Reality Conditions

Wednesday, November 29, 2006

Mathematicians and computers

[UPDATE: I apologize to all those who couldn't see the images and were asked for a password yesterday. I have fixed the mistake I made when uploading the images.]

There is an old joke about mathematicians that comes in many variations, but the basic idea is something like this:

A mathematician is asked how he would prepare tea given a mug, an empty kettle, a heater, and a jar with cold water. After thinking a minute, he answers he would fill the kettle with cold water, put it on the heater, and when it is hot pour it into the mug and make tea. Then he is asked what would he do if the kettle was already full with hot water. He now immediately answers that he would empty the kettle, thus reducing the problem to a previously solved one.

I was strongly reminded of it when I saw two amusing chess positions from computer games, both at Tim Krabbe's wonderful chess site. It seems that modern chess programs come with a table of theoretically won and drawn endings and the complete algorithm to win and draw them; they are also programmed to strive to reach one of the won endings at any cost. This makes sense because reaching it is exactly equivalent to reaching checkmate from the computer's point of view, but it gives rise to curious situations like the following:

Instead of playing the natural 1.Qxf4+, or the even stronger 1.Kb2 which leads to mate in 6, the program Hiarcs 7.32 plays 1.Qf7+!! The reason is, of course, that the resulting ending with two pawns against one is in the tablebase of won positions. Krabbe comments: "He'd rather look something up than think - how human." (You can find the position and the commentary at the bottom of this page).

An even more amusing case:

From a game between programs Deep Junior and Deep Fritz. White is a rook and a pawn up and things should be easy for it. Junior decides that it would be even easier if it had only a pawn up, because then the position is "theoretically won". So it played 1.Rc6+! But Fritz is no fool -it has the same tablebase and knows better than to fall into the trap, so it played 1...Kb5! The game continued in a display of masterful chess: 2.Rc5+! Kb4! 3.Rb5+! Kc4! 4.Rd4+! Kc3! 5. Rc5+! and now Black inexplicably gave up and played 5... Kxd4?, which after 6.Rf5 reaches a tablebase and White wins.

Krabbe's comment on this (item 114 of this page):

It's like buying a can of beer, then taking the plane to Zimbabwe because you have a friend there who knows how to open them.

Monday, November 27, 2006

What people search for here

Life imitates Mathematics far more than Mathematics imitates Life

An interesting variation on Wilde's dictum, which brings to mind the old joke: engineers think that their equations approximate reality, physicists think that reality approximates their equations, and mathematicians don't think about reality.

bayes in pictures

If you wanted pictures of Thomas Bayes, here is one. Google Images is more useful for this than ordinary Google, you know.

what is time but the correspondance of your mind with reality


Scientists don't agree on whether zombies exist

Philosophers, and also some philosophically minded scientists, don't agree on whether zombies could exist. But I am not aware of any scientist thinking that they do in fact exist. In fact, I would be very surprised if any one did.

forma de la tierra

Manolito: "Un esferoide"
Maestra: "Muy bien! Con un ligero achatamiento en..."
Manolito: ..................... "En el animo?"

cuanto es un centimetro

Ehhh... la centesima parte de un metro? O preguntabas en pulgadas o en codos egipcios?

What are the laws of nature and physics in Tolkien's world

An interesting question! I don't think we have enough information from canon to write them up. Probably there are fundamental laws, but they are different enough in character from those of our world (involving, for example, irreducible ethical and aesthetical concepts) that to call them laws of physics is misleading.

time for earth to go round sun
One year. (You wouldn't believe how often I get variations of this question.)

Monday, November 20, 2006

Platonic solids, 1500 years before Plato

My next post was scheduled to be my long review of The Trouble with Physics, almost finished by now, but I saw this in John Baez's last This Week's Finds column and thought it was too cool not to post it. The Neolithic inhabitants of what now is Scotland were familiar with the five Platonic solids already by the year 2000 BC or so, as evidenced by these stone carvings dating from that period:

Baez points to this paper for more on regular polyhedra in different areas of science, and to this great talk by himself on the dodecahedron.

Tuesday, November 14, 2006

More Shameless Self-Promotion

If you wondered wht I had not posted during the past week, the answer is that I was busy finishing this:

Then again, how often does the Unruh-DeWitt detector click if we switch it carefully?

The transition probability in first-order perturbation theory for an Unruh-DeWitt detector coupled to a massless scalar field in Minkowski space is calculated. It has been shown recently that the conventional $i\epsilon$ regularisation prescription for the correlation function leads to non-Lorentz invariant results for the transition rate, and a different regularisation, involving spatial smearing of the field, has been advocated to replace it. We show that the non-Lorentz invariance arises solely from the assumption of sudden switch-on and switch-off of the detector, and that when the model includes a smooth switching function the results from the conventional regularisation are both finite and Lorentz invariant. The sharp switching limit of the model is also discussed, as well as the falloff properties of the spectrum for large frequencies.

Monday, November 06, 2006


- What has contributed more to our basic comprehension of the universe, computer science or cosmology and particle physics? Scott Aaronson says the former; Sean Carroll (and surely most other people with him) the latter.

- While we are at it, the lecture notes on quantum computation Scott Aaronson is putting on the Web are an unmissable read. The title says it all: Quantum Computing since Democritus.

- If you just can't get enough of the Dawkins wars, go to Evolution Blog where Jason is reviewing the reviews of The God Delusion, and mostly defending Dawkins against them. I skimmed a bit through the book at the university bookshop a few days ago, and it seemed more substantial that I had been lead to expect. I may even buy it when it comes in paperback.

- A discussion at The Volokh Conspiracy on wether voting is rational according to rational choice theory. Ilya Somin says yes (also here and here); Jim Lindgren says no (also here), or at least no according to Ilya's arguments (which are inspired by philosopher Derek Parfit). Of course, if the answer turned out to be "no" we could say "so much the worse for rational choice theory" instead of deciding not to vote.

- A philosophy blog that will enter my blogroll soon (or in the next update, which may not be so soon): The Splintered Mind. Recent highlights are a thumbnail summary of positions in philosophy of mind and why all of them are "weird"; a discussion on what is metaphysics, and an intriguing puzzle about vision: when we have our eyes closed, do we see the interior of our eyelids?

Wednesday, November 01, 2006

On not taking a stance

After a typically excellent explanation of the hierarchy of energy scales that is crucial to allow life as we know it to exist in the universe, Sean Carroll says:

Because we don’t yet fully understand the origin of these fantastic hierarchies, we can conclude that God exists. Okay, no we can’t. Really we can conclude that we live in a multiverse in which all of the constants of nature take on different values in different places. Okay, we can’t actually conclude that either. What we can do is keep thinking about it, not jumping to too many conclusions while we try to fill one of those pesky “gaps” in our understanding that people like to insist must be evidence for their personal favorite story of reality.

This is exactly the kind of thing I was going to say in a post scheduled to write one of these days, but not on the fine-tuning problem but on the interpretation of quantum mechanics.

Just as in the fine-tuning problem we have theologians pressing on one side that the most rational solution is to accept the existence of God, and people like Leonard Susskind pressing on the other side that the only rational solution is to accept the real existence of the multiverse, on the interpretation of quantum mechanics we are also pressed on all sides by people who want to convince us of accepting "their personal favorite story of reality". Many physicists insist that we should give up the goal of a physical theory that describes reality "as it really is" and accept that theories are only tools to predict experimental outcomes. Some others urge that the most rational interpretation of quantum mechanics is one that allows a complete and deterministic description like in classical physics, even if this requires nonlocal hidden variables or backwards causation. Still others think that the only reasonable thing is to expect orthodox quantum mechanics to break down at a certain level, replacing unitary evolution of the state vector by a real, physical "collapse". And many others vehemently insist that the only interpretation that makes justice to quantum theory as it is, without adding any extra element nor relinquising realism, is the Everettian one that implies that millions of copies of us "branch out" into other universes at every minute.

And I... find every one of these alternatives unpalatable. And I don't think I am rationally required to take a stance and accept one of them, not even provisionally, any more here than in the fine-tuning case. The day we have a final theory of nature (meaning one that predicts correctly and explains all actual and possible experiments we can think of, including quantum gravity and everything else under the sun), and if it still includes quantum mechanics in its present form, I will have to decide which interpretation to suscribe to. But meanwhile, I think it is perfectly acceptable to go on, using quantum mechanics as every other physicist does, but without accepting any interpretation of it; not even the pragmatical one that rejects all interpretations as a matter of principle.

There is still much we don't know, and not only just "facts" but also whole realsm of nature we do not know how to think coherently about; not the lesser one, spacetime itself at a quantum level. It seems to me a reasonable expectation that a correct theory of quantum gravity could involve changes in the very structure of quatum theory, that would reveal the theory as we know it to be a weak-energy limit of some other kind of physics, with a conceptual structure we cannot even guess at the moment, but which would not be as "paradoxical" and "un-interpretable" as quantum mechanics as we know it, while not involving in any sense a return to classical (pre-quantum) notions.

Someone might say that this (and the similar position on the fine-tuning issue) is just a cop-out. If all the alternative ways of understanding something are on the table, and I can't think of any other, am I not supposed to decide which of the alternatives seems most likely to be true, and accept it until something else comes up? Am I? But why? There is a similar and very familiar fallacy commited by Intelligent Design defenders: if they point to some biological system which we can't explain at present how it evolved, then the only available explanation for the moment is God and we ought to accept it until we can give an evolutionary explanation. The fallacy is much more obvious here, because in the biological case we have already a good idea of what kind of explanation is needed, and we have excellent reasons to believe that with more research we will find it. While in the physical problem I discussed we have no idea at present of how to develope deeper theories that may solve them, which makes some people insist that quantum mechanics as we know it (and particle physics, string theory and cosmology as we know them) are final; that we have already reason to believe that we will be no further revolutionary overturning of our knowledge on those areas. This sounds hubristic to me. If the history of science shows something, it is that Nature is cleverer than we are.

I have a particular historical analogy on my side. When Newton proposed his theory of gravity, it was considered a strong criticism against it that it involved action at distance. The prevailing philosophy of nature, Cartesianism, implied that all physical action occured by direct contact, and the idea of a body exerting a gravitational force directly on another one, without any intermediate, seemed philosophically absurd. When it became clear the Newton's theory predicted accurately the planetary orbits, people had to come to grips with the fact of action at distance; and sure enough, just as with quantum mechanics there were many that said: "You are not supposed to understand how it works -that is a metaphysical question! It predicts the movements we observe, what else do you want?" Still others try to develope theories that mimic Newton's Law starting fom Cartesian models, like Le Sage's theory, and these efforts (which ultimately failed) can be compared to the "hidden variables" or the "physical collapse" models for quantum mechanics, which try to limit the weirdness going back to something more familiar. And there were certainly no lack of people who thought that the model of particles affecting each other at distance was there to stay forever; I think some even said that it could be known a priori that Nature behaved in that way, which shows how much familiarity with an initially weird idea can make for you. (I have seen also a priori deductions of quantum mechanics.) What finally happened, of course, was that Einstein came up with General Relativity, which explained how the gravitational force is transmitted through spacetime using mathematical tools, concepts, and a whole way of seeing nature which were completely unthinkable in the 18th century. The puzzle was finally solved when a much deeper and comprehensive theory was found. That, exactly, is what I am hoping for the puzzle of quantum mechanics

[Note: Does the expression "to take a stance" strike native speakers of English as an eggcorn? I hesitated between it and "take a stand"; checking only the latter phrase appeared, but Google finds results for "take a stance" in a ratio of 1/10 to it. Which seems high enough to be linguistically acceptable, and it sounded much better to my ears. What do you think?]