Harristotelian Logic

For some time several posters have gotten away with pushing bogus mathematics in their efforts to argue with me. Possibly they got sucked in as I worked out the mathematical ideas, and when faced with finally correct arguments, after my many failures, decided to just keep arguing with me, and in doing so taught those of you who trusted them bogus math.

Here finally I've chased down their objection and can explain it to you simply enough.

Given an expression like

P(X) = b^2((b^4 X^3 - 3b^2 X^2 + 3X) t^3 - 3(-1 + b^2 X )t u^2 + b u^3)

where the odd grouping is so that I can factor P(X) into non-polynomial factors, for instance,

P(X) = (r_1(X) t + bu)(r_2(X) t + bu)(r_3(X) t + bu)

they would claim that my factorization meant that really the polynomial is P(t) or P(X,t).

The gist of their complaint being that the factorization changed the polynomial. (Mathematical version of tail wagging the dog?)

Luckily for me, as it is mathematics and a general principle, I could switch to something less complicated and used

P(x) = 11^2 + 11x + 2

where again you have a special grouping simply to allow the non-polynomial factorization, as you can see that P(x) is also

P(x) = 11x + 123

so I've just used the 11's before as placemarkers, so I can act like it's the polynomial y^2 + xy + 2, to get the factorization

P(x) = (11 + (x+sqrt(x^2-8))/2)(11 + (x-sqrt(x^2-8))/2)

but the polynomial is STILL P(x)= 11x + 123. These posters worked to convince that the factorization, with more complicated expressions, changed the polynomial in some way. Apparently plenty of sci.math readers and especially alt.math.undergrad readers, who may be more susceptible, were convinced by them.

They were very successful which can be seen by the date on the following and the fact that they've been arguing with me up until now. Think of all the months pumping false information out to readers.

Consider with my early use of non-polynomial factorization Arturo Magidin's reply claiming that it is a "new polynomial".

>From: magidin@math.berkeley.edu (Arturo Magidin)
Newsgroups: sci.math
>Subject: Re: Google, prime counting, and me
>Date: Sun, 13 Oct 2002 02:17:24 +0000 (UTC)

Message-ID:


The "constant term" here does NOT correspond to the constant term of the original polynomial; the coefficients a1,a2,a3,b1,b2,b3 have nothing to do with this "new" polynomial. They correspond to the original one.

======================================================================
"It's not denial. I'm just very selective about what I accept as reality."
--- Calvin ("Calvin and Hobbes")
======================================================================

Arturo Magidin
magidin@math.berkeley.edu
<\Quote>

And oddly enough for the complicated expression people seemed to believe him.

Now Arturo Magidin has a PhD from Berkeley in mathematics, and is talking about a factorization changing the polynomial, where also he has a telling statement at the end of his posts? What would you think?

I think that some of you would agree with posters like Arturo Magidin and "Nora Baron" on anything or sit idly by without caring about some people thinking they're learning correct mathematics from them, as long as it makes me miserable.

Well that might seem like good fun to many of you, or something I deserve, but think back to when some of you were kids and the more popular kids or bullies picked on you, and consider the position that you deserved it.

My fear is that many of you didn't wish they'd behave, but instead wished that you were popular enough or big enough to do what they were doing.

And now you're adults with math degrees, and you think you have me to tease and mock.

But you see, I have mathematics, which makes me the one who actually has the power. Those kids never had anything important on any of you, and it's foolish to give them power they didn't have, by tossing out the one thing that doesn't change—mathematical truth.

[A reply to David C. Ullrich.]

And notice that David Ullrich deleted out the gist of "Nora Baron" and Arturo Magidin's complaints. I've also noticed an outpouring of hostile posts recently, as apparently, mathematics isn't good enough for many of you.

Here's an excerpt that David Ullrich deleted out.

Luckily for me, as it is mathematics and a general principle, I could switch to something less complicated and used

P(x) = 11^2 + 11x + 2

where again you have a special grouping simply to allow the non-polynomial factorization, as you can see that P(x) is also

P(x) = 11x + 123

so I've just used the 11's before as placemarkers, so I can act like it's the polynomial y^2 + xy + 2, to get the factorization

P(x) = (11 + (x+sqrt(x^2-8))/2)(11 + (x-sqrt(x^2-8))/2)

but the polynomial is STILL P(x)= 11x + 123. These posters worked to convince that the factorization, with more complicated expressions, changed the polynomial in some way. Apparently plenty of sci.math readers and especially alt.math.undergrad readers, who may be more susceptible, were convinced by them.

It's actually rather amazing that a few posters could convince so many people to follow along with something so odd, as to believe that the factorization changed the polynomial.

But then, maybe for many of you an expression like

P(X) = b^2((b^4 X^3 - 3b^2 X^2 + 3X) t^3 - 3(-1 + b^2 X )t u^2 + b u^3)

where the odd grouping is so that I can factor P(X) into non-polynomial factors, for instance,

P(X) = (r_1(X) t + bu)(r_2(X) t + bu)(r_3(X) t + bu)

is just so weird and outside of your mathematical knowledge that you'd figure, hey, if those people say it's no longer P(X) because of the factorization, you'd just go along and trust the majority.

But you see, mathematics isn't a democracy.

# posted by James Harris @ 08:39