|
For hundreds of years people "knew" that geometry only needed four axioms, and the parallel postulate was a dodgy hack that was only needed because Euclid wasn't quite able to prove it. Then it turns out that whoops, actually you do need it. And the alternate geometries that you get when you replace the parallel postulate with something that's different and incompatible with it are actually pretty drat useful. That's the thing with unsolved questions - if you know what the answer probably is, then you tend to build up lots of other stuff based on that assumption of what the answer is. So if it turns out that you're wrong, that discovery is a massive game-changer.
|
#
¿
May 15, 2017 03:46
|
|
|
|
| # ¿ May 14, 2024 11:52 |
|
|
A Pinball Wizard posted:how is polynomial time defined? im guessing "in one lifetime" isn't an actual si unit. basically, you have some number n that represents how large the input to your problem is - for example, how many cities your travelling salesman is trying to visit if your algorithm runs in "polynomial time", that means that you can pick some finite number c so that it takes less than nc operations to complete, no matter what input you run it on note that this doesn't mean it runs "fast". there are lots of situations where people use brute-force exponential algorithms even though polynomial-time algorithms exist, because on all the inputs small enough to be feasibly solved the brute-force method is faster. Jabor fucked around with this message at 12:43 on May 15, 2017 |
|
#
¿
May 15, 2017 12:41
|
|