Posted on 11/08/2005 8:48:52 AM PST by RightWingAtheist
Our brains have become too small to understand math, says a rebel mathematician from Britain. Or rather, math problems have grown too big to fit inside our heads. And that means mathematicians are finally losing the power to prove things with absolute certainty.
Math has been the only sure form of knowledge since the ancient Greeks, 2,500 years ago.
You can't prove the sun will rise tomorrow, but you can prove two plus two equals four, always and everywhere.
But suddenly, Brian Davies of King's College London is shaking the foundations of certainty.
He says our brains can't grasp today's complex, computer-generated math proofs.
"We are beginning to see the limits of our ability to understand things. We are animals, and our brains have a certain amount of capacity to understand things, and there are parts of mathematics where we are beginning to reach our limit.
"It is almost an inevitable consequence of the way mathematics has been done in the last century," he said in an interview.
Mathematicians work in huge groups, and with big computers.
A few still do it the old-fashioned way, he says: "By individuals sitting in their rooms for long periods, thinking.
"But there are other areas where the complexity of the problems is forcing people to work in groups or to use computers to solve large bits of work, ending up with the computer saying: 'Look, if you formulated the problem correctly, I've gone through all the 15 million cases and they all are OK, so your theorem's true'."
But the human brain can't grasp all this. And for Davies, knowing that a computer checked something isn't what matters most. It's understanding why the thing works that matters.
"What mathematicians are trying to get is insight and understanding. If God were to say, 'Look, here's your list of conjectures. This one's true, then false, false, true, true,' mathematicians would say: 'Look, I don't care what the answers are. I want to know why (and) understand it.' And a computer doesn't understand it.
"This idea that we can understand anything we believe is gradually disappearing over the horizon."
One example is the Four Colour Theorem.
Imagine a mapmaker wants to produce a colour map, where each country will be a different colour from any country touching it. In other words, France and Germany can't both be blue. That would be confusing.
So, what's the smallest number of colours that will work?
A kid can work out you need four colours. But can you prove it? Can anyone be certain, as with two-plus-two?
The answer turns out to be a hesitant Yes, but the proof depends on having a computer to work through page after page of stuff so complex that no single person can take it all in.
And it's getting worse, Davies writes in an article called "Whither Mathematics?" in today's edition of Notices of the American Mathematical Society, a math journal.
Math has tried to write a grand scheme for classifying "finite simple groups," a range of mathematical objects as basic to this discipline as the table of the elements is to chemistry -- but much bigger.
The full body of work runs to some 10,000 difficult pages. No human can ever understand all of it, either.
A year ago, Britain's Royal Society held a special symposium to tackle this question of certainty.
But many in the math community still shrug off the issue, Davies says. "Basically, mathematicians are not very good philosophers."
See, it wasn't my fault.
This is a conspiratorial news release by the big computer companies to promote their new products. Pencil pusher mathmeticians, UNITE!!!
Too small to understand self responsibility, now math.
Getting ready for the new P.C. Social Theory: Kids fail at math because humans weren't designed to understand math. It's not their fault if they bring home 'F'.
Everything that can be invented has already been invented. Didn't someone say that over 100 years ago?
Nothing new here. I told my mother this as I handed her my report card in 1958.
So easy a three year old can do it! Somebody run out and get me a three year old.
I agree it's not your fault, but Bush?
This is too funny. I'm a math teacher on a professional development day. I just took a break. and this is the top story!
This is too funny. I'm a math teacher on a professional development day. I just took a break. and this is the top story!
Nope. It's Darks' fault...
What mathematicians are trying to get is insight and understanding. If God were to say, 'Look, here's your list of conjectures. This one's true, then false, false, true, true,' mathematicians would say: 'Look, I don't care what the answers are. I want to know why (and) understand it.' And a computer doesn't understand it.
Ummm, build better computers?
"You can't prove the sun will rise tomorrow, but you can prove two plus two equals four, always and everywhere. "
I knew it all along.
Depending on what you pay me...I can make any amount add up to what you want.
Um, I beg to differ. My spouse and I know a different kind of knowledge. And it's not Greek.
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