Re: JSH: The Math

From: Nora Baron (norabaron_at_hotmail.com)
Date: 09/26/04 

Date: 26 Sep 2004 12:25:59 -0700

jstevh@msn.com (James Harris) wrote in message news:<3c65f87.0409251337.2e23d714@posting.google.com>...
> Not surprisingly, since mathematics IS mathematics, my position can be
> defended rather easily:
>
> f^2((m^3 f^4 - 3m^2 f^2 + 3m) x^3 - 3(-1+mf^2 )x u^2 + u^3 f) =
>
> (a_1 x + uf)(a_2 x + uf)(a_3 x + uf)
>
> where on the left side you have independent variables, and they are f,
> m, x and u.
>
> One the right side you have x, u and f, but also the dependent
> variables a_1, a_2, and a_3.
>
> Note that you have f^2 as a multiple of the left side, and divide it
> off to get
>
> (m^3 f^4 - 3m^2 f^2 + 3m) x^3 - 3(-1+mf^2 )x u^2 + u^3 f =
>
> (a_1 x + uf)(a_2 x + uf)(a_3 x + uf)/f^2
>
> and to determine how that factor f^2 divides through rely on f being
> independent of m, x and u, so you can set m = 0 to get
>
>
> - 3(-1)x u^2 + u^3 f =
>
> (a_1 x + uf)(a_2 x + uf)(a_3 x + uf)/f^2
>
> which is
>
> u^2(3x + uf) = (a_1 x + uf)(a_2 x + uf)(a_3 x + uf)/f^2
>
> and you can tell how the factorization goes by observation, as the
> only way you can get what you have on the left from what you have on
> the right is for two of the a's to equal 0, while one equals 3, when
> m=0.
>
> Given that m is independent of f, and f is independent of m, it
> follows that the result holds without regard to the value of m.
>

  Here we have the New Mathematics: The Harris Independence Principle
(HIP). Here is a concise statement:

    THE HARRIS INDEPENDENCE PRINCIPLE

      Suppose two variables m and f both occurring in the same
      equation are *independent* of each other. Then if some
      fact regarding f is true when m = 0, it must be true for
      all other values of m also.

  Of course we should define 'independent'. Two variables
in an equation are independent if, when you choose a value
for one of them, the other one can be chosen to be anything
you want.

  Terrific new principle! Why haven't mathematicians noticed
it before? I bet it can be used to prove all sorts of new
theorems!

  Here is an example:

  Say m and f are nonnegative integers.

         (m + f) * (m + f + 1) = a * b,

where a and b are integers. First I pick m and f. Then once
I have picked m and f, a and b are dependent on them, though
m and f are themselves completely INDEPENDENT! Remember,
first I pick m, then I can pick f to be anything I want. Of
course I am not as free to pick a and b: they are DEPENDENT
on m and f.

  Note that when m = 0, either a or b (or both)
is non-coprime to f, since

        f * (f + 1) = a * b.

  Therefore by the Harris Independence Principle (HIP),
for all other values of m, either a or b (or both) is noncoprime
to f !

  Hmm, let's see. I'll let m = 1 and f = 5. The equation
is

      (1 + 5)*(1 + 5 + 1) = a * b, or

         6 * 7 = 42 = a * b.

  Now, the HIP says that either a or b must be noncoprime
to 5. That is, 42 must have a nonunit factor in common with 5 !
Immediately I get a new result! And one nobody every suspected!

  Yes, the HIP is great! I say, HIP HIP HOORAY for the
Harris Independence Principle!

> Therefore, algebraically, it is proven that two of the factors
>
> (a_1 x + uf), (a_2 x + uf), and (a_3 x + uf)
>
> have f as a factor.
>
> Notice that the proof follows easily, as long as you accept algebra.
>

  Yep, the HIP: it's JUST ALGEBRA!

> The central point is the independence relationship which is basic.
>
> The independent variables are just independent.
>

  Yep, they just *are*.

  Really, this is not just another James Harris bullshit
pseudomath argument. It is getting so annoying to see him
accused of that all the time. And this is not just some fancy
untrustworthy BS put out by those Galois fanatics. Grow up,
people! This is the HIP ! This is ALGEBRA!

> Some of you may have kept up with arguments on sci.math that have
> raged over this algebra for OVER TWO YEARS NOW and might consider that
> posters who even attempt to challenge the algebra algebraically try to
> FORCE a dependency relationship, like by claiming there exists w_1(m),
> w_2(m), and w_3(m), that are factors of the a's where
>
> w_1 (m) w_2(m) w_3(m) = f^2
>
> and where the w's are to vary as m varies, and notice you now have a
> dependency relationship!
>

  Shocking. You know, when I write

         m*f = a1,

where a1 is some integer, m and f are the independent variables -
I am perfectly free to choose m and f - and a1 is the DEPENDENT
variable. First I pick m and f, and then a1 is determined (i.e.,
DEPENDENT). For fixed f, I could write

         m*f = a1(m),

to express that dependency. Whoa, now it looks like m and f
are both in one equation, so now they must be DEPENDENT. But
you know what? m and f are still INDEPENDENT. No dependency
of m and f has been imposed! If you pick one of them, you
are still perfectly free to pick the other one however you
wish! Why? Because a1 is a *dependent* variable! It's the
one ending up with the short end of the stick! The other two
can do pretty much anything they want. They're INDEPENDENT.

  Still, I must say, this was a pretty good attempt to lead
yourself astray. You were probably thoroughly confused by the
time you got through it. Was anyone else? Maybe not.

> That is, fighting the independent reality of the variables, posters
> would simply try to add in a dependency of their own.
>

  You can't fight Independence!

> It's completely bogus but there are psychological reasons.
>

  Right. When people deny that 42 and 5 have common factos,
that's just for psychological reasons. They are after all
denying the HIP!

> Most of you, despite your labels, are not mathematicians.
>
> Real mathematicians are like me.
 

  You mean, they're full of crap???

> Quirky sense of humor, persistence
> to the point of insanity

  or well beyond

> as far as "normal" people are concerned,
> extraordinary consistency over periods of years, and oh yeah, a
> tremendous love of the truth above all else, even at the expense of
> other people.
>

  [snip the part not concerned with the HIP]

>
> Get it now?
>

  Oh, sure. HIP HIP HOORAY!

  Nora B.

>
> James Harris
> http://mathforprofit.blogspot.com/

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