Something about certainty, proofs in math, induction/abduction

This conversation followed me posting the post just before, and several people bringing up the same proof.

Aowpwtomsihermng = Afraid of what people will think of me, so i had Emil remove my name-guy

[09:57:00] Emil - Deleet: http://mathbin.net/109013 [09:58:50] Aowpwtomsihermng: Your mates know their algebra. [10:00:09] Emil - Deleet: this guy is a mathematician [10:00:27] Emil - Deleet: fysicist ppl have not chimed in yet [10:00:32] Emil - Deleet: they are having classes i think [10:08:18] Aowpwtomsihermng: Have you worked out the inductive proof yet? [10:09:33] Emil - Deleet: no [10:09:40] Emil - Deleet: i dont know how they work in detail [10:09:43] Emil - Deleet: and it takes time [10:09:49] Emil - Deleet: and i already crowdsourced the problem [10:10:00] Emil - Deleet: so... doesnt pay for me to look for it [10:10:19] Aowpwtomsihermng: CBA, right? [10:10:24] Emil - Deleet: i didnt even need any fancy math proof to begin with [10:10:30] Emil - Deleet: since i already proved it to my satisfaction [10:10:54] Aowpwtomsihermng: Induction in the logical rather than mathematical sense... [10:11:00] Emil - Deleet: yes [10:11:17] Aowpwtomsihermng: Not as rigorous, but useful anyway. [10:11:23] Emil - Deleet: or abduction [10:11:46] Emil - Deleet: mathematical certainty is overrated [10:11:48] Emil - Deleet: ;) [10:11:59] Emil - Deleet: just look at economics [10:12:02] Emil - Deleet: :P [10:12:27] Aowpwtomsihermng: You never know, it might have worked for the first twenty numbers then stopped working. Unlikely, but possible. [10:12:48] Aowpwtomsihermng: At least now you know that's not the case. [10:12:49] Emil - Deleet: astronomically unlikely [10:12:56] Emil - Deleet: and i also tried other random numbers [10:13:02] Emil - Deleet: like 3242 [10:13:21] Emil - Deleet: IMO, not much certainty was gained [10:13:50 | Edited 10:14:04] Emil - Deleet: its approximately as likely that we missed an error in the proof as it is that abduction/induction fails in this case [10:14:26] Aowpwtomsihermng: But once you have two or three proofs, then that likelihood drops dramatically. [10:14:46] Emil - Deleet: perhaps [10:15:00] Aowpwtomsihermng: But I take your point, it's not a *great* deal of extra certainty. [10:15:15] Emil - Deleet: for practice, its an irrelevant increase [10:15:34] Emil - Deleet: if it comes at a great time cost - not worth it [10:15:41] Emil - Deleet: thats what mathematicians are for ;) [10:15:50] Emil - Deleet: (with the implication that their time isnt worth much! :D) [10:16:55 | Edited 10:17:14] Aowpwtomsihermng: Right, right. We programmers and mathematicians are mere cogs in the machinery of your grand device. [10:17:19] Emil - Deleet: ^^ [10:17:36] Emil - Deleet: at least ure part of something great ^^ [10:17:37] Emil - Deleet: :P