10 • Problem solving and combinatorial explosion
But many problems we face are not at all clearly defined, they are ambiguous. A logical proof of certainty for those is beyond our capabilities, beyond our understanding of those problems.
Today I want to dig deeper into what exactly makes deductive reasoning and logical proofs often challenging and inaccessible to us, when we are trying to solve real-world problems.
What's an algorithm? An algorithm is a problem solving technique that is guaranteed to find a solution or prove — and I'm using that term technically, not “give evidence for” but prove — that a solution cannot be found. And of course there are algorithmic things you do: You know the algorithm for doing multiplication, for example, 33 times 4. There is a way to do that in which you can reliably guarantee to get an answer.
This is important, and I remember I said I'd come back to you and explain why Descartes' project was doomed for failure? Because algorithmic processing is processing that is held to the standard of certainty. You use an algorithm when you are pursuing certainty.
