Sunday, December 21, 2008
JSH: So why all the arguing?
The situation is critical so I need to give you a synopsis so you understand why, and understand the weird arguments.
You may have noticed me talking a lot about a trivial example:
7(x^2 + 3x + 2) = (7x + 7)(x+2)
where it's clear how I multiplied by 7. That's trivial, so why would anyone argue about it?
Well, I one-upped the trivial with something more complicated:
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.
So I switched from linear to non-linear functions. That picture is somewhat muddled so I made one more minor step, which is to normalize with a_1(x) = b_1(x), and a_2(x) = b_2(x) - 1, so that the b's equal 0 when x=0, and I have
7*(175x^2 - 15x + 2) = (5b_1(x) + 7)(5a_2(x)+ 2)
and if
7(x^2 + 3x + 2) = (7x + 7)(x+2)
is a guide--after all I only switched from linear functions to non-linear ones—then one would suppose that I picked 7 to multiply the same as before but that implies that with
a^2 - (7x-1)a + (49x^2 - 14x) = 0
one of the roots is a product of 7 and some other unknown numbers, which is a HUGE shift in mathematical thinking, as if you plug in numbers like x=1, then that means that with
a^2 - 6a + 35 = 0
only one of the roots one would suppose actually has 7 as a factor, but by standard mathematical teaching NEITHER of the roots can possibly have 7 as a factor in what is called by mathematicians the ring of algebraic integers, as the belief is that the 7 splits up in some way, and mathematicians can make calculations to GIVE you that split, so it's an odd situation.
To hold on to their current mathematical beliefs, posters are arguing that the 7 can shift around depending on the value of x, while I'm arguing that how the 7 distributes is independent of what is being multiplied and the argument is mostly the same as it has been for about six years or so, except at times (recently is the second time) I've pointed out that my distribution argument holds true on the complex plane, as it's not really a factor argument, so I've tried to hold math people to the complex plane.
Now all that may make you wonder, what's the big deal?
Well, I can explain ALL of their current mathematical teaching and include my distribution argument, and explain why they think the 7 splits up and think they can give you evidence that it splits up, but they can't answer my distribution argument, which is why I emphasize
7(x^2 + 3x + 2) = (7x + 7)(x + 2)
as it's simple enough that you can know intuitively that I'm right, but then of course, the idea of authority figures kicks in, and I'm sure most of you suppose that I just can't be completely right because, well, for instance, if a math error entered over a hundred years ago, wouldn't somebody notice?
And what about the massive success of our current science and technology using mathematics?
Well I have a degree in physics so I know that most of the mathematical underpinnings of modern science and technology actually existed long before the error was introduced. Also the error is in number theory where mathematicians often say their research is "pure" as in, it has no practical application.
That is not a relief though as in, none of it matters, as some of this research actually seems related to quantum physics, so we may not be able to do certain things or explain certain things, say, in quantum chromodynamics without the correct number theory, as number theory not being a bigger part of modern physics may simply be because of the error.
This error while it can impact the explanations of some current theory doesn't impact the predictive value from what I've gathered of any working modern theory, while it may completely shoot down "string theory" which is kind of infamous for lacking predictive value.
Given the stature of the modern math field and many of its practitioners and their refusal to follow their own rules regarding acceptance of mathematical proof, it's not clear if the error will be acknowledged any time soon, but that is not really a win for them.
Given our history as a species eventually the tide will turn, the error will be acknowledged and over one hundred years of mathematical work will be re-thought. A lot of big names in the math field may turn into much lesser names, or even simply be considered to be examples of people who never discovered anything of value but were only thought to have done so.
I strongly suspect that it will be the largest upheaval in the intellectual history of the human race. And it is inevitable, but it's not clear when it will occur.
In the meantime, the arguing continues. Math people with YEARS of their lives invested in false information are holding on to it, and society is rewarding them as usual, so they have validation in that way, but it's just a delay of the inevitable when society will turn. From what I've gathered though, they're hanging on for every day with the error as a precious gift. Sadly enough, but if you understand all the issues, I guess it's understandable for people who may, if they acknowledge the truth, wake up to a world where all their "great" "accomplishments" are gone.
For many of them, their faith in society in terms of mathematical knowledge was simply not realized in what they were taught at even the best institutions.
It is clearly a case of a massive it's not fair situation.
The weight of history is against them, but for now they are considered geniuses, leading researchers, and "brilliant minds".
Losing that fantasy is the last thing they want to do.
You may have noticed me talking a lot about a trivial example:
7(x^2 + 3x + 2) = (7x + 7)(x+2)
where it's clear how I multiplied by 7. That's trivial, so why would anyone argue about it?
Well, I one-upped the trivial with something more complicated:
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.
So I switched from linear to non-linear functions. That picture is somewhat muddled so I made one more minor step, which is to normalize with a_1(x) = b_1(x), and a_2(x) = b_2(x) - 1, so that the b's equal 0 when x=0, and I have
7*(175x^2 - 15x + 2) = (5b_1(x) + 7)(5a_2(x)+ 2)
and if
7(x^2 + 3x + 2) = (7x + 7)(x+2)
is a guide--after all I only switched from linear functions to non-linear ones—then one would suppose that I picked 7 to multiply the same as before but that implies that with
a^2 - (7x-1)a + (49x^2 - 14x) = 0
one of the roots is a product of 7 and some other unknown numbers, which is a HUGE shift in mathematical thinking, as if you plug in numbers like x=1, then that means that with
a^2 - 6a + 35 = 0
only one of the roots one would suppose actually has 7 as a factor, but by standard mathematical teaching NEITHER of the roots can possibly have 7 as a factor in what is called by mathematicians the ring of algebraic integers, as the belief is that the 7 splits up in some way, and mathematicians can make calculations to GIVE you that split, so it's an odd situation.
To hold on to their current mathematical beliefs, posters are arguing that the 7 can shift around depending on the value of x, while I'm arguing that how the 7 distributes is independent of what is being multiplied and the argument is mostly the same as it has been for about six years or so, except at times (recently is the second time) I've pointed out that my distribution argument holds true on the complex plane, as it's not really a factor argument, so I've tried to hold math people to the complex plane.
Now all that may make you wonder, what's the big deal?
Well, I can explain ALL of their current mathematical teaching and include my distribution argument, and explain why they think the 7 splits up and think they can give you evidence that it splits up, but they can't answer my distribution argument, which is why I emphasize
7(x^2 + 3x + 2) = (7x + 7)(x + 2)
as it's simple enough that you can know intuitively that I'm right, but then of course, the idea of authority figures kicks in, and I'm sure most of you suppose that I just can't be completely right because, well, for instance, if a math error entered over a hundred years ago, wouldn't somebody notice?
And what about the massive success of our current science and technology using mathematics?
Well I have a degree in physics so I know that most of the mathematical underpinnings of modern science and technology actually existed long before the error was introduced. Also the error is in number theory where mathematicians often say their research is "pure" as in, it has no practical application.
That is not a relief though as in, none of it matters, as some of this research actually seems related to quantum physics, so we may not be able to do certain things or explain certain things, say, in quantum chromodynamics without the correct number theory, as number theory not being a bigger part of modern physics may simply be because of the error.
This error while it can impact the explanations of some current theory doesn't impact the predictive value from what I've gathered of any working modern theory, while it may completely shoot down "string theory" which is kind of infamous for lacking predictive value.
Given the stature of the modern math field and many of its practitioners and their refusal to follow their own rules regarding acceptance of mathematical proof, it's not clear if the error will be acknowledged any time soon, but that is not really a win for them.
Given our history as a species eventually the tide will turn, the error will be acknowledged and over one hundred years of mathematical work will be re-thought. A lot of big names in the math field may turn into much lesser names, or even simply be considered to be examples of people who never discovered anything of value but were only thought to have done so.
I strongly suspect that it will be the largest upheaval in the intellectual history of the human race. And it is inevitable, but it's not clear when it will occur.
In the meantime, the arguing continues. Math people with YEARS of their lives invested in false information are holding on to it, and society is rewarding them as usual, so they have validation in that way, but it's just a delay of the inevitable when society will turn. From what I've gathered though, they're hanging on for every day with the error as a precious gift. Sadly enough, but if you understand all the issues, I guess it's understandable for people who may, if they acknowledge the truth, wake up to a world where all their "great" "accomplishments" are gone.
For many of them, their faith in society in terms of mathematical knowledge was simply not realized in what they were taught at even the best institutions.
It is clearly a case of a massive it's not fair situation.
The weight of history is against them, but for now they are considered geniuses, leading researchers, and "brilliant minds".
Losing that fantasy is the last thing they want to do.
# posted by James Harris @ 20:58 
