FSTDT February Awards

I have to confess I guilty pleasure I have. Do you see, on my sidebar, the link named "Fundies Say The Darndest Things!"? Have you ever clicked on it, or been to the site by other means? Then you will understand my confession, which is that I go into FSTDT at least once per day, usually more, just to have a good laugh.

FSTDT is a website where you can submit bizarre, absurd, ridiculous or bigoted quotes by fundamentalists, taken form discussion boards anywhere in the Internet. The topics can be Creationism, the Rapture, examples of homophobia, or just plain religious or political fanaticism. But only the really, really darndest sayings get approved by the webmaster and are published there to be commented an laughed upon by site visitors. An ordinary "Evolution is not a fact, just a theory promoted by atheistic scientists!" or "God is on the side of America!" won't make it there; much too vulgar. Instead, you can read things like:

"how could organisms complexity develop, without first having an organism to start with? Wouldn't that then mean an organism was dormant even before our earth supposedly broke away from one giant rock? And if this organism was dormant even before the big bang, how is it more believable to say that something existed, without anything to make it exist?"

or

"Part of the reason evolution was offered was they were looking for more sex, and didn't like Christianity telling them about morality."

or

"I don't care what they do. They can do now rong to me. Everynight and every waking moment , I thank God that we have Pres.Bush and VP Cheney and Tom Delay and Bill Frist to watch over us. They can do no wrong. I love them."

which, believe it or not, are not really extreme at all compared to the average stuff you find there. I just picked them at random.

So that is my confession. I feel guilty about it because it is not really nice to be deliberatly getting so many laughs from the stupidity of others. It is a low form of pleasure, and a form of arrogance as well. But I can't stop it. These darn fundies make me laugh too much.

And, to get to the title of the post and the reason I am writing it today, the "FSTDT Awards" for the best posts submitted in February have been given, and you can read them (along with all the February posts, if you are patient enough) by entering the main page and then clicking on the February link. There are 30 awards, with categories like "Non-sequitur of the Month" and "Marching Proudly into the Sixteenth Century Award", and all are incredibly funny, except when they make you feel sick for your fellow humans. Be sure not to miss the "WTF? Award" or the "Drugs are Bad Award" which make me laugh till I cry every time I read them. And the first "Post of the Week", which is just... let's say revolting but also funny. Also go down in the page till you see the hilarious yellow sign that starts "You make me sick" (not an award but should have been; was a submission of yours truly).

Note: the site is not about mocking religion, it is about mocking fundamentalism. There is even a "Secular Fundie of the Month" award, for an especially arrogant atheist. So you can go there without problem if you are a sensible religious person... only that you will feel sad for the silliness of so many of your fellow believers.

This blog performs a useful function, or perhaps not

Somebody reached this blog via this google search. I hope they found satisfaction to their doubts in the post they got to. Although if they were not thinking of the question taking into account general relativity, but just in its plain, ordinary sense, then probably the answer was not too enlightening.

Dr. Kripkenstein: a horror story (Part 1)

Dr. Kripkenstein is not a cousin of Dr. Viktor Frankenstein, the famous creator of a nameless monster, but a sort of monster himself. He is a philosophical chimera, a combination of Ludwig Wittgenstein and Saul Kripke, defined as "the philosopher whose views are put forward in Kripke's book Wittgenstein on Rules and Private Language" (a book with I read recently as told here). The reason for this invention is that the book contains interesting and important arguments and theories which Kripke presents as his interpretation of Wittgenstein, but which many Wittgenstein scholars do not accept as a reconstruction of his views. As Kripke says he does not endorse himself the views presented on the book, they can’t be said to be neither his nor Wittgenstein’s. Hence the invention of "Kripkenstein", or as I shall call him, Dr. K.

And apart of their author being a sort of hybrid monster, the arguments contained in the book mark it as a sort of philosopher's nightmare. They are skeptical arguments, that aim at showing that there is no fact of the matter corresponding to a person "meaning" something when using an expression.

The example Dr. K. uses is addition. In my life so far I have only performed, considered, or thought of, a finite number of sums. Suppose none of them has been greater than 1000 (there must be one number greater than all of them; assume for example it is 1000). Define a function "quus", represented by ++, in the following way: x ++ y is equal to x + y for all x and y smaller or equal than 1000, and equal to 5 whenever x or y is greater than 1000. If now somebody asked me "How much is 1007 plus 24?" I would surely answer 1031. But, Dr. K. asks, what justifies me in answering 1031 instead of 5? How do I know that by the word "plus" as I used it in the past I meant the function plus, and not the function quus?

This is not an ordinary skeptical question of the style "how do you know your memory is reliable?" It is accepted that I remember perfectly well all the past sums I have done, and all the thoughts I had while doing them and while learning about addition in general. The question is, if I never had any concrete thought of a sum greater than 1000 before, how do I know the function I was using and calling "addition" was the plus function (the "real" addition) and not the quus function? Of course that, as a matter of brute fact, I am disposed to answer 1031 instead of 5, but what is my justification for this?

Many of you are surely tempted to say something like: "What I mean by plus is not restricted to a list of particular answers. It is a general rule, that tells me when asked for a sum, to do it applying an algorithm learnt in school (to add 1007 + 24 I have to add 7 + 4, carry the 1, and so on). When meeting a new case I apply this algorithm and get the answer 1031, not 5". But this won't do. It is true, of course -just plain common sense. But it doesn't really answer Dr. K.'s question. Because the algorithm itself I have applied only in a finite number of cases so far, all smaller than 1000. So how do I know how to apply it to greater cases? How do I know that the words in which I express the algorithm don't themselves have meanings like that of "quus", that change when applied to numbers greater than 1000?

The real question is how the mind, being finite, can grasp unambiguously a rule that applies to an infinity of cases. Dr. K. says "It can't. So there is no real fact corresponding to whether we mean plus or quus. We just follow a rule blindly, giving always the plus answer, but there is nothing that justifies us in doing so." And so we are left in a sort of nightmarish uncertainity, all our words and thought suddenly devoid of meaning, and we here at distance the satanic laughter of Dr. K…

Enough of cheap horror movie scenery. Is the argument sound? Well, of course it has not been widely accepted as so. The argument can be read as a challenge: Construct, if you can, an account of meaning and rule-following that does not fall to the skeptical hypothesis. Kripke himself makes some suggestions, only to conclude none of them work; but other philosophers (including this humble amateur philosopher) have not necessarily agreed with him. In following posts I shall discuss some solutions, the objections to them, and try to sketch my own views.

Meanwhile, if you want to read further on Dr. K., try this comprehensive webpage.

Space and Time in Special Relativity (continued)

(This is a follow-up to this post, and should only be read after it, especially if you have no technical knowledge of Special Relativity.)

I had promised to make clearer the differences between space and time according to SR. The similarities I mentioned already are the following three facts:

a) Just as there is no unique, absolute "Forwards" direction in space (what is forwards for one observer is a combination of forwards and sideways to another one rotated with respect to him) there is no unique, absolute "Time" direction in spacetime (what is time for one observer is a combination of time and space for another one that moves with respect to him). As a consequence there is no unique, absolute state of rest.

b) Just like observers that are rotated which respect to each other give different values for forward distance dx and sideway distance dy between points, but agree in the total distance ds, observers moving with respect to each other will give different values to spatial distance ds between events and temporal interval dt between them, while agreeing in the total spacetime distance DS.

c) The spatial distance ds is related to the three distances in the spatial directions by Pythagoras' Theorem ds^2 = dx^2 + dy^2 + dz^2; the spacetime distance DS is related to the four distances in the four spacetime directions by DS^2 = dx^2 + dy^2 + dz^2 – dt^2 (a formula called "Minkowski's Metric"). In both these formulas the right hand side is an absolute which all observers agree in* but each term in the left hand side is relative to the orientation and state of motion of the observer.

So space and time are not identical: Minkowski's Metric** has a minus where a four-dimensional Pythagorean Theorem would have a plus. What concrete differences follow from that sign difference? I will explain them with an analogy: I will describe a set of observers rotated at different angles with respect to each other, in a two-dimensional plane, as they would be if the two directions in that plane behaved like space and time. In the following, "Forwards" is an analogy for the future direction in time and "Sideways" is an analogy for the space dimension.

So imagine you are standing, facing forwards, in a room with many other people. The people have their bodies rotated at different angles with respect to yours, but none at more than 45 degrees in either direction. That is, you see people turned a bit to your right, and a bit to your left, perhaps some at (almost) 45 degrees to your right or to your left, but nobody more than that. The analogy with space and time is that the "rotation" in spacetime, which is to be moving at a certain velocity, cannot be more than a certain amount: it is impossible to move faster than the speed of light. (And yes. This limitation in "spacetime rotations" as opposed to spatial rotations is a direct consequence of the minus sign. But I can't explain that without maths.)

But now you must be thinking that what I said contradicted fact a) above. After all, if you see someone rotated (say) 44 degrees to the right and someone else rotated 44 degrees to the left, then the first of them "must" see the second rotated at 88 degrees to the left. [Translation: if you see someone moving to the right at almost the speed of light, and someone else moving to the left at almost the speed of light, then the first one "must" see the second one moving at almost twice the speed of light to the left.] The only way out of this seems to be saying that you are special: you, only you, are looking to the true forwards [translation: only you are truly at rest] and so the rule of "no rotation of more than 45 degrees" [no speed greater than light] applies only to you. Contrary to what I wrote in a) there is an absolute, unique "Forwards" direction [an absolute, unique "Time" direction], which is the one valid for you. In short: an absolute, unsurpassable angle of rotation [speed] seems incompatible with the relativity, non-absoluteness, of spatial [spacetime] directions.

This conclusion is intuitive, but false. In our analogy, what would happen is that if you see John rotated 44 degrees to the right and Mary rotated 44 degrees to the left, then John would see you rotated 44 degrees to the left, and… Mary rotated 44.99 degrees to the left! Which means in reality, that if you see John moving at 99% of the speed of light to the right, and Mary. moving at 99% of it to the left, then John sees Mary moving at about 99.995% of it to the left. In reality, giving up our analogy, angles are additive: if you are rotated A degrees with respect to John, and Mary is rotated B degrees with respect to you, Mary is rotated A+B degrees with respect to John. Velocities, on the other hand, are not additive. If you are moving at A km/h with respect to John, and Mary moves at B km/h with respect to you, then Mary does not move at A+B km/h with respect to John.

(If you insist on knowing the real formula for the velocity of Mary with respect to John, it is (A+B) / (1+ AB/c^2), where c is the speed of light. You can check by yourself that this is very close to the commonsense answer A+B if A and B are much smaller than c, which is the reason we usually don't notice this effect, but that if A and B are close to c the answer is very close to c but not larger than it. And if both A and B are exactly c, then their "addittion" with this law is c again!)

So here there is a big difference between space and time: rotations in space are additive, rotations in spacetime not (at least not in the same way). And this is also a direct consequence of the minus sign, although once more I can't get into the details***. From this it is clear how the speed of light can be an absolute and unsurpassable constant while still keeping fully the "Principle of Relativity" that there is no unique and absolute "Time direction", or what is the same, that there is no unique and absolute "state of rest" (motion is relative). Historically, Einstein thought first that the absoluteness of the speed of light and the relativity of motion should both be true principles (both had experimental support, specially from the Michelson-Morley experiment****) and noticing that they seemed to be contradictory, discovered that they were actually compatible if velocities were not additive. A few years later Minkowski came and showed that all of Einstein's theory followed naturally if one started from the expression for DS^2 that has the famous extra minus sign.

Another difference between space and time that follows from this: with rotations in space you can go "all the way round", including facing backwards when you have rotated 180 degrees; but with rotations in spacetime (movement) you cannot "rotate more than 45 degrees" (go faster than light) and so you cannot go backwards in time. (Maybe you saw in some sci-fi movie the assertion that going faster than light amounts to time traveling. It is true, but both are impossible, at least in the sense intended.)

And I think that will be all for today. I'll be most happy to answer questions that might be unclear.


* Well, in the first one, all observers agree about ds^2 as long as they are not moving.

** Actually it is called Minkowski's metric, with no capital M in "metric", but it looked better like that.

*** For those of you who are curious and know some calculus, this has to do with the difference between trigonometric functions (which parametrize circles) and hyperbolic functions (which parametrize hyperbolas). I can also mention that the analogy between rotation in space and motion in spacetime becomes mathematically an equivalence if time is measured with imaginary numbers

**** Recently voted the greatest physics experiment ever, though I gave my vote to Galileo (who ended up in fourth place).

This and That on Books

This is a long post, because it covers what could have been two, three or four separate posts on books I have read or am about to read.

- I got today from the philosophy of physics section of the university library two books which I had been intending to read for a long time: Quantum Mechanics and Experience, by David Albert, and The Philosophy of Physics, by Roberto Torretti. I don't promise book reviews anymore (see below) but they may come anyway if I feel disposed to writing them. I have started Albert's already, and it has the best nontechnical presentation I've ever read of quantum "weirdness" except for Feynman's unforgettable description of the two-slit experiment.

- Last week I borrowed from the samesaid library Kripke's Wittgenstein on Rules and Private Language. I was prompted to read it by this discussion Brandon at Siris made of Nagel's The Last Word, in which he mentions my previous review. Brandon spelled out a justification for Nagel's defense of a Platonic faculty of Reason by reference to the philosophy of Malebranche, where emphasis is given to the capacity of the mind to grasp infinities, and this reminded me of what I knew of Kripke's book (and he acknowledged the relation in the comments to the post). So I got Kripke for reading instead of Malebranche, beacuse I find it quite easier to understand a twentieth-century analytic philosopher than a seventeenth century rationalistic one!

I had to return the book to the library already as it was only for one week loan (unlike the two others I got today and indeed most of the books, which can be borrowed for the whole academic year; this is something that never ceases to amaze me used as I am to the zeal with which Argentinian academic libraries keep the books from being borrowed for more than a week at the very most). I made some notes from the section in with Kripke tries to refute a "dispositionalist" account of meaning, and probably will blog these arguments and attempt to respond to them sometime in the following days. Kripke's argument is powerful and unsettling for any theory of mind and meaning. I think a naturalistic theory can answer it, but (for what it's worth) I admit that the answer may have to be counter-intuitive in some respects, so I'm no longer as complacent with the picture of Platonism as a wild "inflating" of commonplace things easily accounted for naturalistically as I was while writing the Nagel review.

- I have read most of J.R.R. Tolkien's Unfinished Tales, which were of course edited and published by his son Christopher Tolkien after his death. They are half-written stories, or in some cases many different incompatible versions of the same story, that cover either aspects of Middle Earth not covered in The Lord of the Rings or The Silmarillion, or cover things narrated in them but with much more detail (as the tale of Túrin). As a Tolkien fan I am finding it both a thrilling and a saddening experience. Thrilling because of the possibility to read such things as why exactly Gandalf chose Bilbo as helper to the Dwarves in The Hobbit, or how exactly did the Nazgûl find the Shire to go searching there for the Ring (who would have guessed it was Grima Wormtongue who gave them the tip?). Saddening because of its demystifying effect: Tolkien's books give such a powerful impression of Middle Earth having a sort of autonomous, self-existing and completely coherent reality that it is a bit of a shock to read three or four different accounts of the story of Celeborn and Galadriel, all extracted from Tolkien's notebooks, without any clue as to which was the "correct" or "preferred" one (or if there was one at all). One yearns for an answer to "But which is the REAL story?", and one's realistic self knows all too well that this answer does not exist, despite all our experience with TLOTR and TS leading us irresistibly to believe that all such questions "must" have an answer.

- I don't think I will ever summon the energy to write the full-scale reviews of Ryle's The Concept of Mind or of Webster's Why Freud was Wrong which I rashly promised, so I will take this chance to make some comments on both books.

I can say little original about Ryle's book, which is one of the classics of twentieth-century philosophy. Those who know nothing about it are invited to read this charming presentation by Dennett. Ryle tries, as everyone knows, to refute Cartesian Dualism, the theory that mind and body are two distinct entities, a view he immortally derided as "The Ghost in the Machine". He is most successful in the first part of the book, when he demolishes the old-faishoned kind of psychology whic talks of "intelligence", "reason", "desire", etc. as specific mental processes that occur in the inmaterial realm of the mental. Ryle argues convincingly (and I think he convinced in fact most philosophers) that such terms must be interpreted in a broadly behaviouristic way (e.g. to act "intelligently" is not to act guided by a particular kind of mental processes, but to be disposed to act in the way we characterize as "intelligent" under a variety of circumstances). Less convincing is the way Ryle disposes of "sensations" or "sense data" as seeing a colour or feeling a pain, which traditionally are concieved as mental events that cannot be accessed from the outside. In this point his argument reduces to an "ordinary language" move that we don't talk of "seeing sensations" but of "seeing things" and "having sensations". Against the powerful set of intuitions that takes us to belief in senations as entities, this argument has little force, and effectively we see that in contemporary philosophy debates on "qualia" go on and on without much regard for the Rylean position. (Even Dennett, who is a follower of Ryle in many regards, does not use his same arguments when trying to quine qualia).

Webster's book presents a strong case against the pretense of psychoanalysis to be a scientific theory of the human mind. I regret that I knew little about psychoanalytic theory, besides what has filtered into common cultural knowledge, before reading the book, so I can't see both sides of the argument. (I have read two or three books by Erich Fromm, but as a psychoanalyst he is very unconventional and unrepresentative). Webster is very convincing in portraying young Freud, with the evidence of his letters and writings, as being eager to make a big discovery and proposing once and again bold theories unsupported by evidence (on the causes of hysteria, especially) which he believed almost fanatically until the weight of evidence was too strong against them; then he hit upon the theory of repressed infantile sexuality as one that could not be disproved by evidence (any absence of evidence could be explained away by repression). He succeded in convincing of its truth first a small group of disciples or "apostoles" (Webster shows how strikingly similar to a religion was the early psychoanalytic movement, with the dissidences of Adler, Jung and other being treated as "heresies" and leading to excommunication) and then a cultural milieu which was ready for this kind of theory. Webster perhaps exaggerates his denial of any truth in some psychoanalytic theories (for example I found difficult to accept his pronouncement that there is no evidence at all for any memories of traumas to be repressed, though I have no evidence in favour expect that I can't understand how it could have become something that "everybody knows" to happen if it didn't). But all in all, he convinced me that there was less of scientific substance in psychoanalysis than I had assumed before. Alas, his proposals at the end of the book for a "true science of Man" to replace psychoanalysis are too vague, even as philosophy, to be of much value.

Scientists playing God, now for real

A cliché from class B science fiction movies and unimaginative news reports on genetics is that scientists are "playing God" when they modify genes, create new species, clone humans to create a slave army, or do other praiseworthy activities of this kind. Bah! That's just "playing natural selection". You want "playing God"? This is playing God!

Monday Quantum Gravity Seminar: Black hole entropy in LQG

Today instead of our usual QG group meeting we had a proper seminar, as Jacobo Díaz Polo from Universidad de Valencia gave a talk on black hole entropy calculations in Loop Quantum Gravity. Kirill Krasnov, who was one of the pioneers of this research, was a sitting in the audience as a memeber of our group but was also willing to give a hand at answering questions, so it was a unique opportunity to learn the real state of affairs here. Warning: I am not an expert of any kind in LQG, knowing only what I have gathered from reading Rovelli's textbook (but not doing most of the math) and hearing quite a few talks on the subject, specially at the Loops '05 conference. So there may be some details (or perhaps more than that) which I get wrong. However this post is not a "popularization" one like the series on special relativity; nonphysicists are unlikely to gather what this is about from what follows.

The question to answer for a BH entropy calculation in LQG is: In how many ways consistent with a given total area can the spin networks states (which describe spatial geometry in loop quantum gravity) puncture the sphere representing the horizon of the black hole? Each puncture has a two quantum spin numbers, j and m, with possible values of j being 1/2, 1, 3/2.... and possible values of m for each j going from -j to j. The logaritm of the total number of states gives the entropy of the black hole, which should agree with the semiclassical Bekenstein-Hawking entropy (one quarter of the area in Planck units) . The diffeomorphism constraint, which represents invariance of GR under spatial diffeomorphisms, is implemented via the requirement that states with the same number of punctures in the horizon are considered equivalent. The Hamiltonian constraint, which should encode the dynamics of the theory, is not implemented at all. I raised my hand at this point of the seminar and asked why; I thought the answer would be "because the black hole is stationary" or something like that, and I wanted to inquire further on how is the "stationarity" defined at the quantum level. But the answer Kirill gave was the Hamiltonian constraint describes the geometry of the bulk (as being a solution to the quantized version of the Einstein equations, I imagine) and we are looking only at the geometry of the horizon surface. We are assuming therefore that of all the states that we can imagine puncturing this surface, "most" of them will be also be extendable to solutions of the Hamiltonian constraint on the bulk.

When we get to the actual counting of states, Jacobo said he would give a lower bound and an upper bound to the total number of states. The lower bound comes from assuming that all the j numbers are 1/2, the lowest possible spin. I couldn't follow exactly how the upper bound was found, it had something to do with how the density of states grows with the area... but the point is that the upper bound gives exactly the same quantity as the lower bound, and therefore this quantity is the number of states. Its logaritm is the entropy and is equal to: ln(2)/(4 Pi Sqrt(3) g) times the classical area of the black hole in Planck units. Here g is the Immirizi parameter, usually represented by a gamma, and Sqrt(3) means square root of 3. (I should get one of those nice math display programs that some other physics bloggers have if I'm going to write posts like this one!) Comparison with the Bekenstein-Hawking entropy fixes the Immirizi paramenter as ln(2)/(Pi Sqrt(3)).

This is the result Kirill and his collaborators had found in their original paper, but since then their result has been submitted to criticism. My supervisor Jorma Louko made a question about this, how does this result contrast with the different one found in this paper. Between Kirill and Jacobo they explained that different definitions can be given of "number of states that give a same total area". The calculation made originally by Kirill et. al. assumed one of those definitions; under it, the 1/2 value for the spins dominates over all others for large values of the area, and therefore it is justified to consider only states with spin 1/2, which is essentially what Jacobo had presented in the talk. Under other definition this is no longer true, higher spins must be taken into account, and the result for the entropy (and consequently the fixing of the Immirizi parameter) are different; g turns out now to be defined by an ugly trascendental equation.

Appearently there is no agreement on which is the correct counting method. I had to leave at this point because I had to get to a class where I am demostrating (answering questions of undergraduates on their classwork), which was a pity because although the talk had ended already I would have liked to go on discussing these matters. I would specially like to know if the uncertainity on the proper counting procedure may be linked to the lack of knowledge on how to impose the Hamiltonian constraint, and the consequent decision to ignore it. (I remember now overhearing John Baez say something that could be interpreted in this direction in a conversation on the subject at the Loops '05 conference).

Knishes!

For first time in my life I tried to cook knishes this evening. (As I have encountered people, even Jewish people, who don't know what they are, probably I have to explain that they are traditional Jewish pastries filled usually with potato and onion. And no, I didn't cook them today because seeing Munich made me rediscover my Jewishness. I had planned it already before.)

When I had the pastries almost prepared and ready to put in the oven, a flatmate of mine reminds me that the oven is not working! D'oh! (as you see I don't use it too often). Fortunately a friend of mine lives just two blocks away and when I called her she agreed to me using her oven and eating at her place, even though she and her boyfriend had eaten already. The knishes were quite good for being a first try, though not as good as my Granny's -not that I was expecting that! Perhaps next time less potato and more onion will get it closer, though the real challenge will be daring to make the dough myself instead of buying it. After coming back home (leaving some of the knishes for my friends to try tomorrow) I took the picture you see above.

Alejandro Simpson

Thanks to The Simpsomaker, I can finally know how would I look like if I appeared in The Simpsons.

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If you want to do the same, after making your character as there is no option to save it you have to press Alt+Prt Sc to save the image, then open the Paint program and paste it there.

Munich

So I've just come back from seeing Steven Spielberg's Munich. In the unlikely case you didn't know, it is about the hunting and killing of the responsibles of the terrorist attack on Israeli representatives during the Olympic Games of Munich 1972 by a special Mossad team operation. Both my suspicious and my cynical friend had been recommending it to me for a while. (There you have, Cynical, don't complain anymore that I don't link to you. I even link to your comments on the film!). So below is my review.

It is certainly a powerful movie. I don't think it is one of Spielberg's best (I can think of several better ones*) but it is perhaps the most complex, less linear and straightforward (of those I have seen at least, which looking at IMDB I reckoned to be about half of those he made since Jaws... less than I thought). It tricks us at the beginning into making us believe that it will be a direct tale of revenge: one by one, the terrorists will be shot or bombed in increasingly suspensful and exciting ways, and at the end the good guys (or those that remain alive) will say "mission accomplished" and return to their lifes. The killings are indeed incredibly suspensful and exciting, to the point that once and again I found myself gasping or jerking at the moment of the shot or the explosion, even if I knew it was coming -a tribute to Spielberg's mastery. But after the third killing or so, things start to get amiss. Things don't go as planned; someone is killed even though he was not in the original target list but is a replacement for one of them; the motivations and sincerity of the mysterious French informers to the group become suspect; the hunters become hunted. The film ends with all the plot threads still open, as if making a point that there is no conclusiveness to the cycle of violence.

Many commentators have focused on the way Spielberg makes the characters doubt and question their own mission, and before seeing I had the impression that the film would leave us a definite moral or message, such as "if we use the same methods than the terrorists we become no better than them". There are a couples of dialogue lines of this kind, but never so explicit and preachy: Spielberg knows better than that. It is true that he displays a typical Hollywood-liberal-sensitivity in making the characters discover moral dilemmas in a perhaps unrealistic way for hardened Mossad agents**, but for me the main "message" of the film insofar as it has one was not a moralistic one in that line, but a deeply pessimistic one. Retail missions against Palestine terrorism are necessary for the survival of Israel, because if they were not done terrorists would only be emboldened; but if they are done, more terrorists appear with fresh cause for revenge and the violence never ends. The movie shows this dialectic but does not offer any way out of it***, and leaves therefore a very sad impression.

There are other important subjects that the film touches upon, but one I would like to mention is the significance the state of Israel has for a Jew. There are several explicit references to this, including one by the protagonist's mother and one by his boss near the end, but there is one moment that does not intend to make such a reference, and nevertheless worked as one for me: After the introduction to the film where the kidnapping of the athletes is shown, news clips with the news of their deaths are shown while the Israel national anthem "Hatikva" is heard in the background. I had not heard it for years, and suddenly hearing it in this context was extremely moving.



*I don't think any of Spielberg's "serious" films, excellent as they are, is as perfect as his earlier adventure masterpieces like the Indiana Jones trilogy or Jurassic Park.

**In fact I have read that paradoxically (or perhaps not) this has lead both pro-Israel and pro-Palestine commenters to criticize the film in a perfectly symmetrical way: the former complain that the movie is anti-Israel because it shows the war on terrorism as something that can be subjected to moral doubts, while the latter complain that the movie is pro-Israel because it portraits Mossad agents as people with ethical principles and conscience instead of as remorseless killing machines.

***Hey Cynical friend, I bet you would never have expected me to use negative dialectics, eh?

2005 film reviews

For those of you who read Spanish and are interested in films, my suspicious friend has posted a list of short reviews for all the movies he saw in 2005.

Useful math

Did anyone say math was useless? It can even address and solve the most complex practical problem known: Should the toilet seat be left up or down?

Space and Time in Special Relativity

Some days ago a non-physicist friend asked me by chat if I could give him a short explanation on the views modern physics has on space. I sent him an email with brief summaries of the concept of space in special relativity, in general relativity, and in quantum gravity speculations. After clarifying some of the doubts the email had left him with, I decided that all that was and should have been blogging material. I just had to translate it to English and expand it, and this is what I shall do now, starting with the Special Relativity part.

As I have been receiving very little feedback recently, I would like to ask my readers to answer, after reading this, if a) those who are not physicists found it understandable, and b) those who are physicists found it a passably good explanation of the issues.

So, let’s get started. The most important new feature about space that arises in Special Relativity (as opposed to Newtonian physics) is that space and time are no longer separated entities but part of a single entity, the much-heard about "space-time continuum". [Trivia question of which I do not know the answer: Does the use of this phrase in popular geeky culture, specially in phrases such as "to disrupt the space-time continuum", trace back to Doc's use of it in Back to the Future, or did it exist previously to the movie, perhaps coming from Star Trek?] But what does it mean exactly to say that space and time are joined in "space-time"? Many people think that it means only that time is the fourth dimension, that objects move through time as well as through space, and that to locate precisely an event one needs to give the full "space-time coordinates", that is four numbers three of which specify position in space and the fourth position in time. All of this is true but not very exciting, it is not the distinctive feature of Einstein's Special Relativity (it is true also in Newtonian physics) and it is not the reason why it is worth talking of "spacetime" as a single entity. The reason for this is rather that time can be "mixed" with spatial dimensions in the same way spatial dimensions can be mixed among themselves.

Imagine you are standing, looking forward with one arm pointing to each side. Your position defines a front-back direction, and a left-right direction which is orthogonal to the other one. ("Orthogonal" is math jargon for "perpendicular" -a strange case in which the jargon word is shorter and easier to say than the common one!) The distinction between these two directions is clear and real -but is relative to your point of view. For another person who is standing like you but rotated in some angle with respect to you, the front-back direction will be different from yours. For example if he is rotated a small angle to the right, then his "front" direction is a combination of your "front" direction and your "right" direction.

In just the same way, observers who are in different states of motion have different "time" and "space" directions. Suppose now you are standing like before, and the other person is not rotated but in motion, moving forwards with respect to you. Your standing defines in the 4-dimensional world a "time" direction and a "front" spatial direction (as well as the other two space directions which do not concern us now). For the other person, there is also a "time" direction and a "front" spatial direction, but these do not correspond to yours. His "time" direction is a combination of your "time" and your "front" directions, in much the same sense as the rotated person's "front" is a combination of your "front" and your "right" directions.

There are more analogies between both cases. If you and a friend standing just by your side but rotated with respect to you calculate the distance to something, you will find the same answer even though you "split" it differently among the different directions. Perhaps what is 5 meters forwards for him will be pehaps 3 meters to the right and 4 meters forwards to you, but the "real distance" (5 meters in this case) is the same for both of you. Pythagoras' Theorem ensures that if dx and dy mean distance forwards and distance sideways for you, dx' and dy’ mean distance forwards and sideways according to him, and ds is the "true distance", then it will be true that dx^2 + dy^2 = dx’^2 + dy’^2 = ds^2. (Make a drawing if you are not convinced. In the particular example before dy' was 0, but it need not be. Of course, "^2" means "squared".) You and your friend see a different forward distance and a different sideway distance to the point you are looking at, but the total distance ds comes out the same. If we allow your friend to be also tilted in the vertical direction, and we look at points that are not in the same plane as yours, the formula generalizes to Pythagoras' theorem in three dimensions, dx^2 + dy^2 + dz^2 = dx’^2 + dy'^2 + dz'^2= ds^2, where dz is the vertical distance according to you, and dz’ the vertical distance according to him. The important thing is that there is an absolute "spatial distance" which can be split differently in a forward part, a sideways part and a vertical part for different observers, but that comes out the same for every observer.

As long as they are not moving, that is. Let's go back to the case when your friend is moving forwards with respect to you. Suppose you and your friend have both rulers and clocks, to measure both spatial and temporal distances between events. Then between any pair of events, you will measure a certain spatial distance ds (which comes from the three separate spatial distances in the three directions as we saw) and a temporal interval dt. Your friend will measure a different spatial distance ds, and a different temporal interval dt’. But both of your measurements will add up to the same "absolute spacetime distance" DS, defined by the formula: ds^2 – dt^2 = ds’^2 – dt’^2 = DS^2. The only difference with the usual Pythagorean formula is a – replacing a +. (After all, some difference exists between time and space!) But what matters is that, just as "forward distance between points" and "sideways distance between points" are not absolute concepts but depend on which way the observer is looking (but the "spatial distance between points" does not depend on that), it turns out that "spatial distance between events" and "temporal interval between events" are not absolute but depend on how the observer is moving (but the "absolute spacetime distance" does not depend on that). This mixture of time and space is the defining characteristic of the Special Theory of Relativity.

It is easy to see from this how other celebrated fact about relativity emerges, the fact that the speed of light is an absolute. The formula above for DS^2 subtracts a time squared from a distance squared; this would not be possible if we were not measuring time and space in the same units. To use the same units for space and time, there must be a velocity which is absolute and serves as conversion factor. This velocity is the speed of light. The formula for DS^2 is correct if we measure for example time in seconds, and distance in light-seconds, defined as the distance traveled by light in a second. (If we were measuring time and space in the usual units, like meters and seconds, the formula would be DS^2 = ds^2 – c^2 dt^2, the appearance in it of the speed of light c showing that it is an universal constant of nature.)

There is one last question my friend made to me, and which I have not answered so far. OK, there is a difference between time and space in that time has a – in a formula where the three spatial dimensions have a +. How does this relate to the ordinary distinction between space and time, to facts such as “we can go backwards in space but not in time”? What other differences between space and time follow from this sign difference? Do ALL of them come from it?

I think that the answer to the last question is yes: all differences between time and space must ultimately be traced to this sign difference. But that does not mean I can spell out a complete answer for the other two questions, partly because the conceptual status of our ordinary notion of “flow of time” is not very clear; it is something related to philosophy and psychology as well as physics. But some of the differences between time and space can be cleared by physics and made more intuitive than just a minus sign. A following post will explain these issues. After that, we’ll be ready to get into General Relativity.

Two (not) unrelated things on global warming

The front page story of today's The Independent is a piece by NASA climate scientist Jim Hansen on the melting of the Artic ice. He says a recent satellite study shows that the ice cap of Greenland is melting faster than current models assumed, and that if no action is made to stop global warming then sea levels may get to rise 25 meters within just one century.

He also says it was for trying to publically announce these discoveries that the Bush administration, via our old friend the five times stupid George Deutsch (who still had his job at that time) tried to censor him.

On the other hand, it has come out that George Bush had a meeting with bestselling author Michael Chrichton about one year ago. The meeting was appearently arranged without the knowledge of Bush's official science advisor, and kept in secret from everyone until now. Chrichton has become a leader of the "global warming denial" party, and his last book State of Fear blames the fear of global warming to an "eco-terrorist conspiracy", which is even accused of causing deliberately natural catastrophes to blame them on climate change. You can read about the Bush-Chrichton meeting here and here, and proof that Chrichton misrepresented the views of scientists he quotes as denying global warming here.

So, to summarise, the most powerful man in the world trusts, in a scientific matter of crucial importance to the welfare of humanity in following centuries, an anthropologist and doctor turned into writer and film producer who has no expertise in climate science and who misrepresents the views of those who he quotes as supporters to build up a paranoid conspiracy theory, and at the same time censors the serious research done by real climate scientists when the results do not suit his interests. We are in good hands.

PS: I am really sorry that Chrichton has turned out this way. I loved his books when I was 15 years old, and still think that Jurassic Park is a great book within the "bestseller genre". It is sad that he has decided to launch a crusade against science and even sadder that he might convince many people.

Kuznicki on liberalism

Jason Kuznicki at Positive Liberty has a very thoughtful post on liberalism as contrasted with fundamentalism and postmodernism. In these days where so much crap is being written on the significance of the Muslim rioting over cartoons, I think that a meta-reflection as this one on why is liberalism better than its opponents is well worth reading.

Chess Match

Today I played for first time in 2006 in the university chess team. To be more precise, the University of Nottingham has 4 chess teams that play in different leagues at different levels, and I play as Board 1 (out of 5) in the Third Team. I had played several times last year in this position, and believe it or not all those games were draws! But today it was different. There were no draws in the match, in fact all the games were exciting (though none had a high quality).

In today's match one of our players was unexpectedly missing, quite a disgrace because we were locals and so one of the memebers of the other team had to come all the way to uni for nothing. Of course it also meant that we started the match being already 0-1. I won my game fairly quickly which set things even, more by luck than by skill: it was a Bird Opening (me with black) that started very closed but soon got complicated when both of us moved knights to King 5, and refused to move them away when they were attacked by pawns. In the confusion that came about I managed to check in h4 forcing him to resign castling, but anyway the position was complex and with chances for both. Just then he made a huge blunder allowing me to checkmate and the game was over at move 15.

Our Board 4 was playing against a schoolchild and it should have been an easy win after he won a rook soon out of the opening. But he managed to complicate it more and more and lost a lot of time, and when he won at last he had only one minute left in his clock (and the match is played with 1 hour 15 minutes per player!). Board 3 started very bad and was a bishop and two pawns down. But somehow he built up a dangerous attack on the opponent's king, recovered the bishop, and could have forced a draw by perpetual check; he missed this chance, blundered and lost a rook, then the opponent blundered and lost a rook as well (!) and in a dramatic ending the opponent promoted two pawns and mated him with the two queens while having only half a minute left.

Thus the match was 2-2 and it was all to the game in Board 2. There they had both less than 5 minutes left and they were still in difficult middle-game position; our player had won the queen but the opponent had rook and bishop to compensate for it so it was still difficult; they were both throwing the places over the board, knocking the clock over when pressing it, terribly nervous... at that moment a security guard came in and told us we had to clear the room because it was booked only till 10:30 and it was time already... we argued that they had just seconds of game left and he insisted that they should finish it outside... but at the same time the players went on playing desperately, knocking pieces in every move and not picking them up, perhaps skipping moves sometimes... until the opponent's flag fell when he was about to get checkmated and a few seconds were left in our player's clock. One of the most dramatic endings I have ever seen. I'm not sure if it would have counted as valid in a proper chess tournment with a referee.

So, at the end, we won 3-2. Hooray! I realise that probably none of this is of interest for the likely readers of this blog. My apologies. It will not hapen again. Or actually, it may happen again next time I play. Be warned.

Science and religion discussion

In my first post I said that among the matters that interested me was the question of the compatibility or oppostion betweeen religion and science. Some of the ideas I have on the subject are appearing in the discussion I am engaged in at Uncredible Hallq. They were triggered by a post in which he mentioned a book by Martin Garnder which has been a long-time favourite of mine. If you want a preview of opinions of mine I was planning to shape into a post some day, just go there. And participate in the discussion! (Just be sure to skip over the ridiculously long and stupid comments of "SocialScientist777". They may produce brain damage.)

Blog Laziness Leads to Shameless Linking

For first time since I started two weeks ago, I am feeling lazy to do real blogging. There are many things I could be talking about, both in physics (I have finished the "trivial couple of steps" I mentioned here and am in position to start writing a paper, so I could well give you the promised explanation of what my work is about, as I shall do tomorrow in a talk for other maths postgraduates at the university) and in philosophy (I have finished reading Ryle's The Concept of Mind and am well into Webster's Why Freud was Wrong, and both books deserve some commenting here). But I somehow don't feel motivated today, so I will keep the blog alive by suggesting you to visit the following places:

* The thread on "Bad physics jokes" at Cosmic Variance (warning: only for those of a very nerdy disposition. Yours truly contributed two jokes.)

* These cool optical illusions: rooms painted in a way that they seem to have circles or lines floating in the middle of the room.

* Bill Vallicella, aka the Maverick Philosopher, is blogging his impressions on Breaking the Spell, the last book by Daniel Dennett. Now Dennett is a scientistic, naturalistic and evolutionistic philosopher whom I admire greatly (he has been the major influence in shaping my current philosophical beliefs, as no other author had been since I was fascinated by Bertrand Russell at age of 17; I promise to blog about him some day) and Vallicella is a conservative and religious metaphysicist, so you might imagine I don't find his criticism very congenial, despite not having read the book. (Malcom Pollack in the comments, on the other hand, is expressing more or less my opinions so far). But Vallicella's thoughts are well worth-reading if only to see a reasoned and consistent articulation of the views I oppose. (Something that keeps me returning to the conservative group blog Right Reason as well).

* Carl Zimmer reviews Flock of Dodos, a documentary movie on the evolution-intelligent design controversy that seems to be really good. I hope it gets to UK.

* Peter Woit points out that two recent physics papers included blog posts among their citations. Dave Beacon, who was one of the cited bloggers, also mentions it and supplements with a list of the funniest "comments" ever on physics papers (the "comments" are a line in the arxiv filing of the paper that usually has only the number of pages and figures... but some are more inventive! Check it out for more nerdy laughs!)

The Grandeur of the Past

Have you ever seen those sequences of pictures which go from a city to country, from country to Earth from space, and so on until we get the largest scale of an infinite system of galaxies? Those that are calculated to make you feel excited about the grandeur of the universe? Well, DarkSyde has a wonderful post making you feel in exactly the same way, about our past. Recommended reading.

It reminded me a bit of this classic by PZ. Also recommended reading.

Chocolate Fondue!

Today was the first event in 2006 of a student organization in the University of Nottingham I am a proud and earnest member of, the Chocolate Society. It consisted of a chocolate fondue held at a bar in city centre. Now the idea of a chocolate fondue is enough to make me feel quite like this, so you will understand I was eager for it while I wrote my post on Hawking's paper. It didn't disappoint me. There were four different kinds of chocolate, and to eat with them we had strawberries, pear, banana, a couple of other fruits, and delicious marshmallows. Here are a couple of pictures. In case you were wondering how this blogger looks, I am the guy about to eat a chocolate-covered marshmallow in the second picture.

Hawking new paper

Every time a new paper by Stephen Hawking appears it sparks inevitably a lot of commentary, and the one that came out last Thursday is no exception. No, sorry to say this is not the one in which he finally gives due credit to H. Simpson (1999) for the toroidal universe theory. This one is written with Thomas Hertog and is called:

Populating the Landscape: A Top Down Approach

Peter and Lubos already have comments, but they are both pretty non-committal. I wouldn't dare at all to make a comment were it not because the most part of the paper is rich in conceptual discussion and scarce in technical math; this makes me feel as if I understood it quite well, which surely isn't the case. I'll try to make a summary of what I felt I understood.

What Hawking and Hertog are proposing is that when you try to apply quantum mechanics in cosmology, that is to regard the whole universe as a quantum system, you have to change the rules for extracting predictions from QM. The standard rules are: you start with a quantum system in state A, and you want to know the probability of finding it some time T later in state B. Assign to each possible way the system could get from A to B in a time T (these ways are called "paths" or "histories") a complex number called the "amplitude" of the history; the rules for assigning amplitudes to histories need not concern us here. Now sum your amplitudes over all possible histories (this is called "the path integral") to get a total amplitude for the A-B transition. Now a simple mathematical operation (multiplying the amplitude by its complex conjugate) gives you the probability of the "A to B in T" transition.

According to H&H, this is not the way you should apply QM to the whole universe. In the universe we don't know and can't know its initial state; we only know the final state, the one we are in now. We are not preparing the system in A and wondering if it will appear later in B; we are now in B, and we are wondering how we got here. So their idea is that we should write a path integral for all the possible histories of the universe that end up in a universe consistent with present data. They expect such a path integral would be dominated by a particular subset of histories (that means, almost all the probability for the present data comes from a restricted set of possible pasts) and then assuming that our history is in this subset we can derive further testable predictions.

This description seems to be lacking something: if normally we need both an initial and a final state to evaluate a path integral, how can we do it with only a final state? The answer is that the notion of a fixed, initial state disappears from Hawking's framework and is replaced by the "no-boundary condition". This means (roughly and so far as I understand it) that there is no initial state for the universe, because the integral sums over universe-geometries in which time is imaginary, and in this case time becomes indistinguishable from a space coordinate. Thus an "initial state in time" is replaced by "all possible states of universes with 4 spatial dimensions" (assuming we have fixed as part of our data that the "really space" dimensions are 3). However I don't really understand completely how this so-called "Euclidean path integral" is supposed to be related to the actual universe in which time is distinct from the other dimensions.

Anyway, I should make clear that H&H do not apply this framework to any calculation in the real universe. (They do a calculation with an ultra-simplified toy model to illustrate how it is supposed to work). What they are doing is proposing a way to frame questions about the state of the universe and the values of its most general parameters (such as the number of dimensions or the masses of elementary particles) which according to the string theory are determined, perhaps, by accidental events in the history of the universe instead of being included or predicted from the ultimate theory of nature. The article is therefore a participant in the enduring "String theory - Landscape - Anthropic principle" controversy, of which I could say a lot more... but I have no time now, so that will be for another day. I have to leave for a delicious event you will learn about in the next post. So long!

Oh, the joy!

Today I finally managed to solve a set of differential equations with which I have been fighting since I arrived back from my holiday three weeks ago. Finishing this was the major remaining prerequisite (a couple of steps are still left, but they are rather trivial) before I could start to write the first paper on my PhD research. Happy this day I am.

Shortly, when I find the time and the energy at the same moment, I will post an explanation of what my research is about and what were these equations for. For the moment I shall only say that it is related to the Unruh effect and how it can be probed by particle detectors.

Does the Earth "really" go around the Sun?

At Pharyngula PZ has pointed to some lunatic geocentrist society and their challenge for anyone to "prove" that the Earth moves. As it is almost inevitable, this has launched a discussion over whether it is correct to state as an absolute fact that the Earth moves around the Sun, or whether motion is purely relative and the only difference between the Sun-centered and the Earth-centered model is pragmatical -calculating and making predictions is easier if one puts the Sun at the center. Popular understanding of the theory of relativity seems to include the second position, but the actual truth is a bit more subtle than that. I copy below the two comments I made in succession there explaining the issue as I see it, and hope to see comments by people more expert than I am approving them or correcting them.



I had once this discussion with a fellow physics student. It lasted about 5 hours, getting more and more intricate all the time. The issue of whether "all motion is really relative" in General Relativity is a lot more trickier than most popularizations make it seem.

My present position is this one: All coodinate systems are equivalent in the sense that one could describe all facts equally well adopting any of them, and the laws of Nature are the same in all of them (this is at the core of GR). In the case of the solar system, the coordinate system in which the Sun is at rest has the feature that the spacetime metric (which encodes the gravitational field) becomes assymptotically Minkowskian at large distances from the solar system (the Minkowski metric is the metric of flat spacetime, where there is no gravity present). By contrast, using the coordinate system in which the Earth is at rest the metric does not become Minkowskian at large distances, but includes constant terms related to the relative rotation of the Earth and Sun. The physical and absolute (not coordinate dependent) fact that the gravitational field of the Sun decreases with distance is therefore better "captured" using the first system. It's up to your philosophy of physics whether you view this as merely a "pragmatical convenience" of the first system or a license to say "the Earth really goes around the Sun". I prefer to say the latter.

Posted by: Alejandro February 9, 2006 04:20 PM

Another way of explaining it, perhaps clearer. If one goes at far distances where the physical gravitational field is too weak to be noticed, one can remain at rest relative to the Sun without any rockets turned on. The reference frame of the Sun becomes assymptotically inertial. The reference frame of the Earth does not; if you try to stay at rest relative to the Earth at large distances of the Solar System, one needs to turn on the rockets and make the spaceship go in circles (from the point of view of an external, inertial observer). I take this as meaning that the Earth "really" moves, while others will (bringing up the valid point that one can use either system to describe the situation) regard it as a convenient, pragmatically useful fact of the Sun-centered system.

Of course all this discussion neglects effects of other stars, the motion of the Sun around the galactic center, the relative motions of the galaxies and the expansion of the Universe. But the essential points remain valid.

Posted by: Alejandro February 9, 2006 04:32 PM


To make the second comment clearer: the important thing is not that to stay at rest relative to the Earth one has to go in circles, because this is a coordinate system dependent fact (in the Earth-centered system one is at rest). The important thing is that to stay at rest in the Earth-centered system one needs the rockets turned on, and in the other one not. This shows that relative to a distant, inertial observer it is the Earth that moves and not the Sun.

Book Review: Thomas Nagel, The Last Word

As promised, I deliver now the first book review on this blog. (Warning to physicists: philosophical discussions of dubious interest to most of them ahead)

The shortest summary of the impression Nagel's book causes to me, is that it strikes me as "quixotic". But I am saying this not meaning that it is idealistic and brave, but in a sense that intends to reflect the original character of Don Quixote: I picture Nagel as charging against windmills. He takes ordinary things and turns them into big deals, blowing out of proportion the philosophical problems they pose. Many of the things he says in the book are true; it's the seriousness and deepness he reads into these things being true what I disagree with.

The main argument of the book can be easily summarized: Reason is universal and fundamental. All positions that describe our rational capabilities (be it in logic, in science, or in ethics) as contingent upon our culture, society, upbringing, genes or evolutionary development, are ultimately inconsistent. The rational kinds of claims they try to subvert (that such-and such method of reasoning is valid, that this-or-that is the way the world is, that a given action is right or wrong) are basic to our thinking; there is no way a psychological, sociological or biological explanation of them can trump over them.

Insofar as his target are the species of subjectivism and relativism so popular in the humanities, Nagel has an easy task, although one that is perhaps beneath a philosopher as well-known and learned as him. His basic argument is that if someone makes for example a scientific claim p, and someone else says for example "but p is just what you believe because of your culture", this is also a claim to be evaluated rationally, just as we evaluate p itself. There is no way of judging reason from the exterior; all our thought is conducted within it. This is an argument and a conclusion with which I basically agree.

The problem is with how Nagel interprets this result. He "inflates" it as establishing a Platonic-Cartesian kind of picture, in which mind has the capacity of grasping reality through reason, and this capacity cannot be accounted for in scientific/naturalistic terms (as the result of evolution for example). Nagel thinks that any naturalistic account of reason must fall guilty of "standing outside it" and calling into question its absoluteness, by transforming it into a contingent feature of an animal species evolved by chance. And he thinks his earlier argument precludes this possibility, and thus dismisses naturalism together with subjectivism. (The fact that most English-speaking philosophers are naturalists and not subjectivists should have warned him that this step is not so easy). So what positive account does he offer of reason? In the last chapter, the most interesting and less predictable, the argument takes an unexpected turn: he admits that the only major option left is a religious or quasi-religious worldview, and confesses that he does not accepts it pehaps for a possible prejudice against it -he says he does not want God to exist! Understandably, religious reviewers (see here and here and here) have shown glee at this pronouncement -they can say (or well, they are too polite to say it, but they surely think) look, a major atheist philosopher admits that reason leads him to religion, and that only his irrational prejudices prevent him from accepting the conclusion!

What leads Nagel in the wrong direction, I think, is that he thinks of our judgments as forming a hierarchy, with things like modus ponens or "2 + 2 = 4" at the top and particular claims in sciences like biology or sociology much lower in the scale. Given this picture, to give an account of "Reason" (which sits at the top) from naturalistic premises is inevitably to degrade it, and a Platonic metaphysics must follow. If one replaces this picture with the Quinean one of a web of beliefs, some of which are more central than others but none of which is ultimately immune to revision, the perplexities mostly disappear. Principles of logic and mathematics are central to our reasoning in fact; a naturalistic account of how we came to believe them (perhaps because they are ways of thought that work in practice and have survival value) can be integrated with the principles themselves in a consistent picture, strengthening them despite having been reached to partially by use of them. Nagel assumes the question is "why is reason justified?", and as neither evolution nor anything else which is contingent can justify it, the answer must be metaphysical (or if there is no answer at all, even worse: Reason with capital R is a fundamental feature of the world). But reason needs no other justification than its lying at the central and most stable position of our web of belief, which does not give it an absolutely privileged status and still permits to give a naturalistic explanation of how it came to be there.

Coherentist, holistic thought of this kind seems to be anathema to Nagel, but he never argues against it. For example, he says that proposals for replacing classical logic with other logic, quantum logic for example, can be answered simply by use of classical logic (by whose standards, obviously, the other logics lead to contradiction). This does not acknowledge the possibility that surprising empirical discoveries may force us into developing new ways of thought to cope with them, which may be absurd and inconsistent by previous standards (just think of quantum mechanics!) He just says that when we discover that something previously thought contradictory is possible and even true, we do it by using higher logical principles which remain unchallenged -again the hierachical picture. This is in my opinion not a good description of scientific revolutions, in which what happens is more like the substitution of a way of thinking about the world for a radically new one when the old one becomes pragmatically inadecuate.

In summary, I found this book a bit disappointing after reading other works of Nagel like Mortal Questions and The View from Nowhere. The essays in the first one contain many interesting discussions on a variety of subjects little discussed by other analytical philosophers, and the second one is a deep exploration of most of the central questions of philosophy; though I disagree with many of the conclusions, they are definitely worth-reading books. This one contains a valid but not very necessary refutation of some trendy postmodernist discourses (after all, they refute themselves, don't they?), plus the attempt to interpret this refutation as meaning the soundness of old-fashioned metaphysics -a misguided attempt and one that accepts the basic mistake of the postmodernists, that the only possible options are "Absolute Reason" or "All is Text", Plato or Derrida. Confronted with this option, most non-religious contemporary thinkers would go for Derrida. Fortunately it is not necessary.


PS: there is a good review by Simon Blackburn here.

Study guide for LQG

If you are interested in studying Loop Quantum Gravity, Christine Dantas has posted a list of must readings, including prerequisites, standard books, primers, introductory reviews, and online courses.

Two updates on previous posts

It seems the five times stupid George Deutsch had to resign his post on the NASA. With all the uproar created by his comments on the Big Bang "theory", the fact emerged that he had lied in his résumé: he had not actually graduated from the college he had claimed he had! This was originally discovered by this blogger. So, who said blogs were useless?

On a different subject, everyone's favourite science blogger PZ Myers is now a God, and is fighting neck-to-neck with Cthulhu and the Flying Spaghetti Monster.

Monday Quantum Gravity Group Meeting

Today my research group had its first meeting on a series of them we are going to have every Monday. The idea is that each of us (students and supervisors) will bring up in turn some aspects of his/her work or other interesting stuff to discuss. Expect me to blog about some of these meetings when they turn out to be interesting.

Richard Johnson kicked off today giving a short talk and starting a nice discussion on group quotients and how they relate to twistor space, among other things. Afterwards he wanted me to write this post starting with "Magnificent and good-looking Richard Johnson gave today the best talk I ever heard..." but I didn't comply. However, you can judge for yourself on the good-looking claim by going here.

Recommended paper of the day

Generalizing Quantum Mechanics for Quantum Spacetime, James B. Hartle

Not overly technical, and full of fascinating ideas and speculation. The table on page 7 is a neat summary of the relation between conceptions of spacetime and corresponding versions of quantum theory. Section 10 is a stunningly brief argument that from the "no boundary wave function of the universe" proposal of Hartle and Hawking it follows that spacetime must have signature (- + + +) instead of (- - + +) or (+ + + +). For non-physicist readers, this means that it explains why (assuming from start the world is 4 dimensional) there is one time dimension and 3 space dimensions instead of 2 and 2, or 0 and 4. Of course, the argument is based on the Hartle-Hawking proposal, which is not generally accepted and part of a speculative research program in quantum gravity. Still, interesting stuff!

On the Manifold Stupidity of Mr. George Deutsch

If you read some of the blogs on my sidebar, such as Cosmic Variance, Pharyngula or Bad Astronomy Blog, you will already know by now of the most recent attack on science by the Bush Administration, which is at least an order of magnitude more egregious than previous ones. George Deutsch, who has been given the position of NASA public relations officer at the young age of 24 and after an experience record large on pro-Republican propaganda and short on science, issued a memo to a Web designer hired by the NASA saying that the word "theory" should be added before every mention of the Big Bang. Now of course the Big Bang theory is a theory, so there should not be cause for quarreling there, except for the reasons given for the recommendation:

'The Big Bang is "not proven fact; it is opinion," Mr. Deutsch wrote, adding, "It is not NASA's place, nor should it be to make a declaration such as this about the existence of the universe that discounts intelligent design by a creator." '

There are so many stupid things in this couple of sentences that I don't know where to start. Let's try to give them in order:

1) "Theory" in science does not mean "opinion"; in fact they are almost opposites. A theory is a wide-ranging system of propositions that explains some features of the world, making testable predictions. Theories that are accepted by the scientific community are so because they have a large body of evidence supporting them and no serious competing theory for explaining the same evidence. A theory can be also a fact, and Big Bang is both (as well as evolution, relativity, and even the non-flatness of the Earth). Scientists have been saying this for decades to creationists that tirelessly parrot "Evolution is just a theory!", so ignoring this marks Mr. Deutsch as a first-class ignoramus already.

2) In science (outside of mathematics and logic) there are no "proven facts". There are theories well-supported by the evidence, and if the evidence is huge and there is no competitor theory, we are justified in considering the theory true and equating it with a fact. Big Bang, just as non-flatness of the Earth, satisfies this.

3) The Big Bang theory asserts that the Universe was much hotter and dense in the past, and it expanded and cooled to its present state. It does not conflict at all with the existence of a creator. In fact the ironic thing is that it is more consistent with a creator than what was its main competitor during decades, the "Steady State theory", in which the universe is eternal and the same at all times. This theory has been refuted, and if one extrapolates the conventional Big Bang theory to its logical conclusion one arrives at a single instant of creation of the universe, in which it was infinitely hot and dense (a singularity). Most cosmologists believe that once quantum effects are properly taken into account it will be shown that there is no singularity, and most speculative models to extend the theory "beyond the singularity" do not contain a moment of creation but some form of an infinite past. But in absence of a reliable theory of quantum gravity, the conventional theory which ignores quantum effects does include a "moment of creation", and so is very compatible with (although of course does not entail) the existence of a creator.

4) So, the only way the Big Bang theory can be in any conflict with religion is if the religion is a literalist reading of Scripture in which the universe was created in six days a few thousand years ago. That someone with this kind of belief (which flatly contradicts the evidence amassed by history, archeology, geology, paleontology, biology, astrophysics, astronomy and cosmology, among other sciences) could be appointed to any position within a scientific organization such as the NASA leaves one speechless.

5) The "Intelligent Design" movement is officially based on the proposition that mechanistic evolution is insufficient for bringing about the appearance of complex biological forms, and that a "Designer" needs to be posited to account for this. Of course they are wrong, but that is not the issue today. The issue is that ID per se has no quarrel with the Big Bang theory. ID is supposed not to be Biblical literalism, but a "scientific" theory based on "biological evidence". Of course the great mass of ID supporters defend it because they interpret it as revindicating the Bible against Darwin, and very likely that is the intention of the leaders of the movement as well; but officially ID proclaims to be independent of any kind of Creationism. So given that as we saw Big Bang denial can only mean biblical literalism, by using the words "intelligent design" as the alternative Deutsch has shown that he does not understand even what ID tries to appear to be, and that he is helping to give the show away.


The scientific blogosphere has been unanimous in its condemnation of Deutsch's words (you go to the linked post at Cosmic Variance to find links to more comments). I am intrigued to see if Lubos Motl, one of the few science bloggers who is an outspoken Bush supporter, will have any comments on the subject.


UPDATE: Here is comprehensive list of blogs commenting on this subject.

Saturday Book Shopping

Saturday is the day in the week I usually dedicate to the boring but necessary tasks of washing my clothes and doing groceries shopping. Today was no exception, but before getting to the supermarket I got into the few secondhand bookstores there are in Beeston (the suburb of Nottingham where I live) and made the following acquisitions:

- Gilbert Ryle, The Concept of Mind (£ 3.49)
- Richard Webster, Why Freud was Wrong (£ 2.99)
- J.R.R Tolkien, Unfinished Tales (£ 3.99)

The corresponding book reviews may take some time to come, due to the large list of reading material that I have at the moment.

You may be pardoned by thinking, seeing the prices of the books, that the bookshop where I bought them always ends the prices of books in "-nine pence". And you would be right, only that it is not that bookshop but all of them, and not only books but all articles. In Britain almost all prices end in "-nine pence". It is difficult to understand why -does the obvious psycological trick of giving non-thinking buyers the visual impression that the article is cheaper, really compensate for the need to have and pass around millions of those useless 1 penny coins? And what do the British consumers do with all those coins they get in change? I put them in a little box and about once per year (when it is full) take it to the bank and exchange it for about £5. Is that the normal practice, or do people actually use the coins?

Rate the gods!

A place where you can rate the many gods of mankind and see how your grade compares to the average of other people. All the usual suspects are there, from Jehovah and Jesus to Vishnu and Buddha, but they face tough competition from modern challengers such as Aslan, Brian and Scientology. For the moment it seems as if His Holy Noodleness the Flying Spaghetti Monster is beating all of them. Ramen!

You can also send submissions for addings to the list. I suggested Cthulhu as a worthy competitor for the FSM -can you think of any others?

Brayton on gender apartheid

Ed Brayton links to this post that comments on the situation of women in Saudi Arabia and wonders why it has much less repercusion in the West than apartheid in South Africa had in its day. Brayton's comment deserves to be quoted:

"The other explanation, I think, lies in cultural and moral relativism. Again, because we viewed the South African oppressors and their victims as being from different cultures (and they were), it seemed uniquely bad to us. But the oppression in Saudi Arabia happens within a single and virtually monolithic culture and ethnic group and we have a kneejerk tendency to fall into the sort of cultural relativism that says, "Who are we to judge other cultures when we are so bad ourselves? Their culture has been this way for centuries and it works for them, so who are we to impose our supposedly enlightened Western values on them?"
Count me as one who thinks this sort of relativism is utter nonsense. If it is wrong to oppress another person and take away their dignity and their self-determination - and I firmly believe that it is, and you will never convince me otherwise - then it is always wrong, regardless of where it takes place, how long it has been taking place, or the ethnic or religious identity of either the tyrant or the victim."

There is nothing I enjoy more than a slap in the face of this kind of relativism. Well said, Ed.

Social Constructivism

I had thought my review of Nagel's book would be my first substantive philosophical post, but today I saw a pretty little essay on Social Constructivism and couldn't resist posting my thoughts on it. Which proves I am already hopelessly addicted to blogging.

I have struggled for a long time to understand what social constructivism is about and whether or not it poses a challange to the objectivity of science, passing from the dismissive rebuttals of Sokal & Bricmont to Putnam's delicate balancing on philosophical tightropes and the greatly enjoyable and deceptively crystal-clear looking essays of Rorty. What I found today is the sharpest attempt I have ever seen at defining what it means to say, for example, that "the solar system is a social construction". And even it slides into ambiguity at the end. So I am beginning to think that social constructivism is an idea that cannot be pin-pointed, that will forever tantalizingly elude us.

If you read the post I have linked to, you will notice (as a commentator there does at well) that while the first two points of the definition are clear, with the last one we get in trouble. Points 1 and 2 say that (1) there would be no concepts and "categorizations" in absense of human beings, something only a Platonist would deny, and (2) different conceptual descriptions of the same reality can be equally valid, if they are used for different purposes, something true as the practical utility of a geocentrical astronomical scheme for navigation shows. None of these claims, properly worded, should bring discomfort to a "scientific realist" that believes that the world described by science is "really there" and is not created by the description. As PTJ says, believing that the description creates the world is not social constructivism but idealism.

But in the third point we start seeing trouble, because it seems we must commit ourselves to say something realistic or something idealistic -and the resolution to avoid both begins to look a lot like fence-sitting. Quoting:

"3) Finally, social practices of meaning-making are complicit in the production of the objects that they purport to study. This is where a claim about social construction looks the most like an idealist claim, so I want to be very careful here: "the solar system is socially constructed" means that it is impossible to refer to the solar system except through the concept of 'the solar system.' We never approach the world as blank slates, and we never get unmediated access to "reality." As such, if we or other meaning-making creatures were to apprehend things differently, there would be no solar system, since 'solar system' only has meaning within a whole set of meaningful social practices."

There is a way to read the last sentence that is clearly idealistic (the solar system, Sun, planets and all, wouldn't exist without our meaning-making activities) but that is clearly not the reading intended. Another reading is that without the concept of "solar system" the solar system wouldn't be "the solar system" because nobody would have conceptualized the combination of Sun, planets, asteroids, etc. into one entity. But it is likely that this is not what is intended either, because any realist can accept that. And it is very difficult to determine a third possible meaning between these two extremes, the absurd and the commonplace.

There is one mistake the realist must avoid in this game (though I realize now that what I wrote above is very close to making it; it is a very tempting mistake!): saying something on the lines of "OK, without the concept of solar system the solar system wouldn't exist, but the planets and other stuff would." Because now the "social constructivist" (and we haven't yet understood what her position is exactly!) has the offensive; she can ask: "And what if we hadn't developed the concept of 'planet'?" The realist will retreat perhaps to atoms and their combinations being "really existent", but the SC can press on until the realist is left with nothing else than "Reality" or "Facts" or "The Thing-In-Itself" as the only mind-independent thing, with atoms, planets and galaxies being only mind-dependent, as they depend on socially created concepts. And now the SC plays her final card: "But isn't your "reality" or "thing in itslef" just another human concept, just like "planet" or "atom"? And even if it is not, why would you cling to something that is unexpressable and unknowable"? Checkmate!

To escape this disastrous dialectical trap (represented by Andreas in the comment thread) we must avoid at all costs conceding to SC that "the solar system wouldn't exist without our concept of it". We can and must agree that many different conceptualizations of the world are possible, and at the same time insist that once we have conceptualized in a certain way, the things we say with those concepts can be true. True, period; true about a mind-independent reality. Concepts are the tools used to think and talk and express truths about the world, and the truths expressed with them can be true unconditioned to anything social, except in the trivial sense that the concepts themselves are socially created.

Emergent spacetime

Via Not Even Wrong, an arxiv article discussing (from a string-theoretical point of view) the possibility that space and time are emergent and not fundamental features of the world:

http://www.arxiv.org/abs/hep-th/0601234


UPDATE

After rereading the article with a little more care, I was struck by the little space dedicated to the possiblity of an emergent time (as opposed to emergent space) and by the perplexities this possibility seems to raise according to the author. That is because from the LQG side of the quantum gravity research, Carlo Rovelli has argued for a long time that time is not a fundamental feature of the world but an emergent one, and for him this has a very precise meaning. A slogan repeated a lot in his book (available online in a draft version) says "Dynamics is not about evolution of observables in time, but about the correlations between different observables". His idea is that the objective of mechanics (classical or quantum) is prediction of correlations between observables, and that only in special cases there is an observable "t", measured by a "clock", that is unaffected by the other variables. Rovelli has put forward an hypothesis about how the appearance of "time" as a special variable emerges from an underlying timeless world, the Thermal Time Hypothesis, in which I am interested because it has surprising connections with my present work (through this paper), a story I will explain some other day.

I don't know if Rovelli's opinions on the subject are dominant in the LQG community, but I find it interesting that apparently from the point of view of string theory space seems to emergent from other more fundamental entities but the emergent quality of time is poorly understood, whereas from the LQG point of view space is built from irreducible "atoms" of space (in spin network models) but time seems to be understood as emergent, at least by Rovelli. Looks as if more dialogue between the two communities is needed...