Thursday, May 25, 2006


Self-serving limitations, math world needs scrutiny

The more I think about the lack of computer checking in the 'pure math' part of the mathematical world, the clearer it is that is must be a deliberate, and important strategy for maintaining the status quo.

Not too long ago a Space Shuttle blew up.

Later another Space Shuttle disintegrated on re-entry.

I am sure plenty of engineers were confident about their work in both cases as human nature is to have an eery confidence on a lot of things—later proven wrong by reality.

Sometimes, no matter how confident you are, or how many people are confident with you, a space shuttle blows up, or a bridge collapses, or people keep dying despite "the cure".

But in our supposedly modern math world, one person presents an argument, supposedly perfect, another looks it over by eye, and says "yea" or "nay" and people go on as if "yea" actually does mean that the argument IS perfect!

And in those areas called pure math, there is no danger of any spacecraft blowing up. No bridges can fall. No patients can look at you with deadening eyes before they die despite your miracle drug.

The one thing that can bring reality testing into those areas of the mathematical field that are impractical—pure as the saying goes—is to have computers check.

But for some reason, computers aren't used to check those arguments.

I suggest to you that the lack of real progress in having computers check is the best evidence that mathematicians know on some level that MUCH of the work being done, would not stand real scrutiny.

Otherwise, why force human beings to continue the tedium of looking over someone else's arguments if a standardized way to do it could be done, so that mathematicians could write arguments proof checker ready? Sure if the checkers says an argument is wrong—humans can check. Or if it's a big deal, and it says something is right, again humans can check.

But why isn't that done already?

I suggest to you that it not being done is a quiet admission by the mathematical community that despite all the talk of mathematical proof, the reality is that human beings screw up, put papers through, or research through that is not correct, but with only other human beings checking, the show can go on.

And they need never worry about a spectacular explosion giving away the errors.

They have, instead, the world's blind trust, and a perfect field, in that you only need to be able to convince that other guy in the field with you.

But why? How could they? Don't mathematicians want to be perfect?

Well, what if more of them are not perfect than are?

The truth can hurt, and computers can push the truth to the front that maybe there aren't that many brilliant mathematical minds on the planet. Maybe most people who get Ph.D's in the math field couldn't hack it if perfection were actually required.

Maybe most of the people in the field could not stay, if their work actually had to be—perfect.

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