1
>>I agree. However, as evidenced by this newsgroup most
mathematicians
>>are naive platonists. They dont understand the 
distinction
between
>>the reality of a table and mathematical ideas.
>> Nonsense! Of course mathematicians understand the
distinction.
>Well, I dont think most of them have even an inkling.
Otherwise, they
>would stop suggesting that PCs are not models of Turing
Machines, or
>that real numbers exist or other silly Platonism.
It is a mistake to assume that exist as used by
mathematicians has
the same meaning as it has when we talk of the existence of
ordinary
things. Likewise, mathematical usage of model is different
from
ordinary usage.
>In particular, they should acknowledge that consistency
alone is no
>indication of reality. That is the issue. I can come up with
a
>completely consistent, and a completely fabricated story,
like the
>Bible. But that is a fairy tale. It is not real.
This is not relevant to mathematics.
> It is not real. Likewise,
>mathematicians can come up with consistent and un-real
stories.
Thats your misunderstanding of mathematics. It is not a
system of
creative fiction.
> Most
>mathematicians do not appreciate that whatever idea they can
think
>about is not automatically real.
Silly. You are confusing the mathematical sense of real with
the
ordinary meaning of the word.
>In my opinion, most mathematicians think that real numbers
existed
>before humanity.
Of course they existed. But thats in the mathematical sense
of
exist. In the ordinary meaning of exist, real numbers do not
exist even today.
> That is seen by their naive reliance on the strict
>truth of their assumptions about real numbers, and by the
fact that
>they think it is clear what is real!
It is clear that you are quite ignorant about mathematics, and
apparently proud of your ignorance.
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===
Subject: Re: Platonism
Hi Neil,
In short, does your position in philosophy of mathematics
have a name?
I found it quite interesting!
Comments follow.
> -----BEGIN PGP SIGNED MESSAGE-----
> Hash: SHA1
>>I agree. However, as evidenced by this newsgroup most
mathematicians
>>are naive platonists. They dont understand the 
distinction
between
>>the reality of a table and mathematical ideas.
>> Nonsense! Of course mathematicians understand the
distinction.
>Well, I dont think most of them have even an inkling.
Otherwise, they
>would stop suggesting that PCs are not models of Turing
Machines, or
>that real numbers exist or other silly Platonism.
> It is a mistake to assume that exist as used by
mathematicians has
> the same meaning as it has when we talk of the existence of
ordinary
> things. Likewise, mathematical usage of model is different
from
> ordinary usage.
I actually like your point about model. But I cannot say if I
like
the point about exist. What is this sense used by *most*
mathematicians then? Would you care to explain? [I dont say
all, I
say most in the above discussion.]
I am hoping you do not mean that in (most!) mathematics
consistency is
identical to existence. That would be quite silly, would not
it?
>In particular, they should acknowledge that consistency
alone is no
>indication of reality. That is the issue. I can come up with
a
>completely consistent, and a completely fabricated story,
like the
>Bible. But that is a fairy tale. It is not real.
> This is not relevant to mathematics.
So in mathematics consistency does not entail existence.
What causes something to mathematically exist then?
> It is not real. Likewise,
>mathematicians can come up with consistent and un-real
stories.
> Thats your misunderstanding of mathematics. It is not a
system of
> creative fiction.
What kind of a system is it, then?
> Most
>mathematicians do not appreciate that whatever idea they can
think
>about is not automatically real.
> Silly. You are confusing the mathematical sense of real
with the
> ordinary meaning of the word.
So, this reality has an altogether different sense than
reality. Good.
So, this reality must be something else!
I think when I say a mathematical object, I usually mean a
mathematical thought.
I assume you may want to explain that, because a kind of
reality I can
attribute to mathematical thoughts is squarely in your head,
which
is itself physical! (regardless of whether these ideas fit
empirical
reality, e.g. real reality) These thoughts are contained in
your
brain, sometimes as good descriptions of physical reality
(e.g.
physical properties can obviously be mathematical!) And
sometimes
their representations are to be found on extraneural marks,
like
Can there be mathematical objects that are not thoughts?
Perhaps. I
dont know. It could be said that the integers necessarily
exist in
any good representation of computations out there. We have an
interesting picture, then. Every version of mathematical
object has
a physical existence. Not surprising if the world is only
physical!
So, reality of mathematical statements seems quite like the
reality of
physical statements! They are theoretical. They are first and
foremost
thoughts (to us!). They can be derived from thought
experiments or
empirical observations. This might be an easier route for you
to
answer. In exactly which fashion can we distinguish physical
statements from mathematical statements?
The only answer I can find is that (in current mathematics)
* They dont have to directly correspond to physical 
systems,
they can
talk about certain mental constructions with desirable
properties such
as abstractness which are not *directly* derived from sensory
experience or empirical trials e.g. graph theory. A graph is
an
abstract concept. But it is wrong to say that graphs do not
exist in
the real world. They certainly do, especially when programmed
on a
computer!
But unfortunately there can be cases in mathematics that are
not even
*indirectly* derived from observations, that are solely the
result of
thought experiments and are indeed incompatible even with the
basic
features of our universe. I dont find this a 
desirable thing,
because
I find these to be misleading thought experiments. I suggest
we put
them aside until we can find a use for them.
>In my opinion, most mathematicians think that real numbers
existed
>before humanity.
> Of course they existed. But thats in the mathematical
sense of
> exist. In the ordinary meaning of exist, real numbers do not
> exist even today.
This mathematical sense of existence you are portraying gets
even
stranger.
I assume you would want to state where I can find this
intriguing
position.
What is it called? If its so common, it ought to have a
name. By now,
it appears that it is not intuitionism, which is something I
might
want to favor.
Is it mathematical realism? And what kind of a mathematical
realism?
Or is it an unnamed fuzzy philosophical position like
Torkels? (He
avoided giving a name, because he probably has no clue what
his
position could be called) Its gotten quite mysterious. 
Im
anxious to
know its name!
> That is seen by their naive reliance on the strict
>truth of their assumptions about real numbers, and by the
fact that
>they think it is clear what is real!
> It is clear that you are quite ignorant about mathematics,
and
> apparently proud of your ignorance.
Educate this ignorant person, then, Neil. What is this unique
philosophical position of yours called? (If its 
determinate,
that is)
Platonism?
But if that is so, I already knew well about it, which is why
I have
taken the chance to show its absurdity. So, then either of the
following is true
1) You are talking about a position other than Platonism, and
Im
sincerely wondering what this position is. Because despite
some
self-study, I cannot predict the name from your post exactly.
2) You dont know what Platonism is.
By the way, another view that I might regard good enough
would be some
kind of mathematical instrumentalism, that might say that
exist is
used only as a figure of speech in mathematics, which is
precisely
what Im suggesting is the current practice. IOW, this exist
has
*nothing* to do with exist in the ordinary sense... Which is
perhaps
what you want to say... Are you an instrumentalist of some
sort? But
we should beware, when we say that, we are really coming to
mathematical solipsism that I talked of a while ago! That
does not
seem desirable either!
--
Eray Ozkural
===
Subject: Re: Platonism
-----BEGIN PGP SIGNED MESSAGE-----
Hash: SHA1
>In short, does your position in philosophy of mathematics
have a name?
None that I am aware of.
>I found it quite interesting!
I wasnt expounding my philosophy.
>> It is a mistake to assume that exist as used by
mathematicians has
>> the same meaning as it has when we talk of the existence
of ordinary
>> things. Likewise, mathematical usage of model is different
from
>> ordinary usage.
>I actually like your point about model. But I cannot say if
I like
>the point about exist. What is this sense used by *most*
>mathematicians then? Would you care to explain? [I dont 
say
all, I
>say most in the above discussion.]
Often, mathematicians demonstrate existence by construction.
Of course,
that is the mathematical sense of construction.
For the ordinary sense of exists, I will note that something
exists after it has been constructed, and only until it has
been
destroyed. But when mathematicians construct an object, they
conclude
that it exists for all time. In particular, it existed before
this
particular construction, and it cannot be destroyed.
This should illustrate why the mathematical sense of
existence is
different from the ordinary sense.
>I am hoping you do not mean that in (most!) mathematics
consistency is
>identical to existence. That would be quite silly, would not
it?
Normally one applies the term consistency to systems of
axioms, and
existence to mathematical objects. An inconsistent system of
axioms could still exist, even though inconsistent.
>I think when I say a mathematical object, I usually mean a
>mathematical thought.
That does not work. For that would make mathematical objects
subjective, and would imply that two different mathematicians
have
two distinct numbers three.
It is important to mathematicians, that mathematical objects
are
objective.
>The only answer I can find is that (in current mathematics)
>* They dont have to directly correspond to physical
systems, they can
>talk about certain mental constructions with desirable
properties such
>as abstractness which are not *directly* derived from sensory
>experience or empirical trials e.g. graph theory. A graph is
an
>abstract concept. But it is wrong to say that graphs do not
exist in
>the real world. They certainly do, especially when
programmed on a
>computer!
The graphs that exist in the real world are not the graphs
that
mathematicians concern themselves with.
>But unfortunately there can be cases in mathematics that are
not even
>*indirectly* derived from observations, that are solely the
result of
>thought experiments and are indeed incompatible even with
the basic
>features of our universe. I dont find this a 
desirable
thing, because
>I find these to be misleading thought experiments. I suggest
we put
>them aside until we can find a use for them.
You only illustrate the extent to which you are confused about
mathematics.
>By the way, another view that I might regard good enough
would be some
>kind of mathematical instrumentalism, that might say that
exist is
>used only as a figure of speech in mathematics, which is
precisely
>what Im suggesting is the current practice.
Thats approximately my own view. But most mathematicians
disagree.
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===
Subject: Re: Platonism
<co59g8$6hg$1@usenet.cso.niu.edu>
<co7gak$2am$1@usenet.cso.niu.eduI actually like your point
about model. But I cannot say if I like
>the point about exist. What is this sense used by *most*
>mathematicians then? Would you care to explain? [I dont 
say
all, I
>say most in the above discussion.]
>I am hoping you do not mean that in (most!) mathematics
consistency is
>identical to existence. That would be quite silly, would not
it?
>Eray Ozkural
This is why you have missed so much of what has been said and
why you
say very naive things about behaviourism. Its also why I 
have
frequently told you that you literally dont know what you
are talking
about.
To be is to be the value of a variable - where is that from?
What does
it have to do with the failure of (existential) quantification
into
intensional contexts such as those of propositional attitude
and the
modalities)? What does that have to do with the extensional
stance?
--
David Longley
http://www.longley.demon.co.uk/Frag.htm
===
Subject: Re: Platonism
> That is in fact what we should do, and I think its been
done fairly
> well for integers,
Apparently not, since you felt prompted to ask whether there
are
integers with an infinite number of digits.
===
Subject: Re: Platonism
> That is in fact what we should do, and I think its been
done fairly
> well for integers,
> Apparently not, since you felt prompted to ask whether
there are
> integers with an infinite number of digits.
That was a pedagogical question (e.g. how do you tell what Z
is to
somebody whos never studied formal set theory, who is *not*
me if you
will try another sore joke), and it was a real explanatory
issue that
I faced trouble with over a coffee table. It has no bearing
on the
ontological status of Z.
Z does not literally exist, but its a good model of certain
computational properties of things in the world, so it can be
said to
exist, in the second order of existence (the conceptual
existence)
sense that Godel talks about, but unlike Godel we should not
overlook
the distinction between 1 and a chair. The nice thing about
integers
is that they are multiply realized, and we should really look
at
them as abstract properties of physical objects, in my
opinion.
Anyway, a complete description of their ontological status
would take
a couple of pages. Try to infer the rest from this paragraph.
(You
will object, anyway. I think you are a platonist. It is not a
position
to be proud of.)
--
Eray Ozkural
===
Subject: Re: Platonism
> (You
> will object, anyway. I think you are a platonist. It is not
a position
> to be proud of.)
Ive heard that in prison pecking order, it lies somewhere
between
car theft and property damage.
--
Mitch Harris
(remove q to reply)
===
Subject: Re: Platonism
> That was a pedagogical question (e.g. how do you tell what
Z is to
> somebody whos never studied formal set theory, who is
*not* me if you
> will try another sore joke), and it was a real explanatory
issue that
> I faced trouble with over a coffee table.
Right. You were wondering if there are integers with an
infinite
number of digits.
===
Subject: Re: Platonism
>> That was a pedagogical question (e.g. how do you tell what
Z is to
>> somebody whos never studied formal set theory, who is
*not* me if you
>> will try another sore joke), and it was a real explanatory
issue that
>> I faced trouble with over a coffee table.
> Right. You were wondering if there are integers with an
infinite
>number of digits.
Im beginning to wonder if there are digits with an 
infinite
number of
digits.
===
Subject: Re: Platonism
>> That was a pedagogical question (e.g. how do you tell what
Z is to
>> somebody whos never studied formal set theory, who is
*not* me if you
>> will try another sore joke), and it was a real explanatory
issue that
>> I faced trouble with over a coffee table.
> Right. You were wondering if there are integers with an
infinite
>number of digits.
> Im beginning to wonder if there are digits with an 
infinite
number of
> digits.
So, can you imagine that? Why, then, that too should be
included in
some strange, nonsense theory, according to mathematical
Platonism,
which does not seem to be concerned with the sensibility or
usefulness
of mathematical theories.
I penned such absurd theories, to show just how absurd and
unreal real
numbers are, and I think they turn out to be much less real
than what
Chaitin or Kronecker may have thought. There is a set that I
call
Absurd numbers, it will be quite fun when I write about it.
With a
little effort, you can construct all kinds of mathematical
absurdities
that are consistent in their own right.
--
Eray Ozkural
===
Subject: Re: Platonism
Originator: harris@tcs.inf.tu-dresden.de (Mitchell Harris)
>> Im beginning to wonder if there are digits with an
infinite number of
>> digits.
>So, can you imagine that? Why, then, that too should be
included in
>some strange, nonsense theory, according to mathematical
Platonism,
>which does not seem to be concerned with the sensibility or
usefulness
>of mathematical theories.
>I penned such absurd theories, to show just how absurd and
unreal real
>numbers are, and I think they turn out to be much less real
than what
>Chaitin or Kronecker may have thought. There is a set that I
call
>Absurd numbers, it will be quite fun when I write about it.
With a
>little effort, you can construct all kinds of mathematical
absurdities
>that are consistent in their own right.
This would make more sense to me if you replaced platonism
with
formalism, where formalism is (very loosely) about playing
games with
symbols irrespective of their meaning.
Mitch
===
Subject: Re: Platonism
...
>>I penned such absurd theories, to show just how absurd and
unreal real
>>numbers are, and I think they turn out to be much less real
than what
>>Chaitin or Kronecker may have thought. There is a set that
I call
>>Absurd numbers, it will be quite fun when I write about it.
With a
>>little effort, you can construct all kinds of mathematical
absurdities
>>that are consistent in their own right.
>This would make more sense to me if you replaced platonism
with
>formalism, where formalism is (very loosely) about playing
games with
>symbols irrespective of their meaning.
I thought playing games with symbols irrespective of their
meaning
was (very loosely) Usenet.
Lee Rudolph
===
Subject: Re: Platonism
> Im beginning to wonder if there are digits with an 
infinite
number of
> digits.
That makes no sense. Every integer is finite so every integer
is
representable by a finite sum of powers of a base > 1.
Bob Kolker
===
Subject: Re: Platonism
>> Im beginning to wonder if there are digits with an
infinite number of
>> digits.
>That makes no sense. Every integer is finite so every integer
is
>representable by a finite sum of powers of a base > 1.
Im not sure the thread makes any sense. Surely there are
more topical
topics in fundamental mathematics than the cryptoplatonism of
mathematicians. Please excuse my boorish observation.
===
Subject: Ozkural was Re: Platonism
>> That was a pedagogical question (e.g. how do you tell what
Z is to
>> somebody whos never studied formal set theory, who is
*not* me if you
>> will try another sore joke), and it was a real explanatory
issue that
>> I faced trouble with over a coffee table.
> Right. You were wondering if there are integers with an
infinite
> number of digits.
Indeed. His question was not
How do I explain to my interlocutors that each integer has
finitely
many digits in its base ten representation?
it was
are there integers with an infinite number of digits?.
--
Robin Chapman, www.maths.ex.ac.uk/~rjc/rjc.html
Lacan, Jacques, 79, 91-92; mistakes his penis for a square
root, 88-9
Francis Wheen, _How Mumbo-Jumbo Conquered the World_
===
Subject: Re: Ozkural was Re: Platonism
>
>> That was a pedagogical question (e.g. how do you tell what
Z is to
>> somebody whos never studied formal set theory, who is
*not* me if you
>> will try another sore joke), and it was a real explanatory
issue that
>> I faced trouble with over a coffee table.
Right. You were wondering if there are integers with an
infinite
> number of digits.
> Indeed. His question was not
> How do I explain to my interlocutors that each integer has
finitely
> many digits in its base ten representation?
> it was
> are there integers with an infinite number of digits?.
Doh! Not interlocutors, friends.
I asked it like that, and why did I do that? Because my
friends asked
me that question. And I had no good answer. They asked me Why
not?,
and I could not answer except by saying that is how we define
things.
doesnt it make sense?... So I forwarded the question here,
and I
quoted the philosophical context later on. I thought that was
the
proper way to do it. Anyway, you two never understood the
gist of that
discussion, or made any useful comment. You did not
understand my
friends well motivated attack against the 
definitional issues
in
Cantors theorem, either. But you are both doing extremely
well in
your ad hominem arguments, and misrepresenting my ideas. I
did try to
develop upon my friends ideas, and I think I had some nice
arguments
philosophically (but quite useless mathematically!).
The question does not belong to me originally. It is someone
elses
who doesnt post here, but I agree with the idea behind the
question
although the answer is obviously NO given the elementary
definitions
they teach us in secondary school in Turkey. (So, I was
surprised that
you guys could think it was possible for a grad. student to
miss such
easy stuff. That may be the case for US or Britain, but its
never the
case in Turkey.) I concluded that the answer might be
definitional
from a more generalist point of view. So, yes, I came close
to being a
formalist of some sort it seems. Im very interested in the
shape of
things. I dont think they necessarily refer to things out
there,
which would be Platonism. Maybe it refers only to things in
here.
But you two naively think that integers are like that,
because they
refer to some truth or reality or whatever out there. You
think it is
not because that is how we define integers, which is precisely
the
case! How can you know that whatever truth is out there, even
if the
outdated doctrine of Platonism holds in our world,
corresponds to
whatever is in your tiny heads? You cannot.
Keep searching. The truth is not quite out there. Its in
your head,
too.
--
Eray
===
Subject: Re: Ozkural was Re: Platonism
> I asked it like that, and why did I do that? Because my
friends asked
> me that question. And I had no good answer.
Right. You were wondering, Are there integers with an infinite
number of digits?
===
Subject: Re: Platonism
>I thought most
>mathematicians who expressed an opinion were generally some
sort of
>Platonists, believing that effective mathematics is
discovered, not
>invented, and that it is the real world which approximates
the ideal.
> ...
>> Mostly, people do not endorse mathematical platonism which
means
>> mathematics pre-exists and is discovered in another realm
by the
>> mathematician.
> I disagree ... sort of. People is a bit too broad. I was
under the
> impression that mathematicians are naively platonistic, in
that, without
> giving too much thought to it, they consider all the things
they work with
> as real as anything a mechanical engineer works with.
and dont ponder too much about the unreasonable
effectiveness of
mathematics.
I knew that mathematicians were cultish about it and I
couldnt
make the assertion that I did about their narrower group so I
used a larger group where my statement is true. Using
mathematician
in the definition of mathematical platonism was a necessary
evil.
I couldnt legitimately say, Mostly, mathematicians do not
endorse
mathematical platonism because they do. So I used the larger
class of people who for varied reasons do not endorse
mathematical
platonism. (Never heard of it; huh, that sounds like a fairy
tale; I dont
have time for that kind of nonsense because I shut up and
calculate.)
> But for those mathematicians who care about philosophy,
they are split
> between those who think that platonism is totally
discredited, and those
> who accept a weak form of it (realism or naturalism).
So I mostly agree with what you say about mathematicains, but
that is
not typical for people like research historians, computer
technicians,
bookies, perhaps some linguists, and the majority of
philosophers.
Were you by any chance thinking of a mathematician as a
person?
> --
> Mitch Harris
> (remove q to reply)
===
Subject: Re: Platonism
>>I thought most
>>mathematicians who expressed an opinion were generally some
sort of
>>Platonists, believing that effective mathematics is
discovered, not
>>invented, and that it is the real world which approximates
the ideal.
>>...
>Mostly, people do not endorse mathematical platonism which
means
>mathematics pre-exists and is discovered in another realm by
the
>mathematician.
>>I disagree ... sort of. People is a bit too broad. I was
under the
>>impression that mathematicians are naively platonistic, in
that, without
>>giving too much thought to it, they consider all the things
they work with
>>as real as anything a mechanical engineer works with.
> and dont ponder too much about the unreasonable
effectiveness of
> mathematics.
> I knew that mathematicians were cultish about it and I
couldnt
> make the assertion that I did about their narrower group so
I
> used a larger group where my statement is true. Using
mathematician
> in the definition of mathematical platonism was a necessary
evil.
> I couldnt legitimately say, Mostly, mathematicians do not
endorse
> mathematical platonism because they do. So I used the larger
> class of people who for varied reasons do not endorse
mathematical
> platonism. (Never heard of it; huh, that sounds like a
fairy tale; I
dont
> have time for that kind of nonsense because I shut up and
calculate.)
OK. I would say (in my own overgeneralized wording) that
those who are
non mathematically oriented (mathematically/philosophically
naive?))
would deny existence of -any- mathematical concept beyond
those
having immediate physical tangibles like specific numbers or
distance.
(taking the oversimplification of platonism as the philosophy
that
mathematical things exist.)
>>But for those mathematicians who care about philosophy,
they are split
>>between those who think that platonism is totally
discredited, and those
>>who accept a weak form of it (realism or naturalism).
> So I mostly agree with what you say about mathematicains,
but that is
> not typical for people like research historians, computer
technicians,
> bookies, perhaps some linguists, and the majority of
philosophers.
> Were you by any chance thinking of a mathematician as a
person?
For actuarial purposes, I suppose one would be forced to. ;)
I think that was my quibble with your use of Mostly, people.
I was
trying to leave out the non-mathematician.
--
Mitch Harris
(remove q to reply)
===
Subject: Re: Platonism
> For actuarial purposes, I suppose one would be forced to. ;)
> I think that was my quibble with your use of Mostly,
people. I was
> trying to leave out the non-mathematician.
> --
Well, in my view mathematical platonism is a philosophical
assumption
rather than an experienced reality. So the mathematician is
closer to
the experienced reality but I dont see that as a
qualification, since
Im not a platonist, which makes a consistent viewpoint.
Their opinion
of their experienced reality has no causal effect on creating
a platonic
realm. A shared delusion rather than a special insight.
So then speaking of mathematicians, I see no special
philosophical
insight demonstrated by mathematicians in general or the
talent for
doing math. I sit here and think of good physicists who were
also
good mathematicians and philosophers, and there are a few.
David
Bohm comes to mind at the top of my list. But pure
mathematicains...
That is my reason for leaving out the mathematican. When I
write
I discover potentials in the writing which I didnt plan or
invent, so
that is a type of discovery. And some artists describe
sculpting
for instance as chipping away the exterior to reveal the
hidden content.
But I dont see that as justifying a platonic realm, rather 
a
cultist
belief,
in the strong version of platonism.
Stephen
===
Subject: Re: Turing Machines and Physical Computation
>You are missing the entire point that computation is meant
to be a
>physical process. That is all there is to computation. It is
a theory
>of computing machines. And it describes a large number of
them. Lets
>get down to your particular objections to my detailed
analysis.
>But every couple of months, a naive mathematician will show
up (not
>you) and try to purport an imaginery dichotomy between
physical
>computation and Turing computation. That is unfortunate, very
>unfortunate indeed, because in my opinion it shows a
systematic mental
>error.
> Although a theory of physical computing machines is
possible, we do not
> have such a theory as yet.
> The Turing Machine, as A. M. Turing specified it, cannot
calculate
pi,
> but it can calculate any finite number of digits of pi, such
as
> (10^(10^(10^(10^(10^1000))))) digits of pi, even though no
> physically-realizable computer could calculate that many
digits of pi.
> Turing _did_ specify the Turing machine that way, so it is
a fact that
> he made the same systematic mental error you refer to. Why
did he do
> such a thing?
> Because it made it possible for him to derive results from
his theory in
> a reasonable amount of time. Determining what the limits of
computation
> in the physical universe are, and what can be done within
those limits,
> is a very complicated problem. Assuming infinite memory
capacity is a
> simplifying assumption that makes for a theory much easier
to derive and
> work with
There is nothing wrong in Turings theory, and Pi is a
computable
real, which means that not that the actual real number can be
ever
generated, but only that arbitrarily many digits of it can be
generated in finite time.
> What is the use of such a theory, a theory that doesnt
refer to the
> real world?
You would be wrong to think it does not refer to the real
world. The
interesting portion of the theory makes predictions squarely
in the
real world, thats why the theory is relevant in everyday
computing.
> If certain things cannot be done with even an infinite
> memory, then they cannot be done with a finite memory.
There is no such thing as infinite memory, the tape is
unbounded, not
infinite. We need to make the distinction. When you above said
capacity, it was potential and therefore admissible exactly
in the
same fashion as that every integer, by definition, is 
finite.
(Integers are *integral*)
> And many things
> that can be computed dont need an infinite 
amount of
memory, or even an
> absurdly large finite one. So the Turing machine is an
*approximation*
> to a real computing machine.
Its more than an approximation. Physical computation does
not mean
that we need to specify the quantum state transitions, or give
physical bounds or formulate a GUT or anything like that. The
Turing
Machine gives an exact characterization of the causal
structure of
computing machines, and that is very physical. The Turing
Machine is a
blueprint. You can take it, and build a variety of machines
using it,
but no information WITH RESPECT TO COMPUTATION is missing in
the
blueprint, which means the blueprint is exact with respect to
computation. (In that it describes exactly HOW to perform the
computation, which is the necessary question to answer to be
able to
compute at all)
There is a difference between a theory which is inexact in
all facts,
and a theory that is exact in many facts, and makes
conditional
predictions in general that would hold in nomologically
similar
(possible) worlds.
In the general sense, the Turing Machine is a metaphysical
model of
causal systems. Is that significant? Yes. But that is so
because it
depicts a set of close-by possible worlds, including our own
world, in
which this causal model corresponds to general mechanical
laws.
Whether our world is infinite or finite (which is 
a matter to be
eventually settled by astrophysics observations), is
irrelevant for
the theory, because its a general theory. However, it
depicts no
worlds that are physically remote from our own. Thats why 
it
carries
a notion of weak physicalism. (There are discussions more to
the
point, but it would be useless to discuss these with Harris,
who does
not seem capable of discussing these within a coherent
metaphysics as
I maintain)
> lines made with real pencils and the pinpricks made by the
point of a
> real compass, mathematicians have always approximated the
real world by
> abstractions which are not physically realizable. This
makes the
> symbolic manipulations in mathematics simpler - and thus
makes them
> realizable instead of impractical. Giving this up would
mean giving up
> mathematics, because taking into account the limitations of
the real
> world in every case would make many fields far too
complicated to
> investigate.
Not bad points, Jon. We abstract at the cost of losing
reality.
The more we lose reality, the less real our theories become.
I suggest that the reality of Turing computation is not
severely
diminished by the fact that it addresses a set of physically
similar
worlds. For the model captures the essence of causality, and
that is
sufficient for it to explain computation. This is a
philosophical
argument.
I would welcome further discussion on individual points, I
hope these
points sound interesting to you.
A tiny argument may be missing in the above exposition. It is
a theory
that deals with possible worlds, and its statements can be
seen as
conditional (If the world has finite space, then we can
construct
*these* machines). However, the approach is constructive, we
take the
coarse-grained causal laws of our universe, and generalize
them,
without positing anything that we are not sure of. Therefore,
its a
scientific way of making metaphysics. Its a 
very very new
thing
(thats why some people still have trouble understanding 
it),
and its
much more powerful than the logical positivist account.
Positivism = Physicalism + Constructivism + Nominalism gives
us a
solution. Its a new foundation not only for mathematics, 
but
also for
computation, which may be more general than mere mathematics
(which
seems to have specific concerns!).
I cannot tell anything about whether the approach of Turing
has a
solipsist favor. I think it does not, but at one level it
might give
rise to a solipsist level (some mental states might be
exactly that).
The level we are interested in at the moment seems quite
real! But
when we talk about these large cardinal axioms, oh, we are
being
solipsists.
--
Eray Ozkural
PS: So, I think I largely agree with Joshua Stern.
===
Subject: Re: Turing Machines and Physical Computation
>>You are missing the entire point that computation is meant
to be a
>>physical process. That is all there is to computation. It
is a theory
>>of computing machines. And it describes a large number of
them. Lets
>>get down to your particular objections to my detailed
analysis.
SH: Eray, his is another one of your premises that conßicts
with the
facts.
Turing was mathematician interested in the foundations of
mathematics.
Hilbert made up a list of 23 questions to put mathematics on
firm footing.
Im pretty sure that it is number 10 on this list that 
Turing
referred to
in
his famous 1936 paper,
On computable numbers, with an application to the
Entscheidungsproblem
The paper had two purposes to define the nature of an
algorithm and
to give a better negative answer to Hilberts challenge:
A decision problem was a general question: Given any sequence
of
symbols,
is it a formula? or Given any formula, is it provable? A
solution to
a
decision problem was an effective procedure, a uniform method
or algorithm,
specified by a finite set of rules, by which each 
instance of
the general
question could be answered in a finite number of steps. An
effective
procedure could not appeal to intuition, understanding,
creativity, or
guesswork, and always generated the correct answer.
http://www.artsci.wustl.edu/~gpiccini/Alan%20Turing%20and%
20the%20Mathematic
al%20Objection.pdf
L. E. J. Brouwer was the main supporter of intuitionism,
according to which
an existence proof for a _mathematical object_ was admissible
only if it
exhibited a construction of the object (Brouwer 1974).
Brouwer was also against Cantorian set theory which also made
use
of the diagonalization process. Turing was improving Godels
result
which answered Hilbert question 10 negatively. Turing was
attempting
to show his answer as a constructive process for exhibiting
proof of a
***mathematical object***, not the physical object you claim.
>>You are missing the entire point that computation is meant
to be a
>>physical process. That is all there is to computation.
Maybe they had an old fashioned hand-driven adding machine
that you
see in old movies. Computation was done by office clerks.
Turing claimed
that his Turing machine could perform mechanical procedures
like these
clerks; that it was mechanical in the sense of by rote, no
ingenuity was
involved, no creativity. That was the computation performed
by human
computer and claimed for turing machines.
computers existing in order to point the purpose of direction
you claim,
realization of a physical computing machine. I think he was
exposed to
a primitive analog computer in 1937. After he worked on
encryption
during WWII I think he got the notion of a physical device.
Then someone
realized that tubes could be used to compute with and I think
the first
proto-digital computer was around 1946. I think it was 1948
when Turing
introduced thinking machines---much after his Turing machine
paper.
You just seem to be ignoring the fact that the theory that
present day
computers borrow heavily from started as a theory. It was a
mathematical-logical theory not at all intended to provide a
blueprint
for physical digital computers. That happened afterward, a
development.
That is why I can find so many quotes on the web describing a
turing
machine as an abstract hypothetical device. That is its
historical origin.
http://www.unidex.com/turing/tm_intro.htm
A Turing machine can be thought of as a primitive, abstract
computer.
Alan
Turing, who was a British mathematician and cryptographer,
invented the
Turing machine as a tool for studying the computability of
mathematical
functions. Turings hypothesis (also known has 
Churchs
thesis) is a widely
held belief that a function is computable if and only if it
can be computed
by a Turing machine. This implies that Turing machines can
solve any
problem
that a modern computer program can solve. There are problems
that can not
be
solved by a Turing machine (e.g., the halting problem); thus,
these
problems
can not be solved by a modern computer program.
Im not arguing with this. I factually stated some problems
are tractable
for TMs that are not tractable for PCs because of time. The
heat death
of the universe comes about because of the passage of time
which means
there is no more energy available in order to power physical
computing.
This is somewhat like the idea that quantum computers are
supposed to
solve some computable problems that are intractable for
conventional PCs.
I say somewhat because this introduces time, which is not a
TM factor.
How many intractable problems are there? Infinite.
>>But every couple of months, a naive mathematician will show
up (not
>>you) and try to purport an imaginery dichotomy between
physical
>>computation and Turing computation. That is unfortunate,
very
>>unfortunate indeed, because in my opinion it shows a
systematic mental
>>error.
You are committing a systematic mental error. The one you
refer to is
when people mistakenly claim that TMs cannot compute what a
digital
computer (pc) can compute. This is true without claiming
inherent
randomness in the physical computer. I have stated the
converse of this
statement. That some problems are intractable for PCs because
of the
time element; but those problems are not intractable for TMs
because
Turing invented TMs without any reference to time and he gave
the
TM an infinite tape so there is no shortage of memory problem
(the
tape doesnt halt unexpectedly because it runs out like an
adding machine)
which eliminates physical constraints from TMs that do impact
PCs.
I made no assertion that the topic of physical computation
was historically
less important now. The physical aspect was certainly less
developed, if at
all, when the mathematical theory of a TM was created. TMs
are not
physical.
> Although a theory of physical computing machines is
possible, we do not
> have such a theory as yet.
> The Turing Machine, as A. M. Turing specified it, cannot
calculate
pi,
> but it can calculate any finite number of digits of pi, such
as
> (10^(10^(10^(10^(10^1000))))) digits of pi, even though no
> physically-realizable computer could calculate that many
digits of pi.
> Turing _did_ specify the Turing machine that way, so it is
a fact that
> he made the same systematic mental error you refer to. Why
did he do
> such a thing?
> Because it made it possible for him to derive results from
his theory in
> a reasonable amount of time. Determining what the limits of
computation
> in the physical universe are, and what can be done within
those limits,
> is a very complicated problem. Assuming infinite memory
capacity is a
> simplifying assumption that makes for a theory much easier
to derive and
> work with.
> What is the use of such a theory, a theory that doesnt
refer to the
> real world? If certain things cannot be done with even an
infinite
> memory, then they cannot be done with a finite memory. And
many things
> that can be computed dont need an infinite 
amount of
memory, or even an
> absurdly large finite one. So the Turing machine is an
*approximation*
> to a real computing machine.
> lines made with real pencils and the pinpricks made by the
point of a
> real compass, mathematicians have always approximated the
real world by
> abstractions which are not physically realizable. This
makes the
> symbolic manipulations in mathematics simpler - and thus
makes them
> realizable instead of impractical. Giving this up would
mean giving up
> mathematics, because taking into account the limitations of
the real
> world in every case would make many fields far too
complicated to
> investigate.
> John Savard
> http://home.ecn.ab.ca/~jsavard/index.html
I think the literature supports your statements:
http://plato.stanford.edu/entries/turing-machine/
In modern terms, the tape serves as the memory of the
machine, while the
read-write head is the memory bus through which data is
accessed (and
updated) by the machine. There are two important things to
notice about the
definition.
The first is that the machines tape is 
infinite in length,
corresponding
to
an assumption that the memory of the machine is infinite. The
second is
similar in nature, but not explicit in the definition of the
machine,
namely
that a function will be Turing-computable if there exists a
set of
instructions that will result in the machine computing the
function
regardless
of the amount of time it takes. One can think of this as
assuming the
availability of infinite time to complete the computation.
[SH: I prefer to think of it as having no time involved,
rather than
infinite.]
These two assumptions are intended to ensure that the
definition of
computation that results is not too narrow. This is, it
ensures that no
computable function will fail to be Turing-computable solely
because there
is insufficient time or memory to complete the computation. If
a function
is
not Turing-computable it is because Turing machines lack the
computational
machinery to carry it out, not because of a lack of
spatio-temporal
resources.
-------------------------------------------------------------
-------
These are called abacus computers by Lambek (Lambek 1961),
and are known
to
be equivalent to Turing machines.
The modern digital computer is subject to finiteness
constraints that we
have abstracted away in the definition of abacus machines,
just as we did
in the case of Turing machines. Physical computers are
limited in the
number
of memory locations that they have, and in the storage
capacity of each of
those locations, while abacus machines are not subject to
those
constraints.
Thus some abacus-computable functions will not be computable
by any
physical
machine. (We wont consider whether Turing machines and
modern digital
computers remain equivalent when both are given external
inputs, since that
would require us to change the definition of a Turing 
machine.)
-------------------------------------------------------------
---------------
-
http://www.alanturing.net/turing_archive/pages/Reference%
20Articles/What%20i
s%20a%20Turing%20Machine.html#head
Commercially available computers are hard-wired to perform
primitive
operations considerably more sophisticated than those of a
Turing machine
--add, multiply, decrement, store-at-address, branch, and so
forth. The
precise constitution of the list of primitives varies from
manufacturer to
manufacturer. It is a remarkable fact that none of these
computers can
outdo
a Turing machine. Despite the Turing machines austere
simplicity, it is
capable of computing anything that any computer on the market
can compute.
Indeed, since it is an abstract or notional machine, a Turing
machine can
compute more than any physical computer. This is because
(1) the physical computer has access to only a bounded amount
of memory,
and
(2) the physical computers speed of operation is limited by
various
real-world constraints.
It is sometimes said, incorrectly, that a Turing machine is
necessarily
slow, since the head is continually shufßing backwards and
forwards,
one square at a time, along a tape of unbounded length. But
since a
Turing machine is an idealised device, it has no real-world
constraints
on its speed of operation.
Stephen
===
Subject: Re: Turing Machines and Physical Computation
<a8d13dcbdca7ae739b921bb2ba3db48e.48257@mygate.mailgate.org>
<ogGFp6BAYAnBFwB6@longley.demon.co.uk>
<419c4735$0$44080$5fc3050@dreader2.news.tiscali.nl>
<Jpfd7EJk2LnBFw1T@longley.demon.co.uk>
<419cd7d4$0$44068$5fc3050@dreader2.news.tiscali.nl>
<4zrnd.46389$QJ3.16198@newssvr21.news.prodigy.com>
<ddEnd.23771$6q2.22891@newssvr14.news.prodigy.comI cant see
how bringing finite TMs into this issue, just because they
>are practical is useful at all. The issue being discussed is
not
>practical/physical
>but theoretical, hypothetical and abstract; an idea not a
physical thing.
Are you sure about that? Are you sure you havent missed the
whole point
of what the first half of 20th century philosophy and earlier
(from
Frege to Goedel and beyond) was really all about? It was, I
suggest, a
record of failure - the failure of analyticity and the
banality of
computing. The collapse of any search for foundations for
philosophy
(of mathematics) led to an enlightened empiricism (which
abandons
intensionalism or analyticity, along with reductionism in
favour of
extensionalism.
Naturalisation of epistemology is behavioural science, and
that comes
down to the experimental and applied analysis of behaviour.
That sadly
often comes down to money management and politics as far as
applied
behaviour analysis is concerned.
Ideas are intensions.
Ive suggested before that you should read some Skinner and
Quine.
Skinners 1945 paper might help some to appreciate how and 
why
Wittgensteins later philosophy is really a therapy for folk
like you
who still havent learned the lessons of the 
first part of the
20th
century. It makes all this talk of AI nonsense as you dont
appreciate
the limits of analyticity - without data its solipsistic or
blind (as
Kant would say). You are just rehashing old words in new ways.
Wittgenstein (or Skinner) would also have shown you (if any
of you would
have listened) that youre largely just talking bosh. I bet
you
wouldnt have liked Wittgenstein either as 
youd have had to
want to
court criticism to benefit, ie youd have to 
have been able to
recognize
that you need therapy.
Note that Ozkural doesnt even like Quine ;-). Do you see a
pattern
emerging here? He doesnt like Sizemore either. No doubt
were all
rude, mentally ill or senile (if not dead). No doubt were 
all
in
your killfiles ;-).
Folk in these newsgroups need to understand that psychiatric
terms are
not terms of abuse (and that all considered, the behaviours
they refer
to are far more common than most folk appreciate (cf. Post
and Goedel,
Turing and many others (the link is in here
k>). These terms classify variants of normal human diversity,
emitted at
higher frequencies than normal. The word idiot on the other
hand seems
to come close to being a synonym or discriminative stimulus
for a
measure of central tendency, so perhaps some of you guys
should, given
your penchant to use psychiatric classifications as terms of
abuse, be
proud to be thought of as idiots?
ÔI have had neither the aptitude nor the temperament for
debate, public or private, when confronted with motives
recognizably other than the pursuit of truth. If in
discussing with a student I sensed that he was animated
rather by some ideological preconception, or by a wish
to have been right for the sake of high marks or self-
esteem, I make short work of the dialogue. A vast gulf,
insufficiently remarked, separates those who are
primarily concerned to have been right from those who
are primarily concerned to be right. The latter, I like
to think, will inherit the earth.
-
W.V. Quine
The Time of My Life (1985).
ÔRhetoric is the literary technology of persuasion, for
good or ill. It is the rallying point for advertisers,
trial lawyers, politicians, and debating teams.
-
Debating teams are promoted in schools as a spur to
effective language and incisive thought. They serve that
purpose, but only by setting the goal of persuasion
above the goal of truth. The debaters strength lies not
in intellectual curiosity nor in amenability to rational
persuasion by others, but in his skill in defending a
preconception come what may. His is a nefarious knack of
disregarding all the discrepancies while regarding every
crepancy.
-
The same skill, along with legal lore, is the strength
of the trial lawyer or barrister, and the strength also
of the successful politician, one or the other of which
careers the captain of the the debating team is clearly
destined for. Happily there are lawyers who will only
take on such cases as they deem to be just, and
politicians who will espouse only a case which is
righteous; but these scruples are not adjuncts of the
rhetorical pole, nor are they keys to success in the
legal or political profession.
-
When an electorate or a jury is the sway of a
demagogues rhetoric, cold reason and the marshaling of
facts bear little promise in rebuttal. Marshaling more
rhetoric, then, in a contrary vein, we fight fire 
with
fire. Rhetoric is invaluable homeopathically in
withstanding its own assaults.
-
In scientific circles there is little demagogy to
combat, but rhetoric is sometimes of service even there;
for in an extremity it may happen that a scientist needs
more than a cold statement of his theory and his
evidence if he is ever to shake the stubborn and
mistaken preconceptions of some of his students, let
alone his dissident colleagues. But rhetoric in the
wrong scientists hands can do disservice to science. It
can help him put his theory across for his reputations
sake despite some shakiness in the evidence.
-
Rhetoric, then, is sometimes nefarious and sometimes
not. In its nefarious use it is the art or practice of
defending a proposition on grounds other than ones own
reasons for defending it. An auxiliary device is
innuendo. A Ôreferentially translucent 
expression, as
Randal Marlin call it, is subtly ambiguous: it can be
taken as objectively stating a result of an action, and
it can be taken as accusing the agent of intending that
result. One of Marlins examples is the headline 
ÔPope
Fouls Up Bar Mitzvah. The Popes arrival in 
town caused
a traffic jam that rendered the synagogue inaccessible
for the Bar Mitzvah; but the headline can be taken as
hinting unjustly of hostility on the Popes part towards
Jews. It is an insidious device, effective in warping
unsuspecting minds while still adhering, in a sense, to
the verifiable.
-
Nefarious rhetoric is rife not only in tendentious
journalism, television commercials, courts of law,
Congress, political rallies, and the United Nations, but
also in homelier settings. In a New England town meeting
a citizen will describe in glowing terms the public
advantages which accrue from some proposed measure, when
what is at stake deep down has to do with his own
interest as proprietor, abutter, investor or contractor.
In such a case we do not cope with abuse by meeting
rhetoric with rhetoric, fire with fire, we just 
expose
the mans motives. What is important is to be alert to
what is going on, and not accept insincere argument at
face value. This much applies to the august and the
humble ones alike.
-
What I have been calling nefarious rhetoric recurs in a
rudimentary form also in impromptu discussions. Someone
interest, and marshals ever more desperate and
threadbare arguments in defence of his position rather
than be swayed by reason or face the facts. Even more
often, perhaps, the deterrent is just stubborn pride:
reluctance to acknowledge error. Unscientific man is
beset by a deplorable desire to have been right. The
scientist is distinguished by a desire to BE right.
-
Rhetoric
-
QUINE (1987)
Quiddities
--
David Longley
http://www.longley.demon.co.uk/Frag.htm
===
Subject: Re: Turing Machines and Physical Computation
>I cant see how bringing finite TMs into this 
issue, just
because they
>are practical is useful at all. The issue being discussed is
not
>practical/physical
>but theoretical, hypothetical and abstract; an idea not a
physical
thing.
> Are you sure about that? Are you sure you havent missed
the whole point
> of what the first half of 20th century philosophy and
earlier (from
> Frege to Goedel and beyond) was really all about?
In this part I might actually agree with Longley! Dolan and
others
miss the whole point! Analytical/synthetic distinction indeed
does not
exist. (And on that point I agree with Quine) Why is this
distinction
relevant? Because saying that an idea is not a physical thing
is a
lot like saying that well, ideas can be purely analytical.
analytical
concepts are DISTINCT from synthetic concepts, so it can be
the case
that an idea is not a physical thing.... Close enough.
This is of course a very confused philosophy. Saying that an
idea is
not a physical thing is an automatic admission of Cartesian
Dualism.
It shows that the person who said it NEVER READ ANY 20th
CENTURY
PHILOSOPHY. And I suggest such ignorant persons like Dolan to
stay
away from philosophical discussions, it is not their league.
> It was, I suggest, a
> record of failure - the failure of analyticity and the
banality of
> computing. The collapse of any search for foundations for
philosophy
> (of mathematics) led to an enlightened empiricism (which
abandons
> intensionalism or analyticity, along with reductionism in
favour of
> extensionalism.
Well, of course I dont agree with this. Computing is not
banal. It is
not analytic either. How did you make that up?
And here is a serious question for you, David. If programming
languages are extensional as you like to proclaim, how come
computing not be an adequate tool for extensional stance?
[snip more stuff I find irrelevant]
--
Eray Ozkural
===
Subject: Re: Turing Machines and Physical Computation
> In this part I might actually agree with Longley! Dolan and
others
> miss the whole point! Analytical/synthetic distinction
indeed does not
> exist. (And on that point I agree with Quine) Why is this
distinction
> relevant? Because saying that an idea is not a physical
thing is a
> lot like saying that well, ideas can be purely analytical.
analytical
> concepts are DISTINCT from synthetic concepts, so it can be
the case
> that an idea is not a physical thing.... Close enough.
An idea is a recognition of a possibility (note it is
physical in an
appropriate ontology). Some ideas go on to become implemented
(or
stick) in our culture ... the WWW was Tim Berners-Lees idea
at some
point. Now what has recognition of a possibility got to do
with the
analytical/synthetic distinction again? Nothing, imho.
patty
===
Subject: Re: Turing Machines and Physical Computation
http://mygate.mailgate.org/mynews/comp/comp.theory/
207fe873374c584e8a375f35c5
b1d9f7.48257%40mygate.mailgate.org
>> I cant see how bringing finite TMs into 
this
>> issue, just because they are practical is useful
>> at all. The issue being discussed is not
>> practical/physical but theoretical, hypothetical
>> and abstract; an idea not a physical thing.
> Are you sure about that? Are you sure you havent
> missed the whole point of what the first half of
> 20th century philosophy and earlier (from Frege to
> Goedel and beyond) was really all about?
David, since you have utterly no concept what the
subject under discussion is (hint philosophy is
the wrong answer), nor education nor inclination
ever to understand the subject matter, how about
learning to hold your peace, rather than riding your
inane hobby horse to trample roughshod over yet
another conversation to which you were not invited,
in which you do not belong, and where all you can do
is (correctly) portray yourself to be a classic
boorish dolt?
HTH
xanthian.
--
===
Subject: Re: Turing Machines and Physical Computation
<a8d13dcbdca7ae739b921bb2ba3db48e.48257@mygate.mailgate.org>
<ogGFp6BAYAnBFwB6@longley.demon.co.uk>
<419c4735$0$44080$5fc3050@dreader2.news.tiscali.nl>
<Jpfd7EJk2LnBFw1T@longley.demon.co.uk>
<419cd7d4$0$44068$5fc3050@dreader2.news.tiscali.nl>
<4zrnd.46389$QJ3.16198@newssvr21.news.prodigy.com>
<ddEnd.23771$6q2.22891@newssvr14.news.prodigy.com>
<pDc1BAEpHynBFwDy@longley.demon.co.uk>
<207fe873374c584e8a375f35c5b1d9f7.48257@mygate.mailgate.org I
cant see how bringing finite TMs into this
> issue, just because they are practical is useful
> at all. The issue being discussed is not
> practical/physical but theoretical, hypothetical
> and abstract; an idea not a physical thing.
>> Are you sure about that? Are you sure you havent
>> missed the whole point of what the first half of
>> 20th century philosophy and earlier (from Frege to
>> Goedel and beyond) was really all about?
>David, since you have utterly no concept what the
>subject under discussion is (hint philosophy is
>the wrong answer), nor education nor inclination
>ever to understand the subject matter, how about
>learning to hold your peace, rather than riding your
>inane hobby horse to trample roughshod over yet
>another conversation to which you were not invited,
>in which you do not belong, and where all you can do
>is (correctly) portray yourself to be a classic
>boorish dolt?
>HTH
>xanthian.
If you want to restrict your metaphysics to sci.maths,
comp.theory or
misc.misc thats fine by me. But you should 
understand that
computers
per se had very little to do with Turing despite what you
think. We had
computers long before. What Turing and the others did was
provide a
theory of computing. The real histories in life are not all
in the
public domain. Its often deemed not to be in the public
interest.
--
David Longley
===
Subject: Re: Turing Machines and Physical Computation
http://mygate.mailgate.org/mynews/comp/comp.theory/
9397b9e1ec6b19e17df4e66701
f8971d.48257%40mygate.mailgate.org
> If you want to restrict your metaphysics to
> sci.maths, comp.theory or misc.misc thats 
fine by
> me.
Which part of you, David Longley butting into
conversations where you have no credentials to
participate, nor ability to talk about anything
currently being discussed there, was so hard for
you to grasp that the above non sequitur about _my_
choices was your reply?
You are not merely mentally ill, David, but
grievously dysfunctionally mentally ill, and with a
severity more than a match for my own sorry
situation. In my case my illness still leaves me a
contributing member of signal on Usenet, mostly in
comp.ai.genetic, in your case your illness limits
you to being part of the noise factor only,
everywhere I see you posting, everything I see you
post.
Based on the other responses you receive, this seems
to be an all but universally held opinion of you. I
can easily count your fellow travelers on the
fingers of one hand, while your (correct) detractors
number beyond my ability to tally at all.
HTH
xanthian.
--
===
Subject: Re: Turing Machines and Physical Computation
<a8d13dcbdca7ae739b921bb2ba3db48e.48257@mygate.mailgate.org>
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<9397b9e1ec6b19e17df4e66701f8971d.48257@mygate.mailgate.org>
If you want to restrict your metaphysics to
>> sci.maths, comp.theory or misc.misc thats 
fine by
>> me.
>Which part of you, David Longley butting into
>conversations where you have no credentials to
>participate, nor ability to talk about anything
>currently being discussed there, was so hard for
>you to grasp that the above non sequitur about _my_
>choices was your reply?
>You are not merely mentally ill, David, but
>grievously dysfunctionally mentally ill, and with a
>severity more than a match for my own sorry
>situation. In my case my illness still leaves me a
>contributing member of signal on Usenet, mostly in
>comp.ai.genetic, in your case your illness limits
>you to being part of the noise factor only,
>everywhere I see you posting, everything I see you
>post.
>Based on the other responses you receive, this seems
>to be an all but universally held opinion of you. I
>can easily count your fellow travelers on the
>fingers of one hand, while your (correct) detractors
>number beyond my ability to tally at all.
>HTH
>xanthian.
Ah, but note that youre nose-counting like many others, and
thats
not a reliable way to pursue truth. Theres nothing
particularly
pathological in what Im doing here, nor is there what 
Ive
been doing
elsewhere. That you think otherwise is largely a function of
your not
having followed up what I have provided, or acting on other
advice that
I (and others) have given you in the past. In other words,
you wilful
ignorance accounts for your poor grasp of what I have been
doing/saying.
Im explicating something about normal behaviour, not just
delinquent or
pathological behaviour. You should look into the differences
between
rule governed behaviour, and behaviour controlled by other
contingencies - and then think about this thread title.
--
David Longley
===
Subject: Re: Turing Machines and Physical Computation
> If you want to restrict your metaphysics to
> sci.maths, comp.theory or misc.misc thats 
fine by
> me.
>>Which part of you, David Longley butting into
>>conversations where you have no credentials to
>>participate, nor ability to talk about anything
>>currently being discussed there, was so hard for
>>you to grasp that the above non sequitur about _my_
>>choices was your reply?
>>You are not merely mentally ill, David, but
>>grievously dysfunctionally mentally ill, and with a
>>severity more than a match for my own sorry
>>situation. In my case my illness still leaves me a
>>contributing member of signal on Usenet, mostly in
>>comp.ai.genetic, in your case your illness limits
>>you to being part of the noise factor only,
>>everywhere I see you posting, everything I see you
>>post.
>>Based on the other responses you receive, this seems
>>to be an all but universally held opinion of you. I
>>can easily count your fellow travelers on the
>>fingers of one hand, while your (correct) detractors
>>number beyond my ability to tally at all.
>>HTH
>>xanthian.
> Ah, but note that youre nose-counting like many others,
and thats
not
> a reliable way to pursue truth. Theres nothing
particularly pathological
> in what Im doing here, nor is there what 
Ive been doing
elsewhere. That
> you think otherwise is largely a function of your not
having followed up
> what I have provided, or acting on other advice that I (and
others) have
> given you in the past. In other words, you wilful ignorance
accounts for
> your poor grasp of what I have been doing/saying.
> Im explicating something about normal behaviour, not just
delinquent or
> pathological behaviour. You should look into the
differences between
rule
> governed behaviour, and behaviour controlled by other
contingencies -
and
> then think about this thread title.
Think about your own NPD.
> --
> David Longley
===
Subject: Re: More on the simple group of order 168
> I dont see why n_3 != 1 for N(I).
> -----------------
> (some hand-waving and babbling follows)
Again youre making things too hard. n_3 <> 1 for N(I) 
because
we already showed that n_3 = 28 for G, so |N_G(P_3)| = 6, so G
cant have a subgroup of order 24 with a normal subgroup of
order 3.
[...]
--
Jim Heckman
===
Subject: Re: More on the simple group of order 168
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posting-account=jcZk7AwAAADXpPEyHtVyWC264SxtppRB
I seems so obvious when someone else says it.
Clearly if P_3 normal in H, then H < N(P_3), which is
impossible
since |N_G(P_3)| = 6 and |H| = 24, as you say.
That does n = 168. The original problem
was to show that GL(3,2) was this simple group, by looking
at characterictic polynomials, which will require further
study before
I can do it.
Van
===
Subject: Re: More on the simple group of order 168
<10pp3hvhlilbd33@corp.supernews.com>
<10prdejast58lf5@corp.supernews.com>
<10pto3od3jl6vf3@corp.supernews.com>
posting-account=jcZk7AwAAADXpPEyHtVyWC264SxtppRB
I came across the following at a new URL for groups, at
http://www.mathreference.com/grp-fin,g168.html
I post it here since there has been a lot on the simple group
of order
168.
--------------
The Simple Group of Order 168
The simple group of order 168 can be described as a
coliniation on 7
points. Label the points a through g and draw the triangle
efg. Arrange
abcd in a square and draw all 6 connecting edges. Then
complete the
following triangles.
(efg) abe cde acf bdf adg bcg
Thus e joins with 2 segments of the square to make two
triangles, f
joins with two segments, and g joins with two segments,
covering all 6
segments. This graph is drawn for purposes of illustration.
The
coliniation is actually on triangles, not edges. If we were
mapping
edges to edges, the group would be S7. After all, we just
drew a
complete graph on 7 points. we might, for instance, map efg
onto abc.
However, abc is not one of the specified triples in our
coliniation.
The group consists of permutations that carry triples to
triples, as
listed above.
Youll notice a symmetry among triangles. If abe were the 
main
triangle, and cdfg the complete square, e connects to fg and
cd, a
connects to cf and dg, and b connects to df and cg.
Our choice of abe was symbolically arbitrary. Any of the 7
triangles
can act as the primary triangle, with 6 triangles connected
to the
remaining 6 edges. Use this to find the order of the group.
Declare one of the 7 triangles as primary, and map efg onto
that
triangle in 6 different ways. Now, how many ways can we
rearrange the
square? We can swap a for b and c for d, or a for c and b for
d. Thats
a group of order 4. If a remains in position, b must as well,
since
there is no ace or ade triangle. Similarly, c and d are fixed.
Once we
know where a is, the square is established. Thus there are
four ways to
map abcd onto the complete square, once the primary triangle
is
selected. That gives a group of order 7[Times]6[Times]4 = 168.
This group is a permutation group on 7 letters. Its order is
divisible
by 7, so it has an element of order 7, which is a 7 cycle.
Two examples
are: efdagcb and efbcgad. These 7 cycles map triples to
triples, as
listed above, and they are independent of each other. We can
now prove
the group is simple.
Since g is transitive and 7 is prime, we can apply an earlier
theorem.
Thus every normal subgroup h of g contains all the elements
of order 7.
By the third Sylow theorem, the number of subgroups of order
7 is 1 mod
7, and divides 24. We produced two independent 7 cycles, so
there must
be 8 subgroups of order 7. These 8 groups define 48 elements
of order
7, so |h| ñ 49. since |h| divides 168, it is either 84 or
56.
If |h| = 84, then h cannot contain 8 instances of Z7 (third
Sylow
theorem). Thus |h| = 56.
Since h has 8 elements not of order 7, these form the Sylow
subgroup of
order 8 in h. This 8-group does not contain the 7 cycles of
g, and is
not normal in g, hence there are other conjugates of this
8-group
ßoating around, outside of h. Something in g/h has even
order, yet
|g/h| = 3. Therefore the subgroup h cannot exist, and g is a
simple
group.
Sometimes g is presented as a permutation group on 7 letters,
with a
circular shift as a 7 cycle. recall our earlier 7 cycle
efdagcb. Remap
abcdefg to 0356142, and g contains the circular shifts of
0123456. If
you relable the 7 triples, you get 013, 124, 235, 346, 450,
561, and
602. Thus the shift maps triples to triples, as it should.
When we relable the permutations on the abcd square, we get
the
involutions 3210465 and 5126403. It is also possible to swap
f and g,
and c and d. This remaps to 0143265. Verify that these
involutions map
triples to triples, as they should. None of these three
permutations is
a circular shift of another. In fact these three involutions
span a
subgroup of order 8.
Let r be the right circular shift, and let x y and z be our
involutions, given below. Then verify the next three
equations.
x = 0143265
y = 3120465
z = 5126403
rrrrxrrrrrrxrrx = y
rrrrrryrryrr = z
rrrzrzrrrrrzr = x
Any of the involutions, combined with the circular shift,
generates the
other two, and the group of order 8. Furthermore, zrzrr is an
element
of order 3. The group generated by the 7 cycle and any of
these
involutions is divisible by 7, 8, and 3, and is contained in
our simple
coliniation, hence it is the simple group of order 168.
--------
Van
===
Subject: Re: (Possibly) New model of compution
> I dont understand the first 
definition.
you (I was wrong). Anyway, the bug is fixed. Please take
another look at
===
Subject: Re: (Possibly) New model of compution
> I dont understand the first 
definition.
(I was wrong.) I believe that my definitions should now meet
with your
sasatisfaction. Please take another look at the paper. Sorry
if this is a
repost. Im not sure if the first one went 
through or not.
===
Subject: Re: (Possibly) New model of compution
>> I dont understand the first 
definition. You seem to be
defining BT
>> via BT^2. What is BT^2 if not pair of elements from BT?
You could
>> before the formula Section 2 line 2, indicate that b is
representing
>> the colour (or color I suppose in American English) of the
node x.
>> I guess you are trying to use a recursive definition.
> Yes I guess technically i have a circular definition. I
should have said
> let TT be the unique set S such that S={x | etc. }. Im
pretty sure that
> TT can be proven to exist in ZF. Anyway I more or less
think you are
> right. Even if TT does exist and behaves as i think it does
its an
awkward
> formulation. I am going to take your advice and define
things in the
> manner you suggest.
Actually, scratch what I said. I am not that used to actually
properly
defining reccursive sets. Im used to informal 
comp. sci.
textbook type
definitions. Upon reßection, I figure now that 
you were
actually 100%
right. I shouldnt have argued with you i guess but i never
know who im
arguing with on usenet. Anyway thank you very much for the
advice. I do
take advice and i am taking your advice.
===
Subject: Mathworld errors
> I just got an email
> inviting me to send him a list of errors on mathworld.
> I havent saved such a list, thought Id 
mention this
> in case anyone else has.
>Recently, on sci.math, you mentioned:
> <<Well, yes - given that youre the kind of guy people
might tend
>to believe, you might at least include a question mark or
>something...
>(Today must be your first visit to mathworld - 
its really
full of
>errors. I admit this is a good one.)>If you would be so kind
as to send us a list, Eric and I will be
>glad to fix them.
>Ed Pegg Jr
>MathWorld Associate
> ************************
> David C. Ullrich
If Eric invited/requested NG directly by posting here reg.
errors,lists...
===
Subject: Re: Mathworld errors
contd..
Two simple examples. For CornuSpiral Ces.88ro intrinsic
equation rho =
c^2/s,c is neither shown in figure nor explained,(as origin to
pole
coordinates along x- or y- ). The detail of KuenSurface
endings appear
distressingly conical due to a too coarse 3D parameter choice
when it
should be seem to be having a negative Gauss Curvature.
===
Subject: Re: Mathworld errors
Ive found these quotes about mathworld.
:mathworld has also blunders in basic combinatorics, etc.
...
:For instance, look at the page about permanent of a matrix.
:The closed formula for computing it is plain wrong!!!
:When I mentioned that mathworld does not give a
:single example of a T1 space which does not satisfy
....
in response to my question ropestretcher spotted another typo:
> http://mathworld.wolfram.com/UniversalSpace.html
> How can we compute minimal d?
> There seems to be a typo in the cited page - a metric
> on R is a certain mapping of R x R to the nonnegative
> reals, not a real number itself. In any event, it is
> unlikely that there is a minimal d in any reasonable
> sense of minimal because scaling a metric yields a
> metric.
...
There are probably other things in theory-edge. They should
look
themselves on individual math/theory forums on the web. They
can ask,
too. Its going to take their time, but its 
probably worth
it. They
can also put some bounties for errors on mathworld, in which
case
theyre going to see a huge list of legitimate errors in
their inbox.
(Now, I claim mine with this post :P )
--
Eray
===
Subject: Re: Mathworld errors
> I just got an email
> inviting me to send him a list of errors on mathworld.
> I havent saved such a list, thought Id 
mention this
> in case anyone else has.
We had spotted some on theory-edge, too, but its so hard to
tell. I
believe Id tried to convince some people to report to
mathworld, but
they said the copyright terms were not good. Google is
mathworlds
friend of course.
On theory-edge they must have a look at the following threads:
Metric question
t1 property
mathworld
post #9215
And probably other places as well, but these would be good
places to
start. Google does not seem to index theory-edge archives for
some
reason. At any rate... Hope this helps Ed.
--
Eray Ozkural
===
Subject: Re: Mathworld errors
Originator: harris@tcs.inf.tu-dresden.de (Mitchell Harris)
>I believe Id tried to convince some people to report to
mathworld, but
>they said the copyright terms were not good.
What do copyright terms have to do with reporting errors?
>Google is mathworlds friend of course.
How is that?
Mitch
===
Subject: Re: Mathworld errors
>I believe Id tried to convince some people to report to
mathworld, but
>they said the copyright terms were not good.
> What do copyright terms have to do with reporting errors?
Youll have to find those threads that I 
mentioned on
theory-edge to
see the arguments of those people. I dont know exactly.
>Google is mathworlds friend of course.
> How is that?
They can search for discussions mentioning mathworld errors.
--
Eray Ozkural
===
Subject: Re: Are Hilberts Axioms independent?
|One feature of Hilberts book is that the axioms are not
first order
|axioms. So, the completeness theorem for first order logic
doesnt apply
|and it is at least conceivable that even if one axiom is
independent of
|the others, there might not exist a model in which it is
false. There
|might exist a model of set theory in which there is a model
of geometry
|in which it is false, but that is a much bigger problem than
one normally
|expects to have to deal with in confronting independence of
axioms for
|geometry.
I dont think its customary to use the term 
independent to
mean
what youre using it to mean, for second-order axioms.
Second-order logic has an associated satisfaction relationship
between sentences and structures. We can define a consequence
relation between sets of sentences and sentences by saying
that
a sentence A is a consequence of a family {B_i} of sentences
if
every structure satisfying all of the B_i also satisfies A.
Trivially,
if one of the axioms is a consequence in this sense of the
others
then it can be omitted without affecting which structures
satisfy
the axioms and conversely.
The failure of the compleness theorem to apply means that
there
isnt a formal deductive system for second-order logic that
suffices to deduce all the consequences of an arbitrary set
of second-order axioms. As far as I know, in fact, there is no
formal deductive system that is treated as standard for it.
Consequently I would assume that there is no canonical
notion of this sentence cannot be deduced in the canonical
way from these other sentences, as distinct from this
sentence is satisfied in all the structures where these other
sentences are satisfied.
It appears that you mean by independent that an axiom
cannot be deduced (or refuted) from the remaining axioms
in (some kind of) set theory. Its true that this entails
only that
there exists a model of that kind of set theory in which there
is a structure satisfying the remaining axioms but not
satisfying
the independent one. But, correct me if I am wrong, I dont
think the term independent is ordinarily used for that.
|Incidentally, Marvin Greenbergs book on non-euclidean
geometry makes
|a fundamental mistake on this point and I think that greatly
impairs its
|usefulness as a textbook, in spite of its many admirable
features.
|Specifically, he claims that because of the Godel
completeness theorem,
|one is entitled to have a model of non-Euclidean geometry,
including the
|continuity axiom, if it is consistent, and organizes a
certain amount of
|the presentation around the belief that is true. Maybe this
problem was
|fixed in a later edition, but Im not aware of 
it.
Thats too bad! If he meant to claim that the parallel
axiom[*] is not a
consequence of the others in the sense I defined above, then
its
tautological to say that there are non-Euclidean geometries;
to show
that there are non-Euclidean geometries is what one would
need to
do to prove that the parallel axiom is not a consequence of
the
other axioms. The Goedel completeness theorem doesnt enter
into it.
It seems like sort of an odd statement anyway. Even if it
were only
a question of the first-order axioms, the easiest way to show
that
there is no proof (in a standard deductive system for
first-order logic)
of the parallel axiom[*] from the remaining axioms is to
exhibit a
model, isnt it?
[*] Or whatever distinguishes Euclidean from non-Euclidean in
his system.
Keith Ramsay
===
Subject: Most Distorted Triangle
> Is there a most scalene/ asymmetric/distorted triangle,
most remote
> from the equilateral triangle? If so, what may be a proper
criterion
> or definition of asymmetry?
> . . .
Yes there is. Squared lengths ratios are:
1 : 4+sqrt(15) : (5+sqrt(15))/2
Theory, criterion, etc..: see my web site.
Michel Petitjean, Email: petitjean@itodys.jussieu.fr
ITODYS (CNRS, UMR 7086) ptitjean@ccr.jussieu.fr
http://petitjeanmichel.free.fr/itoweb.petitjean.html
===
Subject: Re: How to apply a filter on raw data...
It sounds like an cellular automata like
a Majority function used in image processing
might be your answer.
There also several edge finder algorithms of this type as 
well.
you get the idea):
http://www.nd.edu/~mtns/papers/17761_4.pdf
>Hallo to everyone,
>Im trying for the last 2 weeks to find a way 
to apply a
filter on raw
>data. The raw data consists of matrices with surface
topography
>values. For example I have a matrix R with size(R) = [512
512] and I
>want to apply a filter in order to find the low 
pass component
>surface and the high-pass component surface. I have tried
with
>matlab using the commands filter2, conv2, but frankly
speaking, this
>is the first time I have to use such methods and I have no
experiance
>whatsoever of what to expect as a result... Can someone here
help
>me... It would really help if someone could explain to me
what to do
>in order to do the filtering. Im using the 
gauss (normal)
>distribution as a filter. If anyone is interested I can send
the
>matlab program.
>Yannis
--
Respectfully, Roger L. Bagula
tftn@earthlink.net, 11759Waterhill Road, Lakeside,Ca
92040-2905,tel:
619-5610814 :
alternative email: rlbtftn@netscape.net
URL : http://home.earthlink.net/~tftn
===
Subject: Re: How to apply a filter on raw data...
Hallo Roger,
thank you very much for your answer. I dont think is what 
you
suggest, is what I need. All I need is someone to tell me the
necessery steps taken in order to do a succesfull filtering of
raw
data concerning the topography of a surface. I have no idea
what to do
with edge finding algorithms...
Bye
Yannis
> It sounds like an cellular automata like
> a Majority function used in image processing
> might be your answer.
> There also several edge finder algorithms of this type as
well.
> you get the idea):
> http://www.nd.edu/~mtns/papers/17761_4.pdf
>Hallo to everyone,
>Im trying for the last 2 weeks to find a way 
to apply a
filter on raw
>data. The raw data consists of matrices with surface
topography
>values. For example I have a matrix R with size(R) = [512
512] and I
>want to apply a filter in order to find the low 
pass component
>surface and the high-pass component surface. I have tried
with
>matlab using the commands filter2, conv2, but frankly
speaking, this
>is the first time I have to use such methods and I have no
experiance
>whatsoever of what to expect as a result... Can someone here
help
>me... It would really help if someone could explain to me
what to do
>in order to do the filtering. Im using the 
gauss (normal)
>distribution as a filter. If anyone is interested I can send
the
>matlab program.
>Yannis
>
===
Subject: Re: Derivative of maximum eigenvalue of a matrix.
Sir, thank you very much. You gave me a very good idea to
solve this.
===
Subject: Re: hard matrix inversion...
> Okay, so for these kind of special matrices, it is good to
plug in Matlab
> and find some special cases for n is small, etc...
Yes, thats a good way to find patterns. I 
believe thats how
Euler did
it, but, umm, Im not a math historian.
> But to prove the pattern in general?
> It seems to me the proof of the inverse matrix has some
pattern is very
> difficult? Maybe use induction on matrix inversion? Not sure
how to do
> induction on matrix inversion?
> Maybe I can divide a matrix into
> [A B
> C D]
> where A is a sub-matrix, D is just 1x1 element, I am not
sure what is the
> inversion of the above block matrices in terms of A B C D?
Are you familiar with The Simpsons? You know how Homer often
whacks
his
forehead and says Dohh!? Get ready to do that.
A good way to prove that some matrix B is the inverse of a
matrix A is to
show that BA = I.
There is a principle here which is applicable to other
branches of math.
For example, if youre asked to show that y=e^x is a 
solution
to dy/dx = y,
your first thought should not be Hmmm, should I solve it as a
separable
or
as a linear equation?
===
Subject: Re: hard matrix inversion...
>Also, Det(a) = (1-a^2)^n, but the eigenvalues and
eigenvectors do not
>simplify to anything nice. (The characteristic polynomial
seems to
>have a nice pattern though.)
> The characteristic polynomial P(t) = Det(A-tI) seems to
always factor as
> a product of two polynomials whose degrees are either n/2
and n/2 (if n
is
> even) or (n-1)/2 and (n+1)/2 (if n is odd). In the even
case, one
> polynomial is obtained from the other by the substitution a
-> -a.
> In the odd case, both factors contain only even powers of a.
> Otherwise I dont quite see the pattern.
I dont quite see the pattern either, but I a can smell it.
If you look
at it like this (i.e., essentially this just divides out
factors of (1-a^2)
from the coefficients of the characteristic polynomial)
p[n_] := Det[Table[a^Abs[i-j], {i,0,n}, {j,0,n}] -
t IdentityMatrix[n+1]];
q[n_] := Factor /@ (Take[CoefficientList[p[n], t], n+1] /
Table[(-1)^i(1-a^2)^(n-i), {i,0,n}]);
r[n_] := Table[Coefficient[q[n][[j]],a,2k], {j,n+1}, {k,0,n}]
//
MatrixForm;
you get this:
In[1]:= r[6]
Out[1]=
1 0 0 0 0 0 0
7 5 0 0 0 0 0
21 24 10 0 0 0 0
35 45 30 10 0 0 0
35 40 30 16 5 0 0
21 15 10 6 3 1 0
7 0 0 0 0 0 0
There are familiar patterns on various rows, columns and
diagonals.
The real kicker is that, as far as I can tell, no coefficient
is ever
divisible by a prime factor > n+1. So I think there must be a
simple
formula. I havent found it, though.
-Jim Ferry
===
Subject: Counterexample to t( (c^n - a^n) mod b ) | phi(b)
I have located a counterexample to the seemingly obvious
assertion that
since
the component pure exponential generators
(c^n) mod b and (a^n) mod b
in the dual subtractive exponential generator with
gcd(a,b,c)=1 and
a<b<c<a+b
(c^n - b^n) mod b
have periods that divide phi(b), it must be true that the
period of the
dual
generator also divides phi(b).
The counterexample is a=5,b=6, c=7. ph(b)=3 and
t( (c^n - a^n) mod b ) = 2.
I have more counterexamples if needed.
Can any of you here verify this? Only one counterexample is
needed.
And can anyone say roughly *how* counterintuitive this is? It
cant be
novel,
can it?
In thread Perky People Prefer Pure Pseudorandom Periodicity
we explored
the
periods of such generators and associated sequences.
Strictly, it is the
sequence that has a period, not the generator. With this
counterexample,
the
notion that the dual additive and two dual subtractive
exponential
congruential
sequences associated with a^n + b^n = c^n are purely periodic
is called
into
question, but not directly. That linear congruential
sequences are
ultimately
periodic is well established. And that pure multiplicative
congruential
generators are a special case of the linear generator is
clear. Likewise,
pure
exponential congruential generators are a special case of
multiplicative
generators. But these dual generator, they are intriguing.
I have been able to determine, with good help from first I. M.
Davidson,
here
in sci.math, in thread A fairly simple proposition, then
Keith Lewis,
that
for gcd(a,b,c)=1 and a<b<c<a+b, not only is Davidsons 
result
c-a !== 0 mod b / c-b !== 0 mod a is true, but Lewiss
stronger
c-a !== 0 mod b & c-b !== 0 mod a is also true.
What this means is that
a^n + b^n = c^n --> n has a factor of two or more,
contradicting n=p, but you see, I dont really understand
n=p, I just sort
of
follow that if a^mp+ b^mp=c^mp that of course
(a^m)^p+(b^m)^p=(c^m)^p.
please, do so and write here.
Certainly it is obvious to me that if gcd(a,b,c)=1 then
gcd(a^m, b^m, c^m) =1. That much is clear.
I tolerance everything and tolerate everyone.
I love: Dona, Jeff, Kim, Kimmie, Mom, Neelix, Tasha, and Teri,
alphabetically.
I drive: A double-step Thunderbolt with 657% range.
I fight terrorism by: Using less gasoline.
===
Subject: Re: Counterexample to t( (c^n - a^n) mod b ) | phi(b)
> I have located a counterexample to the seemingly obvious
assertion that
since
> the component pure exponential generators
> (c^n) mod b and (a^n) mod b
> in the dual subtractive exponential generator with
gcd(a,b,c)=1 and
a<b<c<a+b
> (c^n - b^n) mod b
> have periods that divide phi(b), it must be true that the
period of the
dual
> generator also divides phi(b).
> The counterexample is a=5,b=6, c=7. ph(b)=3 and
> t( (c^n - a^n) mod b ) = 2.
> I have more counterexamples if needed.
phi(b) = 2.
--
... one Marine noticed one of the prisoners was still
breathing. A Marine
can be heard saying on the pool footage provided to Reuters
Television:
Hes ing faking hes dead. He faking 
hes ing dead.
The Marine then raises his riße and fires into the 
mans head.
The pictures are too graphic for us to broadcast, Sites said.
===
Subject: Re: Counterexample to t( (c^n - a^n) mod b ) | phi(b)
phi(6)=2 (5 and 1 do not divide 6)
error in function phi(n) in Mathcad document cf NB times NA,
N = 1.mcd.
Its written correctly. My other group is reminding me I am
writing a bit
stressed. ÔTil after the holiday, then.
I tolerance everything and tolerate everyone.
I love: Dona, Jeff, Kim, Kimmie, Mom, Neelix, Tasha, and Teri,
alphabetically.
I drive: A double-step Thunderbolt with 657% range.
I fight terrorism by: Using less gasoline.
===
Subject: Re: Counterexample to t( (c^n - a^n) mod b ) | phi(b)
>phi(6)=2 (5 and 1 do not divide 6)
Neither does 4.
I just misspelled ph(b)=3, it wasnt calculated correctly.
So does the period of (c^n-a^n) mod b divide phi(b) or
doesnt it?
I say it doesnt always divide phi(b).
I tolerance everything and tolerate everyone.
I love: Dona, Jeff, Kim, Kimmie, Mom, Neelix, Tasha, and Teri,
alphabetically.
I drive: A double-step Thunderbolt with 657% range.
I fight terrorism by: Using less gasoline.
===
Subject: Re: Counterexample to t( (c^n - a^n) mod b ) | phi(b)
>phi(6)=2 (5 and 1 do not divide 6)
> Neither does 4.
> I just misspelled ph(b)=3, it wasnt calculated correctly.
> So does the period of (c^n-a^n) mod b divide phi(b) or
doesnt it?
> I say it doesnt always divide phi(b).
I say youre wrong.
c^(n+phi(b)) - c^n is a multiple of b (for sufficiently large
n in the
case that gcd(b,c) > 1). The same is true of a^(n+phi(b)) -
a^n.
Therefore (c^(n+phi(b)) - a^(n+phi(b))) - (c^n - a^n) is a
multiple of
b.
Therefore (c^(n+phi(b)) - a^(n+phi(b))) mod b = (c^n - a^n)
mod b
If that doesnt establish that the period of (c^n - a^n) mod
b is a
factor of phi(b), what does?
--
Daniel W. Johnson
panoptes@iquest.net
http://members.iquest.net/~panoptes/
039 53 36 N / 086 11 55 W
===
Subject: Re: Counterexample to t( (c^n - a^n) mod b ) | phi(b)
>c^(n+phi(b)) - c^n is a multiple of b (for sufficiently large
n in the
>case that gcd(b,c) > 1).
This seems to be a misapplication of Eulers totient 
theorem,
that for
relatively prime a and n
a^(phi(n)) == 1 mod n
Is it?
We dont need to consider the case gcd(b,c)>1. gcd(a,b,c)=1
is given in the
OP
to this thread.
Given b | c^(n+phi(b))-c^n, what you say would be true.
Whence cometh this
assertion? Its as if you are implying
c^(n+phi(b)) - c^n = c^(phi(b))
and we know this cant be true because while subtraction is
associative
under
multiplication, it is not associative under exponentiation.
The counter example a,b,c = 5,6,7 shows that the period of
c^n - a^n (mod b)
does not necessarily divide phi(b).
>The same is true of a^(n+phi(b)) - a^n.
>Therefore (c^(n+phi(b)) - a^(n+phi(b))) - (c^n - a^n) is a
multiple of
>Therefore (c^(n+phi(b)) - a^(n+phi(b))) mod b = (c^n - a^n)
mod b
>If that doesnt establish that the period of (c^n - a^n) 
mod
b is a
>factor of phi(b), what does?
Nothing does. I argued the same way to myself, that the
period of the
component
exponential generators c^n mod b and a^n mod b | phi(b), and
so t(c^n - a^n
(mod b)) | phi(b). It simply isnt true. Yes, 0-0=0, but for
some other n, b
|
c^n - a^n. Theres no reason these two powers 
cant combine
with
subtraction
because subtraction doesnt associate with exponentiation.
(cn - an) = (c-a)n but
(c^n - a^n) != (c-a)^n
multiplication does associate with exponentation:
(c^n * a^n) = (ca)^n
thats what makes FLT such a hard nut to crack.
I tolerance everything and tolerate everyone.
I love: Dona, Jeff, Kim, Kimmie, Mom, Neelix, Tasha, and Teri,
alphabetically.
I drive: A double-step Thunderbolt with 657% range.
I fight terrorism by: Using less gasoline.
===
Subject: Re: Counterexample to t( (c^n - a^n) mod b ) | phi(b)
>c^(n+phi(b)) - c^n is a multiple of b (for sufficiently large
n in the
>case that gcd(b,c) > 1).
> This seems to be a misapplication of Eulers totient
theorem, that for
> relatively prime a and n
> a^(phi(n)) == 1 mod n
> Is it?
> We dont need to consider the case gcd(b,c)>1. 
gcd(a,b,c)=1
is given in
the OP
> to this thread.
Right. You gave gcd(a,b,c)=1. You did not give
gcd(a,b)=gcd(a,c)=gcd(b,c)=1. Consider a=6, b=10, c=15. Then
gcd(b,c)=5 but gcd(a,b,c)=1.
> Given b | c^(n+phi(b))-c^n, what you say would be true.
Whence cometh
this
> assertion? Its as if you are implying
> c^(n+phi(b)) - c^n = c^(phi(b))
No. Eulers totient theorem gives us b | c^(phi(b)) - 1
Since c^(n+phi(b))-c^n = c^n*(c^(phi(b)) - 1), the result is
immediate.
> The counter example a,b,c = 5,6,7 shows that the period of
> c^n - a^n (mod b)
> does not necessarily divide phi(b).
Thats not a counterexample, as has already been pointed out
to you.
7^n - 5^n (mod 6) is 0 for even n and 2 for odd n. Thats
periodic with
a period of 2, just like 5^n mod 6, and 2 divides phi(6) = 2.
(7^n mod
6 actually has a period of 1.)
>The same is true of a^(n+phi(b)) - a^n.
>Therefore (c^(n+phi(b)) - a^(n+phi(b))) - (c^n - a^n) is a
multiple of
>b.
>Therefore (c^(n+phi(b)) - a^(n+phi(b))) mod b = (c^n - a^n)
mod b
>If that doesnt establish that the period of (c^n - a^n) 
mod
b is a
>factor of phi(b), what does?
> Nothing does. I argued the same way to myself, that the
period of the
> component exponential generators c^n mod b and a^n mod b |
phi(b), and so
> t(c^n - a^n (mod b)) | phi(b). It simply isnt true. Yes,
0-0=0, but for
> some other n, b | c^n - a^n. Theres no reason these two
powers cant
> combine with subtraction because subtraction doesnt
associate with
> exponentiation.
> (cn - an) = (c-a)n but
> (c^n - a^n) != (c-a)^n
> multiplication does associate with exponentation:
> (c^n * a^n) = (ca)^n
Multiplication does distribute over subtraction, which is all
that
matters.
More generally, suppose f(n) and g(n) both have periods that
divide k.
In other words, f(n+k) - f(n) and g(n+k) - f(n) are 0 for all
n. In
this case, f(n) = c^n mod b and g(n) = a^n mod b, and the
period k is
phi(b). Define h(n) = f(n) - g(n). We then have, for all n:
h(n+k) - h(n) = (f(n+k) - g(n+k)) - (f(n) - g(n))
= f(n+k) - f(n) - g(n+k) + g(n)
= (f(n+k) - f(n)) - (g(n+k) - g(n))
= 0 - 0
= 0
Q.E.D.
--
Daniel W. Johnson
panoptes@iquest.net
http://members.iquest.net/~panoptes/
039 53 36 N / 086 11 55 W
===
Subject: Re: Counterexample to t( (c^n - a^n) mod b ) | phi(b)
>phi(6)=2 (5 and 1 do not divide 6)
> Neither does 4.
> I just misspelled ph(b)=3, it wasnt calculated correctly.
> So does the period of (c^n-a^n) mod b divide phi(b) or
doesnt it?
> I say it doesnt always divide phi(b).
Dont just say, prove.
(17:38) gp > for(a=0,5,for(b=0,5,print1(a b :
);for(n=1,6,print1(
(a^n-b^n)%6));print()))
0 0 : 0 0 0 0 0 0
0 1 : 5 5 5 5 5 5
0 2 : 4 2 4 2 4 2
0 3 : 3 3 3 3 3 3
0 4 : 2 2 2 2 2 2
0 5 : 1 5 1 5 1 5
1 0 : 1 1 1 1 1 1
1 1 : 0 0 0 0 0 0
1 2 : 5 3 5 3 5 3
1 3 : 4 4 4 4 4 4
1 4 : 3 3 3 3 3 3
1 5 : 2 0 2 0 2 0
2 0 : 2 4 2 4 2 4
2 1 : 1 3 1 3 1 3
2 2 : 0 0 0 0 0 0
2 3 : 5 1 5 1 5 1
2 4 : 4 0 4 0 4 0
2 5 : 3 3 3 3 3 3
3 0 : 3 3 3 3 3 3
3 1 : 2 2 2 2 2 2
3 2 : 1 5 1 5 1 5
3 3 : 0 0 0 0 0 0
3 4 : 5 5 5 5 5 5
3 5 : 4 2 4 2 4 2
4 0 : 4 4 4 4 4 4
4 1 : 3 3 3 3 3 3
4 2 : 2 0 2 0 2 0
4 3 : 1 1 1 1 1 1
4 4 : 0 0 0 0 0 0
4 5 : 5 3 5 3 5 3
5 0 : 5 1 5 1 5 1
5 1 : 4 0 4 0 4 0
5 2 : 3 3 3 3 3 3
5 3 : 2 4 2 4 2 4
5 4 : 1 3 1 3 1 3
5 5 : 0 0 0 0 0 0
Either constant (period 1) or alternating (period 2).
Phil
--
... one Marine noticed one of the prisoners was still
breathing. A Marine
can be heard saying on the pool footage provided to Reuters
Television:
Hes ing faking hes dead. He faking 
hes ing dead.
The Marine then raises his riße and fires into the 
mans head.
The pictures are too graphic for us to broadcast, Sites said.
===
Subject: Re: Counterexample to t( (c^n - a^n) mod b ) | phi(b)
>Dont just say, prove.
Good advice.
a b c (c^n - a^n) mod b
5 6 7 0 2 0 2 0 2...
period is two (2).
The totatives of b=6 are 1, 4, and 5. 1 has no factor and can
have no factor
in
common with 6. phi(6) = 3.
The period of the dual subtractive exponential generator with
gcd(a,b,c)=1
and
a<b<c<a+b
(c^n - a^n) mod b
does not always divide the phi of its corresponding base.
I tolerance everything and tolerate everyone.
I love: Dona, Jeff, Kim, Kimmie, Mom, Neelix, Tasha, and Teri,
alphabetically.
I drive: A double-step Thunderbolt with 657% range.
I fight terrorism by: Using less gasoline.
===
Subject: Re: Counterexample to t( (c^n - a^n) mod b ) | phi(b)
Doug Goncz <dgoncz@aol.com> blithered:
>Dont just say, prove.
> Good advice.
> a b c (c^n - a^n) mod b
> 5 6 7 0 2 0 2 0 2...
> period is two (2).
> The totatives of b=6 are 1, 4, and 5. 1 has no factor and
can have no
> factor in common with 6. phi(6) = 3.
gcd(4,6) = 2 > 1. 4 is not a totative of 6.
So, what is 5^phi(6) mod 6 ?
--
Daniel W. Johnson
panoptes@iquest.net
http://members.iquest.net/~panoptes/
039 53 36 N / 086 11 55 W
===
Subject: Re: new twist to the Crossover Technique of the
VonNeumann
Gametheory in
playing StockMarket; BCE, SBC, drug companies
I did not talk about the new twist very much. So let me
detail it further.
When I started the PAF portfolio in October of 2002 I was
immediately
challenged with a Crossover technique applied to Verizon and
Wyeth. If my
memory serves me correctly, these two stocks were in the
general price
range of about $32 to $35 a share and one day Wyeth would be
32 and Verizon
be 35 and a couple of weeks later VZ be 32 and Wyeth be 35
allowing me to
sell one and buy the other and gain in total number of shares
and this
switching campaign lasted for several months. In every switch
Crossover,
the extra shares are like getting something for free (before
taxes of
course).
Then I remember the switching Crossover campaign between BMY
and SBC and
that lasted for several months.
But the trouble is that the Crossovers last only brießy
before one partner
of a switching campaign zooms ahead and stays ahead for years
at a time.
One of the very best examples of Crossover Switching
Campaigns for the last
5 years has been SBC and BLS. In fact if I were forced to
stick to just 2
stocks to run the switching for the 1990s and up to 2005 it
would have
probably, no doubt, been SBC and BLS. For most of 1990s SBC
has been priced
above BLS but around 2001 and thereafter BLS has traded about
1 to 2
dollars higher than SBC. Today SBC is about $26.50 and BLS is
about $28.
So an astute Crossover Switch player could have just profited
both in terms
of increasing number of total shares in the portfolio by
taking advantage
of price discrepancies between SBC and BLS but also increased
in terms of
extra cash in the switches as well as happy over the steady
dividends every
3 months.
But again the main trouble with Crossover Switches is that
they come few
and far between. I remember the Crossover of Verizon to SBC
way back years
ago. Verizon usually trades about $10 premium above SBC but
many years ago
there was a union strike at VZ to where its price dropped
below that of
SBC. In those days VZ and SBC were trading around 40 to 52
dollars per
share and VZ dropped to around 44 and SBC kept rising to over
52. So that
was a glorious Crossover to have made.
Then again, I probably should be trading less in the
portfolio and just sit
back and wait for years to move by and then jump in with a
crossover such
as VZ to SBC when they Crossover in a big manner.
But the new twist that I have recently learned is that of
applying the
Crossover not just to 2 companies such as Wyeth to VZ or BMY
to SBC or BLS
to SBC. Instead, apply the Crossover to 1 company and to cash.
If you watch stocks as much as I do, that is track them for
every day for
years at a time or even decades then, we trackers or fellow
trackers, soon
develop a sense of the price going too high for what it is
worth. Not only
the stocks we track but other stocks such as for example does
anyone really
believe that Microsoft is worth over 300 billion in
capitalization or does
anyone really believe Pfizer should be worth nearly 300
billion in
capitalization when its brethren of Merck fell to 60 billion
with one
fiasco of Vioxx. Does anyone really believe that Lipitor and
Celebrex is
worth 300 billion in capitalization when Sanofi has a drug
that promises to
lose weight as well as reduce cholesterol.
So what I am saying is that playing the Crossover, such as
yesterday there
was a clearcut crossover of BCE with BMY in that BCE was
trading at 24.30
and BMY was trading at 24.15 and that was the first Crossover
of BCE to BMY
in the last 3 or 4 or 5 or even more years. Perhaps I should
have taken
advantage of that Crossover and sold some BCE to buy BMY but
I doubt it
because the entire drug industry is clouded by Vioxx.
So the new partner to Crossover Switching is Cash. Where I
feel a company
has gone ahead too fast and too steep of a price that I sell
a chunk and
sit in cash for days or several weeks and then hopefully buy
back the same
company at a more reasonable price. For instance, Verizon is
overpriced and
so is Microsoft and so was the oil companies during the
recent run up in
oil where it went over $50 a barrel.
So I need to augment the clearcut Crossover of say company A
going higher
than company B and weeks later Company B going higher than
Company A and
switching back having profited with more shares than
originally. Augment
that Crossover with Company X and cash. So if I feel Company
X has priced
itself too high, then sell a chunk, sit back and wait and
hopefully it
drops enough in price to rebuy and profit with more shares
plus cash
extras.
So the new twist is to augment the Crossover Switch Campaign
with Company X
and cash alongside the clearcut Crossover Switch Campaign
between Company A
and Company B.
Archimedes Plutonium
www.iw.net/~a_plutonium
whole entire Universe is just one big atom where dots
of the electron-dot-cloud are galaxies
===
Subject: Re: a question on continuous functions, please
help...
at 01:40 PM, kinki_best@hotmail.com (mindy) said:
>Let f: R-> R be continuous on R. Given a,b in R, a=<b,
consider the
>set A = {x in R: a =< f(x) =< b}. Show that if (x_1, x_2,
x_3,...)
>is a sequence in A that converges to a number x, then x lies
in A.
>My thoughts: Since f is continuous on R, (x_1, x_2, x_3,....)
>converges to x implies (f(x_1), f(x_2), f(x_3),...)
converges to
>f(x). Then I have no idea what to do next. Please enlighten.
Apply the Triangle Inequality and the definiyion of
convergence.
--
Shmuel (Seymour J.) Metz, SysProg and JOAT
<http://patriot.net/~shmuel>
Unsolicited bulk E-mail subject to legal action. I reserve the
right to publicly post or ridicule any abusive E-mail. Reply
to
domain Patriot dot net user shmuel+news to contact me. Do not
===
Subject: Re: Predicting the Stockmarket throughout the 21st
century
> You need to read from the wise book that says that when
someone is
> working on
> an idea that the wise person looks for true bits and
pieces. Whereas
the
> dumb
> guy jumps into the discussion with attack, attack and
attack.
> Looking at a rise in population as the development of
modern civilization
is
> interesting.
> But China is developing into a middle-class society while
controlling
> population. India is just as smart and a thousand years
from now Africa
may
> be developing into a middle-class society. So this is an
idea of the
> development of existing populations...
> Economics is a major discipline with multiple levels of
fundamentals. The
> fundamentals truly coorelate and fail to truly coorelate
all over the map.
I
> just mention productivity, development of new technology,
and development
of
> existing populations.
Well I am thinking that a Barrier Concept exists for the
StockMarket. We
know
and agree that oil is finite so there is a barrier to oil in
that once we
find
the last of it and use it up, we have to make it artificially.
We know that
human population is finite and that once we fill 
this planet
there comes a
moment where we cannot add one more single person. We know
that gold on
Earth
is finite and that it is neither created or destroyed (in
practice) and so
gold
and oil and number of humans is finite and have a barrier.
But now let us look at the StockMarket. Is it infinite? Does
it have no
barrier? Is it different from oil from gold and from the
number of humans?
Those questions suggest to me that the StockMarket is just a
passing
phenomenon. I would not call it a fade of history for it is
stronger than a
passing fade or trend. It certainly has its mark on history
but I suspect
that
in a few future centuries from now that the StockMarket will
be nothing that
we
recognize today.
I suspect that the Bond Market of today will be the
StockMarket of the
future.
And that the StockMarket we recognize today will have become
defunct.
Because in a sense, the reason you have a 10 fold increase in
DJIA, and a
10
fold increase in price of gold and a 10 fold increase in
human population
from
day in work and someone in New York City raking in $1 million
per day from
trading stocks. The poorness of billions of humans is at the
expense of a
few
who simply lavish in riches and do nothing but place a trade
order and rake
in
millions.
The reason DJIA went 10 times and gold went 10 times is
because human
population went 10 times over that period of history. But the
spread of
that
of Africa, Asia, South America payed the price. The
StockMarket is an avenue
of
siphoning off the wealth of continents and placing it into
the hands of a
few.
In that sense, the StockMarket of today is doomed to become
something
unrecognizable in future centuries.
We see it already in GlobalWarming that we cannot increase
human population.
We
see it in the fact that today it was announced that 10,000
species
including
sharks, turtles, fir trees, frogs are going extinct.
The StockMarket as set up today increases GlobalWarming.
Increases human
overpopulation. Increases extinctions of species.
Archimedes Plutonium
www.iw.net/~a_plutonium
whole entire Universe is just one big atom where dots
of the electron-dot-cloud are galaxies
===
Subject: help! a probablilty problem about ßipping coins...
Suppose we ßip a unfair coin with prob. p it is head, with
prob. 1-p it is
tail.
So the prob. of head is p, a prior probablity.
I ßip the coin N times,
what is the a posterprior prob. of head if I know that there
are at least K
heads? i.e. given at least K heads?
what is the prob. of getting M heads out of these N ßippings
given at least
K heads occurred?
===
Subject: Re: help! a probablilty problem about ßipping
coins...
> So the prob. of head is p, a prior probablity.
Note that typically we apply the term prior in a different
sense. It is a probability density function of the possible
values
of some unknown parameter.
If in this case the parameter is Pr(H), then our knowledge
that
Pr(H) = p can be expressed as a prior pdf over the possible
values of this probability: f(w) = delta(w-p) .
Back to the problem now. If we are unshakeably sure about the
value of Pr(H) (as you assume) then we cannot learn anything
from
the data.
~ George Kahrimanis
===
Subject: Re: help! a probablilty problem about ßipping
coins...
>> So the prob. of head is p, a prior probablity.
> Note that typically we apply the term prior in a different
> sense. It is a probability density function of the possible
values
> of some unknown parameter.
> If in this case the parameter is Pr(H), then our knowledge
that
> Pr(H) = p can be expressed as a prior pdf over the possible
> values of this probability: f(w) = delta(w-p) .
> Back to the problem now. If we are unshakeably sure about
the
> value of Pr(H) (as you assume) then we cannot learn
anything from
> the data.
> ~ George Kahrimanis
What if the bias P is a random variable and we dont know 
P...
So from data -- given that at least K ßips are heads -- ...
we should learn
something about P...
===
Subject: Re: help! a probablilty problem about ßipping
coins...
>So the prob. of head is p, a prior probablity.
>>Note that typically we apply the term prior in a different
>>sense. It is a probability density function of the possible
values
>>of some unknown parameter.
>>If in this case the parameter is Pr(H), then our knowledge
that
>>Pr(H) = p can be expressed as a prior pdf over the possible
>>values of this probability: f(w) = delta(w-p) .
>>Back to the problem now. If we are unshakeably sure about
the
>>value of Pr(H) (as you assume) then we cannot learn
anything from
>>the data.
>>~ George Kahrimanis
> What if the bias P is a random variable and we dont know
P...
> So from data -- given that at least K ßips are heads -- ...
we should
learn
> something about P...
This should be covered in any basic book on Bayesian
analysis: if you
knew that exactly K ßips were heads, then it would be about
the
simplest example of using Bayesian probability as a model of
learning.
The rest is just mathematics.
Bob
--
Bob OHara
Dept. of Mathematics and Statistics
P.O. Box 68 (Gustaf H.84llstr.94min katu 2b)
FIN-00014 University of Helsinki
Finland
Telephone: +358-9-191 51479
Mobile: +358 50 599 0540
Fax: +358-9-191 51400
WWW: http://www.RNI.Helsinki.FI/~boh/
Journal of Negative Results - EEB: http://www.jnr-eeb.org
===
Subject: Re: help! a probablilty problem about ßipping
coins...
>Suppose we ßip a unfair coin with prob. p it is head, with
prob. 1-p it
is
>tail.
>So the prob. of head is p, a prior probablity.
>I ßip the coin N times,
>what is the a posterprior prob. of head if I know that there
are at least
K
>heads? i.e. given at least K heads?
>what is the prob. of getting M heads out of these N ßippings
given at
least
>K heads occurred?
The probability of exactly M heads is given by the binomial
distribution.
P(M) = p^M * (1-p)^(N-M) * choose(N,M)
The probability of event A given event B is:
P(A|B) = P(A&B) / P(B)
[The | character means given in this context; & means and]
That should get you started.
--Keith Lewis klewis {at} mitre.org
The above may not (yet) represent the opinions of my employer.
===
Subject: Re: help! a probablilty problem about ßipping
coins...
> Suppose we ßip a unfair coin with prob. p it is head, with
prob. 1-p
> it is
> tail.
> So the prob. of head is p, a prior probablity.
> I ßip the coin N times,
> what is the a posterprior prob. of head if I know that
there are at
> least K
> heads? i.e. given at least K heads?
> what is the prob. of getting M heads out of these N
ßippings given at
> least K heads occurred?
Fellers book, Vol. 1.
John Lowry
Flight Physics
(and former geneticist)
===
Subject: Inversion of complicated Laplace transform
Im trying to obtain the inverse Laplace transform of the
following
expression:
( 400 * (10 + Sqrt(15 + 300*s)) ) /
( 10410 + 41*Sqrt(15 + 300*s) + 40*s^2*(10010 + Sqrt(15 +
300*s)) +
22*s*(10210 + 21*Sqrt(15 + 300*s)) )
It appears as if the usual factorization of the denominator
does not
apply here due to the appearance of the Sqrt(15 + 300*s)
terms. Any
ideas? In principle, an asymptotic expansion valid for long t
would
suffice. Im thankful for every proposal that 
would help to
avoid a
numerical inversion.
Johan
===
Subject: Re: Inversion of complicated Laplace transform
Hi Johan,
I hab a look at your function. Since it is not the usual
rational
function, one has to look at the expansions of it at the
zeros of the
denominator with the largest real parts to get an asymptotic
expansion.
I tried a little bit; a further problem here is that it looks
to me that
these zeros are two conjugate zeros very near. The expansions
are
different, if one has two zeros or if they coalesce into one
point.
First case gives here something like t^{-1/2}exp(-at) with a
the real
part of the zeros or exp(-at) if they coalesce into one.
(see f.e. G. Doetsch, Intro t. t. Theory and Appl. o. t.
Laplace
transform, Springer, 1974).
Any ideas which might be the right order of magnitude in your
case?
Ciao
Karl
> Im trying to obtain the inverse Laplace transform of the
following
> expression:
> ( 400 * (10 + Sqrt(15 + 300*s)) ) /
> ( 10410 + 41*Sqrt(15 + 300*s) + 40*s^2*(10010 + Sqrt(15 +
300*s)) +
> 22*s*(10210 + 21*Sqrt(15 + 300*s)) )
> It appears as if the usual factorization of the denominator
does not
> apply here due to the appearance of the Sqrt(15 + 300*s)
terms. Any
> ideas? In principle, an asymptotic expansion valid for long
t would
> suffice. Im thankful for every proposal that 
would help to
avoid a
> numerical inversion.
> Johan
===
Subject: astonishingly many numbers with abundace 12 and 56
hi,
im currently writing a text about perfect numbers and many
things related
to
it for my final school exam. in order to get an idea of how
the whole thing
isnt good enough) which are supposed to tell me how many
numbers are
perfect, abundant, deficient, and similar things. what i got
was a
frighteningly long list of numbers, so i visualized it using
gnuplot.
the results were surprinsing for me. i knew from books that
there is just a
little amount of perfect numbers, there are several numbers
with deficiency
1
and none with abundance 1 (plz correct me if i use wrong
terms, english is
not my mother tongue).
but it struck me how many numbers there are with an abundance
of 12 and 56.
observing integers from 1 to 100,000, i found 505 numbers
abundant by 56
and
even 1929 numbers abundant by 12. this is especially
astonishing as the
next
frequent abundance is 992, found in just 47 numbers in the
observed range,
all the others only occur 21 times or even rarer.
i tried to find out why i get such extreme values, but 
didnt
find
anything.
if anyone wants to have a look at it, i can post the scripts
(unfortunately,
not knowing that i would ask here, variable and function
names are german)
or
gnuplot plots (please tell me which format you prefer).
if you have any idea why these things are as they are, please
let me know!
btw: i also let gnuplot draw a diagram with N on the x-axis
and sigma(N)-n
on
the y-axis. drawing everything from 1 to 50,000, the
accumulations of
points
on y=x+12 and y=x+56 are invisible, but several other
Ôlines, i.e.,
accumulations of abundancies as a linear function of n, are,
which resemble
functions of simple fractions of x. these are just special
ones -- i
couldnt
find out which until now; y=1/2*x and y=3/4*x are such lines,
y=2/3*x isnt.
i could send images of that as well.
greetings
webograph
===
Subject: Re: astonishingly many numbers with abundace 12 and
56
format=ßowed;
reply-type=response