mm-1058


Interesting!
12=2^2*3 and 56=2^3*7 and 992=2^5*31
These are of the form 2^n*(2^n-1) which if 2^n-1 is prime are
perfect
numbers!
BF
> hi,
> iım currently writing a text about perfect numbers and many
things related

> to
> it for my Ŝnal school exam. in order to get an idea of how
the whole
> thing
> isnıt good enough) which are supposed to tell me how many
numbers are
> perfect, abundant, deŜcient, and similar things. what i got
was a
> frighteningly long list of numbers, so i visualized it
using gnuplot.
> the results were surprinsing for me. i knew from books that
there is just

> little amount of perfect numbers, there are several numbers
with
> deŜciency 1
> and none with abundance 1 (plz correct me if i use wrong
terms, english
is
> not my mother tongue).
> but it struck me how many numbers there are with an
abundance of 12 and
> 56.
> observing integers from 1 to 100,000, i found 505 numbers
abundant by 56
> and
> even 1929 numbers abundant by 12. this is especially
astonishing as the
> next
> frequent abundance is 992, found in just 47 numbers in the
observed
range,
> all the others only occur 21 times or even rarer.
> i tried to Ŝnd out why i get such extreme values, but
didnıt Ŝnd
> anything.
> if anyone wants to have a look at it, i can post the scripts
> (unfortunately,
> not knowing that i would ask here, variable and function
names are german)

> or
> gnuplot plots (please tell me which format you prefer).
> if you have any idea why these things are as they are,
please let me
know!
> btw: i also let gnuplot draw a diagram with N on the x-axis
and sigma(N)-n

> on
> the y-axis. drawing everything from 1 to 50,000, the
accumulations of
> points
> on y=x+12 and y=x+56 are invisible, but several other
Œlinesı, i.e.,
> accumulations of abundancies as a linear function of n,
are, which
> resemble functions of simple fractions of x. these are just
special
> ones -- i couldnıt Ŝnd out which until now; y=1/2*x and
y=3/4*x are such

> lines, y=2/3*x isnıt. i could send images of that as well.
> greetings
> webograph
===
Subject: Re: astonishingly many numbers with abundace 12 and
56
format=ŝowed;
reply-type=response
Sorry i should have said these numbers are double the perfect
numbers.
Since perfect numbers are 2^(n-1)*(2^n-1) ...
BF
> Interesting!
> 12=2^2*3 and 56=2^3*7 and 992=2^5*31
> These are of the form 2^n*(2^n-1) which if 2^n-1 is prime
are perfect
> numbers!
> BF
>> hi,
>> iım currently writing a text about perfect numbers and
many things
>> related to
>> it for my Ŝnal school exam. in order to get an idea of how
the whole
>> thing
>> c
>> isnıt good enough) which are supposed to tell me how many
numbers are
>> perfect, abundant, deŜcient, and similar things. what i
got was a
>> frighteningly long list of numbers, so i visualized it
using gnuplot.
>> the results were surprinsing for me. i knew from books
that there is just

>> a
>> little amount of perfect numbers, there are several
numbers with
>> deŜciency 1
>> and none with abundance 1 (plz correct me if i use wrong
terms, english
>> is
>> not my mother tongue).
>> but it struck me how many numbers there are with an
abundance of 12 and
>> 56.
>> observing integers from 1 to 100,000, i found 505 numbers
abundant by 56

>> and
>> even 1929 numbers abundant by 12. this is especially
astonishing as the
>> next
>> frequent abundance is 992, found in just 47 numbers in the
observed
>> range,
>> all the others only occur 21 times or even rarer.
>> i tried to Ŝnd out why i get such extreme values, but
didnıt Ŝnd
>> anything.
>> if anyone wants to have a look at it, i can post the
scripts
>> (unfortunately,
>> not knowing that i would ask here, variable and function
names are
>> german) or
>> gnuplot plots (please tell me which format you prefer).
>> if you have any idea why these things are as they are,
please let me
>> know!
>> btw: i also let gnuplot draw a diagram with N on the
x-axis and
>> sigma(N)-n on
>> the y-axis. drawing everything from 1 to 50,000, the
accumulations of
>> points
>> on y=x+12 and y=x+56 are invisible, but several other
Œlinesı, i.e.,
>> accumulations of abundancies as a linear function of n,
are, which
>> resemble functions of simple fractions of x. these are
just special
>> ones -- i couldnıt Ŝnd out which until now; y=1/2*x and
y=3/4*x are such

>> lines, y=2/3*x isnıt. i could send images of that as well.
>> greetings
>> webograph
===
Subject: Re: astonishingly many numbers with abundace 12 and
56
monsieur Webograph,
there is nothing unusual about this seeming abundancy
of such abundancies, although Iım not perfectly clear
on the meaning of the term from numbertheory, since
it hasnıt struck my interest of yet.
you could prove the inŜnitude of both abundancies,
for instance, or ratios to other abundancies
at arbitrary limits.

> observing integers from 1 to 100,000, i found 505 numbers
abundant by 56
and
> even 1929 numbers abundant by 12. this is especially
astonishing as the
next
> frequent abundance is 992, found in just 47 numbers in the
observed
range,
> all the others only occur 21 times or even rarer.

> btw: i also let gnuplot draw a diagram with N on the x-axis
and sigma(N)-n
on
> the y-axis. drawing everything from 1 to 50,000, the
accumulations of
points
> on y=x+12 and y=x+56 are invisible, but several other
Œlinesı, i.e.,
> accumulations of abundancies as a linear function of n,
are, which
resemble
> functions of simple fractions of x. these are just special
ones -- i
couldnıt
> Ŝnd out which until now; y=1/2*x and y=3/4*x are such
lines, y=2/3*x
isnıt.
> i could send images of that as well.
--Chairman George and Trickier Dick at Watergate!
http://tarpley.net/bush12.htm
===
Subject: Re: astonishingly many numbers with abundace 12 and
56
> the results were surprinsing for me. i knew from books that
there is just
a
> little amount of perfect numbers, there are several numbers
with
deŜciency 1
> and none with abundance 1 (plz correct me if i use wrong
terms, english
is
> not my mother tongue).
> but it struck me how many numbers there are with an
abundance of 12 and
56.
> observing integers from 1 to 100,000, i found 505 numbers
abundant by 56
and
> even 1929 numbers abundant by 12. this is especially
astonishing as the
next
> frequent abundance is 992, found in just 47 numbers in the
observed
range,
> all the others only occur 21 times or even rarer.
> btw: i also let gnuplot draw a diagram with N on the x-axis
and sigma(N)-n
on
> the y-axis. drawing everything from 1 to 50,000,
I donıt have anything helpful to say on the abundance of
numbers
with abundance 12, but I think thereıs something a bit
non-standard
about your terminology. sigma(n) is generally taken to mean
the sum
of all the positive divisors of n, including n itself.
Abundance
of n would be measured by sigma(n) - 2n, not sigma(n) - n.
--
Gerry Myerson (gerry@maths.mq.edi.ai) (i -> u for email)
===
Subject: Re: astonishingly many numbers with abundace 12 and
56
X-Enigmail-Version: 0.86.0.0
X-Enigmail-Supports: pgp-inline, pgp-mime
> sigma(n) is generally taken to mean the sum
> of all the positive divisors of n, including n itself.
Abundance
> of n would be measured by sigma(n) - 2n, not sigma(n) - n.
although i know that there is a huge possibility for errors
in my
terminology, in this special case i think i didnıt express
myself clearly.
sigma(n)-n is what i meant in the last paragraph. i drew a
diagram of
sigma(n)-n, that is, perfect numbers show up as points
P(n|n), primes as
P(n|1) and so on (i hope this is clearer).
> you could prove the inŜnitude of both abundancies,
> for instance, or ratios to other abundancies
> at arbitrary limits.
i played around a bit and found the following proof that
there are
inŜnitely
many numbers with abundance 12 (iım afraid this will become
formally ugly,
but my former mathematical activities were all restricted to
school maths,
please correct me):
let n be any number 6*p with p being prime
then n can be factorized 2*3*p
this means that sigma(n) is 2+3+p+6+2p+3p+6p=12p+12
the abundance sigma(n)-2n of n is therefor 12p+12-2*6p=12
since there is an inŜnite number of primes, there is an
inŜnite number of

numbers with abundance 12.
there are more numbers with abundance 12, though (24 -
sigma(24)-48=36,
abundance 12).
the same proof can be done for abundance 56 using n=28p
until now, i donıt have an idea of how to prove ratios to
other abundancies,

because as far as i know there is no rule for the amount of
primes in a
certain area.
webograph
===
Subject: Re: astonishingly many numbers with abundace 12 and
56
> sigma(n) is generally taken to mean the sum
>of all the positive divisors of n, including n itself.
Abundance
>of n would be measured by sigma(n) - 2n, not sigma(n) - n.
> although i know that there is a huge possibility for errors
in my
> terminology, in this special case i think i didnıt express
myself clearly.

> sigma(n)-n is what i meant in the last paragraph. i drew a
diagram of
> sigma(n)-n, that is, perfect numbers show up as points
P(n|n), primes as
> P(n|1) and so on (i hope this is clearer).
OK. Then if p is prime you get the point (2p, p + 3); if you
plot just
these points for lots of p they resemble the line y = x/2,
which may
explain one of the observations you made in your original
post.
> you could prove the inŜnitude of both abundancies,
> for instance, or ratios to other abundancies
> at arbitrary limits.
> i played around a bit and found the following proof that
there are
inŜnitely
> many numbers with abundance 12 (iım afraid this will become
formally ugly,

> but my former mathematical activities were all restricted
to school maths,

> please correct me):
> let n be any number 6*p with p being prime
> then n can be factorized 2*3*p
> this means that sigma(n) is 2+3+p+6+2p+3p+6p=12p+12
typo - right side correct, left side missing 1.
> the abundance sigma(n)-2n of n is therefor 12p+12-2*6p=12
> since there is an inŜnite number of primes, there is an
inŜnite number
of
> numbers with abundance 12.
> there are more numbers with abundance 12, though (24 -
sigma(24)-48=36,
> abundance 12).
> the same proof can be done for abundance 56 using n=28p
> until now, i donıt have an idea of how to prove ratios to
other
abundancies,
> because as far as i know there is no rule for the amount of
primes in a
> certain area.
There are very good estimates for the number of primes in an
interval.
Youıll Ŝnd them in texts on analytic number theory, and
possibly in
chapters on analytic number theory in more elementary texts,
and
possibly even in one or more of the recently published popular
treatments of the Riemann Hypothesis.
Are there numbers not of the form 6p, p prime, with abundance
12?
Lots of them?
--
Gerry Myerson (gerry@maths.mq.edi.ai) (i -> u for email)
===
Subject: Re: astonishingly many numbers with abundace 12 and
56
> Are there numbers not of the form 6p, p prime, with
abundance 12?
> Lots of them?
24 = 2^3*3
54 = 2*3^3
304 = 2^4*19
Seems to be all of them.
Phil
--
... one Marine noticed one of the prisoners was still
breathing. A Marine
can be heard saying on the pool footage provided to Reuters
Television:
Heıs ing faking heıs dead. He faking heıs ing dead.
The Marine then raises his riŝe and Ŝres into the manıs head.
The pictures are too graphic for us to broadcast, Sites said.
===
Subject: Unknown operation
X-RFC2646: Format=Flowed; Original
Let A be the product ring ZxZ_20. Consider the following
function F:A-->Z_20

:
F((x,[y]_20))= [9xy]_20.
If * is the usual multiplicative law in Z_20, Ŝnd the
operation .
such
that F is a homomorphism from A(.) to Z_20(*).
TIA
===
Subject: Re: Unknown operation
X-RFC2646: Format=Flowed; Response
fake <fakkicini@invalid.com> ha scritto nel messaggio
> Let A be the product ring ZxZ_20. Consider the following
function
> F:A-->Z_20 :
> F((x,[y]_20))= [9xy]_20.
> If * is the usual multiplicative law in Z_20, Ŝnd the
operation .

> such that F is a homomorphism from A(.) to Z_20(*).
> TIA
Maybe (a,[x]).(b,[y]) =def (ab,9[xy]) ????
===
Subject: Re: Probability Question -- Polymer Chain Breaking
Originator: jeyadev@kaveri
Ah! I did win my bet. I had put money down on you responding
:-)
>>The polymeric chains can be seen a chains made up of links,
which are
>>broken to produce smaller chains. Links that are broken
once cannot
>>be broken again. Let the average number (or, fraction)
>>of chains with Œiı links (i=0, 1, 2, ...) at time t_k be
given by
>>n_i(t_k). The initial distribtion at t = 0, {n_i(0)} is
given.
>>Assume that
>> 1) there is a constant ŝux of entities that attack the
links
>> and break them
>> 2) At any time, any of the links is equally likely ot be
broken
>> 3) The number of links broken at at time t_k is
proportional to
>> the total number of links present at that time (this just
takes
>> into account that as the number of unbroken links reduces,
the
>> breaking entities will become less ŒefŜcientı as there are
>> fewer links to break due to Œdilutionı)
>>What we seek is the time evolution of the {n_i(t_k)}.
>One way to do this, I think, is to use a continuous-time
Markov chain.
>In time interval t to t+dt, any given unbroken link breaks
>with probability f dt + O(dt^2), independent of all other
links.
>The probability of an initially unbroken link being still
unbroken
>at time t is then exp(-f t), and the expected number of
unbroken
>links is C exp(-f t) where C is the number of unbroken links
at time 0.

Got that. I had framed it in the discrete time version just
because I
am already thinking of Monte Carlo .... :-) What is really
bothering
me is expected number of the broken bits.

>If you take an initial chain of N unbroken links and break
links
>independently with probability p, if I understand you
>correctly the subchains of unbroken links that remain
correspond
>to runs of successes in a sequence of N Bernoulli trials with
>success probability 1-p. There should be well-known results
>about these, I think.
I thought about it along similar lines, but I think that it
is not
correct. If we assume that all links are equivalent, then, I
believe
that it is not possible to think in terms of individual
chains. Consdier
the n_i chains. One can now make zero link chains by breaking
1) the
Ŝrst link of a chain, 2) the last link or 3) adjacent links
anywhere
in any of n_i chains ... Thus, one has to look at the entire
i*n_i
links, even though the fact that each chain has only i links
is
important. In other words, the ŒNı that you have is itself a
random
variable and there are n_i values such that they add up to
f*i*n_i,
the total number of links broken in the i link chains.
Now, I hope that I am understanding *you* correctly :-)
--
Surendar Jeyadev jeyadev1@wrc.xerox.com

Remove 1 for email address
===
Subject: Re: Probability Question -- Polymer Chain Breaking
Originator: jeyadev@kaveri
>Howdy, Surendar,
>Just curious... any chance the polymers are genetic material?
>Bob H
Nope. Very mundane. Mylar, actually.
This is just to see if some data that we have on mylar
degradation
makes sense. Physical intuition says it does not!
--
Surendar Jeyadev jeyadev1@wrc.xerox.com

Remove 1 for email address
===
Subject: Re: Skolemıs Paradox and why is math the way it is?
[snip: I think I understand that now, thank you.]
> | I think itıs just that the
> |teachers I had before werenıt clear, it seems like
something has to
> |come Ŝrst.
> It can be difŜcult to be clear without being philosophically
> heavy-handed. This happens when people teach quantum
mechanics
> in a similar way. One has these several different
interpretations.
> One could pick one and teach as if it were so, which can be
somewhat
> misleading. On the other hand, one could try to teach the
various
> interpretations along with the more essential material,
which could
> make it confusing. An instructor could try to stick to just
the
> most essential material-- that part you need to understand
to be
> able to compute the probability of observed outcomes.
I think the best way to teach quantum mechanics is to assume
that the
wave-function is real (exists), and that the equations
describe how it
moves, and thatıs it, in practise thatıs all you need and
every
interpretation takes that seriously to the extent that the
interpretation takes anything seriously at all.

> To be completely unbiased and transparent with regard to
such
> possible qualms as doubting that the natural numbers really
exist
> probably seems like too much of a distraction. So the usual
approach
> is basically not to worry about it. The platonist and the
formalist
> will tend to sound the same as they are developing a
theory, since
> deducing consequences from some assumptions typically
sounds just
> like you believe the assumptions to be actually true in some
> domain. And then one can divert discussion of qualms to
such venues
> as sci.math.
This seems rather ahistorical, the problem is that at one
point people
took the existance of classes for granted and it created
problems.
And the point of the modern theory is to avoid those
problems, so
you have to be clear that everybody is doing the same thing
so that if
someone gets a problem itıs clear that the system is to
fault, not the
person.

> | We can assume induction in the langauge and then latter
> |show there there is an induction INSIDE the theory as
well, so that we
> |donıt have to use induction outside the theory, but thatıs
very very
> |different than proving induction without proving
induction. Thatıs
> |proving induction in a theory using induction outside the
theory.
> Yes, *if* you assume induction for your original concept of
string,
> itıs an informal assumption that canıt come from inside the
theory.
> Having proven mathematical induction from the axioms, to
conclude that
> it applies to actual strings is a further step, requiring
either
> believing the axioms are correct in some sense or something
like that.
As I mentioned before, the PURPOSE of the formal theory was
to avoid
problems, if you actually are depending on the informal
theory (Iım
reading Quine now and so far it looks like formulas will be
built out
of philosophical statements and not strings and that
statements of
set theory will be based on other statements, and that the
axioms will
likely be about assuming the truth of some statements (which
is like
interpreting a schemata), I havenıt Ŝnished it yet, so donıt
think
thatıs how Iım characterizing Quine, itıs just my expectation
based on
where I am so far and it seems at least not to be circular at
this
point.

> | Set
> |theory canıt do itıs own model theory and have every
existentionally
> |possible set be in the model,
> Note that I only have a vague idea of what existentionally
possible
> set means. Existentionally looks like a cross between
existentially
> and extentionally.
> I also donıt really know what you think do itıs own model
theory
> should mean. I donıt consider any particular kind of
self-application
> (do your own model theory, deŜne your own truth-predicate,
and
> the like) to be an important criterion for a theory. I can
see how if
> one were looking for a theory to be the be-all and end-all
of theories,
> one would need for it to be able to do to itself anything
that any
> other theory could do to it. But the quest for the be-all
and end-all
> of theories seems a bit quixotic. One surely would need to
quit
> focussing on particular formal theories to serve as the
be-all and
> end-all, and look instead at such things as the process by
which we
> develop theories, and try to Ŝnd the ultimate
theory-development
> process.
Set theory was billed to me as the type-free be-all theory,
and Iım
not sure if you are refuting that as a misrepresentation that
my
teachers made or if yoy are agreeing with them, I canıt tell.
But IF
logic avoids having inŜnite regresses into higher-order
logics so
that we CAN sit down and discuss how you make theories, so
isnıt that
worth considering? Consistent theories imply strategies.
Thatıs a
REAL implication. But people complain against IF-logic exactly
because itıs the right size to do that because it isnıt the
right
size for NOT doing that (not the right size for formal
deduction).
And thatıs silly because IF-logic has ordinary FOL as a part
of it
anyway, so anything you do with oFOL you can do with
IF-logic, just
stop using the / or // symbols.

> For theories with more realistic goals, I would say
self-application
> is a bit like being able to lift all the rocks that one can
make.
> It could be a sign that one is strong. Or it could be a
sign that one
> has a limited ability to make rocks. IF logic can deŜne its
own
> truth-predicate, yes. But thatıs a combination of being
strong in some
> ways, and being weak in others.
In what way do you think it is weak?

> | but that doesnıt mean there isnıt a
> |strong theory that *can* do itıs own model theory that has
set theory
> |(and hence everything based on it) as a component. Thatıs
what Iım
> |looking for now, and I think the excluded middle is the
only thing in
> |the way really. There is a subsection of the universe
where the
> |excluded middle holds, and thatıs what we call set theory,
but itıs
> |intended models (if it has any) live outside that
subsection.
> Why?
Every model of set theory lacks a set that should exist as
much as the
alleged uncounted real should exist. The proof depends on the
excluded middle, that every set A either has to belong to a
set B or
not belong to B. That assumption has no basis real except for
mantaining an excluded middle. You could still have SOME sets
with
that property (that everything is either in them or not in
them), but
they simply wouldnıt be all sets. And if your goal is to have
every
set that should be, then it looks like you have to have those
nonexclusive sets too because any axiomatic way to carve them
out
takes other (normal) sets with it.
> I mean, I have no big problem with abandoning LEM. Perhaps
itıs a
> bit of a big step to propose that it be abandoned
generally... but
> constructive mathematics proceeds without making any blanket
> assumption of LEM.
> It is consistent to assume that there exists a function
from some
> subset of the integers onto the reals, e.g. the function
taking the
> indices of Turing machines that compute real numbers to the
real
> numbers that they compute. (Compute is in the sense of
computing
> rational approximations to them.) Perhaps something of that
nature
> would be more agreeable to you. It still doesnıt mean that
the reals
> are countable, however.
And once you extend the deŜnition of set to have non-excluded
middles, the standard proof about the lack of a set with a
speciŜc
property goes away, the theorem becomes the graph of the
bijection
between a set and itıs power set does not have an excluded
middle,
even if it exists. And yes we can make a hierarchy based on
equivalnce classes of sets based on graphs with excluded
middles,
itıll be just like cardinality theory if we do it right.
> |The math classes I took assumed that for every sentance
T(x) such that
> |for every set X such that for all x (x in X) => ((T(x) is
true ) or
> |(T(x) is false)) there exists a set Y such that for all y
(y in Y) <= |((x in X) and T(x)), where set and sentance were
both undeŜned, then
> |the standard interpretation of set and sentance were
assumed outside
> |the theory, but maybe the set part is Ŝne, but they should
have been
> |more honest about what was a valid sentance, some
professors actually
> |it is true.
> Well, you do realize that a lot of people consider it
rather artiŜcial
> to go around talking about what is true inside the theory
and what
> is true outside the theory as if they were two very
different spheres
> of discourse? It just sounds like a course being taught as
if
> a standard realist point of view were valid.
> I donıt see any problem with sets of natural numbers such as
> {n : there exists an Oscar award winner who has had n
divorces}.
> To the extent that the sky being blue or actually being
divorced have
> some degree of grey area, these may be somewhat fuzzily
deŜned. But
> itıs only when you decide to formalize the theory that you
need to
> specify what kind of formulas are allowed.
> The problem only comes in when you want to formalize the
axioms. If
> your instructor stated the selection axiom as above without
noting
> that itıs an axiom schema, and that the axioms generated by
the
> schema can only have T(x) that is expressible in the
language, then
> theyıve made a rather technical inaccuracy in the
presentation. But
> if for some speciŜc formula T(x) the above is an axiom in
the language
> of ZFC, it obviously must be a T expressible in the
language of ZFC.
I can grant that no deception was intended if you think it
was just a
technical inaccuracy, Iım a bit scarred (as in maimed, not as
in
afraid) in that I still do not know the order in which to
resolve
things, but Iım still hoping this book of Quineıs Iım reading
will get
everything in the right order.

> Judging by the kinds of questions people ask on sci.math,
imposing
> this kind of technical detail right away tends to be
confusing to
> many students. Moreover, the informal assumption that this
axiom
> continues to be true for any predicate is the more basic
assumption
> than the axiom schema is.
Students should study a Ŝnitely axiomized version of ZFC Ŝrst
(IMO)
with clearly stated and deŜned terms of language (thereıs
only a few
formulas in this baby-set-theory) and satisfaction and
everything, and
then later you bring in the whole schemata, but why not take
the
IF-logic Ŝrst order translation of the negation of a second
order
axiom, speciŜcally the IF-logic Ŝrst order translation of:
EF ~ (Ax Ey Az (zey) <-> (zex and 0=F[z]))
Then to say T is a theorem you can state that it is true that
either the above true, or the some other axiom is false, or T
is
true. I donıt know why we need informal sentances or
metalanguages
or schema at all. Just If-logic Ŝrst order sentances, and
assertions
(hypotheticals) that the universe of discourse is such as to
make some
sentances false (like the f.o. translation of EF ~ (Ax Ey Az
(zey)
<-> (zex and 0=F[z]))).

> | But this sneaks a truth predicate into set theory that
> |isnıt supposed to be there, and I know they were smart
enough to know
> |better, so Iım left to conclude that they did it on
purpose.
> Youıre a mighty suspicious guy.
> Including the phrase is true, as you have it above, is
often just
> a kind of verbal ŝourish. If someone deŜnes A or B to mean
either
> A is true or B is true, that does not mean that theyıre
intending to
> deŜne or in terms of a truth-predicate. Failing to restrict
to
> formulas in the language of ZF is a matter of allowing set
theoretical
> language to intermix with ordinary language.
I am totally familiar with how to translate either A is true
or B is
true into (A or B) is true by using ordinary language, I
could even
evalute (A or ~A) as being true in the case that there is no
excluded
middle without someone saying A is true or A is false to me, I
know that excluded middle is assumed to mean that one of
those holds
regardless of what A is AND that ~A is true when A is false is
true. I donıt think this is about colloquialism. I think this
is
about describing separation badly, I donıt think itıs about
logic or
language at all, so is EF ~ (Ax Ey Az (zey) <-> (zex and
0=F[z])) a
good descrpition of what is intended by separation or not? I
still
donıt know.
> Donıt confuse smartness with being sufŜciently persnickety
to avoid
> making technical slips on the order of the things youıre
describing
> here, or caring a lot about them. I realize that to you,
the fact that
> the axiom schema in ZFC only guarantees selection for
formulas in ZFC
> seems very important, but thatıs because of the kind of
concern you
> have for explaining to yourself how models of ZFC can
manage to be
> countable and things of that kind.
Smartness is related to knowing things, if someone asks if
youıre sure
and you say you are sure when in fact you are wrong, then
either (1)
you were dishonest when you replied yes Iım sure or (2) you
are not
a master of your material because you WERE sure and yet you
were
wrong. Does that make sense yet? I tend to assume (1) because
if I
assume (2) to everyone who makes an error then I have to
reinvent
absolutely everything myself, and force everyone to use *my*
deŜnitions and so on, which is socially too akword. Honestly,
people
can be un-persnickety in general, but to persist when someone
asks
if you are sure is what makes people be capable of calling you
dishonest, especially when later conversations reveal that
not only do
you know it was wrong, but if you claim you knew better at
the time.
I agree that it could still just be a slip of the tongue, and
a
mistake, but how many books and how many teachers before this
persistant slip seems to be a concerted case of either (1) or
(2).

> NB: the technical error here is ONLY an issue if the
instructor in
> question was stating the selection axiom schema this way
*as a part
> of ZFC*. If theyıre just stating it as an axiom, then
theyıre just
> giving an informal axiom.
The only thing the instructor talk about was ZFC, he never
mentioned
schemas or formulas, he said sentance and he gave the sky is
blue
as an example and he assumed truth and falseness of the
sentance T(x)
for every x in a set X. And he said this was set theory, not
we-havenıt-gotten-to-set-theory-yet.

> | And I
> |shouldnıt have to wait for weeks to get a book that deŜnes
formulas
> |without assuming set theory Ŝrst, itıs a bit sad that so
many people
> |do this in a non-rigorous way.
> Donıt confuse rigor with formality. Only a formalist needs
to have
> formula deŜned *inside* of a formal theory separately from
outside.
Iım unfamiliar with your deŜnitions of realist, formalist and
so
on, it just wasnıt covered in my education. Some people on
this
Usenet group have told me to take a set theory class, I have,
they
didnıt cover those terms. Are they covered inmost classes and
was I
just unlucky?
Iım Ŝne with IF-logic saying that some string represent
well-deŜned
games and that some games have winning strategies for one
side, and
some for the other, and some donıt. Iım Ŝnd with someone
making a
claim that the set theoretical universe is such as to make
the string
(~A1)or(~A2)or...(~An)or(T) true (when ŝeshed out with the
right
axioms for A1 through An and the theorem for T, and if they
say that
itıs true for all theorems, then that just leads to the
question what
are the theorems, but that isnıt confusing because we are
forever
talking about actual games and these questions are about what
elements
can be selected for substitution in the games and which atomic
sentances AeB are going to be true, and which are going to be
false.
Itıs forever a discussion about the rules of the game, no
inŜnite
regress into types.
This is FINE for physics because in physics we ALSO play
veriŜcation
and falsiŜcation games in the laboratory, so I can make them
match
universe is such that when I do this experiment I get this
kind of
results, and one can make DIFFERENT models to help CHOOSE new
things
to TEST (in both math and physics). And based on the results,
you
might decide to change the rules of the game (new axioms), or
just
make new deŜnitions to make existing questions easier (for
people) to
ask, verify, or falsify.

> |Then there is the whole colloquialness of truth, theorem,
theory,
> |model, proof, that people use. I donıt think they were
trying to be
> |dishonest there, but itıs very very very difŜcult for
students to
> |learn when people are using the words different ways.
> The responsibility for making an author-reader or
teacher-student
> relationship work is a shared one. I donıt think your
teachers or
> the authors of the books youıve read have failed you to the
degree
> youıre suggesting. Most students, although they may have
some
> difŜculties, tend not to get so hung up on the particular
issues
> that youıve described. I donıt think you need to have
regarded it
> as such an impediment.
The physics classes Iıve taken I can teach myself, why is
math so into
hiding things? I couldnıt honestly teach set theory today,
even a
basic one, because I havenıt seen a logical presentation. My
physics
teachers would answer questions when the students got
together and
demanded resolution (like when we asked to know how you know
when to
treat a stick as single object versus each molecule like a
separate
object, versus each atom as an object versus electrons and
nucleuses
versus electons and quarks and gluons), and they did so in
non-circular ways. But the math proffessors just say why are
you so
interested in foundations, I thought you liked physics?, Iım
just
simply tired of being discriminated with, Iım certain that
they talk
not in circles amongst themselves, and I think itıs down
right rude to
hide the actual logical developement from people just for not
being
in the club, this isnıt middle school this is science. I
consider
math to be science.
One of the differences is that as a physicists Iım rewarded
and
respected for being skeptical of everything, my work, the
owrk of
others, results I see, etc., but in math thatıs praised until
you ask
about ZFC, and then itıs like surely you donıt doubt ZFC, but
how
can I either doubt or trust it if no one tells me what it is?

> |> Mathematicians seem generally, even the ones who are not
formalists,
> |> to treat the job of deducing consequences from axioms as
playing a
> |> special role in doing mathematics. It is supposed to be
what we can
> |> all agree on. I certainly hope that there is no
circularity in your
> |> set theory books in that part! Your set theory books
should contain
> |> many theorems that follow deŜnitely from one of the
usual sets of
> |> axioms for set theory.
> |If the axioms arenıt described clearly enough, itıs not
much an
> |exercise in anything.
> Clearly enough for *what*? I donıt think you can name any
exercise
> where you are asked to prove a result, and where the reason
why it
> is difŜcult for you to complete the exercise is that it
wasnıt
> clear enough what the axioms were.
There is the translation from English to set theory and back
constantly, there is no way for me to tell that Iım doing it
the same
way. The point is that someone can say X is a theorem: Y, QED
but
if you donıt know WHAT it is a thoerem of, then I canıt turn
around to
the guy next to me and say X is a theorem because if Iım asked
theorem of what then I canıt answer, so the theoremhood of the
statement isnıt really proven (I canıt carry it around with
me or
apply it outside of the set theory class), it was only stated
as a
theorem of SOMETHING. Only after we know the axioms can we
know that
X is IN FACT a theorem of THAT axiom system.
> [...]
> |Lost you on the deŜnitions again. Is a theorem a truth of
all models
> |or a provable statement of a language (assuming a Ŝxed
standard of
> |proof)?
> If a system of axioms is a formal system, then theorem
means a well-
> formed formula that follows from the axioms by the rules of
the system.
> If we simply give a set of statements as axioms, the
theorems are the
> statements that logically follow from the axioms. If the
language of
> a system is understood as being statements about a
(variable) model,
> then this becomes true in all models, since in that case,
for a
> statement to follow logically from a collection of other
statements
> simply means that it holds for all models in which the
premises do.
With you so far then.

> I had in mind the common situation where one has a
Ŝrst-order theory.
> In that case, we have the Goedel completeness theorem that
says the
> logical consequences of a set of axioms are the same as the
consequences
> that can be deduced using standard Ŝrst-order logic.
Are you sure about how you stated that? Iım assuming standard
Ŝrst-order logic is ordinary Ŝrst order logic (so not
IF-logic or
SOL), but with IF-logic you can make Ŝrst order statements
that
arenıt statements of ordinary Ŝrst order logic, so you claim
seems,
... a bit sensational. If itıs true, then thatıs great, but I
want to
know if thatıs what you meant.

> |If the latter, then what does it MEAN to be interested in
> |whether a theorem follows from the axioms, since they all
do?
> What I should have written was whether a statement follows
from
> the axioms, or whether a statement is a theorem.
> In any case, those of us who are not formalists seldom care
whether
> the Riemann hypothesis is a theorem of ZFC or PA or
whatever, or
> whether the twin prime conjecture is a theorem of ZFC. We
do care
> about whether theyıre true, however. The formalist thinks
somehow
> that these questions are not well enough deŜned, but
everybody
> else aside from Essenin Volpin as far as I know disagrees.
You totally lost me here, people care about whether a
statement is
true when itıs true in some models and false in others? Just
consider the models where itıs true, now itıs true. Or
consider the
ones where itıs false, now itıs false. Why would anyone care
about
this? Am I therefore a formalist to Ŝnd this silly?

> [...]
> |The dependancy was in deŜning the axioms. What I think you
call
> |formal (what Iım used to called pure,a s opposed to
applied)
> |mathematics is about propositional relations, like x is a
y, where you
> |donıt say (or know) what x is or y is or even is a is or
means, and
> |the statement x is a y is obviously netihre true or false,
itıs
> |meaningless. But what you do is assume that certain
relations BETWEEN
> |propositional relations hold, like for all x, for all y,
(x is a y)
> |or (y is a x), then you can consider what other
propositional
> |relations must ALSO hold that hold INDEPENDANT of any
meaning ascribed
> |to x, y, or is a. Then later if a model exists, that means
someone
> |can make an interpretation where the xıs, yıs, and is a
> |propositional relations are interpreted to be mean
something, and the
> |model is faithful is the axioms (as propositional
relations) hold true
> |in the model (as meaningful statements), and a theorem of
the axiom
> |system is a statement in the language of the thoery that
is true in
> |all faithful models of the axioms. Thatıs how it works for
group
> |theory,
> I donıt think so.
> I just went over to my bookshelf and opened a group theory
> textbook at a random page. The theorem there was that the
center
> of the group GL(n,F) consists of the set of diagonal
matrices.
> GL(n,F) consists of the invertible n by n matrices with
entries
> in the Ŝeld F.
> What are the axioms that supposedly deŜne GL(n,F)? We all
know
> what natural numbers are, and what invertible n by n
matricies
> are, but not because there are axioms for them. An n by n
> matrix is a function from {1,2,...,n}x{1,2,...,n} to F;
invertibility
> means that there exists another such one that is its
inverse, etc.
> The starting point is arithmetic, i.e., knowing what it
means
> to have a natural number n. What complete axiomatization of
> arithmetic do you have in mind when doing group theory?
Iım really confused, I took this course called abstract
algebra and
we didnıt assume any axiomatization of arithmetic, if fact
the whole
point was to avoid that, but instead to axiomize a group so
that
later anything that was a group would have the group theory
theorems
true of it. The group GL(n,F) satisŜes the group axiom with
the
multiplication that you would expect for it (any in fact
since F
satisŜes the Ŝeld axioms by hypothesis, you can prove that
GL(n,F)
is a group, which is GOOD because that makes the nomen group
well-deŜnedish with the fact that GL(n,F) satisifes the group
axioms,
the whole point is that the results we proved about the
center of
abstract groups can then be applied to the subcase of groups
GL(n,F).
Why you think this starts with arithmetic is comletely behind
me, you
have an abstract Ŝeld F, and from it you make a group
GL(n,F), where
does arthemetic come in?

> | Ŝeld theory,
> I donıt really have a book just on Ŝeld theory as far as I
know,
> but it occurs to me that one Ŝeld being algebraic over
another
> isnıt Ŝrst-order deŜnable. The property of a Ŝeld extension,
> that the overŜeld is a *Ŝnite* dimensional vector space over
> the subŜeld, comes up often. The Ŝniteness intended is what
we
> (foolishly?) understood as just plain Ŝniteness, not
Ŝniteness
> relative to a model of [something].
The common axiomization of Ŝeld include the term set, hence
the
importance of the question what is a set. If you threw in F
is a
Ŝeld iff (FA1, and FA2, ... FAn, and STA1, STA2, ... , and
STAn)
(where FAk is a Ŝeld axiom and STAk is a set theory axioms)
then
youıd know what the models of Ŝelds are, but without, you
have to beg
the question over to set theory and ask is this a set to know
if
something is a model of the Ŝeld axioms.

> | geometry, etc.
> How many colors are needed to color the points inside a unit
> square, so that no two points of the same color are a
distance
> of 1/2 apart?
> When people doing Euclidean geometry talk about the
Euclidean
> plane, they are talking about the one thatıs isometric to
R^2,
> pairs of real numbers, not an arbitrary model of some
Ŝrst-order
> axiomatization of it.
Classical geometry is both complete (every statement with the
uninterpreted primatives or geometry is either a theorem or
the
negation of a theorem) and categorical (all models are
isomorphic) as
an axiomatic theory, so what is arbitrary about itıs models?
And
geometry doesnıt have a primative color. Youıve lost me
completely
again. Isnıt that really a question about functions from
manifolds
into integers?

> Generally, your statement comes much closer to correct if we
> are considering relationships between second-order
statements.
> But thereıs no formal deductive system for second-order
statements
> that captures all the valid deductions that can be made in
> second-order logic. Second-order logic also involves
referring
> to arbitrary subsets of the domain, which is the usual
bugaboo
> of set theory.
Formal deductive methods donıt work for set theory correct,
but they
do for geometry I donıt know why you think they donıt. I
donıt know
why you keep bringing up formal deduction anyway, we donıt use
deduction to design theories, so what is this prima facie
reason for
such a hubbub about it? Work at Ŝnding the valid deductions
in SOL
or IF-logic if you care about set theory, use formal
deduction if you
care about geometry. How does this relate to anything we are
talking
about?
And if someone is concerned about arbitrary subsets, donıt
quantify
over them, just stick to the IF-f.o. translations all the
time, and
then it becomes a question of models and strategies the way
it ALWASY
is. You donıt have to consider arbitrary subsets, just
strategies of
games based on formulas, and the ZFC games are the ones that
start a
particular way, and the theorems are the one where you win
regardless
of the model (because either the model fails to satisfy the
axioms, or
you satisfy the statement of the theorem).
> [...]
> |> A formalist considers everything above the bottom line
to be just a
> |> kind of rhetorical ŝourish. A Platonist will tend to
regard the
formal
> |> side as being just another technique for reŜning
informal reasoning.
> |> Not many mathematicians are very much interested in
either reŜning
> |> our explanation of what the undeŜned terms like set
mean, or
justifying
> |> the truth of the axioms in those terms, however. Whether
a given
> |> mathematician believes the axiom of choice tends to be
treated as a
> |> matter of personal belief.
> |Thatıs VERY annoying. I took a class in functional
analysis where the
> |professor actually changed whether the axiom of choice was
true
> |halfway through the semester, I basically had to go redo
everything.
> Thatıs a great story, and I agree that thatıs annoying, at
least if
> he did it in a way that forced the class to redo work. If
he had
> meant to do this, he should at least have started with the
neutral
> theorems (ones not needing choice) and then added the
additional ones
> that can be proven with choice.
> But whether to believe the axiom of choice is really true
or not has
> no necessary connection with whether someone works using it
or not. One
> formalist who doesnıt believe that 10^n exists for each
natural number
> n has proven results in set theory using all the usual
highfalutinı
> assumptions.
The PROBLEM is using ONE word set when people ARBITRARILY
CHOOSE to
have the word essentially MEAN different things, itıs bad bad
bad. If
the word electron meant something different depending on who
said
it, physics would get nowhere fast. I agree that someone
could write
out a proof (so could a Turing machine) without believing the
theorem
to be true (so could a Turing machine), but if we are going
to use the
word set it should mean something, not whatever the speaker
imagines
in his head, thatıs one of my biggest problems, Iım trying to
get a
straight answer about what is and is not a set, and Iım not
getting
one.

> |Hintikka gives a justiŜcation about why mathematicians
like the axiom
> |of choice because it translates the standard
interpretation second
> |order formulas into equivalent Ŝrst order formulas, but
then he shows
> |that that doesnıt work in general.
> Mathematicians do tend to like instances of
quantiŜer-elimination,
> even when they are unaware of the concept of
quantiŜer-elimination.
Iım not sure how thatıs a response to my statement, there is
NO model
of set theory where all such translations are valid. Thatıs
what the
proof-predicate at the Ŝrst-order level shows. And if you
start
dancind around the issue by taking a non-standard
interpretation of
SOL, thatıs just silly to then insist on a standard
interpretation of
ordinary FOL theories. Something seems to have to give here.
> | I think thatıs because he was
> |holding onto an excluded middle for atomic sentances when
he didnıt
> |need to, but thatıs his problem, there is no reason I
canıt assume no
> |excluded middle.
> Some properties of structures seem simply to be
second-order and
> not Ŝrst-order. Whether a graph is connected or not, for
example.
> I donıt see how one can get around it.
> Keith Ramsay
Set theory is supposed to be type free, e.g. you have a set of
points AND a set of edges AND they are both sets, everything
is a set.
So let A be the set of points and let B be a the set of
unordered
pairs of elements of A such that {a,b}eB iff there is an edge
between
a and b. Now let f: N->P(A) be a function such that f(0) = B,
and
such that f(n+1)={CeP(A):ExEyEz (yeS(n)) & (zeS(n)) & (xey) &
(xez) &
C=U({y,z})}, then the Ŝnite graph A is connected iff En
Aef(n),
thatıs all f.o. set theory. If you had an inŜnite graph, then
youıd
need a better deŜnition of course, but Iıd have to know what
the
exact deŜnition of connected is to get an iff going, for
instance
A is disconnected iff ErEs An ~ Et (tef(n)) & (ret) & (set)
might be
correct, I donıt know. I think itıs obvious that Iım failing
to get
your point though, sorry.
===
Subject: Eqautions for generating a sphere?
This is proabably a simple question, but does anyone have a
set
of equations that could be used to generate a set of vertex
data
to model a sphere for a computer graphics application?
===
Subject: Re: Eqautions for generating a sphere?
>This is proabably a simple question, but does anyone have a
set
>of equations that could be used to generate a set of vertex
data
>to model a sphere for a computer graphics application?
Do you mean you want to generate a set of N (pseudo-)random
points
uniformly distributed on a sphere? One way is this.
Generate three random numbers x_i with uniform distribution
in the
interval [-1,1].
If x_1^2 + x_2^2 + x^3^2 > 1 reject these,
otherwise take the point [x_1/r, x_2/r, x_3/r] on the sphere
x^2 + y^2 + z^2 = 1, where r = sqrt(x_1^2 + x_2^2 + x_3^2).
Repeat until you have N points.
Robert Israel israel@math.ubc.ca
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia Vancouver, BC, Canada
===
Subject: Re: Eqautions for generating a sphere?
>This is proabably a simple question, but does anyone have a
set
>of equations that could be used to generate a set of vertex
data
>to model a sphere for a computer graphics application?
> Do you mean you want to generate a set of N (pseudo-)random
points
> uniformly distributed on a sphere? One way is this.
> Generate three random numbers x_i with uniform distribution
in the
> interval [-1,1].
> If x_1^2 + x_2^2 + x^3^2 > 1 reject these,
> otherwise take the point [x_1/r, x_2/r, x_3/r] on the sphere
> x^2 + y^2 + z^2 = 1, where r = sqrt(x_1^2 + x_2^2 + x_3^2).
> Repeat until you have N points.
> Robert Israel israel@math.ubc.ca
> Department of Mathematics http://www.math.ubc.ca/~israel
> University of British Columbia Vancouver, BC, Canada
Actually although a Pusedo random approach to a sphere would
work for some applications, for the one in the original
enquiry, Perhaps a polyhedrial approximation
to a sphere in which face was a quadrilatrel
could be considered?
The reason for needing 4 vertexıs to from a face is to do
with the way the grpahics engine does texture mapping.
Essentialy the texture mapping is deŜned as a series of u,v
pairs
for a given vertex. (U and V being the number of
Œtexture-diatncesı
to display.
for a simple face the code might look like this..
Vertex 0,0,0
Vertex 0,1,0
Veretx 0,1,1
Vertex 0,0,1
Face,0,1,2,3
Texture Grass,Bmp
TextureCoordinate 0,0,0,
TextureCoordinate 1,1,0,
TextureCoordinate 2,1,1,
TextureCoordinate 3,0,1
Texture mappings across a mesh are more complicated in that
they can
use % values for U and V but in general follow a simmilar
pattern, Of
course a
u,v pair has to be deŜned for each vertex deŜned.
I knows this probably doesnıt help with spheres but it helps
explain
why
faces with at least 2 parrallel sides would be useful..
(Thinking about the parrallel sides wil;l probably be
Œlongditude;
or Œlatitudeı in an approximation but obviously not both at
the same
time across the whole sphere...)
Generating an approximation to a donut(ie ring torus) should
be
eaiser...
Alex
===
Subject: Re: Eqautions for generating a sphere?
X-Enigmail-Version: 0.86.0.0
X-Enigmail-Supports: pgp-inline, pgp-mime
hi,
there are basically two approaches: uv-spheres and subdivded
icospheres.
which one do you want?
> This is proabably a simple question, but does anyone have a
set
> of equations that could be used to generate a set of vertex
data
> to model a sphere for a computer graphics application?
===
Subject: Re: Eqautions for generating a sphere?
> hi,
> there are basically two approaches: uv-spheres and
subdivded icospheres.
> which one do you want?
> This is proabably a simple question, but does anyone have
a set
> of equations that could be used to generate a set of
vertex data
> to model a sphere for a computer graphics application?
Do you want to Ŝt data to a spherical surface? Is radius
known? Are
points same or near to Platonic/Archimedean solid vertices?
===
Subject: Re: Eqautions for generating a sphere?
>hi,
>there are basically two approaches: uv-spheres and subdivded
icospheres.
>which one do you want?
This is proabably a simple question, but does anyone have a
set
> of equations that could be used to generate a set of vertex
data
> to model a sphere for a computer graphics application?
> Do you want to Ŝt data to a spherical surface? Is radius
known? Are
> points same or near to Platonic/Archimedean solid vertices?
This is not about Ŝtting a data set.
The aim is to have some kind of polyhedron approximation to a
spehere,
that appears speherical by means of a texture mapping (or
shading...)
UV Spheres and icospheres sound intresting, please say more
:-)
===
Subject: New Model of Computation
Iıve got an idea for a new model of computation using
2-colored binary
trees. It has probably been thought of already or whatever
but check it
out. The paper is now just a draft sketch. Iıll get it into a
Ŝnal form
sooner or later if people think its worth pursuing.
See the paper at:
http://arxiv.org/abs/cs.CC/0411064
Comments appreciated.
===
Subject: Re: New Model of Computation
X-Enigmail-Version: 0.86.0.0
X-Enigmail-Supports: pgp-inline, pgp-mime
> See the paper at:
> http://arxiv.org/abs/cs.CC/0411064
you donıt want to tell us how to access it, do you?
webograph
===
Subject: Re: New Model of Computation
>> See the paper at:
>> http://arxiv.org/abs/cs.CC/0411064
> you donıt want to tell us how to access it, do you?
> webograph
In the bottom of the page with the abstract is a link to the
pdf document.
Here is the link explicitly.
http://arxiv.org/pdf/cs.CC/0411064
===
Subject: Re: New Model of Computation
Originator: tchow@lagrange.mit.edu.mit.edu (Timothy Chow)
> See the paper at:
> http://arxiv.org/abs/cs.CC/0411064
>> you donıt want to tell us how to access it, do you?
>In the bottom of the page with the abstract is a link to the
pdf document.
Is the problem that you just submitted it and itıs not
publicly viewable
yet? After a day that problem should disappear.
--
Tim Chow tchow-at-alum-dot-mit-dot-edu
The range of our projectiles---even ... the
artillery---however great, will
never exceed four of those miles of which as many thousand
separate us from
the center of the earth. ---Galileo, Dialogues Concerning Two
New Sciences
===
Subject: Re: New Model of Computation
> Is the problem that you just submitted it and itıs not
publicly viewable
> yet? After a day that problem should disappear.
You are probably right. I am not familiar with the system yet.
===
Subject: Re: what is the unit of the Matlab 2D FFT output
matrix?
>Hi all,

I just have a question about using Matlabıs FFT2 to compute
the 2D DFT
of an
>image...

An image is input as MxN pixels, what should be the unit of
the
frequency
>domain, thatıs to say, what should be the unit of the 2D DFT
matrix
returned
>by the Matlab FFT2 command? What does each grid of those MxN
output
matrix
>represent?
> inches per pixel (I think) - but the grid spacing is
dependent on M
> and N

>If I attach some physical units to the input image, say,
each input
pixel is
>in fact the sampled value of a physical image at sampling
rate 96
DPI(=96
>dot or samples per inch)... In this case, what should each
grid of
those
>MxN DFT output matrix represent?
In one direction they are units of 1/(N*96) inches per pixel
(I
> think) and in the other 1/(M*96) inches per pixel.

>I guess the FFT2 output matrix has no meaning if the MxN
input image
matrix
>is not associated with a physical units...
Too deep for me - if you do the inverse transform to get back
into
> some space where you are conŜdent of the meaning of your
output I
> donıt see that you need to worry.

> Best of Luck - Mike
Aaah! Inches per pixel - I must be going barmy. Take no
notice of me
kiki - Armanıs quite right! You can see it more or less
immediately by
:
ft=zeros(27,41);
ft(2,40)=1;,ft(2,2)=-1;,ft(26,40)=1;,ft(40,40)=-1;
plot3d(1:27,1:41,abs(ifft(ft)));
playing around with the values at the corners lets you put in
1/2
cycles or DC levels and itıs all very pretty.
Best of luck - Mike
===
Subject: Constructing analysis counterexample
I know the following theorem is true:
If {f_n} is sequence in L which converges uniformly on X to a
function f, and if mu(X) < +inŜnity, then the integral of f
with
respect to mu is the same as the limit of the integral of f_n
with
respect to mu. (L is the set of Lebesgue integrable functions
deŜned
on X.)
Iım trying to prove that the theorem fails if the
hypothesis mu(X) < +inŜnity is dropped. Any ideas?
D. Dewey
===
Subject: Re: Constructing analysis counterexample
> I know the following theorem is true:
> If {f_n} is sequence in L which converges uniformly on X to
a
> function f, and if mu(X) < +inŜnity, then the integral of f
with
> respect to mu is the same as the limit of the integral of
f_n with
> respect to mu. (L is the set of Lebesgue integrable
functions deŜned
> on X.)
> Iım trying to prove that the theorem fails if the
> hypothesis mu(X) < +inŜnity is dropped. Any ideas?
> D. Dewey
Let f_n = { 1/n if 0 < x < n, 0 otherwise.
===
Subject: Re: Help with Diagonal subgroup problem
days. My association with the Department is that of an
alumnus.
[.snip.]
Once you have proven this, try your understanding by proving
the
generalization known as Goursatıs Lemma:
DEF. A subdirect product of two groups H and K is a subgroup
G of
the direct product H x K, such that the canonical projections
p_1:G->H
and p_2:G->K are both surjective (that is, for every h in H
there
exists y in K such that (h,y) in G, and for every k in K
there exists
x in H such that (x,k) is in G).
GOURSATıS LEMMA. Let H and K be two groups. There exist normal
subgroup M of H and N of K such that H/M is isomorphic to K/N
if and
only if there exists a subdirect product G of H and K such
that (G
intersect H) = M and (G intersect K)=N.
--
Itıs not denial. Iım just very selective about
what I accept as reality.
--- Calvin (Calvin and Hobbes)
Arturo Magidin
magidin@math.berkeley.edu
===
Subject: Re: Help with Diagonal subgroup problem
days. My association with the Department is that of an
alumnus.
===
>>Subject: Re: Help with Diagonal subgroup problem
>D is a subgroup of G=M x N (INTERNAL direct product) is a
diagonal
subgroup
>>if
>(D intersect M) = 1 = (D intersect N) and DM=G=DN.
>Show that G has a diagonal subgroup IFF M is isomorphic to N.
><== ?????????????
>>Let D be the graph of the isomorphism from M to N: Ŝx
f:M->N which
>>is an isomorphism, and let D = {(m,f(m)) : m in M}.
>I had asked another student about this and they basically
said something
>similar -- (m, f(m)) and they claimed it was just Œtrivialı
after that. I
>guess that I just donıt Œseeı anything. It says diagonal
subgroup, so
I
>assume that means on a Œgraphı it would be the diagonal from
left to right
>across only.
As someone pointed out, it is called diagonal because in the
special
case when M=N (which you can assume up to isomorphism if M is
isomorphic to N) and f=id, you get the literal diagonal.
>I need to show that DM=G=DN and (D intersect M)=1=(D
intersect N). Unless
D
>itself is just the identity (doesnıt make sense to me), it
would seem that
M
>and N could Ŝll up the entire graph and equal G.
G is not the graph. G would be more like the plane: G=MxN.
So, assume f:M->N is an isomorphism. let G = MxN, and let
D = {(m,f(m)) in G: m in M}.
Notice that for each point on the x-axis M, there is one and
only
one point on the y-axis, N; thatıs why this is sometimes
called
the graph of the isomorphism.
M is identiŜed with the subgroup {(m,1) in G: m in M} of G; N
corresponds to the subgroup {(1,n) in G: n in N}.
Then D intersect M = {(m,f(m)) in G: m in M, f(m)=1}.
Since f is an isomorphism, it is injective, so the only m for
which
f(m)=1 is m=1. Thus, D intersect M = {(1,1)}, the trivial
element of
G.
Likewise, D intersect N = {(m,f(m)) in G: m in M, m=1}. Since
f is a
group homomorphism, f(m)=1, so D intersect N = {(1,1)}, the
trivial
element of G.
Now we want to show that DM = G. That is, that the set of all
products
of the form
(r,f(r))(m,1) = (rm, f(r)1) = (rm, f(r)).
with m, r in M, cover all elements of G.
Well, let (x,y) be an element of G. We want to express it in
the form
(r,f(r))(m,1) = (rm, f(r)) for some r,m in M.
Since f is an isomorphism, it is surjective, so there exists
r in M
such that f(r)=y. And then if we let m = r^{-1}x, which lies
in M, we
have
(r,f(r))(m,1) = (rm,f(r)) = (rr^{-1}x,y) = (x,y). Thus, G is
contained
in DM, and hence (since DM is certainly contained in G),
equal to DM.
Now do something similar to show that G = DN.
--
Itıs not denial. Iım just very selective about
what I accept as reality.
--- Calvin (Calvin and Hobbes)
Arturo Magidin
magidin@math.berkeley.edu
===
Subject: Two new math jokes (Physicistıs vector space, and
compact math
curriculum)
Ok, here we go with 2 new math jokes! The Ŝrst one...
Q: What is the physicistıs deŜnition of a vector space?
A: A set V satisfying the axiom that for any x in V, x has a
little
arrow drawn over it
Ok now for the second one!
I was talking with a friend in my graph theory class and he
pointed
out that a lot of the material is review from his geometric
topology
class. I thought about this for a moment and said, Ah!
Mathematics
curriculum is compact! He asked me what I meant and I
answered:
Any material covered by an inŜnite number of math courses can
be
covered by some Ŝnite subset of those courses
Ok letıs see some other original jokes on this thread... :-)
Snis Pilbor
===
Subject: Re: Two new math jokes (Physicistıs vector space,
and compact
math
curriculum)
> Ok, here we go with 2 new math jokes! The Ŝrst one...
New? Oh, I get it. The redundant new.
> Q: What is the physicistıs deŜnition of a vector space?
> A: A set V satisfying the axiom that for any x in V, x has
a little
> arrow drawn over it
> Ok now for the second one!
For the second time.
> I was talking with a friend in my graph theory class and he
pointed
> out that a lot of the material is review from his geometric
topology
> class. I thought about this for a moment and said, Ah!
Mathematics
> curriculum is compact! He asked me what I meant and I
answered:
> Any material covered by an inŜnite number of math courses
can be
> covered by some Ŝnite subset of those courses
> Ok letıs see some other original jokes on this thread... :-)
Have you consider getting a metaphysical? ;-)
===
Subject: Re: Two new math jokes (Physicistıs vector space,
and compact math
curriculum)
In reply:
There are three kinds of people:
those who understand mathematics
and
those who donıt!
--
Casey
===
Subject: Re: Two new math jokes (Physicistıs vector space,
and compact
math
curriculum)
> In reply:
> There are three kinds of people:
> those who understand mathematics
> and
> those who donıt!
> --
> Casey
I think arithmetic works better than mathematics.
===
Subject: Re: Two new math jokes (Physicistıs vector space,
and compact
math
curriculum)
> In reply:
> There are three kinds of people:
> those who understand mathematics
> and
> those who donıt!
> --
> Casey
I prefer this old joke:
There are 10 kinds of people, those who understand binary,
and those who
donıt.
===
Subject: Re: Geometrodynamics of inertial force in ŝat
spacetime
> this case
> {LC}^1ı0ı0ı = F(non-gravity reaction force)/mc^2
> Therefore
> -g ~ F(non-gravity reaction force)/m
> QED!
Jack has neatly disassembled a VW in spaceport One,
but the work order calls for servicing the Rolls
in spaceport Two.
Have a look at Tolmanıs Eq.(103.1), and sub
the RHS Lorentz force/m for Jacks,
F(non-gravity reaction force)/m
Jackıs using Tolmanıs manual, unless there is
another way to depart from the conventional
geodesic , besides EMF.
Iım going to work on the Rollıs.
For clarity, Iım resetting notation for
an absolute derivative of the 4 velocity to,
DU^u/ds = dU^u/ds + Gamma^u_ab U^a U^b.
Then Tolmanıs (103.1) becomes, (m=1),
DU^u - q*F^u_a dx^a = 0 .
I expect that an outer with g_uv gets,
DU_v - q*F_va dx^a = 0
and I expect an outer with dx^v gets us
DU - q*F_va dx^a dx^v = 0 = power (F*V)
the RHS vanishes by antisymmetry then
DU = 0
is the geodesic equation in the presence of
EMF.
DU/ds = (dU^u/ds + Gamma^u_ab) U^a U^b U_u = 0
Now watch this, do an outer using U^v and get,
0 = (dU^v/ds + Gamma^v_ab) U^a U^b = 0
i.e. DU^v = 0 in the presence of EMF.
Jackıs old VW in Spaceport One has a
non-zero DU^v. My Rollıs in Spaceport Two
has a DU^v =0 all the time.
Ken S. Tucker
Let us not forget the Tucker Automobile,
that occupies Spaceport Three.
===
Subject: Joel shifting ignored
>this case
{LC}^1ı0ı0ı = F(non-gravity reaction force)/mc^2
Therefore
-g ~ F(non-gravity reaction force)/m
QED!
> Jack has neatly disassembled a VW in spaceport One,
> but the work order calls for servicing the Rolls
> in spaceport Two.
> Have a look at Tolmanıs Eq.(103.1), and sub
> the RHS Lorentz force/m for Jacks,
> F(non-gravity reaction force)/m
> Jackıs using Tolmanıs manual, unless there is
> another way to depart from the conventional
> geodesic , besides EMF.
> Iım going to work on the Rollıs.
> For clarity, Iım resetting notation for
> an absolute derivative of the 4 velocity to,
> DU^u/ds = dU^u/ds + Gamma^u_ab U^a U^b.
> Then Tolmanıs (103.1) becomes, (m=1),
> DU^u - q*F^u_a dx^a = 0 .
> I expect that an outer with g_uv gets,
> DU_v - q*F_va dx^a = 0
> and I expect an outer with dx^v gets us
> DU - q*F_va dx^a dx^v = 0 = power (F*V)
> the RHS vanishes by antisymmetry then
> DU = 0
> is the geodesic equation in the presence of
> EMF.
> DU/ds = (dU^u/ds + Gamma^u_ab) U^a U^b U_u = 0
> Now watch this, do an outer using U^v and get,
> 0 = (dU^v/ds + Gamma^v_ab) U^a U^b = 0
> i.e. DU^v = 0 in the presence of EMF.
> Jackıs old VW in Spaceport One has a
> non-zero DU^v. My Rollıs in Spaceport Two
> has a DU^v =0 all the time.
> Ken S. Tucker
> Let us not forget the Tucker Automobile,
> that occupies Spaceport Three.
Ooont Billy Joel Das singin Uptown girl dah dah dah diddy doo
daaaah
===
Subject: How to solve Diff eq. dx/dt*(f(x)+h(t))=0
Hi Every one
Can Some one give me a clue?
Oren
===
Subject: Re: How to solve Diff eq. dx/dt*(f(x)+h(t))=0
>Can Some one give me a clue?
Hint: There are two ways you can have a*b = 0.
Robert Israel israel@math.ubc.ca
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia Vancouver, BC, Canada
===
Subject: a tiling egroup has been formed a yahoo: you are
invited to join.

http://groups.yahoo.com/group/true_tile/
This group is about tiles in Euclidean n space, and
Non-Euclidean n space.
Discusions of crystalography, quasicrystalography,
substitution groups,
L systems, aperiodic tiles, Wang tiles.
Pisot numbers and space Ŝlling curves are all welcome here.
Send us your tile deŜnitions and a picture.
We are trying to get a registry of new tiles.
Respectfully, Roger L. Bagula
tftn@earthlink.net, 11759Waterhill Road, Lakeside,Ca
92040-2905,tel:
619-5610814 :
alternative email: rlbtftn@netscape.net
URL : http://home.earthlink.net/~tftn
===
Subject: Re: Root Finder vii.
> Root Finder vii.
> by Jon Giffen
> [...]
> t^3+2t^2+t-4=0 t=1
> a[0]= -4
> a[1]= 1 a[2]=2 a[3]=1 N=(1,2,1) |N|^2=6 Q=(2/3)(1,2,1)
> |Q|=(2/3)6^(1/2)
> D=(1,2,3) S=(1,4,3) S*N=(1,4,3)*(1,2,1)=1+8+3=12
> D*N=(1,2,3)*(1,2,1)=1+4+3=8
>
C=12(1,2,3)+8(1,4,3)=(12+8,24+32,36+24)=(20,56,60)=4(5,14,15)
> |C|=(4)446^(1/2)
> (2/3)6^(1/2)
> (t,t^2,t^3)=(2/3)(1,2,1)+/- ------------ (5,14,15)
> 446^(1/2)
> (t,t^2,t^3)=(2/3)(1,2,1)+/- 0.07732(5,14,15)
> (t,t^2,t^3)=(0.6666,1.3333,0.6666)+/-(0.3866,1.08254,1.1599)
> Selecting the Ŝrst component,
> t = 0.6666+0.3866 = 1.0532 ~ 1
Strike Seven. Approximations are not acceptable.
> then
> t^2 + 3t + 4
> ------------------------------
> t-1/ t^3 + 2t^2 + t - 4
> t^3 - t^2
> --------------------
> 3t^2 + t - 4
> 3t^2 -3t
> -------------
> 4t - 4
> and the remaining roots are
> -3+/-{9-16|^(1/2)
> t = ----------------- = -1.5+/-1.3229i
> 2
> Dividing t^3 by t^2,
> t^3 = 0.6666+1.1599 = 2.2656
> -----------------------------
> t^2 = 1.3333+1.0825 = 2.4158
> or
> t = 0.9378 ~ 1
Strike Seven(A). If t^2 > 1, then we must have t > 1 or t <
-1. But you
have t = 0.9378 < 1 (and t > -1). So all this has shown is
that your
method fails (again).
-- Christopher Heckman
===
Subject: Re: Root Finder vii.
The fact that the method you present consistently produces
wrong
answers would have prompted most researchers to go back to the
drawing board until the problem was understood and solved or
to
abandon the method. Doesnıt that sound appropriate?
--
There are two things you must never attempt to prove: the
unprovable -- and the obvious.
--
Democracy: The triumph of popularity over principle.
--
http://www.crbond.com
===
Subject: Please help with problem
X-RFC2646: Format=Flowed; Original
Find a cubic fcn f(x)=9x^3 +bx^2+cx+d that has a local max
value of 3 at -2

and a local min value of 0 at 1.
===
Subject: Re: Please help with problem
>Find a cubic fcn f(x)=9x^3 +bx^2+cx+d that has a local max
value of 3 at -2

>and a local min value of 0 at 1.
Review how you Ŝnd local max and min, using the second
derivative
test. You know fı(-2) = fı(1) = 0; you know f(-2) = 3 and
f(1) = 0;
and you know the signs of fıı(-2) and fıı(1).
Unfortunately the problem is overdetermined, and (if my
calculations are correct) there is no cubic curve that Ŝts
all the
conditions. Are you sure you copied the problem correctly?
--
Stan Brown, Oak Road Systems, Tompkins County, New York, USA
http://OakRoadSystems.com/
And if youıre afraid of butter, which many people are nowa-
days, (long pause) you just put in cream. --Julia Child
===
Subject: Re: Please help with problem
X-RFC2646: Format=Flowed; Original
>>Find a cubic fcn f(x)=9x^3 +bx^2+cx+d that has a local max
value of 3
>>at -2
>>and a local min value of 0 at 1.
> Review how you Ŝnd local max and min, using the second
derivative
> test. You know fı(-2) = fı(1) = 0; you know f(-2) = 3 and
f(1) = 0;
> and you know the signs of fıı(-2) and fıı(1).
> Unfortunately the problem is overdetermined, and (if my
> calculations are correct) there is no cubic curve that Ŝts
all the
> conditions. Are you sure you copied the problem correctly?
Something is wrong.......
27x^2 + 2bx + c = 0 when x = -2
27x^2 + 2bx + c = 0 when x = 1
108 -4b + c = 0.............(1)
27 + 2b + c = 0.............(2)
Subtracting (1) from (2)
6b = 81
b = 13.5
c = 54
-72 + 54 - 108 + d = 3 .............(3)
9 + 13.5 + 54 + d = 0................(4)
d = 129.......from (3)
d = -76.5 ......from (4)
PH
===
Subject: Re: Please help with problem
X-RFC2646: Format=Flowed; Response
hgl <HGL@COX.NET> escribi.97:
> Find a cubic fcn f(x)=9x^3 +bx^2+cx+d that has a local max
value of 3
> at -2 and a local min value of 0 at 1.
That conditions are inconsistent. Or the coefŜcient of x^3 is
a an mot 9?
--
Ignacio Larrosa Ca.96estro
A Coru.96a (Espa.96a)
ilarrosaQUITARMAYUSCULAS@mundo-r.com
===
Subject: correlation functions of uncorrrelated random
variables
Suppose x and y are two uncorrelated random variables with
Ŝnite
expectation values.
Then, by deŜnition, cov(x,y)=0.
Is it true then that
cov(x^2,y)=0?
cov(x^2,y^2) = E[x^2] E[y^2] ?
Roger
===
Subject: Re: correlation functions of uncorrrelated random
variables
>Suppose x and y are two uncorrelated random variables with
Ŝnite
>expectation values.
>Then, by deŜnition, cov(x,y)=0.
>Is it true then that
>cov(x^2,y)=0?
No. For example, it could be that y = x^2.
>cov(x^2,y^2) = E[x^2] E[y^2] ?
No. For example, it could be that x and y are
independent (and neither is ever 0).
Robert Israel israel@math.ubc.ca
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia Vancouver, BC, Canada
===
Subject: SORRY, I corrected the equation
X-RFC2646: Format=Flowed; Original
Find a cubic fcn f(x) = ax^3 +bx^2+cx+d that has a local max
value of 3
at -2
and a local min value of 0 at 1.
===
Subject: Re: SORRY, I corrected the equation
X-RFC2646: Format=Flowed; Response
> Find a cubic fcn f(x) = ax^3 +bx^2+cx+d that has a local
max value of 3
> at -2
> and a local min value of 0 at 1.
===
Subject: Re: SORRY, I corrected the equation
max/min at -2,+1 implies constant times (x+2)(x-1)=0=dy/dx
Integrate, interpret this constant as 3a and last as d, to
give form
y= a[x^3 +(3/2)x^2 -6x] +d which leads to 2 eqns with 2
unknowns.
1,0] 0=(-7/2)a +d
-2,3] 3= 10a +d,
so a =2/9, d=3-20/9=7/9 and the required cubic is
y= (2/9)x^3+(1/3)x^2 -(4/3)x +7/9. Check it and see.
Hope this helps
Ian Hutcheson
===
Subject: Re: SORRY, I corrected the equation
X-RFC2646: Format=Flowed; Response
hgl <HGL@COX.NET> escribi.97:
> Find a cubic fcn f(x) = ax^3 +bx^2+cx+d that has a local
max value of
> 3 at -2
> and a local min value of 0 at 1.
Well, you know that f(-2) = 3 and f(1) = 0. Do you know the
value of fı(x)
at -2 an 1?
You have a system of 4 equations in 4 indetermined, it is
easy. To check
your result, 9*f(x) has all coefŜcients integers.
--
Ignacio Larrosa Ca.96estro
A Coru.96a (Espa.96a)
ilarrosaQUITARMAYUSCULAS@mundo-r.com
===
Subject: Re: SORRY, I corrected the equation
X-RFC2646: Format=Flowed; Response
just to check ur answer
a = 2/9
b = 1/3
c = -4/3
d = 7/9
> hgl <HGL@COX.NET> escribi.97:
>> Find a cubic fcn f(x) = ax^3 +bx^2+cx+d that has a local
max value of
>> 3 at -2
>> and a local min value of 0 at 1.
> Well, you know that f(-2) = 3 and f(1) = 0. Do you know the
value of fı(x)

> at -2 an 1?
> You have a system of 4 equations in 4 indetermined, it is
easy. To check
> your result, 9*f(x) has all coefŜcients integers.
> --
> Ignacio Larrosa Ca.96estro
> A Coru.96a (Espa.96a)
> ilarrosaQUITARMAYUSCULAS@mundo-r.com
===
Subject: RE generalized algebraic laws
This is a followup on a posting of the same title. The initial
posting, in august of last year, by Elaine, starts, No matter
where I
look I canıt Ŝnd a... rigorous statement of the laws of
associativity... in... general form. Everybody knows them...
And whoıs
put a proof in writing? ...on my own, Iıve discovered that
the only
way I can produce a... proof is by
disregarding meaning... and proving theorems about properties
of
formal
languages...
I was thinking about the same problem, that is, deŜning
mathematically n-ary products of an operation that is not
apriori
associative. I guess it could be said that the description of
generalized associativity is metamathematical in most algebra
texts.
The mathematical proof needs to be done in a way that
coincides with
the intuitive idea, or with the formal generalized inductive
deŜnition of the class of valid brackettings (sic?):
the class of terms A satisfying either
a) A is a letter
b) A is a combination BıCı for elements B and C
of the class, where Bı is the term (B) if B is not
a letter and Bı is the term B when B is a letter, and
the same for Cı.
(here AB means combining the two assemblies of symbols in the
suggested order.)
I will give one construction. Please comment if it seems
inefŜcient
in applications, if a standard deŜnition already exists, or
etc. It
is a set of functions on X*, i.e., the union of X^n for the
naturals
n, where X is the algebraic structure, with operation u. In
particular, the set P of functions phi for each of which
exists for
every n an m<n such that
(a_1,a_2,...,a_n) -->
(a_1,a_2,...,a_m-1,u(a_m,a_m+1),a_m+2,...,a_n),
(with some abuse of notation in the image) noting in this
case this
image is in X^n-1. Then given any Ŝnite sequence a in X, all
the
different possible ways to apply u to aıs elements are
represented by
some function phi in particular, the set of products of
a_1,a_2,...,a_n is the set {phi^n-1(a)}_(phi in P).
Some simple observations about such functions involves a
construction
like parents Iım taking this word since these functions
could be
imagined as an overly simplistic model of a single-child
baring
population [they technically would have to be hemaphrotides
(sic?) but
Iıll leave a margin for non-logical thinking in the
imagination, and I
recommend imagining them as being of opposite sexes].
According to
this model, for instance, if n is the population of China,
then in n-1
generations there will be exactly 1 Chinese person.
The jth generation parents of a term aı_i in the sequence
phi^k+j(a)
would then be the elements of
phi^k(a) who either are already j-1th gen. parents or whose
child
is a j-1th gen. parent, the latter meaning that the value m
described
above equals the index of the parent with the smaller index.
The 1st
gen. parent is aı_i if it remains from phi^k+j-1(a) or
otherwise
aıı_i and aıı_i+1, where aıı=phi^k+j-1(a).
Easy observations include, that the jth generation parents
are always
consecutive in the sequence in which they appear. The jth
gen. parents
of aı_i+1 appear immediately after aı_iıs jth gen. parents.
Furthermore, one should be able to apply the standard
inductive
proof of generalized associativity to the construction P,
with the
aid of these and several other observations, the hypothesis
being that
phi^n(a)=phiı^n(a) for all phi, phiı in P and a in X^n+1. I am
conŜdent of that, although I havenıt gone through all the
details,
which I must admit can loose my interest.
I will consider this construction a little more, but thatıs
what I
wish to say about it now and in this connection. I donıt know
that
there are no mistypes. Many liberties have been taken for the
sake of
===
Subject: RE generalized algebraic laws
This is a followup on a posting of the same title. The initial
posting, in august of last year, by Elaine, starts, No matter
where I
look I canıt Ŝnd a... rigorous statement of the laws of
associativity... in... general form. Everybody knows them...
And whoıs
put a proof in writing? ...on my own, Iıve discovered that
the only
way I can produce a... proof is by
disregarding meaning... and proving theorems about properties
of
formal
languages...
I was thinking about the same problem, that is, deŜning
mathematically n-ary products of an operation that is not
apriori
associative. I guess it could be said that the description of
generalized associativity is metamathematical in most algebra
texts.
The mathematical proof needs to be done in a way that
coincides with
the intuitive idea, or with the formal generalized inductive
deŜnition of the class of valid brackettings (sic?):
the class of terms A satisfying either
a) A is a letter
b) A is a combination BıCı for elements B and C
of the class, where Bı is the term (B) if B is not
a letter and Bı is the term B when B is a letter, and
the same for Cı.
(here AB means combining the two assemblies of symbols in the
suggested order.)
I will give one construction. Please comment if it seems
inefŜcient
in applications, if a standard deŜnition already exists, or
etc. It
is a set of functions on X*, i.e., the union of X^n for the
naturals
n, where X is the algebraic structure, with operation u. In
particular, the set P of functions phi for each of which
exists for
every n an m<n such that
(a_1,a_2,...,a_n) -->
(a_1,a_2,...,a_m-1,u(a_m,a_m+1),a_m+2,...,a_n),
(with some abuse of notation in the image) noting in this
case this
image is in X^n-1. Then given any Ŝnite sequence a in X, all
the
different possible ways to apply u to aıs elements are
represented by
some function phi in particular, the set of products of
a_1,a_2,...,a_n is the set {phi^n-1(a)}_(phi in P).
Some simple observations about such functions involves a
construction
like parents Iım taking this word since these functions
could be
imagined as an overly simplistic model of a single-child
baring
population [they technically would have to be hemaphrotides
(sic?) but
Iıll leave a margin for non-logical thinking in the
imagination, and I
recommend imagining them as being of opposite sexes].
According to
this model, for instance, if n is the population of China,
then in n-1
generations there will be exactly 1 Chinese person.
The jth generation parents of a term aı_i in the sequence
phi^k+j(a)
would then be the elements of
phi^k(a) who either are already j-1th gen. parents or whose
child
is a j-1th gen. parent, the latter meaning that the value m
described
above equals the index of the parent with the smaller index.
The 1st
gen. parent is aı_i if it remains from phi^k+j-1(a) or
otherwise
aıı_i and aıı_i+1, where aıı=phi^k+j-1(a).
Easy observations include, that the jth generation parents
are always
consecutive in the sequence in which they appear. The jth
gen. parents
of aı_i+1 appear immediately after aı_iıs jth gen. parents.
Furthermore, one should be able to apply the standard
inductive
proof of generalized associativity to the construction P,
with the
aid of these and several other observations, the hypothesis
being that
phi^n(a)=phiı^n(a) for all phi, phiı in P and a in X^n+1. I am
conŜdent of that, although I havenıt gone through all the
details,
which I must admit can loose my interest.
I will consider this construction a little more, but thatıs
what I
wish to say about it now and in this connection. I donıt know
that
there are no mistypes. Many liberties have been taken for the
sake of
===
Subject: Re: sparse matrices and eigenvalue computation
> I am in the position where I may need to implement an
eigenvalue solver
> myself. The objective is to obtain only the lower n
eigenvalues (in
> magnitude). I do the eigenvalue computation at present (in
C++ using TNT
> few of the lower n eigenvalues will be much faster.
> In MATLAB, I have seen some people use sparse matrices to
compute
> eigenvalues (usually when the input matrix, X, is quite
large).
> First, where do I Ŝnd information on what sparse matrices
are and why,
> where and how to use them? I would like to go from easy to
more detailed
> explanations.
> Second, are there any C++ programs that already compute
only a subset of
> eigenvalues of a given input matrix?
> ->HS
Have a look at
http://www.caam.rice.edu/software/ARPACK/arpack++.html
Hans Mittelmann
===
Subject: Modern censorship
You read in history books about individuals harried by mobs,
continually barraged with various attacks, who face outrageous
behavior at the hands of some group, and then we come to a
supposedly
enlightened age with extraordinary tools for sharing
information--and
the same damn thing happens again.
Over the years that Iıve posted on PUBLIC forums the thing
that has
stood out is how out there, without shame, and without even
hesitating
to hide what theyıre doing--groups of people have made it
their
business to try to censor what I write.
Time after time theyıd post to tell me to go away, or to tell
others
to ignore me, as these people made it their business to try to
control.
When harassing me on Usenet wasnıt enough, they took to
putting up
webpage--and if another one of you tries to claim that I
harassed
David Ullrich, a math professor who after harassing me for
years
dragged race into the picture talking about racial slurs,
because I
complained about him bringing race into the picture to his
university,
then you just make my point that much more forcefully. Race
is not a
tool to be used by some unethical math professor who thinks
itıs a
neat way to insult someone on Usenet. David Ullrich was wrong
to try
to attack me with race, and I was right to call him on it, and
complain to his school.
You people cheat.
to a journal, so some of you emailed that journal to get the
paper
censored.
You are disgusting cretins who follow no rules, no moral
obligations,
and you are irrational.
I can argue point for point, point by point, explain over and
over
again, as Iıve done for years, and one of you will just
disagree to be
disagreeable!
I offer compromise and get spat upon.
History shows that there are always those of the mob, who
take it upon
themselves to try and control the few, or especially, the one.
Iım thankful that this plays out over the Internet.
In the past you are the people who would be tying someone to
a stake
to burn them and then, blaming the victim, shout your
morality to the
heavens, as if God listens to loudness above reason.
You are the reason that we have a society of today where so
many
problems will not get addressed because a few people Ŝght for
control
they do not have.
You wish to control others, to dominate the conversation, to
force
your will upon people who might want to say something you
donıt want
to hear.
So still the webpages are there--some of you illegally using
my
copyrighted material to insult me--and you people refuse to
give up
your attempts at control despite the years, despite the
stupidity of
it all, despite the immorality.
But you do not control me. I post as I will despite your
webpages,
despite emails you might send, despite the dedication with
which you
try to push me this way or that, or to push others, though,
yes, most
posters bend to your will.
They are cows, and cowards. I watch them come and go over the
years
terriŜed to ever say anything at all objective about my work
for fear
that theyıll be mobbed, as they will.
But I will not be ruled. I will not be controlled by you. I
will not
be conquered.
And I will win. I have a paper at a major math journal. If
they try
to slide out of publication like others before them, it will
go to
another, and another, and another, as I adjust, shift the
wording,
learn the game, play the politics necessary to get published.
And if it takes a decade I WILL GET PUBLISHED.
And then you will be part of history, part of the sad story of
mobbings, and angry people willing to do so much wrong for
the sake of
their own sense of control. Yet another sad sorry tale among
so many
in a world of people who never learn their history.
In a world where people refuse to learn from the mistakes of
the past,
not only to repeat them, but to wallow in the misery they
create for
others, to celebrate the destruction they wreak, and to pride
themselves until the day they Ŝnally fall.
And humanity is so much the worse for all of the stink of it.
James Harris
===
Subject: Re: Modern censorship
James Harris <jstevh@msn.com> scribbled the following:
> You read in history books about individuals harried by mobs,
> continually barraged with various attacks, who face
outrageous
> behavior at the hands of some group, and then we come to a
supposedly
> enlightened age with extraordinary tools for sharing
information--and
> the same damn thing happens again.
(snip further crap)
James, no one cares. When you get published, notify us. Last
I recall,
you were working on proving Fermatıs Last Theorem and Ŝnding a
polynomial-time prime Ŝnding algorithm. Thatıs great. If you
make any
progress with them, tell us. But donıt whine and whine about
how
everyone is against you. The only way to make people know
about your
proŜciency in math is to actually show your work, not to
whine about
persecution and brag about how great you are.
--
/-- Joona Palaste (palaste@cc.helsinki.Ŝ) -------------
Finland --------
--------------------------------------------------------
rules! --------/
No, Maggie, not Aztec, Olmec! Ol-mec!
- Lisa Simpson
===
Subject: Re: Modern censorship
> You read in history books about individuals harried by mobs,
[snip lengthy diatribe]
> You people cheat.
[snip whining about cheats]
> They are cows, and cowards.
[snip whining about cows and cowards]
> And I will win. I have a paper at a major math journal. If
they try
> to slide out of publication like others before them, it
will go to
> another, and another, and another, as I adjust, shift the
wording,
> learn the game, play the politics necessary to get
published.
Just curious: the most recent version of your paper on
polynomial
factorization, co-authored by you and A. Beckwith, at:
http://www.ne-plus-ultra.net/index.php?option=content&task=
view&id=46&Itemid
=26
includes the following material toward the end:
Now letting m = 1, f = sqrt(5), where I can let u = 1 as its
value doesnıt change the aıs, I have
(m^3 f^6 - 3 m^2 f^4 + 3 m) x^3 - 3 (-1 + m f^2) x u^2 + u^3
= 65 x^3 - 12 x + 1 ...
But clearly, if you substitute m = 1, f = sqrt(5), and u = 1
into the expresson on the left side, you get:
53 x^3 - 12 x + 1.

So thatıs obviously wrong.
Not only that, but your original polynomial in that paper is
written as
P(m) = f^2 ((m^3 f^4 - 3 m^2 f^2 + 3 m) x^3 - 3(-1 + m f^2)x
u^2 + u^3
f).
Now, if I substitute m = 1, f = sqrt(5), u = 1 into THIS
expression, I get:
P(m) = 65 x^3 - 60 x + 15 sqrt(5)
which of course ALSO does not equal
65 x^3 - 12 x + 1.
So what I am curious about is: is this the version you have
submitted to a journal?
Andrzej
[snip still more whining]
> And humanity is so much the worse for all of the stink of
it.
> James Harris
===
Subject: Re: Modern censorship

!3KEIp?*w`|bL5qr,H)LFO6Q=qx~iH4DN;i;/yuIsqbLLCh/!U#X[S~(
5eZ41to5f%E@ıELIi
$t^
VcLWP@J5p^rst0+(Œ>Er0=^1{]M9!p?&:z]|;&=NP3AhB!B_bi^]Pfkw
> Over the years that Iıve posted on PUBLIC forums the thing
that has
> stood out is how out there, without shame, and without even
hesitating
> to hide what theyıre doing--groups of people have made it
their
> business to try to censor what I write.
[...]
> So still the webpages are there--some of you illegally
using my
> copyrighted material to insult me--
Oh, they would not want to have you censored.
--
David Kastrup, Kriemhildstr. 15, 44793 Bochum
===
Subject: Re: Modern censorship
>You read in history books about individuals harried by mobs,
>continually barraged with various attacks, who face
outrageous
>behavior at the hands of some group, and then we come to a
supposedly
>enlightened age with extraordinary tools for sharing
information--and
>the same damn thing happens again.
>Over the years that Iıve posted on PUBLIC forums the thing
that has
>stood out is how out there, without shame, and without even
hesitating
>to hide what theyıre doing--groups of people have made it
their
>business to try to censor what I write.
You continue to make this ridiculous claim, no matter how
many times people point out that they canıt possibly censor
what you write.
Hmm. Sounds like Iım surprised that you continue to say
something
stupid after the stupidity of it has been pointed out. Never
mind.
>Time after time theyıd post to tell me to go away, or to
tell others
>to ignore me, as these people made it their business to try
to
>control.
>When harassing me on Usenet wasnıt enough, they took to
putting up
>webpage--and if another one of you tries to claim that I
harassed
>David Ullrich, a math professor who after harassing me for
years
>dragged race into the picture talking about racial slurs,
because I
>complained about him bringing race into the picture to his
university,
>then you just make my point that much more forcefully. Race
is not a
>tool to be used by some unethical math professor who thinks
itıs a
>neat way to insult someone on Usenet. David Ullrich was
wrong to try
>to attack me with race, and I was right to call him on it,
and
>complain to his school.
If Iıd done what you say you might be right, perhaps.
[*] But youıve _stated_ right here that the reason you
complained
about me to OSU was to get me to stop posting in your threads.
That makes _you_ the _only_ person Iım aware of who _has_
taken
actual steps to try to censor someone on usenet.
>You people cheat.
>to a journal, so some of you emailed that journal to get the
paper
>censored.
Nobody here said the journal should yank the paper - the
concensus
here is that they did the wrong thing in doing so.
>You are disgusting cretins who follow no rules, no moral
obligations,
>and you are irrational.
See [*] above.
>I can argue point for point, point by point, explain over
and over
>again, as Iıve done for years, and one of you will just
disagree to be
>disagreeable!
>I offer compromise and get spat upon.
The compromise you offered was in regard to mathematical
facts -
it doesnıt work that way.
Also, as I pointed out once, that compromise would not have
had
the effect you wanted anyway: It was something about how
youıd make
some modiŜcation to some paper if weıd agree not to be against
its publication. That wouldnıt work, because sci.math has
nothing
to do with why journals reject your papers.
>History shows that there are always those of the mob, who
take it upon
>themselves to try and control the few, or especially, the
one.
>Iım thankful that this plays out over the Internet.
>In the past you are the people who would be tying someone to
a stake
>to burn them and then, blaming the victim, shout your
morality to the
>heavens, as if God listens to loudness above reason.
Hint: the previous paragraph is _very_ funny, for at least two
reasons. Can you identify one or both?
>You are the reason that we have a society of today where so
many
>problems will not get addressed because a few people Ŝght
for control
>they do not have.
>You wish to control others, to dominate the conversation, to
force
>your will upon people who might want to say something you
donıt want
>to hear.
>So still the webpages are there--some of you illegally using
my
>copyrighted material to insult me--and you people refuse to
give up
>your attempts at control despite the years, despite the
stupidity of
>it all, despite the immorality.
>But you do not control me.
True. So whatıs this nonsense about censorship? A censor
_does_
control things, by deŜnition.
>I post as I will despite your webpages,
>despite emails you might send, despite the dedication with
which you
>try to push me this way or that, or to push others, though,
yes, most
>posters bend to your will.
>They are cows, and cowards. I watch them come and go over
the years
>terriŜed to ever say anything at all objective about my work
for fear
>that theyıll be mobbed, as they will.
>But I will not be ruled. I will not be controlled by you. I
will not
>be conquered.
>And I will win. I have a paper at a major math journal. If
they try
>to slide out of publication like others before them, it will
go to
>another, and another, and another, as I adjust, shift the
wording,
>learn the game, play the politics necessary to get published.
>And if it takes a decade I WILL GET PUBLISHED.
Might happen - itıs happened before that respectable journals
have
published total nonsense.
(I forget the name of the journal, but it was a big one that
published a paper where the main result started by covering
the unit sphere by Ŝntely many disjoint spherical caps. People
were talking about how the entire editorial staff should
resign...
Rudin published a well, duh sort of refutation in the same
journal.)
>And then you will be part of history, part of the sad story
of
>mobbings, and angry people willing to do so much wrong for
the sake of
>their own sense of control. Yet another sad sorry tale among
so many
>in a world of people who never learn their history.
>In a world where people refuse to learn from the mistakes of
the past,
>not only to repeat them, but to wallow in the misery they
create for
>others, to celebrate the destruction they wreak, and to pride
>themselves until the day they Ŝnally fall.
>And humanity is so much the worse for all of the stink of it.
>James Harris
************************
David C. Ullrich
===
Subject: Re: Modern censorship
Discussion, linux)
> So still the webpages are there--some of you illegally
using my
> copyrighted material to insult me--and you people refuse to
give up
> your attempts at control despite the years, despite the
stupidity of
> it all, despite the immorality.
*Because* theyıre using your material to insult you, itıs
probably
perfectly legal. Your posts have been excerpted and
paraphrased for
the purpose of criticism. This is a well-established fair use
exception in U.S. copyright law and likely elsewhere, too.
You keep ignoring this fact. You prefer to pretend that youıve
obviously been wronged by scofŝaws. But it just ainıt so.
--
Jesse F. Hughes
My experience indicates that the people who post on this
newsgroup
are about at the level of a 10 year old in the year 2060.
-- More wisdom from James Harris, time traveler
===
Subject: Re: Modern censorship
[snippage]
> You read in history books about individuals harried by mobs,
> continually barraged with various attacks, who face
outrageous
> behavior at the hands of some group, and then we come to a
supposedly
> enlightened age with extraordinary tools for sharing
information--and
> the same damn thing happens again.
> Over the years that Iıve posted on PUBLIC forums the thing
that has
> stood out is how out there, without shame, and without even
hesitating
> to hide what theyıre doing--groups of people have made it
their
> business to try to censor what I write.
> Time after time theyıd post to tell me to go away, or to
tell others
> to ignore me, as these people made it their business to try
to
> control.
You seem to be confusing Œdisagreementı with Œattempted
censorshipı.
> You are the reason that we have a society of today where so
many
> problems will not get addressed because a few people Ŝght
for control
> they do not have.
Ooh, political.
> You wish to control others, to dominate the conversation,
to force
> your will upon people who might want to say something you
donıt want
> to hear.
> So still the webpages are there--some of you illegally
using my
> copyrighted material to insult me
So you still havenıt learned anything about copyright law.
Hint: the
relevant bits are the ones dealing with Œfair useı.
> I have a paper at a major math journal. If they try
> to slide out of publication like others before them, it
will go to
> another, and another, and another, as I adjust, shift the
wording,
> learn the game, play the politics necessary to get
published.
Your mistake is not failing to Œplay ... politicsı, itıs
failing to
Œlearn mathematicsı.
> And if it takes a decade I WILL GET PUBLISHED.
Hey, youıve already been published, remember? You got
published in
GET A CORRECT RESULT PUBLISHEDı ?
By the way, what exactly will that achieve?
--
Larry Lard
Replies to group please
===
Subject: Re: Modern censorship

!3KEIp?*w`|bL5qr,H)LFO6Q=qx~iH4DN;i;/yuIsqbLLCh/!U#X[S~(
5eZ41to5f%E@ıELIi
$t^
VcLWP@J5p^rst0+(Œ>Er0=^1{]M9!p?&:z]|;&=NP3AhB!B_bi^]Pfkw
> And if it takes a decade I WILL GET PUBLISHED.
> And then you will be part of history, part of the sad story
of
> mobbings, and angry people willing to do so much wrong for
the sake
> of their own sense of control. Yet another sad sorry tale
among so
> many in a world of people who never learn their history.
You are laboring under the delusion that getting published is
equivalent to make an impact. It isnıt. It is merely a tiny
Ŝrst
step. And it is no substitute for having something worthwhile
to
say. You might trick somebody into publishing you. It wonıt
make a
difference. Except for the reputation of the publisher.
> In a world where people refuse to learn from the mistakes
of the
> past, not only to repeat them, but to wallow in the misery
they
> create for others, to celebrate the destruction they wreak,
and to
> pride themselves until the day they Ŝnally fall.
> And humanity is so much the worse for all of the stink of
it.
No hammer this time?
--
David Kastrup, Kriemhildstr. 15, 44793 Bochum
===
Subject: Re: Modern censorship
> You read in history books about individuals harried by mobs,
> continually barraged with various attacks, who face
outrageous
> behavior at the hands of some group, and then we come to a
supposedly
> enlightened age with extraordinary tools for sharing
information--and
> the same damn thing happens again.
> Over the years that Iıve posted on PUBLIC forums the thing
that has
> stood out is how out there, without shame, and without even
hesitating
> to hide what theyıre doing--groups of people have made it
their
> business to try to censor what I write.
No-one makes it their business to censor what you write.
<snip>
===
Subject: Re: Modern censorship
Hoorah! A new season of JSH!
===
Subject: Re: Modern censorship
> Hoorah! A new season of JSH!
Yeah, but itıs just not the same. Iım not sure what future
Harrisologians
will demark as the Golden Age, but it seems to have been over
for some time
now. The farce has grown stale. Once upon a time James
emulated a
mathematician in the same fascinating way that a Tamagotchi
emulated
something
alive. Now it just emits an annoying series of beeps over and
over: beeps
that used to mean feed me back when it was engaging enough
that we
amused
ourselves by ascribing to it an intelligence, some sense of
purpose.
He hoped for blazing glory; we awaited the blazing crash. But
nothing is
burning. All that remains is an incessant beep.
Beep. Beep. Beep.
===
Subject: Re: Modern censorship
>We awaited the blazing crash. But nothing is
>burning. All that remains is an incessant beep.
>Beep. Beep. Beep.
So sci.math = Wile E. Coyote?
===
Subject: [JSH] Re: Modern censorship
In sci.math, Dave Rusin
<rusin@vesuvius.math.niu.edu>
<cnnvm4$ph0$1@news.math.niu.edu>:
>>We awaited the blazing crash. But nothing is
>>burning. All that remains is an incessant beep.
>>Beep. Beep. Beep.
> So sci.math = Wile E. Coyote?
No, sci.math is the other side of the equation. :-)
JSH has yet to catch us, on, or up.
Note subject change.
--
#191, ewill3@earthlink.net
Itıs still legal to go .sigless.
===
Subject: Re: Modern censorship
> But you do not control me.
If so, why do you devote an entire lengthy post to the people
who donıt
control you, instead of devoting it to the nominal topic of
the
newsgroup?
--
Transpose hotmail and mxsmanic in my e-mail address to reach
me directly.
===
Subject: Re: Modern censorship
>But you do not control me.
> If so, why do you devote an entire lengthy post to the
people who donıt
> control you, instead of devoting it to the nominal topic of
the
> newsgroup?
That at least is a good question.
The full answer is that the attempts at control involve
whatıs in the
subject line: censorship.
That involves limiting or stopping content, like people
telling me not
to post, or to post only on certain subjects or various other
types of
control type requests.
The only such requests I acknowledge as being pertinent are
ones about
limiting to math and topics related to the newsgroup itself.
The
topic here is troubling censorship attempts from newsgroup
members
acting often as a gang determined to control my postings, so
itıs
topical.
Here you have *mob* behavior as well, with a lot of unfair
tactics as
various groups of people do more than one thing in an attempt
to
control what and how I post.
Itıs actually kind of bizarre, and really, really strange
given my
history of ignoring such requests and using them instead to
simply
gain more attention.
But these people keep trying. Thatıs kind of interesting, as
what can
go so wrong in peopleıs heads that no matter what they just
keep at
the same losing proposition, year after year? Like what
motivates an
Erik Max Francis or a Dik Winter, or a David Ullrich, among
others?
Why do they keep trying given their lack of success so far?
Theyıre not only losing, theyıre losing big, but they keep
going.
Why?
Part of me Ŝnds such dedication admirable, but then again,
how do you
justify continuing when you NEVER win? Like if you think Iım
deluded
and they do win, name one victory. Name a single victory from
any of
those people.
Not something fake, but some way theyıve actually won, a
single time.
Yet here I am, more dominant than ever, waiting on a math
paper likely
to get published, when I will come and really stomp them into
the
ground, so their losses become complete, and more biting, as
well as
more direct.
So, whatıs their motivation?
James Harris
===
Subject: Re: Modern censorship
> Yet here I am, more dominant than ever
/ ____
<> ( oo )
<>_| ^^ |_
<> @
/~~ . . _ |
/~~~~ | |
/~~~~~~/ _| |
|[][][]/ / [m]
|[][][[m]
|[][][]|
|[][][]|
|[][][]|
|[][][]|
|[][][]|
|[][][]|
|[][][]|
|[][][]|
|[|--|]|
|[| |]|
|[[ ]]|
> James Harris
===
Subject: Re: Modern censorship
> Yet here I am, more dominant than ever,
You must be proud of your earthshaking contributions to
mathematics.
Tell me, are you aware of any buzz about you winning a Fields
Medal?
Oh, I know youıre probably not supposed to talk about it, but
Iım
really looking forward to seeing a transcript of your
acceptance
speech. That is, if you decide to accept. The thing is, when
they
award you a Fields Medal, I guess youıre supposed to feel
humbled to
be included in such an elite group. Douglas, Kodaira, Roth,
Hironaka,
Lions, . . . there are dozens of these jokers! Adding Harris
to the
list doesnıt really seem appropriate. Rather, there should be
a list
like Archimedes, Newton, Gauss, Harris. Period. I mean, maybe
you
should take it -- be in their little club -- just to avoid
pissing
them off even more than you already have. Or maybe you just
deliver
an acceptance speech that *really* pisses them off. Like I
said, Iıd
love to hear it.
> waiting on a math paper likely
> to get published,
This is something you have in common with most, if not all,
of the
other Fields Medalists. They had math papers which were
likely to
get published. Indeed, later many of their papers were
published. Oh,
maybe a few of these guys just sort of espoused their
theories on the
internet or whatever preceded it, but most did, in fact,
publish their
work. So youıre in good company there, when you do get it
published,
that is. But only *good* company. Not the great company you
deserve.
> when I will come and really stomp them into the
> ground, so their losses become complete, and more biting,
as well as
> more direct.
Well thatıs a good reason to accept your Fields Medal right
there. It
is well documented that Fields Medalists typically go on a
rampage of
revenge within a few weeks of accepting their prize. Itıs as
if the
Medal were some powerful talisman out of Dungeons and Dragons
-- one
which delights in being wielded by a powerful, chaotic evil
mathematician.
It is said that the math departments of seven universities
were decimated
by the wrath of Grothendieck. In the hands of a Harris, it
would wreak a
veritable mathematical apocalypse. Mathematics as we know it
would not
survive.
Of course, the committee is probably waiting for Jamesıs
paper to get
published before awarding him the medal.
===
Subject: Re: Modern censorship
===
>Subject: Re: Modern censorship
>>But you do not control me.
>> If so, why do you devote an entire lengthy post to the
people who donıt
>> control you, instead of devoting it to the nominal topic
of the
>> newsgroup?
>That at least is a good question.
>The full answer is that the attempts at control involve
whatıs in the
>subject line: censorship.
>That involves limiting or stopping content, like people
telling me not
>to post, or to post only on certain subjects or various
other types of
>control type requests.
>The only such requests I acknowledge as being pertinent are
ones about
>limiting to math and topics related to the newsgroup itself.
The
>topic here is troubling censorship attempts from newsgroup
members
>acting often as a gang determined to control my postings, so
itıs
>topical.
>Here you have *mob* behavior as well, with a lot of unfair
tactics as
>various groups of people do more than one thing in an
attempt to
>control what and how I post.
>Itıs actually kind of bizarre, and really, really strange
given my
>history of ignoring such requests and using them instead to
simply
>gain more attention.
>But these people keep trying. Thatıs kind of interesting, as
what can
>go so wrong in peopleıs heads that no matter what they just
keep at
>the same losing proposition, year after year? Like what
motivates an
>Erik Max Francis or a Dik Winter, or a David Ullrich, among
others?
>Why do they keep trying given their lack of success so far?
Surely _you_ of all people know the answer to that.
>Theyıre not only losing, theyıre losing big, but they keep
going.
>Why?
>Part of me Ŝnds such dedication admirable, but then again,
how do you
>justify continuing when you NEVER win? Like if you think Iım
deluded
>and they do win, name one victory. Name a single victory
from any of
>those people.
>Not something fake, but some way theyıve actually won, a
single time.
How about getting your paper yanked from that journal?
That was pretty impressive to me, given that journals donıt
normally do that. But then, most papers with errors arenıt
submitted by people comitting fraud.
>Yet here I am, more dominant than ever, waiting on a math
paper likely
>to get published, when I will come and really stomp them
into the
>ground, so their losses become complete, and more biting, as
well as
>more direct.
>So, whatıs their motivation?
Whatıs yours?
>James Harris
--
Mensanator
Ace of Clubs
===
Subject: Re: Modern censorship
Discussion, linux)
> Part of me Ŝnds such dedication admirable, but then again,
how do you
> justify continuing when you NEVER win? Like if you think
Iım deluded
> and they do win, name one victory. Name a single victory
from any of
> those people.
> Not something fake, but some way theyıve actually won, a
single
> time.
Golly. That *is* an interesting observation. What would make
someone
go on and on and on for *years* without accomplishing a damn
thing?
--
Jesse F. Hughes
Thatıs whatıs brutal about mathematics! When youıre wrong,
you can
have spent years, and lots of effort, and come out at the end
with
nothing. -- James S. Harris on the path of self-discovery (?)
===
Subject: Re: Modern censorship
> Thatıs whatıs brutal about mathematics! When youıre wrong,
you can
> have spent years, and lots of effort, and come out at the
end with
> nothing. -- James S. Harris on the path of self-discovery
(?)
My son, you are on the path to enlightenment. Itıs back
thataway.
--
Chris Henrich
God just doesnıt Ŝt inside a single religion.
===
Subject: Re: Modern censorship
>Thatıs whatıs brutal about mathematics! When youıre wrong,
you can
>have spent years, and lots of effort, and come out at the
end with
>nothing. -- James S. Harris on the path of self-discovery (?)
> My son, you are on the path to enlightenment. Itıs back
thataway.
Hey, Iım taking the supposedly proper path to being
recognized as I
send papers to math journals.
So whatıs wrong with the picture here?
Oh, wait, you people send emails to math journals attacking
the
journal process by cowing editors. I play by the rules. You
people
cheat, and then come back talking as if youıre on the level.
You CHEAT, and then you go on as if itıs nothing, and youıre
in the
right, when Iım the researcher writing up papers and sending
them in
for review.
Posting is just a sideline now, though IN THE PAST, Iıd hoped
itıd be
a short-cut to introducing new ideas, but faced a mob, which
is still
continuing but has muted effect now, until the mob can Ŝnd
another
journal to target, I guess.
The reality of publishing papers is that you donıt
necessarily get a
journal that will publish on the Ŝrst try, as thereıs
politics in the
process.
Usually the editors have been nice, and Iıve had thoughtful
replies
that donıt claim error, but basically come down to politics.
Iıve learned THATıS NORMAL in the publication process and Iım
NOT
being singled out here, which is nice :-).
In any event, you people can be as negative as you like, and
keep
playing your old games but the real story is not here--itıs
with the
journals.
So now Iım just kind of gooŜng off, as I admit it, itıs fun
to post.
And I am not going to be censored by you people. So why are
you
replying then, eh?
Whatıs your motivation if youıre not here to try and stop me
from
posting, and Iım not interested in being stopped, and Iım
sending
papers to journals anyway?
Why are you dimwits hounding me now? Eh?
James Harris
===
Subject: Re: Modern censorship
...
> Oh, wait, you people send emails to math journals attacking
the
> journal process by cowing editors. I play by the rules. You
people
> cheat, and then come back talking as if youıre on the level.
Eh? It was not the journal process that was attacked in the
email, it
was the paper. The proper way for the journal would have been
to
publish the rebuttal of your paper in a later issue.
> You CHEAT, and then you go on as if itıs nothing, and
youıre in the
> right, when Iım the researcher writing up papers and
sending them in
> for review.
Sending in rebuttals is not cheating.
--
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: Modern censorship
>> But you do not control me.
>If so, why do you devote an entire lengthy post to the
people who donıt
>control you, instead of devoting it to the nominal topic of
the
>newsgroup?
> That at least is a good question.
> The full answer is that the attempts at control involve
whatıs in the
> subject line: censorship.
> That involves limiting or stopping content, like people
telling me not
> to post, or to post only on certain subjects or various
other types of
> control type requests.
I think you should post to sci.math every day. It keeps me
and people like
me interested in the group.
> The only such requests I acknowledge as being pertinent are
ones about
> limiting to math and topics related to the newsgroup
itself. The
> topic here is troubling censorship attempts from newsgroup
members
> acting often as a gang determined to control my postings,
so itıs
> topical.
> Here you have *mob* behavior as well, with a lot of unfair
tactics as
> various groups of people do more than one thing in an
attempt to
> control what and how I post.
> Itıs actually kind of bizarre, and really, really strange
given my
> history of ignoring such requests and using them instead to
simply
> gain more attention.
> But these people keep trying. Thatıs kind of interesting,
as what can
> go so wrong in peopleıs heads that no matter what they just
keep at
> the same losing proposition, year after year? Like what
motivates an
> Erik Max Francis or a Dik Winter, or a David Ullrich, among
others?
> Why do they keep trying given their lack of success so far?
> Theyıre not only losing, theyıre losing big, but they keep
going.
> Why?
> Part of me Ŝnds such dedication admirable, but then again,
how do you
> justify continuing when you NEVER win? Like if you think
Iım deluded
> and they do win, name one victory. Name a single victory
from any of
> those people.
> Not something fake, but some way theyıve actually won, a
single time.
was good and published and unretractable, and then published
their own
> Yet here I am, more dominant than ever, waiting on a math
paper likely
> to get published, when I will come and really stomp them
into the
> ground, so their losses become complete, and more biting,
as well as
> more direct.
> So, whatıs their motivation?
Truth, justice, and the American way!
===
Subject: Re: Modern censorship
===
>Subject: Re: Modern censorship
>Message-id: <vlgop0thlctv1c7amsoleŜ0c995b9smcu@4ax.com> But
you do not control me.
>If so, why do you devote an entire lengthy post to the
people who donıt
>control you, instead of devoting it to the nominal topic of
the
>newsgroup?
At a meta-level, heıs controlling us by forcing us to try to
control him.
But what he doesnıt realize is that at a
meta-meta-level...oh, never mind.
>--
>Transpose hotmail and mxsmanic in my e-mail address to reach
me directly.
--
Mensanator
Ace of Clubs
===
Subject: Re: Modern censorship
You are a vile human being!
===
Subject: Re: Modern censorship
===
>Subject: Modern censorship
>You read in history books about individuals harried by mobs,
>continually barraged with various attacks, who face
outrageous
>behavior at the hands of some group, and then we come to a
supposedly
>enlightened age with extraordinary tools for sharing
information--and
>the same damn thing happens again.
Oh, youıre back again. I thought you said you didnıt need us
anymore.
>Over the years that Iıve posted on PUBLIC forums the thing
that has
>stood out is how out there, without shame, and without even
hesitating
>to hide what theyıre doing--groups of people have made it
their
>business to try to censor what I write.
Yeah, so what? Itıs a free country. Thereıs no law against
censoring you.
>Time after time theyıd post to tell me to go away, or to
tell others
>to ignore me, as these people made it their business to try
to
>control.
Go away.
>When harassing me on Usenet wasnıt enough, they took to
putting up
>webpage--and if another one of you tries to claim that I
harassed
>David Ullrich, a math professor who after harassing me for
years
>dragged race into the picture talking about racial slurs,
because I
>complained about him bringing race into the picture to his
university,
>then you just make my point that much more forcefully. Race
is not a
>tool to be used by some unethical math professor who thinks
itıs a
>neat way to insult someone on Usenet. David Ullrich was
wrong to try
>to attack me with race, and I was right to call him on it,
and
>complain to his school.
You were wrong. You were an asshole then and youıre still an
asshole.
>You people cheat.
Tough titty for you, isnıt it?
>to a journal, so some of you emailed that journal to get the
paper
>censored.
So what are you going to do about it?
>You are disgusting cretins who follow no rules, no moral
obligations,
>and you are irrational.
<blows raspberryI can argue point for point, point by point,
explain over and over
>again, as Iıve done for years, and one of you will just
disagree to be
>disagreeable!
You can argue the points Œtil youıre blue in the face, youıre
still wrong.
>I offer compromise and get spat upon.
P-tui!
>History shows that there are always those of the mob, who
take it upon
>themselves to try and control the few, or especially, the
one.
>Iım thankful that this plays out over the Internet.
Weıre not. Whatıs the matter, not getting any hits on your
blog?
>In the past you are the people who would be tying someone to
a stake
>to burn them and then, blaming the victim, shout your
morality to the
>heavens, as if God listens to loudness above reason.
>You are the reason that we have a society of today where so
many
>problems will not get addressed because a few people Ŝght
for control
>they do not have.
Most people just blame the Republicans.
>You wish to control others, to dominate the conversation, to
force
>your will upon people who might want to say something you
donıt want
>to hear.
So?
>So still the webpages are there--some of you illegally using
my
>copyrighted material to insult me--and you people refuse to
give up
>your attempts at control despite the years, despite the
stupidity of
>it all, despite the immorality.
Boo-hoo.
>But you do not control me. I post as I will despite your
webpages,
Weıve already noticed that.
>despite emails you might send, despite the dedication with
which you
>try to push me this way or that, or to push others, though,
yes, most
>posters bend to your will.
>They are cows, and cowards. I watch them come and go over
the years
>terriŜed to ever say anything at all objective about my work
for fear
>that theyıll be mobbed, as they will.
As they should. Anyone who supports you deserves to have a
new asshole
reamed.
>But I will not be ruled. I will not be controlled by you. I
will not
>be conquered.
And you wonıt get published, either. Guess what matters.
>And I will win. I have a paper at a major math journal. If
they try
>to slide out of publication like others before them, it will
go to
>another, and another, and another, as I adjust, shift the
wording,
>learn the game, play the politics necessary to get published.
Sure, if one journal got suckered by your fraud, thereıs
probably another.
Not that it matters. It wonıt survive being made public.
>And if it takes a decade I WILL GET PUBLISHED.
Care to make a wager on that?
>And then you will be part of history, part of the sad story
of
>mobbings, and angry people willing to do so much wrong for
the sake of
>their own sense of control. Yet another sad sorry tale among
so many
>in a world of people who never learn their history.
You mean there was another math crank who turned out to be
right all along?
>In a world where people refuse to learn from the mistakes of
the past,
>not only to repeat them, but to wallow in the misery they
create for
>others, to celebrate the destruction they wreak, and to pride
>themselves until the day they Ŝnally fall.
Please, please tell us what happened to The Hammer. My theory
is that
you accidentally deleted it off your computer. Am I right?
>And humanity is so much the worse for all of the stink of it.
Gee, weıll just have to muddle through, deprived of your
insights.
>James Harris
--
Mensanator
Ace of Clubs
===
Subject: Re: Modern censorship
> You read in history books about individuals harried by mobs,
> continually barraged with various attacks, who face
outrageous
> behavior at the hands of some group, and then we come to a
supposedly
> enlightened age with extraordinary tools for sharing
information--and
> the same damn thing happens again.
And the one thing they all have in common: They are dead.
Perhaps that is
your problem, you are still alive. Maybe we will see your
brilliance only
in your death.
- Tim
--
Timothy M. Brauch
NSF Fellow
Department of Mathematics
University of Louisville
email is:
news (dot) post (at) tbrauch (dot) com
===
Subject: Re: Modern censorship
> I can argue point for point, point by point, explain over
and over
> again, as Iıve done for years,
But you donıt. You just start a new thread and repeat
yourself.
===
Subject: Re: Modern censorship
> You read in history books about individuals harried by mobs,
I think thereıs a movie called Married to the Mob. Your movie
could be
Harried by the Mob!
===
Subject: Re: Modern censorship
>Time after time theyıd post to tell me to go away, or to
tell others
>to ignore me, as these people made it their business to try
to
>control.
When people brush away annoying ŝies, theyıre not trying to
control
anything; they just want to be left in peace.
--
Stan Brown, Oak Road Systems, Tompkins County, New York, USA
http://OakRoadSystems.com/
And if youıre afraid of butter, which many people are nowa-
days, (long pause) you just put in cream. --Julia Child
===
Subject: Help on a probabilty problem, HELP
Consider a particular Ph.D. student; we know that after she
begins her
Ph.D.
program, the number of years it takes her to complete her
studies is a
random
variable with distribution exp(1/4) (independent of when she
started).
Suppose
you know that the student completed her Ph.D. today. We wish
to estimate
how
long ago she started. Assume that the a priori distribution
of X is uniform
on
[3, 6].
a. Let X represent the number of years ago the student
started. Let Y
represent the observation of when she completes, relative to
today (so the
given observation is Y = 0).
Find fY | X(y | x) for x >= 0.
can not understand the meaning very precisely ,Can not
understand the
===
Subject: Re: meta-proof that p is not np
Hi Torkel,
>The halting probability Omega is the chain of irreducible
mathematical
>facts which he refers to. If these facts are computationally
>irreducible, it follows that you, as a computational agent,
cannot
>arrive at them using simpler (shorter) facts, that is to use
reasoning
>to Ŝnd a solution, etc. etc.
> Chaitin is indeed referring to Omega. What is the argument
for the
> claim that the only way to prove the logically irreducible
true
> statements of the form the n-th bit of Omega is i is to
directly
> asume them as a new mathematical axiom, without using
reasoning at all?
Well, I presented at least two arguments, one of which was
identical
to Chaitinıs own argument, but you donıt seem to like them.
Let me try
a slightly different approach, simpler hopefully. (But alas,
you do
not seem to like any argument that you think would be wrong
wrt your
point of view, so...)
Take any bit of Omega, there is no way to know _in general_
this
single bit of information from something else, in the sense of
computing it from something, or more mathematically speaking
proving it from some axioms (which are not distinct things, of
course). We can however, use some clever procedures to
compute some
bits of Omega exactly below, as in Caludeıs paper.
http://www.cs.auckland.ac.nz/CDMTCS/researchreports/
167omega.pdf
The answer to your question is contained in the Theorem 5 and
Theorem
6 of this paper. There are no philosophical points to be made
about
these theorems. If you are unsure of their relevance, you can
ask me
Ŝrst. If youıre not satisŜed with my explanation of this
paper or
your comprehension of it, you can always ask either Calude or
Chaitin,
and Iım sure as respectable scholars they would gladly answer
your
inquiries.
That is, we are basing our argument on Chaitinıs version of
Godelian
incompleteness. We say that no (Ŝnite) formal axiomatic
system can
ever settle arbitrarily many bits of Omega. In fact, for the
case of
ZFC, this is quite bad already, it can _know_ only very few
bits of
Omega (a reminder: all Omegas have essentially identical
information
content due to universality of computation!). Why? Because
ZFC is a
really simple system. It knows so little!
If reasoning is proving or computation, as is implicitly
assumed in
Chaitinıs writings, then his conclusions easily follow.
However, he
does not make the kind of exact metaphysical arguments that I
like. I
would have talked much more precisely, as was the case with my
previously presented arguments.
Now, this is a _very_ arguable assumption. Perhaps, there are
other
paths to knowledge, other than empirical trials, but my
magic-ball
says no. (So, if I were to write a philosophical paper, I
would try to
rest this on some principle which is easier to accept, like
some
all-sweeping empiricist statement or physicalism which was
how I
argued for Chaitinıs thesis before. ) How about yours?
--
Eray Ozkural
PS: Iım hoping that you will actually read the referred
theorems.
PS2: It should not come as a surprise that the shakey part of
Raatikainenıs arguments have no place in this discussion.
There is no
such thing as a computer that can simply compute any n-bits
of Omega
in Ŝnite time.
===
Subject: Re: meta-proof that p is not np
> Take any bit of Omega, there is no way to know _in general_
this
> single bit of information from something else, in the sense
of
> computing it from something, or more mathematically speaking
> proving it from some axioms (which are not distinct things,
of
> course).
There is indeed no computational procedure which proves all
true
statements of the form the n-th bit of Omega is i. The same
is true
of any undecidable set of true statements - nothing special
about
Omega here. What I am asking about is the claim that
statements
of the form the n-th bit of Omega is i are true for no reason
and can only be postulated, not proved.
> That is, we are basing our argument on Chaitinıs version of
Godelian
> incompleteness. We say that no (Ŝnite) formal axiomatic
system can
> ever settle arbitrarily many bits of Omega.
And how does this fact imply that the truth of a statement of
the
form the n-th bit of Omega is i can only be postulated, not
arrived
at by reasoning?
Your rambling is nothing to the point.
===
Subject: Re: inŜnitesimal calculation ?
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>I am trying to get addtionnal data on inŜnitesimal numbers
dx.
A Mathematical perspective or a historical perspective?
Historically, you are talking about what Newton called
ŝuxions, and
the whole concept is inconsistent. However, there are two
modern[1]
concepts using similar nomenclature.
1. Differential forms, which are deŜned in terms of germs of
functions, that is, dF_X is the set of all continuous[2]
functions that agr