### Sunday, April 05, 2009

## JSH: Math society realities

This wacky story about the one stop equation for 3 of the 4 conic sections in rationals should be more than enough to convince those of you who haven't completely gone over to the Dark Side that math people follow their own wacky rules, where a lot of what they do is anti-thesis to physicists, but it can be kind of appealing to lazy people.

Given x^2 - Dy^2 = 1, in rationals:

y = 2t/(D - t^2)

and

x = (D + t^2)/(D - t^2)

showing it more traditionally versus the way that results from my own re-derivation. (Some of you may remember I screwed up my own derivation and for a while thought I'd solved the factoring problem partly as a result!)

And you get a parameterization for hyperbolas with integer D>0, for circles with D=-1, and for ellipses with D<-1.

But to math people x^2 - Dy^2 = 1 is just "Pell's Equation" so who cares if you can rationally solve ellipses, circles and hyperbolas with it, and categorize 3 of the 4 conic section with one number? The D number?

To THEM it's just a Diophantine equation inappropriately attributed to this Pell guy by Euler, and that is that.

But even more wackily, even as a Diophantine equation they missed reporting on very obvious stuff, like that if D = n^2 - 2, where n is a natural number greater than 1, that is positive integers greater than 1, then D+1 is the first solution for x in Pell's Equation:

Which also means—for various reasons I won't go into for this post—that n^2 - 2 tends to be prime, or the product of few prime numbers.

I mean, that's just cool! And it even has prime numbers!!! It's sexy even by math society "pure math" standards.

In my own battles with that community, where I discovered a HUGE error at the base of what they call number theory which blows Galois Theory out of the water as a useful methodology, I've seen a worship of past mathematicians which the rest of the world refuses to accept.

These people will not accept corrections to their own story about their history.

Mathematics for them is a religion.

Modern mathematicians today are a priesthood.

I have no doubt that they will happily ignore everything I've discovered or re-discovered about "Pell's Equation", and that they could teach as they have for thousands of years without feeling at all that they are missing anything—just like people in any religion.

But physicists give in to this behavior at their peril.

Who knows how many theoretical physicists have blown their futures or any chance of decent research by working with Galois Theory.

And the rational solutions for ellipses and hyperbolas could at a minimum allow, say, a categorization of orbits by a SINGLE NUMBER, the D number, that might yield crucial clues about things like the stability of our own solar system.

Math people, I fear, and I know some of you may think I'm being too hard but hey I found a deep ERROR IN THEIR FIELD AND THEY LIED ABOUT IT TO LIVE IN ERROR—do not care.

They live in error like people in any religion because they do not see it as error.

Did Jesus walk on water? Come on. The laws of physics say, no.

But if you're a Christian, do you go with what you know MUST be true by reason, or do you go with your BELIEFS, by faith?

Mathematicians live by faith, not reason. Or find another explanation for their errors and omissions with "Pell's Equation" as I assure you these postings will have little impact on that wack group of religious freaks.

And tomorrow they will still be with you, asking your to give them full prestige as researchers and academics, despite their ability to have fascinating amnesia on certain issues.

They live in their own little world.

I don't. But they say I do because I'm out here "preaching heresy" to them.

I live in the real world where many of you waste your lives, your intellectual energy, and your careers because the task in front of you seems too hard—facing mathematicians as they are.

Real physics though is your victim.

Given x^2 - Dy^2 = 1, in rationals:

y = 2t/(D - t^2)

and

x = (D + t^2)/(D - t^2)

showing it more traditionally versus the way that results from my own re-derivation. (Some of you may remember I screwed up my own derivation and for a while thought I'd solved the factoring problem partly as a result!)

And you get a parameterization for hyperbolas with integer D>0, for circles with D=-1, and for ellipses with D<-1.

But to math people x^2 - Dy^2 = 1 is just "Pell's Equation" so who cares if you can rationally solve ellipses, circles and hyperbolas with it, and categorize 3 of the 4 conic section with one number? The D number?

To THEM it's just a Diophantine equation inappropriately attributed to this Pell guy by Euler, and that is that.

But even more wackily, even as a Diophantine equation they missed reporting on very obvious stuff, like that if D = n^2 - 2, where n is a natural number greater than 1, that is positive integers greater than 1, then D+1 is the first solution for x in Pell's Equation:

Which also means—for various reasons I won't go into for this post—that n^2 - 2 tends to be prime, or the product of few prime numbers.

I mean, that's just cool! And it even has prime numbers!!! It's sexy even by math society "pure math" standards.

In my own battles with that community, where I discovered a HUGE error at the base of what they call number theory which blows Galois Theory out of the water as a useful methodology, I've seen a worship of past mathematicians which the rest of the world refuses to accept.

These people will not accept corrections to their own story about their history.

Mathematics for them is a religion.

Modern mathematicians today are a priesthood.

I have no doubt that they will happily ignore everything I've discovered or re-discovered about "Pell's Equation", and that they could teach as they have for thousands of years without feeling at all that they are missing anything—just like people in any religion.

But physicists give in to this behavior at their peril.

Who knows how many theoretical physicists have blown their futures or any chance of decent research by working with Galois Theory.

And the rational solutions for ellipses and hyperbolas could at a minimum allow, say, a categorization of orbits by a SINGLE NUMBER, the D number, that might yield crucial clues about things like the stability of our own solar system.

Math people, I fear, and I know some of you may think I'm being too hard but hey I found a deep ERROR IN THEIR FIELD AND THEY LIED ABOUT IT TO LIVE IN ERROR—do not care.

They live in error like people in any religion because they do not see it as error.

Did Jesus walk on water? Come on. The laws of physics say, no.

But if you're a Christian, do you go with what you know MUST be true by reason, or do you go with your BELIEFS, by faith?

Mathematicians live by faith, not reason. Or find another explanation for their errors and omissions with "Pell's Equation" as I assure you these postings will have little impact on that wack group of religious freaks.

And tomorrow they will still be with you, asking your to give them full prestige as researchers and academics, despite their ability to have fascinating amnesia on certain issues.

They live in their own little world.

I don't. But they say I do because I'm out here "preaching heresy" to them.

I live in the real world where many of you waste your lives, your intellectual energy, and your careers because the task in front of you seems too hard—facing mathematicians as they are.

Real physics though is your victim.