Re: Amateur takes on Wiles's work
From: W. Dale Hall (mailtowd-hall_at_pacbell.net)
Date: 09/10/04
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Date: Fri, 10 Sep 2004 21:54:34 GMT
James Harris wrote:
> Paul Murray <paul@murray.net> wrote in message news:<NZT%c.440998$ic1.42833@news.easynews.com>...
>
>>In article <3c65f87.0409081500.3b2cc427@posting.google.com>, James Harris wrote:
>>
>>>The statement did NOT follow logically from what that poster gave.
>>>
>>>He simply made an assertion.
>>
>>You statement that Wiles' proof is incorrect does not follow logically from
>>what you have posted. You have simply made an assertion.
>>
>
>
> Yes, I have asserted that the *approach* Wiles uses fails logically as
> it fails by Cum Hoc, Ergo Propter Hoc.
>
> I make that assertion based on statements about his work, and hold to
> it after looking over his paper.
>
So, you used what amounts to *hearsay* to form your opinion, and now you
say that you looked over his (Wiles's) paper and have decided to hold
your opinion.
Based on the few comments you've made in sci.math that are relevant to
Wiles's paper, it's clear that your "looking at" the paper didn't really
yield anything other than a string of disconnected words. After all,
your complaint that he was assuming modularity in Theorem 0.2 made it
evident that you believed the theorem to be about elliptic curves, when
it was really about Galois representations.
Of course, you didn't have any axe to grind here at all. You didn't
enter the fray with any sort of agenda, believing, for instance, that
mathematicians operate a secret society that enriches itself from
the public coffers, denies outsiders access to its prestige, yet acts
to hinder progress. You didn't actually come in to this discussion
holding to the position that mathematicians are actually the
beneficiaries of some sort of "white collar welfare".
Or did you?
You probably wouldn't be interested in providing any sort of rationale
for basing a conclusion such as yours on *hearsay*, would you? After
all, many mathematicians have not only "looked over" his paper, but
have worked through it in all its gory detail, only to come up with
a contrary conclusion, and it's through the filter of *hearsay* that
you've established that mathematicians are behaving in a corrupt
fashion, believing what they wish to be true!
-- No matter that an error *was* found in the first version of Wiles's
paper to emerge! Just what are we supposed to be conclude: that they
still believed what they wished to be true, only they had actually
wished for the first version to have been false?
Of course, to your credit, you did go and "look over" Wiles's paper,
only to conclude, er, the same thing: he uses the argument "Cum Hoc,
Ergo Propter Hoc". That raises a little question in my mind, that being
How can you tell the form of an argument
if you can't even read the language?
Hey, call me stupid, but I imagine that language has several levels,
the lowest consisting of the physical characteristics of the units:
the look of the words, or the sounds of the phonemes; the next level
might be the level of vocabulary: meanings of terms; at the next level,
perhaps the syntactical structure or grammar might be visible, and only
after that can one discuss stylistic issues, such as argumentation.
It seems to me that one cannot even *begin* to establish what a
person's *form* of argument is, prior to the level at which one can
*recognize the argument itself*. That is, the *form* of an argument
exists at a level of abstraction *above* that of the *details* of the
argument.
Let me make myself clear. I don't mean to suggest that you need to
follow the entire argument to be able to establish its form. What I'm
saying is that you have to be able to identify the various facets of
argumentation: here are the assumptions, here are sub-arguments intended
to nail down certain details, these are the logical inferences, and this
is the conclusion. You can identify those without fully understanding
their content or derivation, but in order to say with *any* confidence
at all that an argument of of some specific form, it is essential to
identify enough of the detail of the argument to be able to characterize
it.
What am I driving at? I say this: you "looked over" Wiles's paper, and
got 5 pages into a paper of 100+ pages. By that time, your intention of
wading through a shallow pool became more like an ordeal of flailing
about in the middle of the ocean. Here you were, clearly taking on
water, when you hoped to fix matters by calling for "a null test".
This does not constitute adequate comprehension of the argument for you
to be able to support the calumny you utter: that not only did Wiles
fall prey to the fallacy of "Cum Hoc, Ergo Propter Hoc" [which fallacy
you *failed* to spot in his article, else you would have displayed the
evidence with annoying pride], but also that the mathematics community
closed ranks around him, forming a conspiracy of support.
One could say "put up or shut up" (and I know I have, on several
occasions, towards several points of discussion with you) but my
words fall on deaf ears, or blind eyes, or unopened Usenet articles.
However, your unwillingness to debate honestly is more your problem
than any of ours, as it should be. Like it or not, if your behavior
in real life is as duplicitous, dishonest, bigotted, and mean-spirited
as it is on Usenet, this life cannot be much of a productive endeavor
for you.
>
>>>I want to emphasize what I said here as it is my way to clear through
>>>posters trying to b.s. their way through, as they need to actually
>>>refer to specific parts of Wiles's work.
>>
>>You have never referred to specific parts of Wiles' work when claiming it is
>>incorrect.
>>
>
>
> That's not necessary for an *approach* problem.
>
Duh. You can't comment intelligently on something in total ignorance
of what that something is. That's something your mama should have told
you.
> It's like if you decide you can prove something using a logically
> fallacious approach, and write volumes of work, it's not necessary for
> people to dig through your efforts.
>
However, it's essential for someone to have a passing familiarity. You
have given a wealth of evidence that for you, and on this subject, it
just ain't so.
> For instance, mathematicians don't need to look at attempts at
> squaring the circle using a square edge as the approach is flawed.
>
"Square edge"? Do tell us how "the approach is flawed", mister
geometer.
> Think of Wiles case as simply being a more dramatic example of a
> person trying a logically flawed approach on a problem.
>
> Just like you don't have to look deeply into an attempt at squaring a
> circle with a straight-edge, I don't have to look deeply into his
> paper.
>
So, tell us all, just how is it that the circle can't be squared? Do you
actually understand the problem? Do you actually know the solution?
What about the trisection of an angle, or doubling the cube?
Do you really understand *any* of these problems?
You said "the approach is flawed". How about you educate us about
the classical problem of squaring the circle?
WHAT IS THE APPROACH?
WHY IS IT FLAWED?
>
>>>As then what they say can be checked against the actual work.
>>>
>>>Such a test is needed on Usenet.
>>
>>So why haven't you provided it?
>>
>>
>>>I just checked it, and that poster did not actually refer to specific
>>>part of Wiles's work.
>>>
>>>I repeat that posters who feel that Wiles's work passes the null test,
>>>and feel they have found the place where it does need to not just SAY
>>>it does but give an actual section.
>>>
>>>That is, they actually need to refer to Wiles's actual work, like to
>>>his paper, you know?
>>
>>So why don't you refer to particular parts of his work when claiming it is
>>false. Like his paper, you know?
>
>
> I have looked his paper over, and to be fair I've offered the null
> test.
>
You've "looked his paper over".
You have not even understood the vocabulary to page 5 from 109 pages.
Yet, you've "looked his paper over".
To be fair, you've "offered the null test".
You don't understand the words, let alone the statements, and God knows,
have not a clue about the combinations of statements that go into
theorems and proofs. However,
TO BE FAIR
you've "offered the null test".
You've come to the conclusion already: mathematics is white-collar
welfare, mathematicians are evil and corrupt, and (because you saw
it written in some men's room stall) Wiles depends on a logical fallacy
to deduce his result. You've "looked his paper over". You don't get the
lingo, but
TO BE FAIR
you've "offered the null test".
Dope.
> The null test is to assume that a non-modular elliptic curve exists
> and trace through his argument to see if that assumption gives a
> contradiction with a logical step.
>
The contradiction? Here's from Arturo Magidin:
From: magidin@math.berkeley.edu (Arturo Magidin)
Newsgroups: sci.math
Subject: Re: JSH: Assocation does not prove
Date: Mon, 30 Aug 2004 22:39:16 +0000 (UTC)
... a buncha stuff deleted ...
Again, I am using the PDF copy at
www.eleves.ens.fr/home/rrichard/wiles.pdf
page numbers refer to the journal page number, i.e.
the page number that appears on the page, not the
one that Acroread gives you. They are the one hundredth
through one hundred and second page of the file;
line numbers ignore headers.
Assume there exists a non-modular semistable elliptic curve.
The following would happen with the argument:
On pp. 542, line 17 through pp. 544 line 3 is the proof that all
semistable elliptic curves are modular.
Assume that the given curve E is semistable, and is non-modular.
Since the argument proceeds by cases, we must change this proof
a bit. That is, currently, the argument is
(a) Either X or not(X) happens;
(a.1) If X, then E is modular;
(a.2) if not(X), then E is modular.
If we assume that E is non-modular, then we need to change the
first part of the proof to
(a) Either X or not (X) happens;
(a.1) If X, then E is modular,
(a'.1) Therefore, not (X).
(a.2) If not(X), then E is modular.
(a.3) not(X) (from (a'.1).
(a.4) Contradiction. Therefore, E is modular.
"X" here is "the representation constructed from E on E[3] is
irreducible".
Explicitly:
pp. 542, line 29, is the conclusion of the argument in the case
that the induced representation on E is irreducible. We must add
"Therefore, by our assumption of non-modularity, the
representation is not irreducible."
pp. 542, line -2 (2 from the bottom). Since we are doing a
reduction ad absurdum proof instead of a direct proof, instead
of "it is enough to show that there are no elliptic curves for
which..." we would have "we conclude that there must exist an
elliptic curve for which...". Instead of using E (which was a
free variable in the original proof, but is not in ours) we
should also switch to some other letter, e.g. F.
pp. 543 through the end of the proof: since we are now working
with the putative F which has the property we want, we should
change the instances of "E" to "F".
pp. 544, line 3. Once we've established that "E' is also
semistable", we must add the following notes to finish the proof
by contradiction:
"But that means that F cannot have the properties we asserted
it did, i.e., it is not an elliptic curve for which the
representation on F[5] is an induced representation[*] over
Q(sqrt(5)) and is semistable at 5. This contradiction arises
from assuming that such an F exists, which follows immediately
from our assumption that E is non-modular and semistable.
Therefore, there cannot exist a non-modular semistable
elliptic curve."
[*] Here, being an "induced representation" is a technical term
about representations. It is not being used in the sense
before of a representation being constructed from a given
elliptic curve.
The problem then arises on line 3 of pp. 544, i.e., the very
last line of the proof of Theorem 5.2.
-- > The nice thing about the null test is that it focuses attention on the > heart of an argument--if it is correct--which is particularly > important with a work like Wiles's because it's so long and supposedly > complicated. > > The null test focuses attention on the keystone of a math proof. > Yeah, whatever. Dope. > If Wiles had a proof then it'd have that keystone logical step, which > could be simply posted. > There it is above. Dope. > I've covered my bases. Now then, if any of you are up to the > challenge, then deliver. > What, are you deef? I just showed you. It's above. Dope. > So far, it's still some kind of freaking political debate. > Hey, I'm not the one who threatened to sic the US Army on us all! > I have a sense that some of you think you're protecting Wiles! > > So ludicrous, like he needs your protection. Besides, I'm challenging > his work. > Challenging? I rather doubt that! > In math, it's the argument that matters. People, soft fluffy stuff, > and feelings are side issues of NO interest when questions of proof > are raised. > Boy, howdy. JSH is sure the master of that proof stuff, lemme yell ya. > Mathematics is a hard discipline. > That whatcha want, tough guy? some.... Hard... Discipline? You got the wrong newsgroup. I think it's alt.booty.spankspankspank > Some of you may soon learn just how hard it is, as your fantasies get > shattered. > Is it? Could it BE????? YESSSSS!!!!! It's the HAMMER!!!!! HAM MER!!! HAM MER!!! HAM MER!!! HAM MER!!! HAM MER!!! HAMM MERRR!! HHHAAAAAMMMMMMMEEEEERRRRRR!!!!!!!!!!!!!!!! YYYYYAAAAAAAYYYYYYYYYYYYYY!!!!! > But playing at math does not change it, and mathematics is no more > your friend than I am. > Awwww. You hurt Mongo's feelings. You no be Mongo's friend? > > James Harris Dale
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