Philosophy – God of the Machine
Aug 012007

It is a cherished belief, in all Objectivist as well as certain fellow-traveling circles, that economic interventionism must collapse under its own weight. Here, for instance, is Ludwig von Mises, in Planned Chaos:

Many advocates of interventionism are bewildered when one tells them that in recommending interventionism they themselves are fostering antidemocratic and dictatorial tendencies and the establishment of totalitarian socialism. …

What these people fail to realize is that the various measures they suggest are not capable of bringing about the beneficial results aimed at. On the contrary they produce a state of affairs which from the point of view of their advocates is worse than the previous state which they were designed to alter. If the government, faced with this failure of its first intervention, is not prepared to undo its interference with the market and to return to a free economy, it must add to its first measure more and more regulations and restrictions. Proceeding step by step on this way it finally reaches a point in which all economic freedom of individuals has disappeared. Then socialism of the German pattern, the Zwangswirtschaft of the Nazis, emerges.

Mises has just asserted, on the previous page, that for interventionists “the main thing is not to improve the conditions of the masses, but to harm the entrepreneurs and capitalists.” If this is true, it puts his claim that interventionism produces “a state of affairs which from the point of view of [its] advocates is worse than the previous state” in doubt. But what really interests me is the slippery-slope argument that interventionism inherently leads to socialism.

The example Mises chooses to support this thesis is price controls. The government begins by controlling the price of milk. The supply of milk declines, as the marginal producers are driven out of business. This is not what the government wants at all; so it continues by controlling the prices of the factors of milk production. The logic repeats itself a few more times, until we arrive at socialism of the German pattern. Mises, being no mean economist, points out that the government could guarantee milk for poor children more effectively by buying it at the market price and giving it away or selling it at a loss. The populace pays for this in taxes, of course, and you might end up with a black market in milk, but it surely beats price controls. Yet this policy is interventionism, just as price controls are. Does socialism emerge in either case? Or do only particularly stupid forms of interventionism produce the slippery slope?

The Objectivists, as is their wont, go a good deal further. Only Objectivism itself can halt the long, slow slide of the mixed economy into slavery. The go-to guy for over-the-top Objectivist pronouncements is not Ayn Rand herself but her “intellectual heir,” Leonard Peikoff. His book The Ominous Parallels is notable as the only work of German historiography ever written by someone who cannot read German. It also contains this gem:

No one can predict the form or timing of the catastrophe that will befall this country if our direction is not changed. No one can know what concatenation of crises, in what progression of steps and across what interval of years, would finally break the nation’s spirit and system of government. No one can know whether such a breakdown would lead to an American dictatorship directly — or indirectly, after a civil war and/or foreign war and/or protracted Dark Ages of primitive roving gangs.

What one can know is only this much: the end result of the country’s present course is some kind of dictatorship; and the cultural-political signs for many years now have been pointing increasingly to one kind in particular. The signs have been pointing to an American form of Nazism. …

There is only one antidote to today’s trend: a new, pro-reason philosophy.

This new pro-reason philosophy, of course, would be Objectivism. Now I think we can agree that in the twenty-five years since this passage was written two things have not happened. Objectivism has not swept the country, and American-style Nazis have not taken over the government. (Anyone who thinks the Bush gang counts needs to acquaint himself with the real Nazis.)

We have had approximately steady-state interventionism in the United States for a long time. Federal spending has hovered around 20% of GDP since the Second World War — no matter who was President, no matter which party controlled Congress, no matter what. Naturally there has been a great deal of expensive tinkering. The airlines are regulated, then deregulated. Savings and loans are encouraged, through insurance, to invest in risky propositions and then, after they lose hundreds of billions, enjoined from doing so. Liberty advances, when the draft is eliminated; and retreats, when the state sponsors offshore torture and suspends habeas corpus for citizens who are classified as “enemy combatants.” On the one hand the Fairness Doctrine is scrapped. On the other Draconian regulations are imposed in quasi-public spaces like offices, stores, and restaurants. To call these changes marginal would be an exaggeration; to call them a lurch toward fascism would be absurd.

Peikoff hastens to say that neither he nor anyone else can predict “the form or timing” of the coming dictatorship. Mises, similarly, disassociates himself from historical determinism, saying that the socialist tide can be stemmed with “common sense and moral courage,” which does not appear to be in any greater supply now than it was then. Their belief, in other words, commits them to nothing whatever. Barring an unlikely sudden upsurge of Objectivism, common sense, or moral courage, Peikoff and Mises are, epistemologically, on all fours with Christians who await the Rapture.

As Eliezer Yudkowsky puts the matter:

The rationalist virtue of empiricism consists of constantly asking which experiences our beliefs predict — or better yet, prohibit. Do you believe that phlogiston is the cause of fire? Then what do you expect to see happen, because of that? Do you believe that Wulky Wulkinsen is a post-utopian? Then what do you expect to see because of that? No, not “colonial alienation”; what experience will happen to you? Do you believe that if a tree falls in the forest, and no one hears it, it still makes a sound? Then what experience must therefore befall you?

It is even better to ask: what experience must not happen to me? Do you believe that elan vital explains the mysterious aliveness of living beings? Then what does this belief not allow to happen — what would definitely falsify this belief? A null answer means that your belief does not constrain experience; it permits anything to happen to you. It floats.

When you argue a seemingly factual question, always keep in mind which difference of anticipation you are arguing about. If you can’t find the difference of anticipation, you’re probably arguing about labels in your belief network — or even worse, floating beliefs, barnacles on your network. If you don’t know what experiences are implied by Wulky Wilkinsen being a post-utopian, you can go on arguing about it forever. (You can also publish papers about it forever.)

Above all, don’t ask what to believe — ask what to anticipate. Every question of belief should flow from a question of anticipation, and that question of anticipation should be the center of the inquiry. Every guess of belief should begin by flowing to a specific guess of anticipation, and should continue to pay rent in future anticipations. If a belief turns deadbeat, evict it.

Consider this an eviction notice.

Mar 132007

Brian Doherty’s Radicals for Capitalism is a comprehensive, highly entertaining history of libertarianism with too many points of interest — Murray Rothbard’s solution to the free rider problem (“so what?”), Milton Friedman’s sterling character, The Unbearable Lightness of Being a Deontologist — to deal with in a single post. Instead I want to talk about the notes.

Radicals for Capitalism is a scholarly, though not an academic, book, and like many such books it does plenty of business in the notes. Not as much as some, like Popper’s The Open Society and Its Enemies, in which the notes are longer than the text, but enough. For instance, my friend (and frequent commenter) Jim Valliant’s book on the Brandens, The Passion of Ayn Rand’s Critics, receives a half-page treatment in the endnotes, but none in the text. Out of 2,000 notes, there are 400 or so that you want to read; the rest are simple source citations.

Doherty’s notes receive the standard treatment, which is to say the worst possible. The notes are renumbered by chapter, but each page of notes is headed, usefully, “Notes”; the chapter titles occur only on the beginning page of the notes for that chapter. To look up an endnote, then, you have to remember the number, remember the chapter number, flip to the notes section, locate the beginning page of the correct chapter, and then flip forward to the right note number, only to be disappointed most of the time with a mere source cite. (Admittedly it would be more efficient to use a bookmark, but I never have one handy, and they tend to fall out. At any rate, the necessity confesses design failure.)

Yet this is all so simple to fix. There are five rules for notes:

1. Footnotes, provided they are short and sparse, are better than endnotes. They can be consulted immediately and without effort. Obviously in a book like Doherty’s endnotes are necessary.

2. Each endnote page should be headed by the page numbers of the notes it contains, to facilitate easy flipping. For example, “Notes, pp. 537-558”; not “Notes: Chapter Seven,” or “Notes: A Stupid Chapter Title That I’ve Forgotten and Now You’re Gonna Make Me Look It Up,” or, God forbid, “Notes.”

3. Notes should not be numbered. Numbers tax the reader needlessly, especially when they reach three figures. They should be marked by a symbol in the text, something like this* or this. In the back they should be referenced by the page number and the last few words of the passage that they annotate, which are the easiest things to remember.

It would be especially helpful to use two symbols, to distinguish substantive comments from simple citations, telling the reader when to flip to the back and when not to bother. I have never seen this in a scholarly book, and I wonder why.

4. The notes must be indexed. In Doherty’s book they are not. Had Jim Valliant gone looking for himself in the index, as I am assured august persons are wont to do, he would have come up empty. Why make trouble for Jim? If he merits a substantive mention, he also merits an index entry. I realize this is extra work. I expect extra work for my thirty-five bones, now marked down to $23.10, plus shipping.

5. The text should contain as little scholarly detritus as possible. Academic books often include source citations in the text, which avails the author the opportunity to look more erudite and avails the reader nothing, since if he wants to look up the source he has to consult the biblliography anyway. If the book has endnotes, that’s where the source cites belong.

A brilliant exception to this rule is Jacques Barzun’s From Dawn to Decadence, which contains no specific source cites, only an occasional parenthesis, when discussing a topic, that “the book to read is…” or “the book to browse in is…” If you are a nonagenarian and the world’s preeminent living intellectual, you can write like that. The rest of us cannot afford to be so peremptory. Still, Barzun’s asides have furthered my education, which is more than I can say for the usual uncommented bibliography.

*Yes, a circle would be better. I can’t get a circle the right size using HTML character codes. Sorry.

Yes, a larger bullet would be better. See above. I trust you get the idea.

Update: Another intransigent opponent of endnotes, Billy Beck, heard from. I thank him for his recommendation of the Zerby book, which I will look up. Kieran Healy comments. Andrew Gelman comments. James Joyner comments. Evan Hughes comments.

Dec 232006

Albert Hirschman has many fans at the arbiter of all things serious, Crooked Timber. Tyler Cowen, in one of his fitful attempts to shore up his left-wing cred, praised Hirschman as deserving of the Nobel Prize in Economics and The Rhetoric of Reaction as “a brilliant study in intellectual self-deception.” Good enough! I ordered up my copy and prepared to be edified.

The Rhetoric of Reaction proposes a taxonomy, or really a nosology, of arguments frequently employed by reactionaries. It begins with T.H. Marshall’s Class, Citizenship, and Social Development and its convenient, if schematic, tripartite division of “the development of citizenship” in the West. According to Marshall, first there were civil rights (freedom of religion, speech, and thought); then political rights (universal suffrage); and finally economic rights (the welfare state). Marshall allots these three developments a century apiece — the eighteenth, nineteenth, and twentieth, respectively. They are “progressive.” Whoever opposes any of them is “reactionary.”

If that’s all it takes, then count me in: I won’t defend universal suffrage, let alone the welfare state. I take solace in my distinguished and eclectic company. Hirschman’s reactionaries range from monarchists like Maistre and Burke to flaming socialists like Mosca and Pareto to welfare state critics like Friedman, Hayek, and Charles Murray, who get an especially raw deal. Friedman, who proposed a negative income tax, and Murray, with his similar grand scheme to replace the welfare state, cannot be fairly characterized as intransigently opposed to “reform.” Violence is being committed on the terms “reactionary” and “reformer.”

But to make a neat taxonomy you have to break a few eggs, and Hirschman’s is very neat indeed. We reactionaries, Hirschman says, argue against a proposed “reform” in three ways. The policy will do the opposite of what was intended (perversity). The policy will do nothing at all (futility). The policy will do other damage unrelated to its ends (jeopardy).

Hirschman’s categories are also more fluid than he acknowledges; the identical argument must be reclassified depending on how the reformer defines his ends. Take gun control. An opponent — the “reactionary” — might, and probably will, argue that it will prevent homeowners from defending themselves. This will reduce the risk to criminals, and thus crime will increase. If the advocate — the “reformer” — defines his end as reducing crime, we have a perversity argument. If he defines his end as reducing household gun accidents, we have a jeopardy argument. Hell, if the reformer defines his end as protecting innocent homeowners, and the additional homeowners who are shot by robbers cancel the ones who no longer shoot themselves, we might even have a futility argument. But it’s the same argument.

Still, Hirschman is on to something here. Jeopardy, futility, and perversity are all variations on unintended consequences, a traditionally rich field for ironists, and his thesis goes a long way toward explaining why “progressives” are so excruciatingly sincere:

There has been a certain lack of balance in the recurring debates between progressives and conservatives: in the effective use of the potent weapon of irony, conservatives have had a clear edge over progressives. In [Tocqueville’s] hands [the French Revolution] begins to look naive and absurd, rather than infamous and sacrilegious — the predominant characterization conveyed by earlier critics such as Maistre and Bonald. This aspect of the conservatives’ attitude toward their opponents was also reflected by the German term Weltverbesserer (world improver), which evokes someone who has taken on far too much and is bound to end up as a ridiculous failure…. In general, a skeptical, mocking attitude toward progressives’ endeavors and likely achievements is an integral and highly effective component of the modern conservative stance.

I once read a news item about an oil-slick cleanup, it might have been the Exxon Valdez spill, I can’t remember. Countless mammals and birds are scrubbed; vast trouble is taken. Finally all is ready: the cosmetologists gather on the beach, and a freshly shampooed otter is ceremoniously released into the sea. It swims to the crest of the first wave, where it is promptly eaten by a killer whale. If you laugh, you are a reactionary.

Of course it is funny. But so what? Maybe the otter ran into extremely bad luck. Maybe so many animals were rescued, and so efficiently, that a few meals for Shamu made no difference. Perhaps what really makes a reactionary is that he finds this story not only funny, but a dispositive argument against oil-slick cleanups. I owe this thought to Hirschman, and it is enough to make me glad to have read the book. “Reactionaries” pride themselves on deep thinking and “hard-headed realism” the same way “progressives” pride themselves on moral superiority, and often with no more justification. Not all reforms fail, and not all unintended consequences are bad. It is salutary to be reminded to cast out the beam from your own eye before beholding the mote in your adversary’s.

But Hirschman has broader aims:

There has indeed been a more basic intent: to establish some presumption, through the demonstration of repetition in basic argument, that the standard “reactionary” reasoning, as here exhibited, is frequently faulty….

A general suspicion of overuse of the arguments is aroused by the demonstration that they are invoked time and again almost routinely to cover a wide variety of real situations. The suspicion is heightened when it can be shown, as I have attempted to do in the preceding pages, that the arguments have considerable intrinsic appeal because they hitch onto powerful myths (Hubris-Nemesis, Divine Providence, Oedipus) and influential interpretive formulas (ceci tuera cela, zero-sum) or because they cast a flattering light on their authors and provide a boost for their egos. In view of these extraneous attractions, it becomes likely that the standard reactionary these will often be embraced regardless of their fit.

Hirschman does not establish, beyond noting the similarity in the stories, that the perversity and futility theses “hitch onto” Oedipus and Hubris-Nemesis. And even if they do, where did the myths themselves originate? Isn’t it likely that both Oedipus and the argument from perversity, both Hubris-Nemesis and the argument from futility, originate in observed facts about events?

And his taxonomy is too comprehensive to sustain the charge of overuse. Throw out perversity, futility, and jeopardy, and what’s left? A reform’s ends are always noble, in the eyes of the reformers. Would Hirschman prefer that reactionaries argue against liberty, democracy, a minimal living for the poor, or clean air? When Charles Fourier tells us that socialism will raise the human average to the level of a Goethe or an Aristotle, should we reply that we prefer the human average as it is? Hirschman professes disappointment in the reactionaries: “Instead of the rich historical argumentation to which I was looking forward, the purveyors of the jeopardy claim, from Robert Lowe to Samuel Huntington, have often satisfied with simple affirmations of the ceci-tuera-cela [this will kill that] type.” The arguments in which, by implication, he thinks reactionaries ought to engage would really let him down.

Hirschman is much given to ironizing about the reactionary propensity to ironize. He surely appreciates the irony that his likely audience, “progressives,” will find nothing but confirmation for its beliefs. Few “reactionaries,” who could profit from the book, will ever read it.

Post scripta: It does not bear directly on Hirschman’s thesis, but the casual dishonesty of some of the footnotes is shocking in a scholar of his reputation. He writes of Gustave Le Bon, the author of The Crowd: “His basic principle being that the crowd is always benighted, he makes it apply with remarkable consistency, regardless of the constituents of the crowd and of their characteristics as individuals: ‘the vote of 40 academicians is no better than that of 40 water carriers’ he wrote, thereby managing to insult in passing the French academy with its forty members, an elite body from which he resentfully felt himself excluded.”

There is a footnote after “excluded,” which simply refers to the passage from The Crowd that he quotes, supplying no evidence for Le Bon’s alleged resentment. Hirschman must know that the note belongs directly after the quoted passage. By placing it where he does he bolsters, with an irrelevant citation, an unsupported slur.

Here is Hirschman later in the same chapter, on the 1834 Poor Law Amendment: “…the new arrangements were meant to deter the poor from resorting to public assistance and to stigmatize those who did by ‘imprisoning [them] in workhouses, compelling them to wear special garb, separating them from their families, cutting them off from communication with the poor outside, and, when they died, permitting their bodies to be disposed of for dissection.'”

Hirschman intends the reader to take the quotation at face value, as a factual description of the effect of the Amendment. But the footnote, at the end of the passage, is to Gertrude Himmelfarb’s classic The Idea of Poverty: England in the Early Industrial Age. The note says, accurately, that Himmelfarb is summarizing William Cobbett. The note does not say that Cobbett was one of the most vigorous contemporary opponents of the Amendment; neither does it say that Himmelfarb spends her next five pages qualifying and disputing him. The very page Hirschman quotes has a note of its own: “Cobbett was especially outraged by the practice of dissection, which he took to be the ultimate degradation and desecration caused by the New Poor Law. This was not, of course, part of the law, and it is not clear how common it was for workhouses to dispose of bodies for this purpose. But it was widely believed to be the case, partly because of Cobbett’s repeated charges to this effect.”

I hope Hirschman footnotes his works in economics, the ones that merit the Nobel Prize, more correctly.

Nov 222006

If I could require every American schoolchild of normal intelligence to read one book, it would be George Pólya’s How To Solve It. (Second choice is Henry Hazlitt’s Economics in One Lesson. I keep extra copies of both books on hand to give away as necessary.) Pólya was born in Hungary and taught mathematics at several European universities before ending up at Stanford. Like the authors of all the best pedagogical texts, he was a superb practitioner. Pólya made important original contributions in probability theory, combinatorics, complex analysis, and other fields. He published How To Solve It in 1945; it has since sold more than a million copies. He died in 1985 at an immense age.

How To Solve It, among its other virtues, is a model of English prose style; I will let Pólya himself describe what he’s up to:

The author remembers the time when he was a student himself, a somewhat ambitious student, eager to understand a little mathematics and physics. He listened to lectures, read books, tried to take in the solutions and the facts presented, but there was a question that disturbed him again and again: “Yes, the solution seems to work, it appears to be correct; but how is it possible to invent such a solution? Yes, this experiment seems to work, this appears to be a fact; but how can people discover such facts? And how could I invent or discover such things by myself?” Today the author is teaching mathematics at a university; he thinks or hopes that some of his more eager students ask similar questions and he tries to satisfy their curiosity.

Math students are regularly exhorted to “show your work,” while the great mathematicians hide theirs. Euclid’s proof that the angles of a triangle sum to 180 degrees is a masterpiece of logical thought, but however he arrived at it, it was assuredly not by the route shown in the Elements. The proofs came first, the axioms after. One can admire but not emulate. In short, what math education lacks is heuristic, and this is what Pólya endeavors to supply.

The way to write about Pólya is to solve problems with his techniques. Abbas Raza at 3 Quarks Daily provided an occasion by posting fourteen moderately difficult logic problems, none requiring mathematical background. I’ve rearranged them slightly. Most of the problems are famous; you have probably seen some of them before. You may want to have at the problems first before you read my solutions and commentary on how I used Pólya’s techniques to find them.

1. You are given two ropes and a lighter. This is the only equipment you can use. You are told that each of the two ropes has the following property: if you light one end of the rope, it will take exactly one hour to burn all the way to the other end. But it doesn’t have to burn at a uniform rate. In other words, half the rope may burn in the first five minutes, and then the other half would take 55 minutes. The rate at which the two ropes burn is not necessarily the same, so the second rope will also take an hour to burn from one end to the other, but may do it at some varying rate, which is not necessarily the same as the one for the first rope. Now you are asked to measure a period of 45 minutes. How will you do it?

Solution: Light the first rope at both ends, and the second at one end. When the first rope has completely burned, 30 minutes have elasped. Now light the other end of the second rope. When the second rope has completely burned, 45 minutes have elapsed.

Commentary: “If you can’t solve a problem,” Pólya says, “there is an easier problem you can solve: find it.” Measuring 45 minutes may seem impossible at first, but how about 30 minutes? Thinking about 30 minutes instead, you may hit on the bright idea of lighting the rope at both ends. From there you need one more bright idea: that you need not light both ends simultaneously. Most people, including me, arrive at the second idea very quickly after thinking of the first; but I once saw an excellent problem solver find the first idea immediately and take quite a while to find the second.

2. You have 50 quarters on the table in front of you. You are blindfolded and cannot discern whether a coin is heads up or tails up by feeling it. You are told that x coins are heads up, where 0 < = x

Solution: You are given x, the number of heads. Create a subgroup of x coins. Flip them all.

Commentary: Pólya asks: Did you use the whole condition? The condition here is more liberal than it looks. You need not know the number of heads in each pile. Neither must the two piles contain the same number of coins, provided the number of heads in the two piles is the same.

Pólya also asks: Did you use all the data? Here we are given the total number of coins, which is doubtfully relevant, except that it is large enough to make the problem difficult. More important, we are given x, the number of coins heads up. The solution is very likely to involve flipping x coins. In fact it is a simple matter of doing just that.

Pólya finally asks: Can you check the solution? Introducing suitable notation, another Pólya suggestion, yields a satisfying way to do so. x is the number of coins that are heads up; 50 – x, then, is the number of coins tails up. We divide the coins into two groups, of x and 50 – x coins. Let y be the number of heads in the x group. Then the number of heads in the 50 – x group is x – y. Now we flip all the coins in the x group. The number of heads becomes x – y. The two groups contain the same number of heads. This also demonstrates, as we suspected, that 50 is indeed irrelevant; the solution works no matter how many coins you begin with.

3. A farmer is returning from town with a dog, a chicken and some corn. He arrives at a river that he must cross, but all that is available to him is a small raft large enough to hold him and one of his three possessions. He may not leave the dog alone with the chicken, for the dog will eat it. Furthermore, he may not leave the chicken alone with the corn, for the chicken will eat it. How can he bring everything across the river safely?

Solution: Bring the chicken across. Return alone and bring the dog across. Return with the chicken, and bring the corn across. Return alone and bring the chicken across.

Commentary: This is a “hill-climbing” problem; you proceed by steps until you reach the goal. It can be difficult to solve because in hill-climbing it is natural to try to proceed directly, which gets you stuck at a local optimum of two items across the river.

Pólya says, translating the Greek mathematician Pappus of Alexandria (circa 300 AD), “start from what is required and assume what is sought as already found.” Next “inquire from what antecedent the desired result could be derived.” Beginning at the end, we can see that on the farmer’s last raft trip he must bring the chicken across, because only the dog and corn can be left together safely. But for the same reason he must also bring the chicken across on his first trip. Putting this to yourself explicitly, you may eventually realize that the chicken must go back and forth and the solution will immediately present itself.

4. Late one evening, four hikers find themselves at a rope bridge spanning a wide river. The bridge is not very secure and can hold only two people at a time. Since it is quite dark, a flashlight is needed to cross the bridge and only one hiker had brought his. One of the hikers can cross the bridge in one minute, another in two minutes, another in five minutes and the fourth in ten minutes. When two people cross, they can only walk as fast as the slower of the two hikers. How can they all cross the bridge in 17 minutes? No, they cannot throw the flashlight across the river.

Solution: Two and One cross (2 minutes). One returns (3 minutes). Ten and Five cross (13 minutes). Two returns (15 minutes). Two and One cross (17 minutes).

Commentary: Pólya asks: If you had a solution, what would it look like? Certainly we know that Ten and Five cannot cross more than once, or we are immediately at 20 minutes plus. But if Ten and Five cross separately we are still over 17 minutes, since there must be three other trips of at least a minute each. Therefore Ten and Five must cross together. This cannot happen at the beginning — otherwise one would have have to return — or at the end — since someone would have to return with the flashlight and would remain. Therefore they must cross in the middle. The solution appears.

Pólya also asks: Do you know a related problem? This problem bears an interesting reciprocal relationship to Problem 3, of the dog, chicken, and corn. There we infer the procedure from the first and last trips; here we infer it from the trip in the middle.

5. You have four chains. Each chain has three links in it. Although it is difficult to cut the links, you wish to make a loop with all 12 links. What is the smallest number of cuts you must make to accomplish this task?

Solution: Three cuts. You cut all three links of a single chain and use them to connect the other three together.

Commentary: Cutting one link in each of the four chains will obviously do the job, but that’s not interesting enough to be the right answer. Can we do better?

Pólya suggests enumerating the solution space, when possible; or guessing, to put it bluntly. How many different ways can we cut three links? Well, we can cut one from each of three chains: that won’t work. We can cut two from one chain: that doesn’t help either. Or we can cut all three from a single chain… aha!

6. Before you lie three closed boxes. They are labeled Blue Jellybeans, Red Jellybeans and Blue & Red Jellybeans. In fact, all the boxes are filled with jellybeans. One with just blue, one with just red and one with both blue and red. However, all the boxes are incorrectly labeled. You may reach into one box and pull out only one jellybean. Which box should you select from to correctly label the boxes?

Solution: Choose from the box labeled Blue & Red.

Commentary: Another good guessing problem. The solution is obvious. It is functionally equivalent to choose from the Blue or Red box, and the problem stipulates a single answer, which must be Blue and Red.

All that is left is the reasoning. Suppose you choose a red jellybean. Then you know the Blue & Red box should be labeled Red, and that, since the other two boxes are also mislabeled, that the Red box must be Blue and the Blue box must be Blue and Red.

Guess first, reason later: it works more often than you’d think.

7. Walking down the street one day, I met a woman strolling with her daughter. “What a lovely child,” I remarked. “In fact, I have two children,” she replied. What is the probability that both of her children are girls?

Solution: There are four prior possibilities for the sex distribution of her two children: boy-boy, girl-girl, boy-girl, and girl-boy. We’ve seen a girl, so boy-boy is out. Of the three remaining possibilities, once you’ve revealed a girl, a boy remains in two of them. Therefore the probability that the other child is a girl, P(G) = 1/3.

Commentary: The difficulty here is less in finding the answer than in believing it. As with the Monty Hall Problem, many people deny that the solution is true, and they have distinguished company. (The solution depends subtly on the precise wording with which the problem is given; this comment thread has an extensive discussion, which is beyond the scope of this discussion.)

Pólya asks: Can you draw a diagram? No, but you can model the problem experimentally. Dump a bunch of coins on the table and pair them up randomly. Remove all the tail/tail pairs. Now tabulate the results for the rest of the pairs. They will be tail/head approximately 2/3 of the time.

8. A glass of water with a single ice cube sits on a table. When the ice has completely melted, will the level of the water have increased, decreased or remain unchanged?

Solution: The water level sinks, because ice has lower specific gravity than water.

Commentary: Pólya asks: Have you seen this problem before? You have. It’s the famous problem Archimedes solved in his bath. A king asked Archimedes to determine if a crown he owned was pure gold, without melting it down. Archimedes stepped into his bath, watched the water rise, and ran naked into the street, shouting “Eureka!” Maybe not. At any rate, he realized that his body displaced an equivalent volume of water, and he could measure the volume of any irregular object the same way, by submerging it.

Once Archimedes determined the volume of the crown, he simply weighed it against a lump of gold of identical volume. Gold is denser than silver, so if the crown was lighter, it had been adulterated. Water is denser than ice, so the water level sinks as the ice melts.

Abbas Raza, after setting this problem, got it wrong. The floating cube does not “displace its own weight in water”; it displaces its own volume in water. Had he regarded Pólya’s advice to check the solution, by melting a few ice cubes in a glass of water, he would have spared himself some embarrassment. (See the update for who’s embarrassed now.)

9. You are given eight coins and told that one of them is counterfeit. The counterfeit one is slightly heavier than the other seven. Otherwise, the coins look identical. Using a simple balance scale, can you determine which coin is counterfeit using the scale only twice?

Solution: Weigh three against three. If they are equal then the counterfeit is one of two coins and it’s easy. If not, then the counterfeit is one of three coins. Take two of the three and weigh them against each other. Whichever is heavier is the counterfeit, or, if they’re equal, the third is counterfeit.

Commentary: This problem would be far easier if it were given with nine coins instead of eight. The same solution applies, but since three divides nine evenly, and two does not, you would immediately think to weigh three against three. With eight coins the opposite is true. You think of weighing four against four, and it may be some time before you disentangle yourself.

10. There are two gallon containers. One is filled with water and the other is filled with wine. Three ounces of the wine are poured into the water container. Then, three ounces from the water container are poured into the wine. Now that each container has a gallon of liquid, which is greater: the amount of water in the wine container or the amount of wine in the water container?

Solution: The water in the wine is equal to the wine in the water.

Commentary: This problem, like Problem 2, is overspecified. In fact almost all of the given data — how much liquid is in each container, the mixing sequence — is irrelevant. It matters only that the two containers begin and end with equal amounts of liquid. Pólya asks: Did you use all the data? Here that question gets you into trouble.

But Pólya also says that sometimes the general problem is easier to solve. (In computer science the general problem is always easier to solve.) He has caught grief for this remark, and the example he gives is somewhat artificial, but here it bears out. The specifics make the problem confusing.

Of course if you solve the general problem then you have, by definition, not used all the data. Sometimes one procedure works; sometimes its opposite.

11. Other than the North Pole, where on this planet is it possible to walk one mile due south, one mile due east and one mile due north and end up exactly where you began?

Solution: Pólya gives this exact problem in How To Solve It in its more famous form, in which a bear does the walking and the problem is what color is the bear. I will quote his solution, if only to demonstrate how comprehensive his thinking is next to mine:

You think that the bear was white and the point P is the North Pole? Can you prove that this is correct? As it was more or less understood, we idealize the question. We regard the globe as exactly spherical and the bear as a moving material point. This point, moving due south or due north, describes an arc of a meridian and it describes an arc of a parallel circle (parallel to the equator) when it moves due east. We have to distinguish two cases.

1. If the bear returns to the point P along a meridian different from the one along which he left P, P is necessarily the North Pole. In fact the only other point of the globe in which two meridians meet is the South Pole, but the bear could leave this pole only in moving northward.

2. The bear could return to the point P along the same meridian he left P if, when walking one mile due east, he describes a parallel circle exactly n times, where n may be 1, 2, 3… In this case P is not the North Pole, but a point on a parallel circle very close to the South Pole (the perimeter of which, expressed in miles, is slightly inferior to 2Ï€ + 1/n).

Commentary: Before solving the problem Pólya offers the following hints:

What is the unknown? The color of a bear — but how could we find the color of a bear from mathematical data? What is given? A geometrical situation — but it seems self-contradictory: how could the bear, after walking three miles in the manner described, return to his starting point?

12. I was visiting a friend one evening and remembered that he had three daughters. I asked him how old they were. “The product of their ages is 72,” he answered. I asked, “Is there anything else you can tell me?” “Yes,” he replied, “the sum of their ages is equal to the number of my house.” I stepped outside to see what the house number was. Upon returning inside, I said to my host, “I’m sorry, but I still can’t figure out their ages.” He responded apologetically, “I’m sorry. I forgot to mention that my oldest daughter likes strawberry shortcake.” With this information, I was able to determine all of their ages. How old is each daughter?

Solution: The factors of 72 can be combined into three factors with identical sums only one way: 6, 6, and 2; and 3, 3, and 8, both of which sum to 14. “My oldest daughter likes strawberry shortcake” implies that there is one daughter who is older than the other two. (This isn’t quite sound, since two of the daughters could be, say, 6 and 1 month and 6 and 11 months, and even twins are not precisely the same age; but, as Pólya would put it, we idealize the question, as it is more or less understood.) Therefore 3, 3, and 8 are the ages.

Commentary: Pólya might suggest introducing suitable notation. Let the ages of the three daughters be x, y, z. There must be a uniqely oldest daughter, so x > y >=z. Let S be the sum of their ages.

We have:

x * y * z = 72

x + y + z = S

Now we enumerate x, y, and z, looking for those with non-unique sums. Since the prime factors of 72 are (2^3) * (3^2), the job is pretty simple. The solution suggests itself shortly.

13. The surface of a distant planet is covered with water except for one small island on the planet’s equator. On this island is an airport with a fleet of identical planes. One pilot has a mission to fly around the planet along its equator and return to the island. The problem is that each plane only has enough fuel to fly a plane half way around the planet. Fortunately, each plane can be refueled by any other plane midair. Assuming that refuelings can happen instantaneously and all the planes fly at the same speed, what is the smallest number of planes needed for this mission?

Solution: Three planes. Send out all three, flying clockwise. At 45 degrees each plane has burned a quarter of its fuel. Plane 1 gives a quarter of its remaining fuel each to Plane 2 and Plane 3 and uses its remaining quarter-tank to return to base. Planes 2 and 3, now both full, continue to 90 degrees. Plane 2 gives Plane 3 one-half of its fuel and uses its remaining half-tank to return to base. Plane 3 continues to 270 degrees. When it reaches 180 degrees, Planes 1 and 2, having refueled at base (Plane 2 will have just returned by then), fly out counter-clockwise, using the same procedure.

Commentary: Pólya says, first be sure you understand the problem. Abbas Raza specified, in reply to a reader’s query, that the planes may not fly suicide missions. Oddly, if they were permitted to, the answer would still be three, although two of them would plunge into the drink. But then the problem would not be interesting.

14. You find yourself in a room with three light switches. In a room upstairs stands a single lamp with a single light bulb on a table. One of the switches controls that lamp, whereas the other two switches do nothing at all. It is your task to determine which of the three switches controls the light upstairs. The catch: once you go upstairs to the room with the lamp, you may not return to the room with the switches. There is no way to see if the lamp is lit without entering the room upstairs. How do you do it?

Solution: You turn one on. You turn a second one on, wait a minute, then turn it off. Then you go upstairs and see if the bulb is off, on, or warm.

Commentary: Here the question that is so effective for Problem 12 — could you restate the problem? — can lead you astray. Introducing notation will probably also steer you wrong. The solution depends on the physical characteristics of the problem elements, and different, more abstract language may cause you to miss it. (This is why many mathematicians hate this problem.) But that’s why it’s called heuristic, as Pólya explains:

You should ask no question, make no suggestion, indiscriminately, following some rigid habit. Be prepared for various questions and suggestions and use your judgment. You are doing a hard and exciting problem; the step you are going to try next should be prompted by an attentive and open-minded consideration of the problem before you….

And if you are inclined to be a pedant and must rely on some rule learn this one: Always use your own brains first.

Update: On Problem 8, as Adam points out in the comments, Abbas Raza is right and I am wrong. The best correct explanation is here. Pólya does not say, but should, that if you insist on solving problems in public you do so at your peril. I will leave up my own foolishness as a lesson in hubris.

Aug 262006

I’m a betting man, and yesterday I was offered a betting proposition. The U.S. Bridge Championships are going on now, and the great Nickell team, which has won the event eight years running, has a bye to the semifinals. My friend Justin Lall, a bridge pro, offered me 6:1 odds on $50 on the field: in other words, he would pay off if any team but Nickell won the event.

Ordinarily I would accept happily. 6:1 is very long odds, and no matter how good Nickell is they still have to win two matches against excellent teams. Except Justin informed me that he was getting 6.5:1 on the same 50 bucks from someone else. So taking the bet gives him a freeroll: plus $25 if Nickell loses, break-even otherwise.

I refused the bet, which, from a strictly economic point of view, is irrational. If I like the odds, then I like them. Why should I care if Justin is using me to hedge his risk?

Anxiety mostly — anxiety, first, about one’s place in the dominance hierarchy. One hates to be a pawn in someone else’s game, Es to his Ich, a means to his end. A moment’s reflection will convince you of the idiocy of this attitude, on which several moral philosophies, like Kant’s and Martin Buber’s, have been erected. Regardless of who initiates the transaction, Justin is just as much a means to my own end — obtaining a bet against Nickell at favorable odds — as I am to his of laying off his risk. Hasn’t he also earned a transaction fee for having done the work of negotiating the bet in the first place and then offering it, at a small profit, to me? I regard the philosophies as foolish and atavistic yet, in this case at least, persist in the attitude. If you want an instance of the dictionary definition of “irrational,” this will serve.

Also involved is a related, slightly different form of anxiety which, for lack of a fancy psychological term, I will call shopping anxiety. Mencken defined Puritanism as the haunting fear that someone, somewhere may be happy: shopping anxiety is the haunting fear that someone, somewhere got a better deal. It is not clear to me why it should detract from someone’s pleasure in his new 56-inch plasma TV to discover that his neighbor bought the same model for $200 less. Neither is it clear why it annoyed me that Justin found a better bet than I had, especially since I hadn’t been out looking. But it did.

Finally there is the fact that Justin is a bridge pro. He knows and has played with members of the Nickell team. He is, in short, far more competent than I to evaluate the odds, and he would rather freeroll than eat the risk. Perhaps the bet isn’t as good as I thought it was. This conceivably sound reason, I am sure, influenced me far less than the stupid ones.

Nickell, as I write, has a huge deficit late in its semifinal match. Who’s sorry now?

Update: Despite a furious comeback, Nickell loses. I’m out 300 bones.

Aug 222006

Possibly the most annoying truth in the world is that good qualities cluster. People who are good at something tend to be good at many things.

The psychometric version of clustering is g, or general intelligence. The existence of g is not seriously disputed in the field, and g-deniers like Howard Gardner, with his theory of “multiple intelligences,” or the late paleontologist-cum-Marxist Stephen Jay Gould, are regarded as cranks or axe-grinders. The Wechsler scale, the most complex (and expensive) of all intelligence tests, measures thirteen apparently widely disparate skills, including vocabulary, picture completion, matrix reasoning, and the ability to repeat back a string of digits. Bad news! Each skill, without exception, correlates positively with all the others. Seventy-eight possible correlations, and every one positive. The correlations range from 0.3 (weakish) to 0.8 (very strong), where 0 indicates no relationship and 1 an exact match. If you suck at math, the parsimonious explanation isn’t that your true talents lie in writing or painting. The parsimonious explanation is that you suck.1

Intelligence isn’t everything, you say. Quite so. Nevertheless intelligence correlates quite highly with other happy outcomes, like money and status (0.5 or so), long, healthy lives, and staying out of jail. Not to mention height. About the only negative quality definitely associated with high IQ is myopia.

The news gets worse, much worse. Smart people tend to be good-looking. Since intelligence also correlates significantly with income and status, this should surprise no one. Rich, high-status men marry better-looking women and sire better-looking offspring. QED. Models aren’t stupid after all.2

Jocks aren’t stupid either. Reaction time, essential in many sports, correlates moderately with IQ. The data is spotty for most sports, but pro football players have a significantly higher average IQ than the population at large.3 Again, no surprise; learning an NFL playbook is probably pretty demanding.

Clustering offends the human sense of fairness. The world is frequently imagined as if God gives out qualities one at a time — brains for you, beauty for her, and for him, let’s see, how about a sense of humor? — seeing to it that things somehow even out in the end. Jocks and models must be dumb; they already expended their early-round draft picks on something else. Geniuses are crazy; it’s their handicap. Ugly girls have nice personalities. And most of all, you can be anything you want to be, in Lake Wobegon, where all the children are above average.

1By “you” I mean an abstract individual, a statistical creation, not you, dear reader. No statistics could possibly apply to you. You are special, and Jesus loves you.

2Again, these remarks should not be construed as a reflection on any particular model, like, say, Claudia Schiffer (Schiffer-Brains, as she is known in the industry).

3Assuming the same racial composition.

Update: Matt McIntosh comments. Elsewhere, I mean. The Mechanical Eye comments. I will reply if I can find the time in my busy schedule of feeding Christians to lions, building palaces, and oppressing the peasantry. Ilkka Kokkarinen comments. Degrees of Freedom comments. Noneuklid comments.

Jul 192005

Brian: I’m not the messiah.
Acolyte: Only the true messiah would deny that he was the messiah!
Brian: OK. I’m the messiah.
Mob: He’s the messiah! He’s the messiah!
Life of Brian

Guy’s out walking in Manhattan when he sees a street vendor selling unmarked aerosol cans. He’s curious and asks what’s in them, and the vendor says, “Tiger repellent.” The guy points out that there are no tigers in New York City, and the vendor replies, “See how well it works?”

Certain ideas enter the world, like Athena, fully armed. Most of these are disreputable. Conspiracy theorists frequently insist that the absence of evidence for their theory constitutes proof of the power of the conspiracy; otherwise how could they cover it all up? Child “therapists” invoke the absence of any memory of sexual abuse as proof of the same; the horrific experience has been repressed. As Renee Fredrickson puts it, with all seriousness, in Repressed Memories: A Journey to Recovery from Sexual Abuse, “The existence of profound disbelief is an indication that the memories are real.” The major religions, of course, are the greatest tiger repellent of all. Good is proof of God’s wisdom and mercy; evil of his subtlety and inscrutability. Throw in a sacred text that it is blasphemy even to translate, and a standing order to slaughter the infidels, and you’ve really built something to last.

Tiger repellent also insinuates itself into more respectable precincts. In 1903 a well-known French physicist named Rene Blondlot announced the discovery of N-rays. Over the next three years more than 300 papers, published by 120 different scientists, enumerated some of the remarkable properties of these rays. They passed through platinum but not rock, dry cigarette paper but not wet. Rabbits and frogs emitted them. They could be conducted along wires. They strengthened faint luminosity, with the aid of a steel file.

N-rays, however, turned out to be highly temperamental. You could produce only so much of them, no matter how many rabbits or frogs you lined up. Noise would spoil their effect. Your instruments had to be tuned just so. Blondlot gave complex instructions for observing them, and still numerous physicists failed, for the excellent reason that N-rays do not exist. The American prankster physicist Robert Wood finally settled the matter by visiting Blondlot’s lab in 1906 and playing several cruel tricks on him. Wood surreptitiously removed the dispersing prism that was supposed to be indispensable to the observation of the rays. Blondlot claimed to see them anyway, and when he died thirty years later he was still firmly convinced of their existence.

It is easy to laugh at Blondlot from a century’s distance. But he was not dishonest, and many of the scientists who replicated his results were highly competent. N-rays were, on the face of it, no more improbable than X-rays, discovered a few years earlier. But a phenomenon so faint, so susceptible to external conditions, so difficult to reproduce, is tiger repellent.

All of this struck Karl Popper with such force that he attempted to erect an entire philosophy of science upon it. One sympathizes. Popper began to formulate his philosophy in the 1920s, when psychology, the largest tiger repellent manufacturer of the 20th century, was coming of age. Popper also, unlike most of his colleagues, does not give the impression of squinting at his subject through binoculars from a distant hill. He knows something of math and science and incorporates examples from them liberally. It is no surprise that of all philosophers of science only Popper, Kuhn possibly excepted, has a significant following among actual scientists.

For Popper a scientific theory must be falsifiable, by which he means that one could imagine an experimental result that would refute it. Scientific theories, it follows, are not verifiable either. No matter how many times a theory has been confirmed, no matter what its explanatory or predictive value, it is on probation, permanently. The very next experiment may blow it all to pieces.

Popper’s imaginary experimental result need not exist in our universe — some theories are true — but merely in some other possible universe far, far away. This possible universe may, indeed must, differ from ours in its particulars but may not violate the laws of logic. That 2 + 2 = 4 is necessary, true in all possible universes; that water boils at 100°C at sea level is contingent, true in ours. Science deals only in the contingent.

This distinction is essential to falsifiability. Some imaginary experimental results are valid, some are not, and this is how you tell the difference. In philosophy it has been formally known, since Kant, as the analytic/synthetic dichotomy. Analytic truths are tautologies; they are necessary; all of the information is contained in the premises. The locus classicus of the analytic is mathematics. Following Wittgenstein, Popper views math as “unpacking tautologies,” and therefore excludes it from science. It is, for him, a form of tiger repellent — useful to be sure, but tiger repellent just the same.

Trouble is, there’s no such distinction, at least not as Popper conceives it. Quine’s refutation in “Two Dogmas of Empiricism” is decisive. His arguments are well-known, if technical, and I will not recount them here. They amount to the contention that the analytic always bleeds into the synthetic and vice versa. Even mathematics turns out not to be strictly analytic, to Wittgenstein’s chagrin. If, as Gödel demonstrated, there are true statements in any formal system that cannot be reached from its axioms, how do we classify them? Are they analytic, or synthetic, or what? When Popper first published The Logic of Scientific Discovery, in 1934, Gödel was already internationally famous. Its index is replete with the names of contemporary scientists and mathematicians. Gödel’s does not appear.

The analytic/synthetic dichotomy has shown considerable staying power, its flaws notwithstanding, because it resembles the way people really think. Gerald Edelman’s theory of consciousness, for one, with its modes of “logic” and “selectionism,” maps quite well to analytic and synthetic. But the philosopher, in his hubris, elevates ways of thinking to categories of knowledge. Matt McIntosh, a convinced Popperian who rejects the analytic/synthetic dichotomy, has promised to salvage falsifiability notwithstanding. He assures me that this post will be coming, as we say in software, real soon now. (Note to Matt: I haven’t grown a beard while waiting, but I could have. Easily.)

The laws of thermodynamics, science by anyone’s standard, are probabilistic. It is not impossible for a stone to roll uphill, merely so unlikely that the contingency can be safely disregarded. Modern physics is statistical, and was in Popper’s day too. Popper acknowledges that respectable science employs probability statements all the time, which leaves him with two choices. He can admit what inituition would say, and what the Law of Large Numbers does say, that probability statements are falsifiable, to any desired degree of certainty, given sufficient trials. But then he would have to abandon his theory. By this same logic probability statements are also verifiable, and verifiability, in science, is what Popper is concerned to deny.

Hence he takes the opposite view: he denies that probability statements are falsifiable. More precisely, he denies it, and then admits it, and then denies it, and then admits it again. The lengthy section on probability in The Logic of Scientific Discovery twists and turns hideously, finally concluding that probability statements, though not falsifiable themselves, can be used as if they were falsifiable. No, really:

Following [the physicist] I shall disallow the unlimited application of probability hypotheses: I propose that we take the methodological decision never to explain physical effects, i.e. reproducible regularities, as accumulation of accidents. [Sec. 67, italics his.]

In other words, let’s pretend that the obvious — probability statements are falsifiable — is, in fact, true. Well, as long as we’re playing Let’s Pretend, I have a better idea: let’s pretend that Popper’s philosophy is true. We can, and should, admit that “what would prove it wrong?” remains an excellent question for any theory, and credit Popper for insisting so strenuously on it. We can, and should, deny that falsifiability demarcates science from non-science absolutely. Falsifiability is a superb heuristic, which is not be confused with a philosophy.

(Update: Matt came through with his post after all, which is well worth reading, along with the rest of his “Knowledge and Information” series. Billy Beck comments. He seems to think I play on Popper’s team.)

Feb 132005

After months of diligent study I have finally become the person you edge away from at parties. At the last one I attended I began, after a few drinks, to dilate on alpha theory as usual. One of the guests suggested that I become a prophet for a new cult, which was certainly a lucky thing, and I want to thank him, because that joke would never have occurred to me on my own.

As with party-goers, so with blog-readers. The vast majority of my (former) readership has greeted alpha theory with some hostility but mostly indifference, and for excellent reason. It is a general theory, and humans have high sales resistance to general theories.

Generality offends in itself. Theories of human behavior apply to all humans, and that means you. If you’re anything like me, and you are, when you look at a graphed distribution of some human characteristic, no matter what it is, you harbor a secret hope that you fall at a tail, or better still, outside the distribution altogether. It is not that we are all above average, like the children of Lake Woebegon. Oh no: we are all extraordinary. Surely the statistician has somehow failed to account for me and my precious unique inviolable self. Nobody wants to be a data point. General theories, including alpha theory, often involve equations, and nobody likes an equation either.

General theories are also susceptible to error, the more susceptible the more general they are. An old academic joke about general surveys applies to general theories as well. I first heard it about Vernon Parrington’s Main Currents in American Thought, a once-common college text, but it has made the rounds in many forms. Whichever English professor you asked about Parrington, he would praise the book, adding parenthetically, “Of course he knows nothing about my particular subject.”

Someone seeking to explain a wide range of apparently disparate phenomena usually overlooks a few facts. By the time these are brought to his attention he is too heavily invested in the theory to give it up. He hides or explains away the offending facts and publishes his theory anyway, to world-wide yawns.

The gravest danger of a general theory is that it might be true — more precisely, that you may come to believe it. Believing a new general theory is a mighty expensive proposition. You’ve built up a whole complicated web of rules that have worked for you in the past, and now you have to go back and reevaluate them all in light of this new theory. This is annoying, and a gigantic energy sink besides. General theories, including alpha theory, tend to attract adherents from among the young, who have less to throw away — lower sunk costs, as the economists say. For most of us dismissing a new theory out of hand is, probabilistically, a winning strategy. Some might call this anti-intellectualism: I call it self-preservation.

(I will not go so far as to claim that alpha theory predicts its own resistance. Down that road lies madness. “You don’t believe in Scientology? Of course you don’t. Scientology can explain that! Wait! Where are you going?”)

General theorists often insist that anyone who disagrees with their theory find a flaw in its derivation. I have been known to take this line myself, and it is utterly unreasonable. If someone showed up at my door with a complicated theory purporting to demonstrate some grotesque proposition, say, that cannibalism conduces to human survival, and demanded that I show where he went wrong, I’d kick him downstairs. Yes, they laughed at Edison, they laughed at Fulton. They also laughed at a hundred thousand crackpot megalomaniacs while they were at it.

So if you still want alpha theory to dry up and blow away, I understand. No hard feelings. And if you’ve written me off as some kind of nut, well, could be. The thought has crossed my mind. I can assure you only that I ardently desire to be delivered from my dementia. It would do wonders for my social life.

(Addendum: I want to make it perfectly clear that, although I have written about alpha theory for several months now, I did not invent it. I am not nearly intelligent enough to have invented it. That honor belongs to “Bourbaki,” well-known to the readers of the comments. Me, I’m a sort of combination PR man and applied alpha engineer. Oh wait — there aren’t any applications yet. Don’t worry, there will be.)

Aug 122004

Humans have suffered three thousand years of philosophy now, and it’s time we took stock.

Explanations. A successful explanation decomposes a complex question into its constituent parts. You ask why blood is bright red in the air and the arteries and darker red in the veins. I tell you that arterial blood has more oxygen, which it collects from the lungs and carries it to the heart, than venous blood, which does the opposite circuit. Then I tell you that blood contains iron, which bonds to oxygen to form oxyhaemoglobin, which is bright red. I can demonstrate by experiment that these are facts. I have offered a successful explanation.

Of course it is incomplete. I haven’t told you how I know the blood circulates, what oxygen is, how chemical bonding works, or what makes red red. But I could tell you all of these things, and even if I don’t you know more about blood than you did when we started.

The explanation succeeds largely because the question is worth asking. You notice an apparently strange fact that you do not understand. You investigate, and if you are lucky and intelligent, maybe you get somewhere. Philosophers, by contrast, when they sit down to philosophize, forget, as a point of honor, everything they know. They begin with pseudo-questions like “Do I exist?” (Descartes) or “Does the external world exist?” (Berkeley and his innumerable successors), the answers to which no sane person, including Descartes and Berkeley, has never seriously doubted. Kant, the great name in modern philosophy, is the great master of the showboating pseudo-question. The one certainty about questions like “how is space possible?”, “how are synthetic judgments possible a priori?”, and, my favorite, “how is nature possible?,” is that you will learn nothing by asking them, no matter how they are answered. Kant rarely bothers to answer them and such answers as he gives are impossible to remember in any case.

Explanations would seem to be philosophy’s best hope, but its track record is dismal. There has been the occasional lucky guess. Democritus held, correctly, that the world was made up of atoms. Now suppose you had inquired of Democritus what the world-stuff was, and he told you “atoms.” Would you be enlightened? In any case he couldn’t prove his guess, or support it, or follow it up in any way. Atoms had to wait 2500 years for Rutherford and modern physics to put them to good use. If you asked Parmenides how a thing can change and remain the same thing, he would have told you that nothing changes. It’s an explanation of a sort. But would you have gone away happy? Grade: Two C’s, two D’s, and an F. Congratulations Kroger, you’re at the top of the Delta pledge class.

Predictions. To be fair, predictions have been the Achilles’ heel of many more reputable disciplines than philosophy, like economics. Human beings have a nasty habit of not doing what the models say they should, and most philosophers retain enough sense of self-preservation to shy away from prediction whenever possible. Still, a few of the less judicious philosophers of history, like Plato, Spengler, and Marx, have taken the plunge. Spenglerian cycles of history take a couple thousand years to check out, fortunately for Spengler, but Plato’s prediction of eternal decline and Marx’s of advanced capitalism preceding communism were — how shall i put this politely? — howlingly wrong. The very belief that history has a direction is a prime piece of foolishness in its own right.

Brute matter is more tractable. Einstein’s equation for the precession of the perihelion of Mercury, which Newtonian mechanics could not explain, is a classical instance of a successful prediction. Although the precession was a matter of a lousy 40 seconds of arc per century, Einstein wrote Eddington that he was prepared to give up on relativity if his equation failed to account for it. Ever met a philosopher willing to throw over a theory of his in the face of an inconvenient fact? Me neither. Grade: No grade point average. All courses incomplete.

Tools. OK, there’s propositional logic, for which Aristotle receives due credit. But really that’s more mathematics than philosophy, Aristotle’s version of it was incomplete, and it took mathematicians, like Boole and Frege, to make a proper algebra of it and tighten it up. With this one shining exception philosophy has been a dead loss in the tools department. Probably its most famous contribution is Karl Popper’s theory of falsifiability, which turns real science exactly on its head. Where real science verifies theories, Popper falsifies them. Most of us consider “irrefutability” (not “untestability,” which is a different affair) a virtue in a scientific theory. For Popper it is a vice. Mathematics, which is obviously not “falsifiable” and equally obviously “irrefutable,” supremely embarrasses Popper’s philosophy of science, and Popper takes the customary philosophic approach of never mentioning it.

Far from supplying us with tools, philosophers have taken every opportunity to disparage the ones we’re born with. According to Berkeley things do not exist outside of our mind because we cannot think of such things without having them in mind. According to Kant we are ignorant because we have senses. I cite these arguments not because they are bad, which they are, but because they are the most influential arguments in modern philosophy.

To modern philosophy in particular also belongs the unique distinction of making the ad hominem respectable. According to Marx we reason badly about economics because we are bourgeois. According to the deconstructionists we are racist, being white; sexist, being male; and speciesist, being homo sapiens. Grade: Fat, drunk, and stupid is no way to go through life, son.

Advice. Moral advice from philosophers divides into two categories, the anodyne and the dangerous. Under the anodyne begin with Plato and “know thyself,” which is to advice what “nothing changes” is to explanation. Kant recommends that we treat our neighbor as we ourselves would be treated, which works well provided our neighbor is exactly like us, and sheds little light on the question of how we would wish to be treated, and why. Rand counsels “rational self-interest,” which might be helpful if she told us what was rational, or what was self-interested.

Under dangerous file Nietzsche’s “will to power,” just what a growing boy needs to hear. (Yes, he is tragically misinterpreted, and no, it doesn’t matter.) But utilitarianism, “the greatest good for the greatest number,” with its utter disregard for the individual, is the real menace. Occasionally some poor deranged soul actually tries to follow it, with predictable consequences. Ladies and gentlemen, I give you the consistent utilitarian, the unblushing advocate of infanticide and cripple-killing, Mr. Peter Singer. The sad fact is that your moral intuition, imperfect though it is, gives you better advice than any moral philosophers have to date. G.E. Moore, confronted with this fact, responded with “the naturalistic fallacy,” from which it follows that the way we do behave has nothing to do with the way we should behave. Well George, natural selection, which largely governs our behavior, has seen us through for quite a long time now, which is more than I can say for moral philosophy. Grade: Zero point zero.

One loose index of the value of a discipline is whether it helped humanity out of the cave. Mathematicians, scientists, engineers, and even a few economists have all made their contributions. As for philosophy — we programmers have a term to characterize a programmer without whom, even if he were paid nothing, the project would be better off. The term is “net negative.”

Is it too late to start over? Tomorrow we will consider a better approach.

(Update: Bill Kaplan notes in the comments that I had the Einstein-Eddington story backwards, which reflects no credit on Einstein but, alas, none on the philosophers either. Umbrae Canarum comments. Colby Cosh wittily points up my debt to David Stove, to whom I owe some, though not more than 95%, of the argument. The original draft contained an acknowledgement of Stove, which was inadvertently omitted in the final version thanks to a transcription error by one of my research assistants. I recommend Stove’s The Plato Cult to anyone with even a mild interest in the topic. You skinflints can find a few of his greatest hits here. Ilia Tulchinsky comments. Jesus von Einstein comments. Ray Davis comments.)

Apr 282004

An old joke has a grocer trying to explain business ethics to his son. “Suppose a lady comes into the store,” he says, “buys two dollars worth of merchandise, pays with a fifty, and leaves, forgetting to take her change. Here’s where business ethics comes in: do you, or do you not, tell your partner?”

Now a harder one, from real life. Suppose you own a second-hand store. You run profitable weekly auctions, the seller’s best friend, by gussying up a window with a few especially nice items and inviting customers to bid. One week you take two lamp bases, outfit them with new shades, and put them in the window, describing them, accurately, as lamps, not as valuable antiques. The lamps find two bidders, who both offer substantial amounts of money. As you wrap them for the winner you both notice price tags at the bottom of the bases, for an embarrassingly small amount, from an embarrassingly modern store. The winning bidder understandably balks at paying several times for the lamps what he would have paid for the bases and shades retail.

Here’s where business ethics comes in. What do you do? You can’t very well demand that the winner pay his bid, giving him a lecture on the subjective theory of value. It’s not gonna happen. Do you simply remove the tags and go to the underbidder, who hasn’t seen them? Are you obliged to tell the underbidder about the tags, which are now essentially public information? If you don’t, what do you tell the winner, now loser, when he comes back to the store, as he surely will, and asks what happened to the lamps? Do you have to tell him anything at all? Or do you ignore the underbidder and renegotiate a deal with the winner?

I honestly don’t know the right approach, and am curious what my readers think.

(Update: John Venlet comments.)