Cyan comments on No Universal Probability Space - Less Wrong

0 Post author: gworley 06 May 2009 02:58AM

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Comment author: Cyan 06 May 2009 05:13:38PM *  1 point [-]

I think smoofra is talking about the same sorts of things Jaynes is when he writes:

The danger here is particularly great because mathematicians generally regard these limit theorems as the most important and sophisticated fruits of probability theory, and have a tendency to use language which implies that they are proving properties of the real world. Our point is that these theorems are valid properties of the abstract mathematical model that was defined and analyzed [emphasis in original]. The issue is: to what extent does that model resemble the real world? It is probably safe to say that no limit theorem is directly applicable in the real world, simply because no mathematical model captures every circumstance that is relevant in the real world.

- PT:LOS, pp 65-66.

Comment author: smoofra 06 May 2009 05:29:54PM *  2 points [-]

ADBOC

Jaynes aggressively scorns abstract mathematics. I love abstract mathematics. We both agree that just because you have a model or a theorem, it doesn't necessarily apply to the real world.

edit: (ADBOC directed to jaynes, not to cyan)

Comment author: Cyan 06 May 2009 08:00:24PM *  2 points [-]

I come to quote Jaynes, not to praise him; the scorn that men write lives after them, the good is oft interred with their bones -- let it not be thus with Jaynes.

Comment author: Vladimir_Nesov 06 May 2009 05:19:21PM 0 points [-]

Yep, you shouldn't wirehead yourself into developing a theory about the mathematical formalism, you should instead develop a theory about the world. But the theory that you develop should be mathematical where possible.

Comment author: smoofra 06 May 2009 05:36:17PM 0 points [-]

There's nothing wrong with doing pure Math, if you know that's what your doing.

Comment author: Vladimir_Nesov 06 May 2009 05:42:56PM 0 points [-]

Arguably there may be, if it can be shown that you normatively should worry only about the real world, even if what you are doing in the real world is thinking math.

Comment author: smoofra 06 May 2009 07:00:45PM 0 points [-]

if it can be shown that you normatively should worry only about the real world,

It can't be. Not in any system of norms I would give a fig about. Art, Fiction, and Math are worthwhile. They don't have to be useful. If you disagree with that, then we simply have different utility functions, and there's no point in arguing further.

Comment author: Vladimir_Nesov 06 May 2009 07:50:02PM 1 point [-]

You are seeing "useful" too narrowly. I only stated that whatever you consider "useful", it's probably a statement exclusively about the real world, and "doing math" is one of the activities in the real world. I don't see how you could place Art in the same cached thought, since it was remarked many times that you shouldn't go Spock.

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