![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
Entry tags:
Yet more fridge poetry, paper, error-estimation in proofs
I'm going away (first to London, then to Nova Scotia) tomorrow, so I'll have to stop work on the fridge poetry for a while. So, here's what I've done so far (100K tarball), in case any of you want to have a crack while I'm away. There are lots of dead-ends and abandoned files there, but you should be able to work it out from the README and the Makefile.
Also, I've now fixed enough errors in my P-categories paper that it's met my rapidly plummeting idea of acceptable quality. Get it while it's hot, it's lovely. If this is the amount of effort required to write a twelve-page paper, I'll be totally screwed in a year when I have to write my thesis.
Actually, this has provoked an interesting philosophical musing: there are statistical techniques available for estimating the number of undiscovered errors in a piece of software, which could be adapted for estimating the number of undiscovered errors in a mathematical paper. So I could keep looking until the chance of an undiscovered error is less than (say) 1%, or the number of estimated errors is lower than some critical threshold, and then release, possibly with a statement like "Error-free with 99% probability". But if I'm only 99% certain that a proof is error-free, does that count as a proof, whose defining characteristic should be 100% confidence? OTOH, that kind of estimation is clearly better than the ad-hoc approach currently favoured...
Also, I've now fixed enough errors in my P-categories paper that it's met my rapidly plummeting idea of acceptable quality. Get it while it's hot, it's lovely. If this is the amount of effort required to write a twelve-page paper, I'll be totally screwed in a year when I have to write my thesis.
Actually, this has provoked an interesting philosophical musing: there are statistical techniques available for estimating the number of undiscovered errors in a piece of software, which could be adapted for estimating the number of undiscovered errors in a mathematical paper. So I could keep looking until the chance of an undiscovered error is less than (say) 1%, or the number of estimated errors is lower than some critical threshold, and then release, possibly with a statement like "Error-free with 99% probability". But if I'm only 99% certain that a proof is error-free, does that count as a proof, whose defining characteristic should be 100% confidence? OTOH, that kind of estimation is clearly better than the ad-hoc approach currently favoured...
no subject