Fundamental mathematical limitation?

Quote:

I don't know how many of you will read through my previous long post,
so here's a shorter version in the same subject area to hopefully
improve my odds.

Basically mathematicians currently teach that there's a fundamental
mathematical limitation on irrational roots of polynomials, like
unless all of their roots have simple radical factors, like sqrt(2),
they can't have an integer other than 1 or -1, like 2, as a factor
where the domain here is one where integers other than -1 or 1 like 2
is itself not a factor of 1.

Quote:

(That is, no 1/2, or 1/3 here, as then you have 3(1/3) = 1.)

That in a very concise space is the area of disagreement as I say
that's wrong.

It turns out that even irrational roots can have the full spectrum of
factors including integer factors, without them all needing to have
the *same* factor, and that the basis for the mathematicians' belief
that they can't is spurious.

That basis is our inability to *look* at the roots of something like

x^2 + 7x + 2, and *see* where that 2 has gone, like we can with

x^2 + 3x + 2 = (x+2)(x+1)

as mathematicians hadn't figured out a way to do it before I came
along, and some of them decided that for that reason it was
mathematically impossible.

The gist of their position is that rational roots, like integers, can
do one thing, but irrational roots must do something different.

The problem is that with the mathematical tools they used, they
couldn't ever get past a fundamental limitation that with irrational
roots you need at *least* two roots to get integers.

That's it. That's what all the fighting and arguing is about, as I
figured out that their current number system was incomplete once you
realized the above, and that you need a more complete arena of numbers
and then you have a concise and consistent system.

It's actually easier, and it makes sense, and you don't have silly
limitations on irrationals.

Is it important for physics or cognitive scientists?

I think it is important for cognitive scientists because I think
mathematicians aren't thinking properly!

As for physics, current physics theories don't necessarily depend, to
my knowledge, on factors between irrational numbers, but if they ever
do, then we're in trouble.

Those of you who believe that discrete physics is the answer should
feel a lot more anxiety, as what I'm saying is that mathematicians
have an idea which may get in the way of those who do research in
discrete physics, if they trust mathematicians!

It's like, they'll train you wrong.

If you don't do research that uses mathematical tools in the area, you
probably are ok, if you do, then you may not have the capacity, based
on the math you're taught, to get a correct theory.

For all we know now, humanity may be stuck at a point that can't be
passed in the arena of physics while we don't have a handle on our
mathematics.

Besides, hey, the mathematicians have an error in thinking here. It's
rather easy to show it's an error, if people will accept logic, and I
just don't see why they should be allowed to just hang on to it.

James Harris