Tuesday, September 26, 2006
JSH: Stop being dense
So why would people known as top number theorists around the world NOT admit the coverage problem with algebraic integers?
Because in admitting it they are taking away that very position.
This thing is huge. It stepped in over a hundred years ago—before anyone currently alive was even born—and in mathematics a small mistake at a key spot can be devastating.
This error re-writes the math history books over a hundred plus years, yanking expert status from so many people over that time, and to admit it now, people called top, would suddenly find they are nowhere near there.
What do they have that this error doesn't touch?
Dedekind in saying that he proved a result that was key in convincing others that the algebraic integers did give full coverage, said he used ideal theory, which at that time was a relatively new idea.
He couldn't figure out any other way to do it, and now we know that was because there was no way to prove full coverage—not correctly.
So one of the first things ideal theory was used for was to convince people of this faux result about algebraic integers and a lot of history passed from that point until today, till we have people who are currently thought brilliant, or even "beautiful minds" who if they admit the truth, are just, well, I guess maybe still highly intelligent, but otherwise, ordinary people.
You have to be fairly dense to look at all the evidence, understand what is at stake, and not go with mathematical proof.
Our civilization can be affected by the decision you people are making.
Mathematics is crucial for our continued development and "pure math" has been dubiously distinguished by being mostly useless.
Now the explanation is that much of it is wrong.
But what about the correct mathematics? What great advances might humanity make with it that it cannot make without it?
Sacrifice the future for the egos of some people who got some math wrong?
Would you be satisfied today if Newton were sidelined for some people who found his ideas troublesome, or Galileo couldn't get past people like these that I'm dealing with, or Gauss himself never got the recognition he deserved?
Maybe there wouldn't be computers, or cars, or planes just for some people doing what many of you are doing today.
But so what, right? We got ours, so screw the future, right? Forget the unborn, who may never be born (maybe better off?) because people like you failed where past generations did not.
If humanity never manages to really get off this planet out to distant stars, and ultimately finally dies sometime in the future having done some things sure, but ultimately falling short, what if it is here and now that the die was cast?
What if here and now you decided to end humanity—take away the future—and put limits on what was possible for all generations to come by failing like no generation before you failed, to protect some people who just can't handle the mathematical truth?
What if here you betrayed humanity and condemned it?
Because in admitting it they are taking away that very position.
This thing is huge. It stepped in over a hundred years ago—before anyone currently alive was even born—and in mathematics a small mistake at a key spot can be devastating.
This error re-writes the math history books over a hundred plus years, yanking expert status from so many people over that time, and to admit it now, people called top, would suddenly find they are nowhere near there.
What do they have that this error doesn't touch?
Dedekind in saying that he proved a result that was key in convincing others that the algebraic integers did give full coverage, said he used ideal theory, which at that time was a relatively new idea.
He couldn't figure out any other way to do it, and now we know that was because there was no way to prove full coverage—not correctly.
So one of the first things ideal theory was used for was to convince people of this faux result about algebraic integers and a lot of history passed from that point until today, till we have people who are currently thought brilliant, or even "beautiful minds" who if they admit the truth, are just, well, I guess maybe still highly intelligent, but otherwise, ordinary people.
You have to be fairly dense to look at all the evidence, understand what is at stake, and not go with mathematical proof.
Our civilization can be affected by the decision you people are making.
Mathematics is crucial for our continued development and "pure math" has been dubiously distinguished by being mostly useless.
Now the explanation is that much of it is wrong.
But what about the correct mathematics? What great advances might humanity make with it that it cannot make without it?
Sacrifice the future for the egos of some people who got some math wrong?
Would you be satisfied today if Newton were sidelined for some people who found his ideas troublesome, or Galileo couldn't get past people like these that I'm dealing with, or Gauss himself never got the recognition he deserved?
Maybe there wouldn't be computers, or cars, or planes just for some people doing what many of you are doing today.
But so what, right? We got ours, so screw the future, right? Forget the unborn, who may never be born (maybe better off?) because people like you failed where past generations did not.
If humanity never manages to really get off this planet out to distant stars, and ultimately finally dies sometime in the future having done some things sure, but ultimately falling short, what if it is here and now that the die was cast?
What if here and now you decided to end humanity—take away the future—and put limits on what was possible for all generations to come by failing like no generation before you failed, to protect some people who just can't handle the mathematical truth?
What if here you betrayed humanity and condemned it?
# posted by James Harris @ 20:47 
