### Tuesday, December 30, 2008

## JSH: Simple proof, but difficult response

I have found an easy demonstration of a very damaging error that has hold of number theory.

Mathematical argument is about as easy as it gets:

In the complex plane:

7*(x^2 + 3x + 2) = (7x + 7)(x + 2)

I can let that be

7*(x^2 + 3x + 2) = (f_1(x) + 7)(f_2(x) + 2)

where f_1(x) = 7x, and f_2(x) = x, to emphasize those are LINEAR functions.

Now compare and contrast with

7*(175x^2 - 15x + 2) = (5b_1(x) + 7)(5b_2(x)+ 2)

where b_1(0) = 0, b_2(0) = 0, a_1(x) = b_1(x), and a_2(x) = b_2(x) - 1,

and the a's are roots of

a^2 - (7x-1)a + (49x^2 - 14x) = 0.

Now you have NON-LINEAR functions.

So in one case 7 multiplies times a linear function, while in the second it multiplies times a non-linear function.

There is no way the type of function changes the distributive property as the distributive property with functions is as follows:

a*(f(x) + b) = a*f(x) + a*b

So all I did was figure out a creative way to put a non-linear function in a position where it had to be multiplied by 7 in a highly specific way, where it's trivial with linear functions, and the answer is also clear with non-linear ones…but I blow up about a hundred years of "pure mathematics" in number theory with the result.

"Pure mathematics" actually arose AFTER this error came into number theory in the late 1800's so it may be an artifact of the error as of course, wrong mathematics can't be useful for situations where you need correct answers.

By claiming "pure" math practitioners escaped having to have mathematics that could be checked against the real world, and the field became corrupted, and now it's VERY difficult to get past that corruption even with a very basic proof.

With the error people can appear to "prove" just about anything, and so Andrew Wiles has no proof of FLT. Guys winning Abel prizes in "pure math" errors related are getting money for failure.

The system broke here, but there is so much social inertia that it is difficult to get the word out.

Go over the argument above. Ask yourself: is there any way the TYPE of the function can change the distributive property?

Ask yourself again and again and again until it sticks.

The answer is, no.

Your heroes are nonesuch, and have proven they will hold on as long as society lets them, then I expect they will run for cover, and use every excuse in the book. Expect it, steel yourselves for it.

Those you respected so much, will come crashing down to the ground very hard, and reveal themselves to be, craven human beings, who held on to failure as long as they could, because they were never great, or even all that good, but just opportunists.

Mathematical argument is about as easy as it gets:

In the complex plane:

7*(x^2 + 3x + 2) = (7x + 7)(x + 2)

I can let that be

7*(x^2 + 3x + 2) = (f_1(x) + 7)(f_2(x) + 2)

where f_1(x) = 7x, and f_2(x) = x, to emphasize those are LINEAR functions.

Now compare and contrast with

7*(175x^2 - 15x + 2) = (5b_1(x) + 7)(5b_2(x)+ 2)

where b_1(0) = 0, b_2(0) = 0, a_1(x) = b_1(x), and a_2(x) = b_2(x) - 1,

and the a's are roots of

a^2 - (7x-1)a + (49x^2 - 14x) = 0.

Now you have NON-LINEAR functions.

So in one case 7 multiplies times a linear function, while in the second it multiplies times a non-linear function.

There is no way the type of function changes the distributive property as the distributive property with functions is as follows:

a*(f(x) + b) = a*f(x) + a*b

So all I did was figure out a creative way to put a non-linear function in a position where it had to be multiplied by 7 in a highly specific way, where it's trivial with linear functions, and the answer is also clear with non-linear ones…but I blow up about a hundred years of "pure mathematics" in number theory with the result.

"Pure mathematics" actually arose AFTER this error came into number theory in the late 1800's so it may be an artifact of the error as of course, wrong mathematics can't be useful for situations where you need correct answers.

By claiming "pure" math practitioners escaped having to have mathematics that could be checked against the real world, and the field became corrupted, and now it's VERY difficult to get past that corruption even with a very basic proof.

With the error people can appear to "prove" just about anything, and so Andrew Wiles has no proof of FLT. Guys winning Abel prizes in "pure math" errors related are getting money for failure.

The system broke here, but there is so much social inertia that it is difficult to get the word out.

Go over the argument above. Ask yourself: is there any way the TYPE of the function can change the distributive property?

Ask yourself again and again and again until it sticks.

The answer is, no.

Your heroes are nonesuch, and have proven they will hold on as long as society lets them, then I expect they will run for cover, and use every excuse in the book. Expect it, steel yourselves for it.

Those you respected so much, will come crashing down to the ground very hard, and reveal themselves to be, craven human beings, who held on to failure as long as they could, because they were never great, or even all that good, but just opportunists.