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None of those require theorems, they require computers.
by marshallp 14y ago
None of those require theorems, they require computers.
- gizmo686 14y agoGreat news, I finally wrote a sorting algorithm that worked for 10/10 of my test cases. Now, I can just plug that number into my unproven statisticle test, and found out how likely it is that my algorithm will work for all inputs. It does not seem to run extra slow for any input, so it probably won't run slowly on any input in actual use. Besides, even if it did I would have no way of proving what types of inputs it failed on, or if another algorithm would do better.
- marshallp 14y agohttp://ertos.nicta.com.au/research/l4.verified/proof.pml http://ertos.nicta.com.au/research/l4.verified/proof.pml Keeping the above in mind, does it actually justify the billions of man hours spent on mathematics.
- saraid216 14y agoThe notion of a computer was a theorem. http://en.wikipedia.org/wiki/Turing_completeness http://en.wikipedia.org/wiki/Turing_completeness
- marshallp 14y agoThe computer industry wasn't built on Turing completeness. It's an evolution of practical technology starting with the invention of textile machinery (but you can also kind of argue it started with abacuses or even lines drawn in sand).
- jonsen 14y agoYou are right. Evolution has its mysterious ways. But maybe it's only mysterious to us because our math has not evolved yet to a point where complex systems can also be properly described by theorems.
- marshallp 14y agoBut then what is the use of the maths. We already have the wealth the comes from the technology. The maths doesn't add much (instead siphons off resources).
- waqf 14y agoYou're arguing for eating our seed corn. Yesterday's maths drove today's technology. Today's maths will drive tomorrow's technology, unless you have your way.