I’m sure this story was heavily slashdotted at some point, and I just missed it, but I’m suprised none of my friends pointed it out to me. I am, after all, the freak who memorized a couple of hundred digits of pi in 3rd grade because I thought it might be fun.
If you don’t like math, just go ahead, skip this entry. It’s ok, really. Just skip on down and find another entry you like. For the numerically inclined (or the bored), follow the journey.
Computers are being used more and more for actual mathematical breakthroughs, much to the chagrin of many mathematicians. You see, the computer was supposed to be a raw number cruncher, and useful, sure, but not actually important to the real work, the true groundbreaking work. They were supposed to be sorta like the strongman at the circus. Fun to look at, and impressive, but not a part of developing the actual mathematical principles, theorems and proofs.
In the last couple of decades, however, computers have been heavily utilized in a number of extremely important proofs. Almost more important than the proofs themselves is the way in which computers were used.
The famous coloring problem; if I give you a map with the outline of countries on it, how many colors do you need to be sure that no two adjacent countries have the same color? It’s easy to see that two isn’t enough, and without too much effort, you can make a map that three colors will not suffice for. But what about four? Just because you can successfully color every map in the atlas doesn’t do a thing for mathematicians. They want a proof. And believe me, that tends to be a lot of work. In fact, for the past few hundred years, a number of ‘proofs’ have sufficed that proved not to pan out under closer inspection. In 1976, a couple of smart fellas were able to build on some previous work and demonstrate that indeed, every map could be colored with four colors. One controversial part (there was another controversial part, but let’s ignore that for now) was that they used a computer to brute force the problem, showing that the problem can be broken down into thousands of subproblems, and then letting the computer check them all. My kinda people. I’ve used my calculator to solve a number of problems that were specifically designed to defeat calculators, but that’s not what we’re talking about.
Mathematicians were divided on this proof, and eventually some other smart purists found a ‘prettier’ (it’s strange, but true: mathematicians often describe proofs in terms of elegance or beauty, and I hate to admit it, but I tend to agree when I can follow the proofs) solution that didn’t require the kludgy computer hack.
Fast forward a dozen years or so, and now people are beginning to use computers even for elegant solutions. In fact, the most elegant I’ve seen relates to my oh so favorite number.
Computing pi tends to be one of those challenges that computers are good at. Obviously; the mathematicians may come up with the algorithms, but it’s the computers that crunch away, computing billions of digits. All known formulas for computing pi (until recently) computed sequentially; there was no shortcut for finding out, say the 10 billionth digit without first computing the first 999,999,999 other digits.
The new breakthrough? PI now looks like this:
Which means that you can compute any particular bit you like (it’s actually a formula for the binary bits, but it’s easy enough to turn into an integer), and is darn simple considering it took mathemticians thousands of years of study of the number before they were able to come up with it. Except it wasn’t a mathematician alone, but his computer. And because of this amazing discovery, you get to play with fun toys like the pi search page.
While none of this may sound quite life-changing yet, we’re getting there. Computers have been crunching away at some of the most outstanding problems in mathematics, many of which have definite application into your life. Maybe not today, but sometime soon a computer is going to solve a formula that will change our understanding of math and the world. A little bit scary, isn’t it?
What a great post! It is cool that pi isn’t completely random after all. Perhaps nothing in nature is completely random… what would that mean? What would we, as a people contrive from the lack of randomness to arrive at a meaning?
Left by David on May 16th, 2003
Wow, this one is even better than your “awk” entry ;-).
Left by Nate on May 17th, 2003
Pi isn’t random, eh?
That is so sexy! God, I LOVE what people can do mathamatically with computers thses days. Lord knows geeks are nice too
Left by Clara on November 26th, 2004