Year: 2010

I am Shiva, destroyer of fireplaces

Posted by – August 20, 2010

The fireplace started smoking out of its right side. There’s a brick wall that’s supposed to meet the mantel and keep the smoke in, but it has started leaning in, letting the smoke out. In fact all the brick lining, especially in the back, is beyond its useful lifespan and failing.

Note leaning right wall

Note leaning right wall


More…

A phrase repeated with delight

Posted by – August 12, 2010

Walk where we will, we cannot help hearing from every side a phrase repeated with delight, and received with laughter, by men with hard hands and dirty faces, by saucy butcher-lads and errand-boys, by loose women, by hackney-coachmen, cabriolet-drivers, and idle fellows who loiter at the corners of streets. It seems applicable to every circumstance, and is the universal answer to every question; in short, it is the favourite slang phrase of the day – a phrase that, while its brief season of popularity lasts, throws a dash of fun and frolicsomeness over the existence of squalid poverty and ill-requited labour, and gives them reason to laugh as well as their more fortunate fellows in a higher stage of society.

Many years ago the favourite phrase was Quoz. When vulgar wit wished to mark its incredulity, and raise a laugh at the same time, there was no resource so sure as this popular piece of slang. When a man was asked a favour which he did not choose to grant, he marked his sense of the suitor’s unparalleled presumption by exclaiming Quoz! When a mischevous urchin wished to annoy a passanger, and create mirth for his comrades, he looked him in the face, and cried out Quoz! and the exclamation never failed in its object. When a disputant was desirous of throwing a doubt upon the veracity of his opponent, and getting summarily rid of an argument which he could not overturn, he uttered the word Quoz, with a contemptuous curl of his lip and an impatient shrug of his shoulders.

(Charles MacKay, Extraordinary Popular Delusions & the Madness of Crowds, 1841)

Today in harsh Chinese pragmatism

Posted by – July 24, 2010

(from Making out in Chinese, via reddit)

Today in postmodernism

Posted by – July 19, 2010

For what it’s worth

Posted by – July 16, 2010

If you’d asked me five minutes ago about the respective values of Apple and Microsoft, I’d have guessed that Microsoft has at least twice the value of Apple. For the benefit of any readers who, like me, have missed the news: Apple is currently worth more than Microsoft. Huh! Apple is worth $230 billion, Microsoft $223 billion.

Microsoft has about three times as many employees as Apple, about a quarter more revenue and about three quarters more profit. Apple’s P/E is about double Microsoft’s, meaning that investors are willing to pay twice as much for Apple’s profit than for Microsoft’s profit. But presumably Apple is the future. Google, by the way, is only worth $156 billion, another number I’d have absolutely no way of coming up with. Nokia is a measly $32 billion.

I wonder what other wildly unexpected valuations there are out there. I’m thankful that my job isn’t to buy and sell international technology companies.

Porn for girls

Posted by – July 12, 2010

I recently watched about 50 hours of Gilmore Girls inside a couple of months, so you may want to take a moment to mentally readjust how seriously you take anything I say.

Now, unless you’re some kind of retarded sexist, you’ll know that women watch pornography just as much as men do – at least for a sufficiently broad definition of porn. The purpose of porn is, ultimately, fantasy depiction. For men, that means

  • having sex with beautiful people
  • getting status (some say: to get sex with more beautiful people)

When men watch Led Zeppelin concerts on dvd, part of what they’re getting is the fantasy of having an incomprehensible amount of status, in the eyes of men and women alike. Of course, men fantasize about sex a lot more than about being in Led Zeppelin – just like most of their meals are stomach-filler, not culinary art.

Women are way more complicated than this, so they need eg. Gilmore Girls. Why did I choose Gilmore Girls? Why not Twilight (the fantasy of being “different” and passionately fought over by impossibly handsome, ancient, powerful and magical non-human creatures without doing much and for no apparent reason) or Sex and the City (live in Manhattan, spend scads of money on fashion while being a useless ditz, enjoy a neverending variety of penis without ever ending up on the trash-heap for being old or slutty)? Gilmore Girls is much more nuanced and wholesome than that – it offers an entire life plan, simultaneously depicting three generations: one on the cusp of adulthood, one in maturity and one in old age. And yet, incredibly, for all its detail and multidimensionality, it is pure fantasy, to a sometimes absurd degree.

At the centre of GG is Lorelai Gilmore, a thirty-something manager of an inn who always has something snappy to say, and her highschool-aged daughter Rory (she goes on to study at her choice of any ivy-league college in subsequent seasons). Their (genuinely) clever-funny banter is a big part of the show. Lorelai’s parents are super-wealthy WASP types, allowing the series to spend a lot of time in their stately mansion and in the higher reaches of society, where Lorelai is courted by powerful, handsome men with fast cars.

But wouldn’t it be boring to have a modern female lead just ride on her family’s money? It sure would, which is why Lorelai ran away from home as a teenager when she got pregnant and never attended college. Pretty cool! Having broken contact with her parents, she raised her daughter as a single mother without getting a single dime (this is reiterated many times during the series) from her parents or, apparently, from the father, who is an elite badboy, also from the upper classes. Normally things end up badly for single mothers with no support, but as I say, Lorelai becomes a manager and a houseowner and her daughter is set for the Ivies (and I meant what I said earlier, she gets acceptance letters from everywhere, all the way up to Harvard). Thusly Lorelai is able to combine cool pop-culture infused disdain and ridicule for the trappings of wealth and high society, actually partake of and enjoy that society and be a hip, non-stuffy single mom whose daughter is her best friend all at the same time.

Watching GG and enjoying its large, complicated cast and intermingling array of plots and then realising that all the contortions are necessary just to maintain this otherwise contradictory fantasy is like looking into a kaleidoscope and suddenly realising it’s a complete engineering plan for a flying ocean-liner.

But that’s not all! I won’t go through every element of perfection (the other best friend is fat but always cheerful; there’s no scary crime or resentful poor people; Lorelai has a gruff, handsome admirer who fixes any mechanical problems but sex takes about five years to come into the picture while she considers her options) but I must mention one because it’s such a delightfully direct, visceral fantasy. Lorelai and her daughter are slim and beautiful, and notorious for constantly eating vast amounts of fast food, ice cream, snacks, fine dinners at the WASP parents’ mansion, everything and anything. This is not just a minor in-joke, this is pointed to in EVERY EPISODE. When the two slim girls decide to order food in, as they do most nights, they might get food from four different restaurants just for the variety. Other characters comment continually on the vast amounts of food they’re putting away (no, the series doesn’t conclude with the fat best friend murdering Lorelai). This becomes a part of their personalities – they’re not some boring losers worrying about calories or fat on their midsection; let’s party, get tubs of Ben & Jerry’s and watch movie classics all night! What do you mean, are they going to get to work and school on time in the morning? This is girl time, and anyway, one of their fun sides is drinking coffee all the time because they’re so HYPER and FUNNY and RANDOM!

Okay, I’m starting to give the impression that I’m somewhat overanimated about this whole thing. Mostly it amuses me, and it’s a fun series anyway, but I guess getting too close to other people’s fantasies can end up being rather distasteful. It’s like how women are always rather intrigued about the idea of men’s sexual fantasies, but might become a bit resentful after watching a tv series depicting them.

Which Wohltemperirte

Posted by – July 12, 2010

About halfway through GEB I decided that I should give this Bach stuff a day in court. I’ve long liked what I’ve known, but known relatively little. Fairly arbitrarily I had pre-decided to start with The Well-Tempered Clavier, which comprises two sets of 24 preludes and fugues (a pair of 24 pairs!). But covetousness always brings more pain: now you have to decide which recording to get. Wanting only a complete set and drawing on the expertise of some friends and the Internet, I came up with this shortlist (all played on the piano, due to no special prejudice):

  1. Edwin Fischer 1933-1936
    Fischer is an extremely big, maybe the biggest, name in the appropriate Germanic tradition. I think this is the most famous of all the recordings, and something of a default. It has authority, but I worried that it’s too old – perhaps by now the consensus on Bach recordings is more settled. Also, I suspect that the standard of top musicianship has been steadily rising.
  2. Glenn Gould 1963-1965 for Book 1, 1968, 1970 and 1971 for Book 2
    Gould is, of course, the big eccentric celebrity, by far the most intriguing as a person and, according to many, as a musician. He certainly cared as much about Bach as anyone, going so far as to revive his music in the Soviet Union on then-unusual tours there, and giving his all to make perfect recordings. But perfect by his own standards: notorious for both a large number of takes and singing along as he played, the recordings have passionate haters as well as lovers. Ultimately I deemed Gould insufficiently neutral, and neutrality is what my heart yearns for.
  3. Angela Hewitt 1997-1999
    Hewitt is probably by consensus the greatest living Bach performer. This recording is currently the most popular choice on eg. Amazon, and according to Wikipedia “the set has often been recommended as a ‘reference’ version”. I can’t find any complaints about it, and Hewitt is certainly the real deal: in 2007-2008 she undertook a six-continent world tour performing the entire Well-Tempered Clavier each concert.
  4. Angela Hewitt 2008
    The recordings I’ve mentioned so far took a long time to complete, but after the aforementioned world tour, Hewitt decided to re-record the whole thing in a week and a day in the Jesus-Christus-Kirche in Berlin. She said that after playing the work so many times on tour and becoming more and more acquainted with a new custom-build piano, she felt that she had a new, refined vision for the recording. Some people who have heard it prefer it, saying that it has a lighter, clearer tone. But I decided for now that I don’t want new, refined visions, thank you very much (as intriguing as it sounds). For neutrality!

I went with choice 3, fairly confident that I’d be completely unable to tell the difference between any of them.

Mathematico-philosophical opinions in Concrete Mathematics, Probability Theory and Principles of Statistics

Posted by – July 4, 2010

These books I recently bought together are curiously interconnected, to the degree that their introductions and various asides seem to be having a conversation (I’ve been popping in and out of each one, finishing none of them). The introduction to Concrete Mathematics sets the stage rather well:

It was a dark and stormy decade when Concrete Mathematics was born. Long-held values were constantly being questioned during those turbulent years; college campuses were hotbeds of controversy. The college curriculum itself was challenged, and mathematics did not escape scrutiny. John Hammersley had just written a thought-provoking article “On the enfeeblement of mathematical skills by ‘Modern Mathematics’ and by similar soft intellectual trash in schools and universities”; other worried mathematicians even asked, “Can mathematics be saved?” One of the present authors had embarked on a series of books called The Art of Computer Programming, and in writing the first volume he had found that there were mathematical tools missing from his repertoire; the mathematics he needed for a thorough, well-grounded understanding of computer programs was quite different from what he’d learned as a mathematics major in college. So he introduced a new course, teaching what he wished somebody had taught him.

The course title “Concrete Mathematics” was originally intended as an antidote to “Abstract Mathematics”, since concrete classical results were rapidly being swept out of the modern mathematical curriculum by a new wave of abstract ideas popularily called the “New Math.” Abstract mathematics is a wonderful subject, and there’s nothing wrong with it: It’s beautiful, general, and useful. But its adherents had become deluded that the rest of mathematics was inferior and no longer worthy of attention. […]

But what exactly is Concrete Mathematics? It is a blend of CONtinuous and disCRETE mathematics. More concretely, it is the controlled manipulation of mathematical formulas, using a collection of techniques for solving problems. Once you, the reader, have learned the material in this book, all you will need is a cool head, a large sheet of paper, and fairly decent handwriting in order to evaluate horrendous-looking sums, to solve complex recurrence relations, and to discover subtle patterns in data. You will be so fluent in algebraic techniques that you will often find it easier to obtain exact results than to settle for approximate answers that are valid only in a limiting sense.

Some deal! By the way, I believe the book more or less delivers on this promise, at the price of a ferocious amount of work and application on the part of the reader. There is an extremely large selection of problems, the solutions to all of which are given in an appendix (except the most difficult ones which were open questions in mathematics at the time of publication). I think anyone who worked through all of them, blood pouring from the forehead, would stand out with their sheer manipulative muscle.

The two works on probability are very much opposites in just such a hotbed of controversy: the correct mathematical formulation of the practical concepts of probability and confidence. Probability Theory is especially pugnacious, weighing in on this and numerous other matters. Its author, E. T. Jaynes, intended in it to bring together in a grand way a vision of Bayesian or inferential probability, but sadly died before the book was finished. It was edited into a publishable form by Larry Bretthorst, according to whom many sections of the manuscript concluded with “MUCH MORE COMING.” Jaynes’ death led not only to an incompleteness of the work, but also to a certain harshness in the various off-topic asides which a living author might have been persuaded to tone down. On the topic of mathematical courtesy:

Nowadays, if you introduce a variable x without repeating the incantation that it is in some set or ‘space’ X, you are accused of dealing with an undefined problem. If you differentiate a function f(x) without first having stated that it is differentiable, you are accused of lack of rigor. If you note that your function f(x) has some special property natural to the application, you are accused of lack of generality. In other words, every statement you make will receive the discourteous interpretation.

[…]


Emancipation Proclamation
[A statement guaranteeing the implications of the previous paragraph]

We could convert many 19th century mathematical works to 20th century standards by making a rubber stamp containing this Proclamation, with perhaps another sentence using the terms ‘sigma-algebra, Borel field, Radon-Nikodym derivative’, and stamping it on the first page.

Modern writers could shorten their works substantially, with improved readability and no decrease in content, by including such a Proclamation in the copyright message, and writing thereafter in 19th century style.

Other contrarian topics include “The Hausdorff sphere paradox and mathematical diseases”, “Counting infinite sets?”, “Bogus nondifferentiable functions” and “What is a legitimate mathematical function?” A less reverent editor would definitely have omitted these, but although they don’t really add anything to the subject matter of the book, they are a lot of fun and I don’t mind hearing Jaynes’ opinion on them. I want to quote just one more of these tangents, on the subject of probability in quantum physics:

Those who cling to a belief in the existence of ‘physical probabilities’ may react to the above arguments by pointing to quantum theory, in which physical probabilities appear to express the most fundamental laws of physics. Therefore let us explain why this is another case of circular reasoning. We need to understand that present quantum theory uses entirely different standards of logic than does the rest of science.

In biology or medicine, if we note that an effect E (for example, muscle contraction, phototropism, digestion of protein) does not occur unless a condition C (nerve impulse, light, pepsin) is present, it seems natural to infer that C is a necessary causative agent for E. Most of what is known in all fields of science has resulted from following up this kind of reasoning. But suppose that condition C does not always lead to effect E; what further inferences should a scientist draw? At this point, the reasoning formats of biology and quantum theory diverge sharply.

In the biological sciences, one takes it for granted that in addition to C there must be some other causative factor F, not yet identified. One searches for it, tracking down the assumed cause by a process of elimination of possibilities that is sometimes extremely tedious. But persistence pays off; over and over again, medically important and intellectually impressive success has been achieved, the conjectured unknown causative factor being finally identified as a definite chemical compound. […]

In quantum theory, one does not reason in this way. Consider, for example, the photo-electric effect (we shine light on a metal surface and find that electrons are ejected from it). The experimental fact is that the electrons do not appear unless light is present. So light must be a causative factor. But light does not always produce ejected electrons; even though the light from a unimode laser is present with absolutely steady amplitude, the electrons appear only at particular times that are not determined by any known parameters of the light. Why then do we not draw the obvious inference, that in addition to the light there must be a second causative factor, still unidentified, and the physicist’s job is to search for it?

In short, Probability Theory, in addition to being a strong and demanding exposition of Bayesian probability, is a font of unconventional, direct thinking. Principles of Statistics stands in contrast, being an absolutely straightforward textbook on the time-tested methods of frequentist probability. Despite this, its introduction happens to present an opinion on the philosophy of probability, dismissing efforts such as Jaynes’ work:

[The introduction first introduces frequentist probability and then various approaches to inductive probability, all stemming from the “principle of indifference” and finding problems in each one]

It has been reluctantly concluded by most statisticians that inductive probability cannot in general be measured and, therefore, cannot be used in the mathematical theory of statistics. This conclusion is not, perhaps, very surprising since there seems to be no reason why rational degrees of belief should be measurable any more than, say, degrees of beauty. Some paintings are very beautiful, some are quite beautiful and some are ugly; but it would be absurd to try to construct a numerical scale of beauty on which the Mona Lisa had a beauty-value of 0.96! Similarily some propositions are highly probable, some are quite probable and some are improbable; but it does not seem possible to construct a numerical scale of such (inductive) probabilities.

Here’s Probability Theory on the same subject:

For many years, there has been controversy over ‘frequentist’ versus ‘Bayesian’ methods of inference, in which the writer has been an outspoken partisan on the Bayesian side. […] In these old works there was a strong tendency, on both sides, to argue on the level of philosophy or ideology. We can now hold ourselves somewhat aloof from this, because, thanks to recent work, there is no longer any need to appeal to such arguments. We are now in possession of proven theorems and masses of worked-out numerical examples. As a result, the superiority of Bayesian methods is now a thoroughly demonstrated fact in a hundred different areas.

If books could fight… Of course, as far as I’m aware, statistical/probabilistic methods as taught at universities are, at least on a low level, still purely frequentist.

The combination of these very practical, mathematically demanding, hard-nosed but nevertheless somehow philosophical, personal and opinionated books is very intriguing – I hope I’m able to put enough work into them to extract for my benefit at least some of the immense work that has gone into them.

On gay marriage and unreasonable demands

Posted by – July 3, 2010

I’ve witnessed variations on the following dialogue more times than I can remember:

A: Gay marriage is a simple human rights issue. We can’t restrict a person’s rights just because they’re homosexual.
B: I agree that homosexuals should have the same rights as everyone else, and they do. Heterosexuals can’t have same-sex marriages either.

At this point A explodes with disbelieving fury, thinking that B is playing the fool. Surely B is disingenously twisting words! But after careful observation, I’ve come to the conclusion that B usually is sincere in his position. We have yet another case of communication breakdown… Let’s expand the dialogue (and the interlocutors’ capacity for mutual understanding):

A: The right to marry is society’s blessing on a loving and committed relationship, and homosexuals have as much a right to that as heterosexuals.
B: Maybe, maybe not – but even if they’re given the right, they still can’t have the kind of marriage heterosexuals have. It would make as much sense for them to demand the right to heterosexual sex between same-sex couples.
A: What do you mean? Are you suggesting that same-sex love is so inherently different from different-sex love that the concept of commitment doesn’t translate?
B: Well… yes.

At this point A again explodes with disbelieving fury, thinking that B is bigoted and prejudiced. We need to expand more – let’s take A and B into the past, to the murky, gender-warring 70’s-80’s.

A: The way men take advantage of women is an outrage comparable to slavery. Women are powerless and unappreciated in their own homes, in the workplace and society as a whole – and why? Pure sexism and prejudice!
B: Well, women just aren’t cut out for some jobs. Men and women are different, you know.
A: Different but equal! What job can’t a woman do?
B: Oh, I’m all for treating women right, but women aren’t going to do the dirty, dangerous physical jobs or be good at leading men. It’s biological.
A: What are you, a caveman? I just read an article about woman miners in the Guardian! Margaret Thatcher is Prime Minister!
B: Sure, there are always exceptions.
A: Ugh, you always say that.

A’s position is that women are essentially equivalent to men, and even if they aren’t, to claim otherwise is to restrict the opportunities of those woman who are willing and able to do “men’s work”. B’s position is that stratification by sex is to be expected because men and women are so different. Some men are closer to the average woman and some women closer to the average man, but to demand women in general to be regarded as men is unreasonable, because people are used to their prejudices about men and women and find them useful. Back to gay marriage:

B: Anyway, same-sex couples already get civil unions or whatever. As far as I’m concerned, anyone can make any partnership contract they like, but I’m going to keep calling only different-sex marriages marriages.
A: What exactly do you find so threatening about the idea of gays marrying? Do you think it’s somehow a bad thing when a gay couple forms a stable family unit, like married couples?
B: Well, that doesn’t usually happen. Gay couples don’t have children and don’t have that incentive to stay together. The dynamics are completely different. Of course, it doesn’t harm anyone if they don’t stay together, and that’s exactly why it’s not like a marriage.
A: Some gay couples do have children, or would if it were easier. Do you just not care about them? And anyway, how is it your place to tell them what their relationships are like?
B: I’m just telling them what I consider marriage to be. And there’s always exceptions.
A: Ugh, you always say that.

Okay… so what do I think about all this? I actually rather sympathise with both viewpoints. Starting with the sexism issue, I think it’s foolish and destructive to equate a person with their sex and to be blind to the individual – but I, like everyone else, allow my first impression of a person to be coloured by their sex. To do otherwise would be to throw out useful information, and I don’t believe that can ever be a moral necessity.

Likewise, I don’t think the day will ever come when my abstract mental images of couples consisting respectively of two women, two men and a man and a woman are identical, and I don’t think the societal importance of those forms of partnership will be the same. Also, I absolutely believe that all three of these relationships are capable of any kind of commitment/meaning/crappiness or whatever else comes to mind when you think about couples. Whether all of those couples “deserve” the same word seems to me a strange question. Personally, I think they’re sufficiently different to justify different words, but if the gay people in my life get married and care about that word, I’ll use it about them. It’s kind of like the question of which word to use about black people – even if you don’t mean anything bad by using the word “nigger”, everyone else believes that you do.

So on balance: I support gay marriage on the grounds that I don’t want to offend people. As for the “social effects” of gay marriage, I have no idea, and I don’t know that it’s feasible or moral to legislate on such a basis – some of the complications of that question are explored rather well in this blog post by someone else.

Today I learned

Posted by – June 7, 2010

Guess what? For variables (a to z) ranging over the nonnegative integers, the set of positive values of this polynomial is the set of prime numbers:

(k+2) *
[1 – [wz+h+j-q]2 – [(gk+2g+k+1)(h+j)+h-z]2 – [2n+p+q+z-e]2 – [16(k+1)3(k+2)(n+1)2+1-f2]2
[e3(e+2)(a+1)2+1-o2]2 – [(a2-1)y2+1-x2]2 – [16r2y4(a2-1)+1-u2]2
[((a+u2(u2-a))2 -1)(n+4dy)2 + 1 – (x+cu)2]2 – [n+l+v-y]2 – [(a2-1)l2+1-m2]2
[ai+k+1-l-i]2 – [p+l(a-n-1)+b(2an+2a-n2-2n-2)-m]2 – [q+y(a-p-1)+s(2ap+2a-p2-2p-2)-x]2
[z+pl(a-p)+t(2ap-p2-1)-pm]2]