Re: Cum Hoc, Ergo Propter Hoc

From: James Harris (jstevh_at_msn.com)
Date: 08/25/04 

Date: 25 Aug 2004 03:47:05 -0700

poespam-trap@yahoo.com (Randy Poe) wrote in message news:<df76407e.0408241942.670afdf1@posting.google.com>...
> jstevh@msn.com (James Harris) wrote in message news:<3c65f87.0408241452.322d12c4@posting.google.com>...
> > poespam-trap@yahoo.com (Randy Poe) wrote in message news:<df76407e.0408241057.423f3563@posting.google.com>...
> > > jstevh@msn.com (James Harris) wrote in message news:<3c65f87.0408221623.400a43da@posting.google.com>...
> > > > Basically there are 4 numbers that you can use to describe a modular
> > > > form and mathematicians found THE SAME 4 numbers could be used to
> > > > describe an elliptic curve, and they noticed the for every set of 4
> > > > numbers for a modular form they could find an elliptic curve with the
> > > > SAME SET OF 4 NUMBERS!!!
> > > >
> > > > It's a perfect setup for a logical error, as rather than do what's
> > > > necessary in such a situation, which is find out what exactly the
> > > > relation is--if there is one--between modular forms and elliptic
> > > > curves, Wiles set out to compare between sets.
> > > >
> > > > He set out to compare every elliptic curve against every modular form,
> > > > which is a logical error called Cum Hoc, Ergo Propter Hoc.
> > >
> > > Wait a minute.
> > >
> > > So are the following also examples of the same logical fallacy?
> > >
> > > (a) I can demonstrate a one-to-one correspondence between
> > > complex numbers and points in the (x,y) plane. There are two
> > > real numbers that correspond to every complex number, and
> > > there are two real numbers that correspond to every point in
> > > the (x,y) plane. Given a point in the (x,y) plane, I can
> > > use the SAME TWO NUMBERS to define a complex value, and
> > > vice versa.
> > >
> > > (b) I can demonstrate a one-to-one correspondence between
> > > rational numbers and repeating decimals, excluding those
> > > whose repeating part consists only of 9's. For every one
> > > of the latter, I can find unique rational number, and
> > > vice versa.
> > >
> > > All I've done is establish one-to-one correspondences of
> > > just the type you accuse Wiles of doing. Is that "cum hoc
> > > ergo propter hoc"? If not, where is the difference?
> > >
> > > - Randy
> >
> > Well now you're lying as it's not the same type as Wiles.
>
> "Lying"? I asked you a question. I expected a yes or no
> answer, but I certainly didn't expect to be told my question
> was a "lie".
>

Ok then you're dumb.

Otherwise how you can try to connect modular forms and elliptic curves
having the 4 same descriptors when compared to repeating decimals
being rational?

I was giving you the benefit of the doubt by saying you lied, but if
you say you didn't lie then you're dumb.

> > Repeating decimals can be shown to be equal to rational numbers,
>
> No, repeating decimals are infinite strings of characters.
> They can be shown to be in one-to-one correspondence with
> the rational numbers (with the caveat I gave above omitting
> certain strings).

No. The simplest way to understand repeating decimals is to look at
an example so consider 1, 3 and x, such that

3x = 1

and if you operate in the field of reals then you can divide that 3
into 1, and notice that as you do, you get a steady stream of 3's,
like if you go a certain distance and quit, you might have
0.3333333333.

Now, the operations don't change, and the output isn't changing,
except at one step you add another 3, so using some basic mathematical
axioms you can rightly assume that giving the same operations the same
output will occur as long as mathematics is consistent.

Therefore, you will get 3's indefinitely.

Sure, the meager mind may wish to leap to infinity, but you show why
that can be a dangerous thing for a meager mind.
 
> They are not "equal". But this correspondence is used to
> show that these two very different representations, one
> finite, one infinite, are EQUIVALENT.
>

Some people see that word "infinite" and their brains are out of their
depth.

You should consider using the word "indefinite length" until you get
it.

Then maybe you can come back to consider infinity.

> > so in
> > fact you actually push my point as the logical fallacy that Wiles
> > makes comes from trying to *prove* through a correspondence.
>
> Please outline the difference between my correspondences
> and Wiles.
>

Mathematicians noted that modular forms and elliptic curves could
*both* be described by 4 numbers. It's like you can be described,
say, by your IQ, you address, your social security number (if in the
US), and your shoe size.

Now the difference between you and modular forms and elliptic curves
here is that mathematicians say that 4 numbers are what's needed to
describe, while there are other numbers that could be used to describe
you, like your waist size or the weight of your brain. (Actually
creatively more numbers could probably be used to describe modular
forms and elliptic curves!)

Now then mathematicians noted that for every elliptic curve they found
they had a modular form with THE SAME FREAKING NUMBERS!!!

Gee, wow, oh my, so Wiles took off on a logically fallacious path of
trying to compare every modular form against every elliptic curve and
since the sets are infinite he used what mathematicians call lifting.

Trouble is, it doesn't matter that he used lifting as his entire
approach is logically flawed and fails by Cum Hoc, Ergo Propter Hoc.

Now readers who decided to look that logical fallacy up, might have
noticed the *solution* to not falling to the fallacy, so all anyone
has to do is show what Wiles did to not fail by it, but the problem is
that he didn't do any of those things, so he failed.

I'm not making this up. Look up the logical fallacy, and look up how
you're supposed to avoid it.

> >
> > The same applies to mapping the complex plane.
>
> What does? That they are "equal"? Again, not true. You're
> just so used to accepting the correspondence that you
> think of them interchangeably. Again, two very different
> kinds of objects which are shown to be EQUIVALENT in that
> they have not only a one-to-one correspondence, but
> can have corresponding arithmetic relationships
> defined.

The mapping of complex numbers into the complex plane *follows* from
various definition and axioms such that if mathematics is *consistent*
it works out a certain way.

Any time you can logically constrain a system such that one conclusion
exists as long as that system is consistent, then you're ok.

No logical fallacy.

Don't mathematicians get taught logic in school?
 
> > In both of your examples, you don't need the correspondence to prove,
> > as you have other means.
>
> Fine. Exhibit one, please.
>
> - Randy

I've explained as much as I'm interested in doing since I know that
Randy Poe is a rather annoying repeat poster, where you explain,
explain, explain, and he just keeps replying, replying, replying.

My suggestion for readers in this thread is to ignore the regular
parasitic sci.math'ers who reply to me for God knows what reason, and
look up the logical fallacy in the subject line.

If you research it, you should also find how it is you protect from
falling prey to it.

Then just ask yourself if Wiles did that or not.

It's freaking LOGIC people. Next thing though, one of these
sci.math'ers might try to claim I'm making it up!!!

Freaking overemotional people. How did they ever get into math?

Math isn't some social club. It's totally unforgiving.

James Harris

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