JSH: Tail does not wag the dog, simply explained
- From: JSH <jstevh@xxxxxxxxx>
- Date: Thu, 30 Oct 2008 21:52:53 -0700 (PDT)
Turns out I did something massively creative which blows up a lot of
previously held beliefs in the mathematical field:
7*(175x^2 - 15x + 2) = (5a_1(x) + 7)(5a_2(x)+ 7)
where the a's are roots of
a^2 - (7x-1)a + (49x^2 - 14x) = 0
was found by me by creatively moving terms with
7*(175x^2 - 15x + 2) = 1225x^2 - 105x + 14 = (49x^2 - 14x)5^2 + (7x-1)
(7)(5) + 7^2
where I have 5 and 7 where you might normally see x and y, or some
other letters, so I came up with this bizarre, wacky factorization,
and started talking about what happens if you try to divide that 7
off, and the mathematical field kind of blew up as a result.
Understanding why requires you understand some esoteric number theory,
as mathematicians do a lot with something they call the ring of
algebraic integers, which is defined to contain numbers that are roots
of monic polynomials with integer coefficients.
That is, by the roots of polynomials like
x^2 + 3x + 2=0, or x^2 + 3x + 1=0,
but NOT ones like 2x^2 + 5x + 1 = 0.
Mathematicians built up a lot of machinery around the use of these
numbers which are integer-like in many ways, like 1/2 cannot be an
algebraic integers as it's 2x - 1 = 0, so it's a root of a non-monic.
Now normally if you see something like
7*(175x^2 - 15x + 2) = (5a_1(x) + 7)(5a_2(x)+ 7)
you can just divide that 7 off as a useless and extra thing, but
weirdly enough, you may notice that with my creative, wacky
factorization, called a non-polynomial factorization as
(5a_1(x) + 7) and (5a_2(x)+ 7)
are NOT polynomials, you cannot so easily divide that 7 off, but it
gets weirder.
Provably, with
7*(175x^2 - 15x + 2) = (5a_1(x) + 7)(5a_2(x)+ 7)
where the a's are roots of
a^2 - (7x-1)a + (49x^2 - 14x) = 0
you cannot in general divide that 7 off, at all, in the ring of
algebraic integers. Some of you may wish to solve for the a's as you
can just use the quadratic formula and substitute into the
factorization to see if you can figure out a way to divide that 7 off,
and I can tell you, there is no way you CAN see.
It's mathematically impossible for you to see a way.
But a way to do it can be proven, but it requires you throw out a lot
of previously held beliefs, which is why mathematicians chose instead
to argue with me for years.
Now the paper that went to the journal that died after publishing it
and retracting it, covered this result.
So you have an entire mathematical journal going belly-up all of a
sudden because of one paper and math people lying all over the place
about it as the situation is THAT BIG.
But still you may wonder, what if the crazy guy is just wrong? Or you
may ponder, how could all those math people be wrong for over a
hundred years? (Oh yeah problem came into the field over a hundred
years ago.)
How are any groups of people wrong for years? It just happens.
In this case to disbelieve me you have to believe some truly wacky
stuff, but primarily you have to ignore the reality that constants
like 2, when multiplied by something like 7, tend to turn into
something like 14.
So with
7*(175x^2 - 15x + 2) = (5a_1(x) + 7)(5a_2(x)+ 7)
where the a's are roots of
a^2 - (7x-1)a + (49x^2 - 14x) = 0
you can just see that the 7 didn't multiply times the 2 because you
don't see 14 on the right side. But yeah, functions can obscure
things, so how do you make sure there isn't something weird going on
with the functions?
Oh, I know, you try a value!!! What a concept. So try x=0 as that's
easy, and it just gives
a^2 + a = 0, so a_1(0) = 0 or -1, and a_2(0) = -1 or 0, and plug those
in and everything works out perfectly and easily.
Know what the math people did when I started talking about constant
terms years ago when I was making a prior attempt at getting them to
do the right thing?
They made fun of me. Argued with me about how you define constant
term. Stuff like that.
My fellow physics people: they killed one of their own math journal to
help obscure this result!
That journal was over 10 years old. There were a lot of other papers
published through it besides mine and the hosting university just
dropped it like a hot potato. EMIS, a European agency, kept the
American math journal's archives alive.
Google: SWJPAM
Math journals do not just die. Supposed crackpots do not get
published in a peer reviewed mathematical journal without it being
news and later the math journal dies, unless there is something truly
massive going on.
So what does this matter to physics?
Well, for one thing, any bleed over from number theory where algebraic
integers are the basis for the mathematical results is probably wrong.
So theoretical physicists playing with these tools are wasting their
times and experimenter's times if they test theories based on bogus
math, but hey, I know, not much useful comes from these "pure math"
areas, but there is some I'm sure.
And it's probably wrong.
(Does "string theory" use any esoteric mathematics? See what I mean?)
Also, I have other research results like my prime counting function
and the people lying about this major result that blows up so much are
lying about it as well and I know there are physicists looking into
ways that prime numbers pop up in physics theories.
Short of it is, the math people are blocking ANYTHING I come up with
now, and need I remind you they killed one of their own freaking math
journals?
Anybody notice I came up with a more general and direct method for
solving binary quadratic Diophantine equations? Think the math people
who supposedly care about such things will trumpet that result? I
haven't seen anything yet, and yes, I'm bugging them about it.
If you want your physics complicated by bogus math where the experts
in the field have been fully informed and they killed one of their own
math journals versus accept a massively important result with
implications over a hundred years then you go right ahead and waste
your life and research dollars when you don't know where the
minefields are.
Mathematical journals do not just die.
I can give the mathematical proof but while the denial goes on, proof
isn't working.
For years now the math people have avoided this result which is
actually peer reviewed and published, but they broke the rules, got
the journal to retract, and it quietly died a little later.
Your own research may be corrupted by bogus math ideas that these
people are trying to keep teaching.
This situation is the biggest intellectual issue maybe in the history
of the human species.
Yes the tactic of calling me crazy is an effective one. But it's the
pursuit of knowledge itself that is at stake when you turn a blind eye
to mathematical proof in the hope that your mathematical colleagues
are actually doing the right thing.
And your lost time and energy if they are not, and you buy into bogus
mathematical concepts just because you were too trusting, or willfully
too naive.
Journals do not just die. Google SWJPAM. Email EMIS and ask them why
they had to save that journal if you have the contacts. But DO
something. Dig. Find out why.
Be real physics people.
Math journals do not just die.
James Harris
.
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