mm-1050

>> I¹m trying to Þnd a series where the sum of a subset of
that
>> is unique. Or in other words, I can Þnd the numbers from
sum.
>>
>> An example would be f(n)=2^n, you add any number of
elements
>> in this set, you¹ll get a number with all those bits set.
>> But I¹m 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
Œmost
efÞcient¹
> 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 doesn¹t
>grow exponentially)?
> I believe this doesn¹t 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 don¹t think I believe this. It¹s anyway not true that if
all size-2
subsets produce a unique sum then all subsets produce a
unique sum,
and it¹s not clear to me why size-10 should differ from
size-2 in this
regard.
There¹s a lot of literature on these problems. A good
starting place
is Guy¹s Unsolved Problems in Number Theory. The 3rd edition
is out,
but I don¹t 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
it¹s
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
it¹s
> 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 couldn¹t do better than powers
of 2, and
I¹d be very interested to see that example. For those of us
who don¹t
have the book, is the example simple enough for you to
reproduce here?
(I¹m 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
it¹s
> 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 couldn¹t do better than powers
of 2, and
> I¹d be very interested to see that example. For those of us
who don¹t
> have the book, is the example simple enough for you to
reproduce here?
> (I¹m 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
doesn¹t 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 deÞned 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 Þxed $n$, 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 $|I|-|J|=1$ $(|á|$ 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 deÞnes 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
$overline{p}$ deÞned 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
coefÞcients in ${0,1}$ and a zero of multiplicity $m$ at
$-1$. A
greedy solution can be deÞned 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-deÞned properties and that $$deg
g_m=frac43á2^m-frac32+frac{(-1)^m}6.$$ Therefore,
$$d(m)lefrac43á2^m-frac32+frac{(-1)^m}6.$$ The authors show
that the
equality holds if and only if $mle5$. In the general case,
they prove
that $$2^m+c_1mle d(m)le frac{103}{96}á2^m+c_2$$ and they
conjecture
that for any $epsilon>0$ the inequality $d(m)<(1+epsilon)2^m$
holds
for sufÞciently large $m$. Also, they consider the related
problem of
Þnding 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 Þnite 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
$f(n) le
0.23513á2sp n$ for $nge 40$. W. F. Lunnon ref[Math. Comp. 50
(1988),
no. 181, 297--320; MR0917837 (89a:11019)] suggested a similar
construction, which implied $f(n) le 0.22096 á2sp n$ for $nge
67$.
In his paper Bohman presents two parametric families of
inÞnite
sequences, which include, for small values of parameters, the
sequences
of Conway-Guy and Lunnon. Using his sequences, he Þnds many
new
examples of DSS-sets, and, in particular, obtains a new upper
estimate
$f(n) le 0.22002 á2sp n$ for sufÞciently large $n$. Bohman¹s
construction is very subtle and interesting and is likely to
Þnd
different applications in combinatorics, cryptography, and
related
Þelds.
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,
deÞne $alpha(A)=(max A)/2^{|A|-1}$, 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] deÞned 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 $kgeq1$,
deÞne
$A_k={u(k+1)-u(i)colon1leq ileq k}$. 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 $k$. DeÞne $f(n)=min{max_{sin S}scolon|S|=n$ 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
modiÞcation of the Conway-Guy sequence, and states that this
leads to a
slight improvement over Lunnon¹s 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
it¹s
>> 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 couldn¹t do better than powers
of 2, and
> I¹d be very interested to see that example. For those of us
who don¹t
> have the book, is the example simple enough for you to
reproduce here?
> (I¹m not asking you to type in ten pages of text!)
C¹est 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
it¹s
>> 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 couldn¹t do better than powers
of 2, and
> I¹d be very interested to see that example. For those of us
who don¹t
> have the book, is the example simple enough for you to
reproduce here?
> (I¹m not asking you to type in ten pages of text!)
> C¹est un forum en fran.8dais, respectez la charte !
Please accept my apologies. I didn¹t notice that this was
being posted
to a French-language group.
===
Subject: Re: Finding unique sums.
> C¹est un forum en fran.8dais, respectez la charte !
> Please accept my apologies. I didn¹t notice that this was
being posted
> to a French-language group.
Don¹t worry Matt, some of us enjoy a little international
þavour on
the French group :-) The bullies won¹t have their ways...
===
Subject: Re: Finding unique sums.
Vous avez aussi poste ce message a des forums anglais, donc
vous
n¹avez 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
it¹s
>> 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 couldn¹t do better than powers
of 2, and
> I¹d be very interested to see that example. For those of us
who don¹t
> have the book, is the example simple enough for you to
reproduce here?
> (I¹m not asking you to type in ten pages of text!)
> C¹est 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 you¹ll
see it depends on the binary expansion of sqrt2. I don¹t
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 you¹ll
>see it depends on the binary expansion of sqrt2. I don¹t
think enough
>is known about the binary expansion of sqrt2 to answer the
question.
It¹s equivalent to the question of whether every Þnite string
of 0¹s and
1¹s 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 you¹ll
> see it depends on the binary expansion of sqrt2. I don¹t
think enough
> is known about the binary expansion of sqrt2 to answer the
question.
Well I don¹t 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: Courant¹s Introduction to Calculus and Analysis I
solutions to
exercises
I¹m 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 I¹m 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: Courant¹s Introduction to Calculus and Analysis
I solutions
to exercises
> I¹m 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 I¹m 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: Courant¹s 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: Courant¹s 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. It¹s a composite of Ed
Witten and Stephen
> Hawking as a murderer - motive to cover up the failure of
his theory.
> The actor is in Hawking¹s wheelchair with two wives - the
one accused of
> abusing him as in the recent Cambridge þap (she¹s 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
Witten¹s i.e.

> 11 dimensions and the guy is an American not a Brit in the
TV story.
> Bizarre.
I didn¹t 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. It¹s 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
won¹t be a
genius at how to commit murder.
It¹s 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 wasn¹t all
that hidden because the actor was madeup to look like Hawking.
But the idiots couldn¹t 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 inÞnite for the
overworked
mathematicians
posting-account=Qiuj5AwAAACmGnmS12qcvqA9IXzD0s4L
You are one person tossing a coin.
I have inÞnite people, for every time you toss a coin, my
inÞnite
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 (inÞnite),
you can
toss your coin as long as you want, you NEVER form a new
sequence to
what an inÞnite set of people can make.
Whatever sequence you form must be a *possible outcome* of
tossing
coins, inÞnite trials at the possible always succeed.
With Þnite people, the length of the sequence where every
combination
is covered is Þnite, about log(#P).
With inÞnite people, the length of the sequence where every
combination is covered is without bound, INFINITE.
InÞnite length sequences are all covered, the diagonal is a
Œcheat¹
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 deÞne
>>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
>>Þrst-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
> he¹s not deÞning provability to be the
> same as truth. (He¹s setting up a _speciÞc_ formal system in
> which the two coincide. There¹s a big difference.)
That doesn¹t make any sense. How can you deÞne provability (or
anything else) without being in a system? Smullyan is setting
up a
speciÞc formal system and you¹re not? So what are you talking
about
if it¹s 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 deÞne
>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
>Þrst-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
>> he¹s not deÞning provability to be the same as truth.
(He¹s setting
>> up a _speciÞc_ formal system in which the two coincide.
There¹s a
>> big difference.)
> That doesn¹t make any sense.
It does. Really.
Given a language:
* Truth (deÞned in the model theory) is a semantic relation
that holds
between a sentence of the language and an interpretation of
the language.
* Provability (deÞned 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 deÞnitions 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. That¹s a simple theorem.
It isn¹t a
deÞnition of truth or provability.
Makes good sense.
HTH.
===
Subject: Re: what are the correct set theory axioms?
X-CompuServe-Customer: Yes
X-Coriate: interspeed.co.nz
X-Ecrate: tanandtanlawyers.com
X-Pose: George Cox
X-Punge: Micro$oft
X-Sanguinate: The MVS Guy
X-Terminate: SPA(GIS)
X-Tinguish: Mark GrifÞth
X-Treme: C&C,DWS
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
>couldn¹t Þnd a statement of the axioms of SO set theory
anywhere in
>the book, so now I¹m still wondering what are the correct
set theory
>axioms?
There are none. It¹s 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
reply to spamtrap@library.lspace.org
===
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. What¹s 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 Þght 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. What¹s 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 Þght terrorism by: Using less gasoline.
************************
David C. Ullrich
===
Subject: Re: a<b<c<a+b
>>What¹s an accepted notation in ASCII for in N
>>and not in N?
>in N and not in N, respectively.
Really? There¹s no little sideways e or member of set
notation? Darn.
Ok, I like words. We¹ll 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 inÞnity, 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 Þght terrorism by: Using less gasoline.
===
Subject: Newbie question about percentiles
Hi group,
This is my Þrst 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) didn¹t 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 Þnd the rank of Œmy¹ 10 if there are more 10¹s
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
There¹s an ambiguity in how you deÞne the quantiles, and the
user thus has some freedom in their deÞnition. Probably any
of those is reasonable, and you can just cite a reference for
the
appropriate deÞnition.
Suppose we wanted to see where the 30-th, 40th and 50th
percentiles are. Let¹s look at a couple of the quantile
deÞnitions
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
deÞnition, we have cutoff = Y_[þoor(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 deÞnition 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_(þoor(x)) + (Y_ceil(x) - Y_(þoor(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 Þnd 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 Œwe¹ had some clearcut
deÞnition.
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 coefÞcients)?
> 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: Inþection 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 Þnd 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 Þnd quartics Q
which split
> over Z and have property D; but so far roots of Q or Q¹
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 Þnd 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 Þrst
derivative
are rational. (z = +27 gives a zero denominator in the
formula for a.)
Setting w = -12 and z = -36, I Þnd a = 432/77, and in that
case the
Þrst derivative does not have rational roots. (On the other
hand,
when z = +36, a = 0, and it Þts, 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
Þnd 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

> Þnd 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 wasn¹t a linear one. In that case, the correlation
coefÞcient 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 wasn¹t in the class and
so I
don¹t 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
Þnd evidence for hidden codes in the Hebrew text of Genesis.
This
number of debates in the scientiÞc 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 scientiÞc community was that the methodology
in the
1994 experiment was þawed 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 þawed. Furthermore, to their
discredit, the journal Statistical Science did not allow the
authors
Þnding, 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 Þnding 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 Haralick¹s
Þndings
are technically correct.
You can download Haralick¹s paper here
http://www.torahcodes.net as
well as other papers in the section marked new. Note that I
am not
claiming that Haralick¹s Þndings 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 Þnding.
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 Þrst and last)
horizontally
pairs with itself or its mirror image. Whether or not you
think that
this is all a coincidence, you¹ll have to agree that there is
a very
interesting pattern in the Þrst verse of Genesis.

Craig
===
Subject: Re: Bible Codes Resurrected?
After thinking about Haralick¹s 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 speciÞed 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 Þrst 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 al¹s Þrst 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 al¹s
second list, but the rules and styles of the appellations and
dates
from Witztum et al¹s Þrst 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 Þnd 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.
> Þnding, 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 Þnding 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 Haralick¹s
Þndings
> 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 Haralick¹s 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 speciÞed 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 Þrst 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 al¹s Þrst 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 al¹s
> second list, but the rules and styles of the appellations
and dates
> from Witztum et al¹s Þrst 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 Þnd 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 didn¹t 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 Þnd 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 won¹t 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 Haralick¹s 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 speciÞed 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 Þrst 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 al¹s Þrst 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 al¹s
> second list, but the rules and styles of the appellations
and dates
> from Witztum et al¹s Þrst 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 Þnd 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 didn¹t 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 Þnd 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 won¹t work is completely
unfounded.
As a follow up, I notiÞed 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 Þnd 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 didn¹t 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 Þnd 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 won¹t work is completely
unfounded.
> As a follow up, I notiÞed 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
(WRR¹s data), combine it with some more data that was openly
cooked (War and Peace data), then suddenly have an objective
list, is breathtaking.
And that¹s 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 notiÞed 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 cc¹ed me. It appears
to me
that he only made a mistake by forgetting about those extra
lists
he already used. I wouldn¹t 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
> (WRR¹s 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 Aaron¹s rod swallowed up their rods.
- that is of course assuming that everything is as Haralick
describes.
> And that¹s 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 þaws in the
Haralick
Craig
> Brendan McKay.
===
Subject: Re: Bible Codes Resurrected?
> As a follow up, I notiÞed 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 cc¹ed me. It
appears to me
> that he only made a mistake by forgetting about those extra
lists
> he already used. I wouldn¹t 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 speciÞc 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 that¹s 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 þaws in the
Haralick
I¹ll 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 signiÞcance
level for
his results. How likely is it for his observations to occur
by chance?
He doesn¹t even ask the question. (I have reason to believe
that
they are not very unlikely.) And let¹s 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 Haralick¹s only
justiÞcation 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
scientiÞc experiments and then concludes with The data for
the above
three experiments can be found at McKay¹s web site (1999b).
> As a follow up, I notiÞed 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 Þnd 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 Þnd 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 ŒDestruction¹. 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 codes¹ 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 ŒDestruction¹. 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 codes¹ 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 þaw
that
makes it completely worthless. I will begin by brieþy
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 Þnd 13,430 of these
ELS¹s in
their 614,400 control texts. They also manually Þnd 8 phrases
that
are somewhat intelligible in these control texts. They
present these
ELS¹s to many subjects with the bin Laden ELS mixed in.
3. They present these ELS¹s 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 Þnd 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 Þnd 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 ŒDestruction¹. 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 Þrst sentence is a little strange. However,
the
grammar in Hebrew is reasonable. The fact that the Þrst
sentence is
strange was reþected 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 codes¹ 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 þaw
that
> makes it completely worthless. I will begin by brieþy
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 Þnd 13,430 of
these ELS¹s in
> their 614,400 control texts. They also manually Þnd 8
phrases that
> are somewhat intelligible in these control texts. They
present these
> ELS¹s to many subjects with the bin Laden ELS mixed in.
> 3. They present these ELS¹s 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 Þnd 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 Þnd 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 Þnd 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 Þnd 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 Þnd to be incorrect? I do
think the
description in the paper supports that statement; for example:
Our method of signiÞcance 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 Þnd 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 Þnd 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 Þnd 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 Þnd to be incorrect? I do
think the
> description in the paper supports that statement; for
example:
> Our method of signiÞcance 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 Þnd 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 speciÞc characteristics.
===
Subject: Re: Bible Codes Resurrected?
> Equidistant Letter Sequences in the Book of Genesis which
claimed to
> Þnd evidence for hidden codes in the Hebrew text of
Genesis. This
> number of debates in the scientiÞc 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 þawed.
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
shufþing 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 Gans¹ cities experiment and found similar
results [1].
3. The several independent studies conducted by qualiÞed
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 scientiÞc community was that the
methodology in the
> 1994 experiment was þawed 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 þawed.
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 al¹s 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
Þnding þaw after þaw in Torah Codes experiments are becoming
tired
of the subject [11].
> The major
> Þnding, 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 Þnding 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 Haralick¹s
Þndings
> are technically correct.
Unfortunately I do not have the expertise to fully evaluate
Haralick¹s
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 Haralick¹s paper here
http://www.torahcodes.net as
> well as other papers in the section marked new. Note that I
am not
> claiming that Haralick¹s Þndings 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 Þnding.
Torah Codes claims have been taken seriously by its critics
for over
10 years. Like you I hope that someone qualiÞed will
intelligently
dispute Haralick¹s 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 Þrst and last)
horizontally
> pairs with itself or its mirror image. Whether or not you
think that
> this is all a coincidence, you¹ll have to agree that there
is a very
> interesting pattern in the Þrst 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 þawed.
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
shufþing 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 Gans¹ 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, Haralick¹s paper renders this argument obsolete,
assuming that
it is correct.
> 3. The several independent studies conducted by qualiÞed
> 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 scientiÞc community was that the
methodology in the
> 1994 experiment was þawed 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 þawed.
> 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 difÞcult to do. Sort of like trying to deÞne
randomness. It¹s relatively easy to show that a sequence is
not random
by Þnding a pattern. However, showing that there is no
conceivable
pattern is much more difÞcult. 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 al¹s 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
> Þnding þaw after þaw in Torah Codes experiments are
becoming tired
> of the subject [11].
I agree with you on this point. Witztum¹s critiques come down
to why
his spellings are more legitimate than McKay¹s monkey list.
This is
very weak since it is subject to so much subjectivity.
> The major
> Þnding, 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 Þnding 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 Haralick¹s
Þndings
> are technically correct.
> Unfortunately I do not have the expertise to fully evaluate
Haralick¹s
> 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 McKay¹s
paper. I just
read it yesterday and could not Þnd obvious fault with the
reasoning.
> You can download Haralick¹s paper here
http://www.torahcodes.net as
> well as other papers in the section marked new. Note that I
am not
> claiming that Haralick¹s Þndings 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 Þnding.
> Torah Codes claims have been taken seriously by its critics
for over
> 10 years. Like you I hope that someone qualiÞed will
intelligently
> dispute Haralick¹s 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 Haralick¹s
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 Þnd 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 Þrst and last)
horizontally
> pairs with itself or its mirror image. Whether or not you
think that
> this is all a coincidence, you¹ll have to agree that there
is a very
> interesting pattern in the Þrst 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 al¹s lists seem to be
tuned to
acheive
remarkable results in Genesis. Nobody has claimed that
combining the War
and
Peace list with these two lists will necessarily cancel out
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
shufþing 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 Gans¹ 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 didn¹t 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 difÞcult to do. Sort of like trying to deÞne
> randomness. It¹s relatively easy to show that a sequence is
not random
> by Þnding a pattern. However, showing that there is no
conceivable
> pattern is much more difÞcult. 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 Haralick¹s
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 Þnd 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 Haralick¹s paper, since the reliability of any experiment
using data
from
Witztum et al¹s 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 I¹m 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, Panin¹s 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.
I choose Polesoft Lockspam to Þght spam, and you?
http://www.polesoft.com/refer.html
===
Subject: Re: Bible Codes Resurrected?
> Yes, but Gans didn¹t 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 Haralick¹s paper, since the reliability of any
experiment using data
from
> Witztum et al¹s 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 Witztum¹s lists.
Craig
===
Subject: Re: Bible Codes Resurrected?
Fortunately they will still be winning even if none of the
experts
respond
> to Haralick¹s paper, since the reliability of any
experiment using data
from
> Witztum et al¹s 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 Witztum¹s 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 speciÞed 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 Þnd 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 didn¹t 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 Þnd 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
Þnd
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 won¹t 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
Witztum¹s 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 Witztum¹s 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.
I choose Polesoft Lockspam to Þght spam, and you?
http://www.polesoft.com/refer.html
===
Subject: Re: Bible Codes Resurrected?
> ----- Original Message -----
===
> Subject: Re: Bible Codes Resurrected?
> Yet we Þnd 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 didn¹t 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 Þnd 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
Þnd
> 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 McKay¹s 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, I¹m not certain they will be
successful. I hope
they will be successful if indeed there is a þaw in
Haralick¹s work.
I saw that you helped McKay write his response to Gans¹
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. That¹s 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 won¹t 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
> Witztum¹s 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 Witztum¹s 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. That¹s not Haralick¹s 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.
> I choose Polesoft Lockspam to Þght spam, and you?
> 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 sufÞciently 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 Þrst and last)
horizontally
> pairs with itself or its mirror image. Whether or not you
think that
> this is all a coincidence, you¹ll have to agree that there
is a very
> interesting pattern in the Þrst 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, you¹ll have to agree that there
is a very
>> interesting pattern in the Þrst 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 he¹s 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.
SpeciÞcally, 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 Craig¹s post.
Bart
===
Subject: Re: Bible Codes Resurrected?
>SpeciÞcally, 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 I¹d 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 Þnd 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?
>SpeciÞcally, 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 scientiÞc 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?
>>SpeciÞcally, 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, that¹s exactly the experiment performed
in the paper. I sure don¹t care one way or the other. My
point was that the responses to the OP were as if the OP¹s
question was much more shallow than it really was.
Bart
===
Subject: Re: Bible Codes Resurrected?
>SpeciÞcally, it appears that the new paper shows that
>the frequency of coincidences is much higher in the Torah
>than in War and Peace.
That¹s hardly surprising, since the Torah allows you o Þll in
any
vowels you like to create meaningful words, whereas with War
and
Peace the spelling is Þxed for vowels and consonants.
--
Stan Brown, Oak Road Systems, Tompkins County, New York, USA
http://OakRoadSystems.com/
And if you¹re afraid of butter, which many people are nowa-
days, (long pause) you just put in cream. --Julia Child
===
Subject: Re: Bible Codes Resurrected?
>>SpeciÞcally, it appears that the new paper shows that
>>the frequency of coincidences is much higher in the Torah
>>than in War and Peace.
> That¹s hardly surprising, since the Torah allows you o Þll
in any
> vowels you like to create meaningful words, whereas with
War and
> Peace the spelling is Þxed for vowels and consonants.
Recall that the original rebuttal paper DID Þnd the high
frequency of coincidences in War and Peace. The OP¹s question
was, In this new investigation, supposedly done with more
statistical sense, the Torah beat War and Peace. Is
this signiÞcant?
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.
> SpeciÞcally, 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.
>> SpeciÞcally, 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 isn¹t.
I just picked up a copy of the U.S. News and World Report¹s
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.
It¹s 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 didn¹t write the paper and I¹m not going to read
it either. All I did was to point out that the responders
didn¹t understand the OP¹s question.
Just like you didn¹t 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 title¹s reserved for JSH!
:-)
--
Stan Brown, Oak Road Systems, Tompkins County, New York, USA
http://OakRoadSystems.com/
And if you¹re 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
>Þnd 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 you¹re 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
>Þnd 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 I¹m a little
disappointed. They state that there are problems with the
1994 paper
but don¹t state what the problems are.
--
Stan Brown, Oak Road Systems, Tompkins County, New York, USA
http://OakRoadSystems.com/
And if you¹re 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 I¹m a
little
> disappointed. They state that there are problems with the
1994 paper
> but don¹t 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 I¹m a
little
>> disappointed. They state that there are problems with the
1994 paper
>> but don¹t 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 you¹re 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 Kaczynski¹s Manifesto,
getting b
mail o
m
b
s, or like that, and
readers are welcome to Þnd 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 Þnd hidden words
in _any_ sufÞciently large piece of text? To demonstrate how
silly
this is, I created
The Shakespeare Code
Start with a well known passage (Hamlet¹s 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 Þnd hidden
messages.
But only use diagonals so as not to pick up actual words from
the
quotation.
I¹ve capitalized three words:
NEWT TERM LOSS
which leads to the conclusion that Shakespeare predicted
Gingrich¹s
defeat in the 1998 Congressional election!
Spooky, eh?
===
Subject: Re: Bible Codes Resurrected?
I don¹t get how you wrapped the text
in a spiral, but that¹s 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 (Hamlet¹s 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 Þnd hidden
messages.
> But only use diagonals so as not to pick up actual words
from the
> quotation.
> I¹ve capitalized three words:
> NEWT TERM LOSS
--Give Earth a Trickier Dick Cheeny -- out of ofÞce, 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/Þgs/plate02.
html
===
Subject: Re: Bible Codes Resurrected?
===
>Subject: Re: Bible Codes Resurrected?
>I don¹t get how you wrapped the text
>in a spiral,
Are you familiar with Ulam¹s 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 that¹s 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 didn¹t use any sort of modulo, I only looked at letter
patterns
that were in contiguous diagonal lines. When I Þrst 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 didn¹t 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 Þgured 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. It¹s easy to predict the
past.
>> Start with a well known passage (Hamlet¹s 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 Þnd hidden
messages.
>> But only use diagonals so as not to pick up actual words
from the
>> quotation.
>> I¹ve capitalized three words:
>> NEWT TERM LOSS
>--Give Earth a Trickier Dick Cheeny -- out of ofÞce, 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/Þgs/plate02
.html
--
Mensanator
Ace of Clubs
===
Subject: Re: Bible Codes Resurrected?
I see; I had seend Ulam¹s spiral, before. it¹s 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 didn¹t use any sort of modulo, I only looked at letter
patterns
> that were in contiguous diagonal lines. When I Þrst 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 didn¹t 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. It¹s easy to predict
the past.
--ils duces d¹Enron!
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.
I¹m trying to Þnd out where I can buy this poster. Can anyone
help?
It¹s 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.
> I¹m trying to Þnd out where I can buy this poster. Can
anyone help?
> It¹s 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 veriÞcations 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
modiÞcations,
>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 inÞnite 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 inÞnite of (-1)^p/(2p+1)^2 ?
I don¹t, 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 inÞnite 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?
Isn¹t 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 haven¹t found a copy of the actual
paper, but
all references I¹ve found to it deÞne 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 Baumgartner¹s statement trivially?
Let f : R/{0} -> R be a purported order-isomorphism. Call f¹s
image
on the negative reals N, and f¹s 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 haven¹t found a copy of the actual paper, but
|all references I¹ve found to it deÞne 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.