![]() ![]() The notion-found in the works of Aristotle-that the structure of human arguments, of human reasoning, can be represented in a stylized form-using logic. But for practical purposes, the notion of creating formal systems from the structure of languages was lost for more than 2000 years.Īnd instead, what emerged in Greek times-probably around 350 BC-was the idea of logic. That idea did reappear a few times in scientific history for example, Lucretius talked about how atoms might make up the universe as letters make up words and sentences. Going from human language-and finding a formal way to describe its structure-and in effect to use that to compute the poetic forms that could be produced. There were other possibilities too, though, even at that time.Īnd indeed on the other side of the world, probably around 400 BC, Panini was coming up with rules-not numbers, just rules-that described the grammar of Sanskrit. But still, with people like Pythagoras around 500 BC, it seemed that nature, and music, and much more-even if not human affairs-could perhaps be described, and computed, using numbers. Things worked in predicting the heavens, so why not predict the weather, the rise and fall of kingdoms, and everything? Of course, that didn’t work so well. Of course, it wasn’t at all clear where the boundaries were. It was the beginning of the tradition of exact science as we know it. To work out the behavior of the planets, and even to say things about spectacular events like eclipses. And then it was realized that one could use arithmetic-the same arithmetic that worked for commerce and for land surveying-to predict things about the heavens. People had known that there were regularities to be seen if not on earth, at least in the heavens. But when it came to working out more about what would happen in the world-well, probably most people just assumed it was all just fate, and that nothing much could be predicted. From which at least it was possible to compute taxes. It didn’t take long before numbers and writing led to kings in Babylon making pretty broad censuses of people and commodities. But it was still a crucial step in perhaps 4000 BC when written language first emerged-and it became possible to systematically record and transmit knowledge about things. Human language lets us describe much more, but it isn’t systematic-it doesn’t allow us to go directly from our knowledge to computing new things. And then that there were definite unchanging rules of arithmetic that could let one abstractly compute things.īut of course just counting things is a very coarse form of systematic knowledge. The big idea that we know pretty much existed by 20,000 BC was that you could just abstractly count objects, independent of what the objects were. Well, I think in history the first really big step in this direction was taken a really long time ago-with the invention of counting and arithmetic. And we have to know methods and models for the world that let us do that computation. Somehow we have to organize-systematize-knowledge to the point that we can build on it-compute from it. So what do I mean by “computable knowledge”? There’s pure knowledge-in a sense just facts we know. And I want to talk about what I think the future holds. I want to talk about my own efforts in this direction. It’s a topic that spans a lot of history, and that I’ve personally spent a long time working on. ![]() I want to talk about a big topic here today: the quest for computable knowledge. The following is a slightly edited transcript of the speech he gave on that occasion. Stephen Wolfram recently received an award for his contributions to computer science.
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