Overview for xrchz - Less Wrong

Comment author: xrchz 03 November 2009 10:18:34PM 0 points [-]

It's a good guess that the actual majority of human cognition consists of cache lookups.

Sounds consistent with Jeff Hawkins's memory prediction framework

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In response to comment by xrchz on Searching for Bayes-Structure

Comment author: gwern 03 November 2009 12:26:58AM 6 points [-]

Turing-equivalent is usually used to mean that one system is at least as powerful as some sort of TM or UTM. Your computer is some sort of TM or UTM, and it exists inside the universe, so the universe (or its laws, rather) is quite obviously Turing-equivalent. That's the trivial observation.

Sometimes Turing-equivalent is said to be true only if a system can both implement some sort of TM or UTM within itself, and if it can also be implemented within some sort of TM or UTM. This is a little more objectionable and not trivial, but so far I haven't seen anyone demolish the various 'digital physics' proposals or the Church-Turing surmise by pointing out some natural process which is incomputable (except perhaps the general area of consciousness, but if you're on Less Wrong you probably accept the Strong AI thesis already).

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In response to comment by gwern on Searching for Bayes-Structure

Comment author: xrchz 03 November 2009 12:45:17AM * 1 point [-]

Thanks for the reply. I want to follow a related issue now.

So are all natural processes computable (as far as we know)?

I want to know whether the question above makes sense, as well as its answer (if it does make sense).

I have trouble interpreting the question because I understand computability to be about effectively enumerating subsets of the natural numbers, but I don't find the correspondence between numbers and nature trivial. I believe there is a correspondence, but I don't understand how correspondence works. Is there something I should read or think about to ease my confusion? (I hope it's not impenetrable nonsense to both believe something and not know what it means.)

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In response to Outside the Laboratory

Comment author: Eliezer_Yudkowsky 24 January 2007 02:30:02AM 5 points [-]

John Thacker:

I consider myself a finitist, but not an ultrafinitist; I believe in the existence of numbers expressed using Conway chained arrow notation. I am also willing to reject finitism iff a physical theory is constructed which requires me to believe in infinite quantities. I tentatively believe in real numbers and differential equations because physics requires (though I also hold out hope that e.g. holographic physics or some other discrete view may enable me to go digital again). However, I don't believe that the real numbers in physics are really made of Dedekind cuts, or any other sort of infinite set. I am willing to relinquish my skepticism if a high-energy supercollider breaks open a real number and we find an infinite number of rational numbers bopping around inside it.

I consider the Axiom of Choice to be a work of literary fiction, like "Lord of the Rings".

Bayesian probability theory works quite well on finite sets. Real-world problems are finite. Why should I need to accept infinity to use Bayes on real-world problems?

The two-envelopes problem shows the necessity of having a finite prior.

Godel's Completeness theorem shows that any first-order statement true in all models of a set of first-order axioms is provable from those axioms. Thus, the failure of Peano Arithmetic to prove itself consistent is because there are many "supernatural" models of PA in which PA itself is not consistent; that is, there exist supernatural numbers corresponding to proofs of P&~P. PA shouldn't prove itself consistent because that assertion does not in fact follow from the axioms of PA. (This view was suggested to me by Steve Omohundro.) Now, I don't believe in these supernatural numbers, but PA hasn't been given enough information to rule them out, and so it is behaving properly in refusing to assert its own consistency.

I have no desperate psychological need for absolute certainty or proof, which, even if PA proved itself sound, I couldn't have in any case, because I would have to believe in PA's soundness before I trusted its proof of soundness. Or maybe I'm in the grips of a Cartesian demon playing with my mathematical abilities.

Correspondence, not coherence, very easily justifies mathematics. Math can make successful predictions, ergo, it's probably true. No one has ever seen an infinite set, ergo, they probably don't exist, and at any rate I have no reason to believe in them.

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In response to comment by Eliezer_Yudkowsky on Outside the Laboratory

Comment author: xrchz 02 November 2009 09:08:50PM 0 points [-]

I tentatively believe in real numbers and differential equations because physics requires (though I also hold out hope that e.g. holographic physics or some other discrete view may enable me to go digital again). However, I don't believe that the real numbers in physics are really made of Dedekind cuts, or any other sort of infinite set.

Shouldn't you add probability theory to the list [physics, differential equations]? Only because probabilities are usually taken to be real numbers. I'm curious what you think of real numbers... how would you construct them? I guess it must be some way that looks a limit of finite processes operating on finite sets, right?

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In response to comment by iwdw on Searching for Bayes-Structure

Comment author: gwern 27 July 2009 07:58:31AM 1 point [-]

It's a trivial observation based on a constructive proof ie. that which I'm writing and you're reading on.

(There is the issue of resource consumption, but then we have the result that the universe is Turing-complete for anything small enough.)

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In response to comment by gwern on Searching for Bayes-Structure

Comment author: xrchz 02 November 2009 07:27:51AM 0 points [-]

I don't quite see the trivial observation yet - can you explain a little further?

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In response to Timeless Control

Comment author: Unknown 07 June 2008 12:15:53PM 3 points [-]

Eliezer's point (a quite justified one) is that the word "choice" is a name for something that human beings do, just as the name "apple" is a name for something human beings find in the world. Whatever you think an apple is, if you say it is only an illusion, then you're not talking about apples, but something else. Likewise, whatever you might think a choice is, if you say it is only an illusion, you're not talking about choices, but something else. For choice just means one of the things that people actually do in the real world, so it is quite real, not an illusion.

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In response to comment by Unknown on Timeless Control

Comment author: xrchz 01 November 2009 09:24:08PM 1 point [-]

I think when people say that apples and choices are illusions, they might mean that they are patterns recognizable by people but not fundamental: if some system couldn't recognize an apple (perhaps only because it never had any reason to form the concept) but did have a model of the amplitude distribution of the universe, it would get along just fine (actually it would probably just have different high-level concepts).

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In response to comment by xrchz on Configurations and Amplitude

Comment author: RichardKennaway 01 November 2009 08:40:30PM 0 points [-]

How does a half-silvered mirror work?

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In response to comment by RichardKennaway on Configurations and Amplitude

Comment author: xrchz 01 November 2009 09:01:24PM * 2 points [-]

You can't explain yourself? I followed your link. It looks like part of why half-silvered mirrors "work" for the purpose of seeing someone without them seeing you is that one side is kept brightly lit while the spying side is kept dark. I think "beam-splitter" is possibly a more accurate term for my question, which I looked up and found

Another design is the use of a half-silvered mirror. This is a plate of glass with a thin coating of aluminum (usually deposited from aluminum vapor) with the thickness of the aluminum coating such that part, typically half, of light incident at a 45 degree angle is transmitted, and the remainder reflected.

(Wikipedia) Of course, this doesn't actually explain anything - why should there be a thickness of aluminum such that part of the light is reflected while the remainder is transmitted?

Would a beam-splitter still work if the silvered and non-silvered parts were much larger (i.e. a chunky block pattern)? If you fired a single photon at that would it still make sense to calculate amplitude as you do in this post (considering the two outward paths and multiplying one by i, the other by 1)? Perhaps the distance between a silvered part and a non-silvered part needs to be close to the wavelength of the photon?

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In response to Configurations and Amplitude

Comment author: xrchz 01 November 2009 08:31:45PM 1 point [-]

I have a question similar to Nate's. How does a half-silvered mirror work? More specifically, what is it about light or about half-silvered mirrors that means there are two paths for a photon out of a half-silvered mirror (compared to a full mirror, for example)? My guess at the moment is that the answer might start "light doesn't actually travel in straight lines..."...