## 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