Vladimir_Nesov comments on Decision theory: Why Pearl helps reduce “could” and “would”, but still leaves us with at least three alternatives - Less Wrong

29 06 September 2009 06:10AM

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Comment author: 07 September 2009 09:51:18AM *  6 points [-]

After reading more Girard, "platonic computation" started to sound to me like "phlogiston". Seriously.

Comment author: 09 September 2009 11:25:27PM 0 points [-]

My UDT1, which makes use of the concept of "platonic computation", seems to work, at least on simple toy problems, so I don't see what's wrong with it. Are you arguing that "platonic computation" will cause difficulties in more complex problems, or what?

Comment author: 09 September 2009 03:18:43PM *  0 points [-]

Can we just remove the word "platonic" and define "computation" in the usual way as an input for a UTM?

Comment author: 09 September 2009 05:07:18PM 0 points [-]

Where's the UTM that runs both in yours and Omega's head?

Comment author: 09 September 2009 10:05:50PM *  0 points [-]

What do you mean by "where" in reference to a mathematical abstraction?

Comment author: 09 September 2009 10:48:48PM *  0 points [-]

What do you mean by "where" in reference to a mathematical abstraction?

That's the thing: you are basically requiring "platonic" to be returned in the explanation (mathematical abstraction that doesn't reside anywhere specifically). "Computation" I can imagine: it's the process running on my PC, or in my head, or wherever. Mathematical abstraction of computation -- not so clear. It's for one thing something that happens in mathematicians' heads, but moving this process to the moon is suspect.

There is always a "where" to any abstract math that anyone ever observed, and the lawfulness with which this phenomenon persists among many instances doesn't need to be explained by something outside the physical laws (or "meta" to them): it's just another regularity in the world, a daunting one, but as always a curiosity-stopper is not the answer (assuming a hidden world of mathematical truths that is not even anywhere in our real world in which you can peek from anywhere with varying levels of success by theories of different strength, never to see it whole, etc. -- a kind of modern dualism, consciousness of reason).

Comment author: 09 September 2009 11:25:06PM 3 points [-]

There is no need for dualism, if we assume that mathematics is all there is, and that consciousness is a property of certain mathematical objects. "Never to see it whole" makes perfect sense, since why would a part be able to see the whole as a whole?

To put it another way, why do you infer a physical world, instead of a mathematical world, from your observations? Is there some reason why a pile of physical particles moving around in a certain pattern can cause a conscious experience, whereas that pattern as an abstract mathematical object can't be conscious?

Comment author: 11 September 2009 06:18:48PM 1 point [-]

why do you infer a physical world, instead of a mathematical world

What's the difference between these two? I think we are getting to the stage of philosophical abstraction where words lose all purchase. I have no idea what image "physical world, instead of a mathematical world" conjures up in Wei and Vladimir's minds, and the words "physical " and "mathematical" don't seem to help me.

Comment author: 12 September 2009 06:32:08PM 2 points [-]

My position is that "physical world" is meaningless, and the question was a rhetorical one that I asked because I thought Nesov was thinking in terms of a physical world.

Comment author: 12 September 2009 09:18:57PM 0 points [-]

I think it is reasonable to eliminate the phrase "physical world". "Hubble volume that we inhabit" seems to do most of the job that it did for me anyway.

Comment author: 10 September 2009 12:10:56AM *  0 points [-]

I can hardly do more than sound my vote, with a few details -- it's a huge debate, with intricate arguments on both sides. My emphasis is on sidestepping the confusion by staying at the level of natural phenomena. Saying that "everything is math" is not an explanation of what math is, in the sense of lawful processes in mathematicians' heads, and more generally in decision-making. There is a danger of losing track of the question.

Comment author: 10 September 2009 10:09:20AM 0 points [-]

Saying that "everything is math" is not an explanation of what math is, in the sense of lawful processes in mathematicians' heads, and more generally in decision-making.

It seems fairly obvious that a mathematician's head is doing a physics computation, which is logically correlated with an abstract neural-network computation (representing its mind), which is logically correlated with whatever part of math that the mathematician is considering. "Everything is math" doesn't tell us the exact nature of those logical correlations, but neither does it hurt our attempt to find out, as far as I can tell.

Also, I don't understand what you mean by "staying at the level of natural phenomena" nor how that helps to "sidestepping the confusion".

Comment author: 10 September 2009 12:53:10PM 1 point [-]

It seems fairly obvious that a mathematician's head is doing a physics computation, which is logically correlated with an abstract neural-network computation (representing its mind), which is logically correlated with whatever part of math that the mathematician is considering.

My point is that you don't need to make that last step, saying that process in the head is related to some abstract math. Instead, take two processes in two heads, and relate them directly, through the physics stuff.

To make an analogy, when you see two similar plants, it's confusing to talk about them being instances of the same platonic plant. Instead, by saying that they are similar, you mean that you formed certain representations of them in your own mind, and the representations considerably match: it's a concrete operation that is performed by one who recognizes the connection.

With math, relating processes (or formulas) through denotational semantics has a danger of losing track of the procedure that relates them, which can in some cases be unfeasible, and limitations on which may be important. Some things you can't even pinpoint to the semantics: are these two programs equal, in the sense of producing the same results for the same inputs? That is, what are those mathematical objects that correspond to each of them? You'll never know, and thus the question is effectively meaningless.

Interaction between specific details of implementation is part of decision-making as well as of the decisions themselves. Introducing abstract representation that abstracts away the details in unspecified fashion and gets communicated through the ether may confuse the situation.

Comment author: 10 September 2009 04:07:58PM *  2 points [-]

Ok, that's much clearer, and while I don't know if I agree with you completely, there's nothing you said that I object to.

I think confusion arose in the first place because you interpreted "platonic computation" to mean the denotational semantics of a computation, whereas Eliezer (and others) were using it to refer to the "abstract neural-network computation" as opposed to the "physics computation" involving wavefunctions and such, or the "physical world" with physical particles/wavefunctions (whatever that means).