23. Computational Complexity

MIT 6.006 Introduction to Algorithms, Fall 2011 View the complete course: http://ocw.mit.edu/6-006F11 Instructor: Erik Demaine License: Creative Commons BY-N…

La Life’s insight:
That’s a truly interesting thing: most of the problems that we’re attempting to solve are computable, whereas mathematically most of the possible problems are uncomputable.

The insight part is here: http://www.youtube.com/watch?v=moPtwq_cVH8&start=18:06&end=18:20

This says a lot to the effect that there are no answers without questions. Or, in other words, that the things we discover are the things that we conceivably are interested in discovering. The set of these problems are therefore those that, somehow, map to our cognitive interests, which have "evolved", or in any event represent thigns that matter to us, that can factor into outcomes that we care about. So, naturally, the questions we ask of the world are questions that actually have answers, whereas most of the actual answers (meaning things that actually come out of the universe’s unfolding) are things that are beyond our cognition, including our computational and mathematical cognition. With some exceptions.

EDIT: Another key insight here, and in fact maybe more significant, is also that there are an infinite number of strings that an infinite roomful of monkeys can type, without all of these strings actually representing a question. To have a question and an answer requires semantics, not just binary information. It’s wholly unclear what the ratio of meaningful strings over meaningless strings is in a random infinite set.

from A quoi sert la connaissance ? What is knowledge for? | Scoop.it http://www.scoop.it/t/a-quoi-sert-la-connaissance-what-is-knowledge-for/p/4010437315/2013/11/05/23-computational-complexity
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