Against The 70s

Someone not so recently asked a big question, "Why does the 1970's inflation matter so much to economic thought?". There are so many stories told about that period that it has passed into myth. It isn't really clear why, at least if you look at it through the lens of high powered macroeconomic theory. Supposedly it all has something to do with the Phillips curve. The Phillips curve is an expression of the observation that the rate of inflation is negatively correlated with the rate of unemployment. The Phillips curve hypothesis is that this correlation is stable (at least, holding institutions constant) and that the order of causation can run from inflation onto unemployment. The usual story is simplistic: "Back then we believed in the Phillips curve, but the 70's taught us not to do so.". That sound you hear is a vortex generated by philosophers of science rolling their eyes.

When you try to put meat on these bones, you find they break too easily. It isn't easy to find a high flying macro theorist who actually believed in a stable, exploitable Phillips curve. The classics certainly couldn't believe in such a money illusion; Keynes couldn't have argued for a stable inflation/unemployment trade-off (if it existed, why would we need G > 0 ?); Samuelson and Solow certainly didn't believe in it; nor did Fed Chairman at the time Arthur Burns. It's hard to find a single person that "believed" in the Phillips curve in the way it is said to have been.

Milton Friedman

These facts - and they are brute historical facts - have led some to believe in a conspiracy theory of the 70's. "Milton Friedman and the Chicago School convinced everyone that the 70's 'proved Keynes wrong because the Phillips Curve was wrong!1!' was all a lie and therefore modern macro is an illusion meant to disguise naked power grabs by The Enemy.". I put it in a way that you could see how fallacious such reasoning is, but I've seen it put almost as bluntly before.

It is strange, you have to admit, that such brilliant people would be snookered by it. Not just right wing radicals who want validation came out of this. Ed Phelps, Stanley Fischer, and Tom Sargent all saw ... something invalidated. But if it wasn't the Phillips curve, what was it?

Stevie Nicks

The first thing that you have to realize about the 1970s is that it was not, in fact, the 2010s. Nobody in 1976 - not Nixon, not Friedman, not Samuelson and not anyone in heterodox economics - was also in 2016. Everybody was groping blindly and if some had more insight than others, well we should be so lucky. The other thing to realize is that high falutin' macro theory is a tiny and rare thing. Nixon certainly never read a single work in the field and didn't have any friends that did. Ed Cole - one of the presidents of General Motors - could tell you a lot about the Chevy Corvair or Vega, but knew and needed to know nothing of the debate over large scale statistical models and certainly he had no opinions worth noting on anything as abstruse as the Cambridge Capital Controversy that was so distracting in the 60's. This is interesting given how macroeconomic his job was. Some basic facts from Wikipedia: GM at its height measured its profits in % of GDP. GM was the second largest employer in the world - behind only the entire Soviet state.

So, given that Cole was no expert in high macroeconomic theory for its own sake, what did he believe? Clearly, I can't read his mind. But I can give you a picture of what he likely believed, even if he would quibble with a nibble or two. If you are a fan of brief summaries, I'll give you one: "He thought he lived in the era of Mad Men.".

John Kenneth Galbraith

The person who most clearly put the vision to paper is J K Galbraith in his books The Affluent Society and The New Industrial State. Since this vision failed, it might seem that I came to pick on him, but I actually a lot of sympathy for him. He was trying his best and had a basically empirical outlook. He was basically right on backing imperfect competition. Even if he went too far and replaced it with something equally simplistic, Galbraith was right to question consumer sovereignty. He worried about the structure of the firm and capture of government legislation by business before it was cool. Galbraith was trying to think through ideas that don't formalize very easily. He was trying to get away from the myth of the rational consumer. Herbert Simon was working on similar ideas and did better work, but never anything macro related. Galbraith tried his hand and if he didn't succeed, well, did anyone?

Carlo Ponzi

Galbraith's method is developed in his second book, The Great Crash, 1929. This is a strange book for a modern to read. The first thing one notices is how little a role the year 1929 plays. The lengthy, hilarious section on the Florida real estate bubble is the best part of the book - but what all does it have to do with the Great Depression? This part of the book is an argument - I don't remember if it is explicit or implicit - that the market is not guided by rational consumers. The masses are irrationally attracted (that is to say, they will invest more than they would expect to receive if held down and forced to think it through) to the promise of easy money, even if it comes from Carlo Ponzi or Donald Trump. They are irrationally repelled by the slightest loss. They put good money after bad. They're moved by emotional displays from the wealthy. They do many things, but they do not maximize net present value like Irving Fisher taught us.

Sigmund Freud

Though the masses are not very good consumers, the advertisers and engineers, they're very good (supposedly). From this vision, the corporation emerges as the fundamental entity of economics. A corporation consists of four parts (my typology, not his): the capitalist, the engineer, the laborer and the advertiser. The advertiser has read his Freud and empirically studied the deep parts of human nature. As depicted in Freud On Madison Avenue, the advertiser designs the aesthetics of the car to be a giant phallus with a clitoral emblem on a vaginal grille. He can then determine exactly how much the irrational consumer will buy in aggregate. The engineer then designs the car as a functional item, which selects the costs of production. The laborer and capitalist then build the cars. The income is then divided among the four parts of the corporation by the labor contract (which is fixed by negotiation between the capitalist and labor, which in practice is represented by union officials). Note that it is not the profit that is divided, but the income. That doesn't matter in this system - income and profit are jointly decided by the engineering and advertising experts. The corporation never has to worry about society wanting less products in general, demand will be simply created by the government if it ever accidentally slackens.

There is much to criticize in the above system. The biggest problem is a very strong difference that is assumed to exist between the irrational common consumer and the tiny echelon of experts that control them. There's no way to get around this, there should be no apologetic for it and there is no question into which class Galbraith put himself. It is assumed, not proven. When pushed on this point, Galbraith would fall back on his endless supply of jokes about irrational consumers. In his economics and his novel, this was all but explicit. The only question was whether people Galbraith would be allowed by his fellow elites to make the masses a comfortable world. There is no freedom to give them.

The role of the state is very strong in Galbraith's mind. I've already mentioned maintaining demand at a full employment level. Another is managing labor unions. The labor unions face a macroeconomic prisoner's dilemma. Imagine two labor unions that have the choice of either asking for higher wages or keeping them stagnant. If they both keep stagnant, then the price level stays the same and everyone is well off. If just one asks for an increase, then its members are much better off. But if both ask for an increase, relative wages stay the same but the money price of everything goes up. Therefore, people are worse off. (This actually happened in England in the 70's) This is one of the state's tasks as countervailing power against the large corporations (and their unions). The simplest and most dangerous way of doing this is wage controls - Galbraith never bothered to ask for another one. Price controls in general follow from the same argument on advertisers instead of laborers.

 Panasonic Space Age Television

Outside of the secluded world of high economic theory, much of what I just exposited was uncontroversial. Arthur Burns, the head of the Federal Reserve at the time, believed much of it. Galbraith's books were best sellers. Further, it was in the general culture. To be an adman in the 60's was to be the king of the world.

What happened in the 70's was the fall of the whole idea. For the first time, the mandarins in charge were forced to admit that demand management was non-trivial. The incoherent system of monetary policy, price supports, unpredictable government regulation and massive war time spending interacted with oil-induced supply shocks and changing culture demand shocks to pull aggregate demand in every direction. The net result was gas queues, stagflation and malaise. The role of the failure of price supports, while not shocking to any theorists, bolstered Friedman's claims that markets were a necessary part of demand management (he didn't put it like this). Friedman prestige didn't come from just getting it right, it came from how he got it right. No high powered macroeconomist denied the possibility of stagflation - but Friedman happened to have the perfect combination of being against price supports, for rule based monetary policy, for smooth government regulation (okay, I'll be fair. He was against government regulation in general) and having done deep work about how the economy can smooth over shocks. It was exactly what people needed in 1971 (well, government regulation in general is arguable, but certainly not basically arbitrary price controls).

The markets upset the Galbraithian vision in a deep way. Recall that GM's deeply learned advertisers decide on how much sales they make this year. The human mind cannot resist the sexual allure of their automobiles ... supposedly. But the oil crisis meant that people wanted smaller, more efficient cars, not rolling slabs of steel. The Japanese entered the automobile market with cars that people wanted and GMs sales declined. Wasn't GM supposed to control sales?

Another example. When GE designed a television, they decided the sales. They knew - knew - what people wanted in a TV: they wanted a wood exterior and a durable stainless steel frame. They wanted furniture (I know they thought this, because I've talked with the people who built them at the time). When Japanese companies started exporting cheaper, lighter all plastic televisions, GE was sure no American would want one. As it turned out, those "irrational" consumers resisted the psychological allure of the expensive American furniture and just bought cheap, functional boxes. This is not how the system was supposed to work! Didn't these consumers know that they were irrational?

The important thing about the 70s is that they seemed to show that irrationality could only be pushed so far. Consumer preferences can't be written off as a minor addendum. The point of Friedman about inflation expectations in the Phillips curve is minor. People had been writing about inflation expectations since monetary analysis began. What was influential was his whole approach. It was part of a general tendency to move toward rationality - game theory began to go deeper into traditional economic realms (such as industrial organization). And damn it, if you presume consumers act basically according to their preferences, then price controls and shocks cannot coexist. Friedman and others hammered on these points as far as they could. And then they were pushed even further...

You see, through the lens of the 70s experience outlined above, purely rational expectations economics starts to look good. However, once the "t"s were crossed and the "i"s dotted, the New Classical school that supposedly took them as their basis didn't live up to its promises. I mean this explicitly - they promised to pass statistical tests that they did not. The New Classicals stopped using these statistical methods because "they were rejecting to many 'good' models". Perhaps this movement toward "rationality" was itself irrational. In many ways, by the time the 80s ended, the rationality revolution of macroeconomics was spent. In other fields (the aforementioned industrial organization, for instance), the move to rationality bore better fruit.

Even with all these qualifiers, it was still the 70's that forced people in power to consider the consumer as an autonomous human being. And that is why it looms so large in our thought.

Idealism And Modern Science: Intentionality

Immanuel Kant

Last time we talked about High German Idealism, I concentrated on giving an example of how it attempts to reconcile the physical portrait of the world with the world of experience and intuition. We constructed a loose picture of what I called The Dang-An-Sich, which was - roughly speaking - the entire universe. I used Kant's name, but it could also be called Schopenhauer's "World As Will" with no loss. I said that The Dang-An-Sich was "empty of content". There was no volumes and pressures, no fluids or gasses, no chairs or minds, etc. I showed where one could find proofs that, among other things, the basic thermodynamic functions such as volume and so forth could be shown to be "minimal statistics" of the behavior of The Dang-An-Sich. Therefore, they or functions of them will be in every living thing's description of the physical world. This is part of what is called in Schopenhauer's language "My Representation", which exists and is well formed even though The Dang-An-Sich cannot be directly probed. This gave us good examples of idealism and showed that their ideas were not empty of content.

Arthur Schopenhauer

Today I'm going to talk about some more philosophical concerns of Idealist philosophers. In particular, it can be shown exactly that Schopenhauer is correct when he says  the universe as a whole, The Dang-An-Sich, must be purposeless in some sense. That is, The Dang-An-Sich has a special property that means that it doesn't care at all what overall state it is in beyond an important technical detail. This demonstration implies that any system that does care about what state it is in, called by Husserl an "intentional system",cannot be the whole universe. Therefore, any subsystem of the Dang-An-Sich that has the property that it prefers some states to others must divide the universe into an inside and outside. This means that an idealist may not be "solipsistic", in a well defined sense.

W R Hamilton

The fundamental thing about the universe as a whole, The Dang-An-Sich, the thing that distinguishes it from any other object is this: it does not interact with anything outside of itself. I will talk about a universe that consists of many, many classical particles. Each particle has a position and momentum at a particular time, so that the entire system can be seen as a vector in a very high dimensional space. This space is called "phase space" and its points are the states of the system. Any particular fact about the system at a given time is a function of the position and momentum of (at most) every particle. There are few essential changes to this picture if we move to quantum mechanics, except the dimension of the space is infinite and the algebra of dealing with the functions is different.

The laws of physics do not depend upon time, which can be derived from the first fact. Any system where the laws of physics depend upon time can be expanded as a subsystem of one where the laws of physics do not, but the universe is not a subsystem of a larger system. Therefore, laws of physics of the universe are time independent. If the laws of physics of a system are time independent, the system described conserves energy. Therefore, the entire evolution of the system is given by the level curve of a so-called "Hamiltonian" function. These functions were named after their discoverer - the above pictured William Rowan Hamilton, based on his work with optics (and Lagrange's equally foundational work). I will throughout call an energy conserving system a Hamiltonian system.

But what is a Hamiltonian? Recall that we've just proved an essential physical fact about a system - it has constant energy. The system can change phase only by moving energy around - between its particles, for instance. The Hamiltonian function captures all of the flow of energy within a system. From a given state, the amount of energy it takes to get to a neighboring state by changing the position or momentum of one or another particle (including that - unique! - neighboring state which requires no energy change) gives the change in the Hamiltonian. As before, if energy is conserved, then the system moves on the level curves of the Hamiltonian.

The most simple Hamiltonian is that of a harmonic oscillator. The idea is of a particle bobbing up and down, as on a spring. As the velocity goes up, the particle gets a little farther (closer) from (to) equilibrium. This causes some of the energy to move from (to) the spring and restore . As a result, the level curves are simply ellipses. We can similarly find the results for pendulums and many other system. Most Hamiltonian systems cannot be solved exactly, but wander around state space almost randomly. Much like a fractal, such curves (nearly) fill the volume of state space.

There are many important facts about Hamiltonians. For instance, their level curves (constant energy trajectories) of a Hamiltonian never intersect, so that no two identical systems will be in the same state unless they also have the same energy. Classically, they can get as close as they like, however quantum mechanics forces a discrete separation. Energy is therefore a macroscopic "state function". There is no cheating here, since non-dependence of the laws of physics everywhere is not a local property, we shouldn't be surprised that one derives global properties from it.

Possibly the most important fact about Hamiltonian systems is what is called Liouville's Theorem (notice, again, there is a proof in the quantum mechanical case as well). This means that a cloud starting points of always has the same "volume" as each point moves on its own curve. Looking at the above example. If one draws a circle of starting points on the above graph and lets follows the lines, the ellipses will stretch and bend but never grow or shrink. This means that, in particular, it is never the case that the circle grows or shrinks. This is perfectly general.

Liouville's Theorem implies that there are no stable equilibria for a Hamiltonian system. In the oscillator example, the system stays still if the spring is left at rest, but every perturbation no matter how small means the system moves forever. Since the universe is a Hamiltonian system, it has no stable equilibrium states. This means that the evolution of the universe cannot be "toward" some final state. The Dang-An-sich, the universe in itself, has no preferences among states. It just wanders around state space. It is not only empty not only of content, but it also has no goals.

Edmund Husserl

Edmund Husserl is often called the "father of phenomenology", supposed to be an exact philosophical science of all perception. Husserl was originally a mathematician trained by no less than Leopold Kronecker and Karl Weierstrass. Like many of Weierstrass's students, he was acutely sensitive to foundational issues in mathematics. This lead him into philosophy, where he was inspired by the philosopher and co-founder of psychology Franz Brentano (you might have heard of another one Brentano's students - Sigmund Freud). Brentano was a Catholic priest and took from the Scholastic's interpretation of Aristotle and Aquinas the idea that conscious is always directed at something. One can be conscious of one's surroundings or of one's goals or (most importantly for the Scholastics) of God, but not conscious in general. As G K Chesterton said in Orthodoxy "The worship of will is the negation of will ... because the essence of will is that it is particular.".

Husserl claimed to invent a psychological/philosophical/transcendental method of achieving absolute certainty by "bracketing" each little bit of sense-data and examining it, disregarding questions of its existence. Every time we bracket a blob of sense-data, either 1) we discover it's content is identical with something we already are certain exists or 2) our world grows by one object (More on this in a bit). Why? We may be absolutely certain that we exist and the existence of an object toward which consciousness is directed toward. If it can be known that it is not an object that we were previously aware of, then it is a new object. Therefore, we can supposedly - very slowly! - build a build a world of absolute certainty.

There are flaws with this idea. A system which is directed may not be conscious. Alfred North Whitehead said that it was a profound mistake to think about what we are doing. Not only may the majority of the activities of a system that is conscious be only scarcely directed by consciousness, some of the activities we value most may be barely conscious. This was pointed out by Heidegger to Husserl, who ignored it. The "bracketing" process is vague on how we can learn enough about a piece of sense-data to absolutely know it consists of an object about which we do know absolutely know, kicking that whole important process over to science per se. It isn't clear whether bracketing is psychological or transcendental. Husserl himself changed his mind about this - initially he thought it was psychological, later transcendental. Husserl was a Christian (a Lutheran), but it isn't clear how to treat things we have no sense-data of - like the divine.

But one of the important assumptions, that the above concept of intentionality (interpreted in a highly minimalistic way) always implies that there is at least two "objects" is rigorously true. It follows from Liouville's theorem above. A system that prefers a given, for example, temperature, it must have an outside. This is not a trivial factoid - it is seen in real physics of Hamiltonian "thermostats". These can be checked theoretically and numerically. One can also consider "barostats", etc. that prefer states with particular values of other thermodynamic potentials.

Since human beings are - among other things - thermostats and barostats, they may not be closed systems. Therefore, one may not be The Dang-An-Sich by oneself. This shows that there should be no idealist solipsists.

I have stated all of this without reference to the higher level phenomena of actual experience. I left out the "minimal statistics" state functions (other than energy) such as pressure, volume, etc. These state functions can be described as functions on every possible state. We can then define a "macrostate" as the set of states such that all the state functions are the same for each state (or "microstate") in that set. Here the story actually gets a bit more complex. It turns out there are some macrostates that have a lot more microstates in them than others. Since "most" Hamiltonians wander around phase space almost at random, we can see that a Hamiltonian system will (probably) spend (almost) all of its time at the unique macrostate with maximum entropy. This can be made much more precise, of course.

It is not clear to me yet how this relates to the simple story of Schopenhauer and his followers (such as Heidegger and Sartre). It is philosophically important that The Dang-An-Sich has no direction, but it is not so clear that the non-intentionality of My Representation follows from any principle. I would like to take up this some time later, but no promises.

Unexamined Life: What Have I Learned From Philosophy?

I have read a lot of philosophy, perhaps more than the subject deserves and perhaps less. Philosophy is odd, everything is obvious to a philosopher but nothing between philosophers. Philosophy has been prepped for the trash pit many times, by religious fundamentalists, by over-reaching scientists, by mad governments, by great philosophers and - most fatally - by many bored readers.

Albert Einstein

The Pythia said "No one is wiser than Socrates.". In his day, he could walk up to what we would call a scientist and defeat them - clearly, nobody knew more than him. Much of the disrepute of modern philosophy is rooted in this no longer being true. No matter who you think the greatest living philosopher is (and I doubt that is a definite description), you probably wouldn't go on to say that they are the smartest person in the world. You'd probably admit Terence Tao is at least a little better at math.

But I didn't put Einstein up there because I think he was smarter than Husserl. The disrepute of philosophy comes from another, related source: philosophers aren't our deepest thinkers any more. Einstein has had more influence on us how we think about time than Carnap or Heidegger, more on how we think about space than Bergson or Whitehead. Nietzsche's philosophers of the future don't call themselves philosophers.

I do think philosophy has an important place. What makes humans unique is that they can understand what they do (this, of course, is a philosophical opinion!). In many instances, philosophy is just thinking about what we do. When you read a paper like (Alchian, 1950) or (Krugman, 1996), you are seeing philosophical argument. In this case, there is complete agreement, but I would say - another economist, another philosopher might disagree.

Daniel Dennett

So, what have I learned from philosophy? What philosophers - and "philosophers" - have influenced me? The answer is simple: Daniel C Dennett III. I'm going to leave him to another post as being too important. I will admit I have been more influenced by the technical/logical philosophers of the so-called "analytical" school. It isn't that I think they are smarter, just as a mathematician their work is often more directly relevant to my daily life. They are almost all black & white, dead men. I should include female philosophers such as Susan Haack & Deborah Mayo. In fact, the only reason I didn't include Mayo because I left her book in America. I'm leaving continental philosophers for another post.

Jaako Hintikka

Despite my fascination with intuitionist/constructive approaches, their philosophical views I find less interesting. The math is neat, but the philosophy is weak. The philosopher that has influenced my view of mathematics the most is Jaako Hinitikka. Unfortunately, he was not as cool as the above picture makes it seem. Hintikka developed what are called "Game Semantics" for quantifiers. This is the best explanation for why classical analysis has the structure it does. The reason is that classical analysis is based on non-refutable arguments. It's best explained with an example.

Let's say that I claim a given function, perhaps the angle of a shower knob and the equilibrium temperature of the water coming out of the shower head, perhaps the solution to a DE, is continuous. What does this mean? One might say that it takes on the value of the limit on that point. But this is not the point of view of classical analysis. In classical analysis, the important thing about my claim is that you can't disprove it. Let's say we know the function takes on a value at a certain point - we know by, say, measuring the heat of the water when the knob is at a certain angle. When I say it is continuous, that means you can't truthfully say it doesn't get close to that value when the angle is close. If it could, you could say it's getting near some over value. We can call the difference between the measured value and the "error". But any given amount of error is too much, I can always just sneak by it. You can't prove that there is a jump, therefore the function is continuous.

Hintikka gave formal rules for interpreting any sentence from classical mathematics like this. That is by itself a huge deal.

Wittgenstein

The first philosopher to genuinely fascinate me was Wittgenstein. I spent a month reading and re-reading his Tractatus Logico-Philosophicus, trying to find the meat hidden on its austere bones. On the technical side, Wittgenstein co-invented the truth table within it. On the more philosophical side, it pointed to a metaphysical semantics of the new logics and set theory. On a deeper level, it pointed to a world beneath language and made sense of the idea that there was more on Heaven and Earth than in our philosophies. In his later work, Wittgenstein would attack the metaphysical parts of the Tractatus, on the grounds that even if the metaphysics was true they had nothing to do with why we believed that they were the case. This attack, laid out in Philosophical Investigations, naturalized language in a way nobody had seen since Hume. Only after this book could we go back and see how wise Hume was. I don't think that the attack affects the value of the Tractatus metaphysics as a semantics of set theory, but certainly no one will take them without a grain of salt anymore...

Thomas Schelling

Thomas Schelling's Micromotives And Macrobehaviors is one of the greatest books on social philosophy I ever read. Along with the Tractatus, it took me apart and put me back together a smarter and wiser person. It is hard for me to summarize, but I don't feel bad - it is hard for him to summarize too. Often we associate game theory with rigorous mathematical analysis - on the grounds that if Von Neumann was doing, so must everyone else. Schelling was given a Nobel Memorial Prize for contributions to game theory, but he never used math in any deep way in his work (contrast with the other winner, Robert Aumann). The important thing for Schelling was that game theory forced the user to consider the effects of his actions on others, and theirs on himself. What mattered to Schelling, in other words, is the notion of an "equilibrium". Game theory then is as much Hume & Kant as Luce & Raiffia. There is no formal "game theory" in Micromotives and Macrobehaviors, but there are hundreds of examples of equilibrium arising from social interactions giving results paradoxical and straightforward.

It was perhaps Hegel who was the first to recognize the importance of self-negating equilibria. Every society comes with it a set of norms & expectations. But every society so far has had some norms that force in conflict with the expectations. Eventually society adjusts its norms to remove this contradiction. Each society is out of equilibrium and therefore history matters to it. Unfortunately, in Hegel, these notions are tied to a history that is, in most matters of fact, false. I will give the Marxist version: In perfect competition, the wages to labor will be subsistence wages (this assumption was common to all classical economists) and technical change will tend to deepen capital (this is a norm). Capitalists expect capital deepening to profit them (this is an expectation), but will find in the long run they can't all deepen against each other (this is called fallacy of composition). Instead, capitalists will be paradoxically trapped underneath a mountain of less profitable goods. This is a Hegelian contradiction, a self-negating equilibrium. Marx's proof used the labor theory of value instead of the fallacy of composition, but it amounts to a different gloss on the same thing. Marx might have been smart enough to make that argument by himself, but I needed Schelling.

David K Lewis

I feel kind of odd putting David K Lewis on this list. He's too important to me to ignore, but my disagreements with him are part of what made me keep reading philosophy. He was the first academic philosopher that I liked, not just the philosophical aspects of a scientist or economist. Lewis made permanent contributions to mathematics, but I have to say - I basically am completely uninfluenced by them. I've never once started a proof with megethology in mind. Lewis is most famous for his adapting Wittgenstein's "The world is everything that is the case" classical logic semantics for modal logic - the so-called "possible world" semantics. They nearly single handedly brought metaphysics back into academia. Lewis (and, to a greater extent, his ally Daniel Dennett and, to the optimum extent, linguist/mathmatician Noam Chomsky) helped bring analytic philosophy out of behaviorism. But Lewis's solution was Bayesianism, which is not to my own taste (though it is important and I'm glad someone was working on it).

Of his ideas, his concept of a coordination game has been the most important and influential. He claimed to have been inspired by Thomas Schelling above. I first read about it in his book Convention, which is also where it was invented. I've gone over this before. His definition of value as what we "desire to desire" is something I've been thinking about recently. I like the way that it reduces the theory to preference theory (for the classic reference on preference theory, see Debreu's Theory of Value - Debreu's "Value" is value in another sense) without impoverishing the value part of the apparatus. The words of Kant are very comprehensible: what we should desire to desire is those desires that are coherent for the population. The words of Bentham too: what we should desire to desire is the satisfaction of the most individual desires. Hegel (and Marx) pointed out: our desires generally conflict, society is out of equilibrium. You could, if you want, do all social philosophy this way.

In fact, one reason I like Lewis is his congenial approach to formalization. Formalizing philosophical concept of value by putting it in terms of (in some sense "reducing" it to) the preference theory of economics allows us to sharpen and clarify the philosophical differences of old - but shouldn't try to artificially "solve" them. This seems to me to be a right way to go about things.

Robert Nozick

Okay, so if I felt odd about David K Lewis, I have to say this about Nozick: I've never read his big book on political philosophy. I've read an article attacking Ayn Rand and another one attacking "Austrian" Economics, but hey, easy targets. I'll come out and say it: Nozick tried to make a philosophical explanation of what we call "libertarianism" or "classical liberalism". I won't address whether his argument fails since, again, I haven't read it. I kind of doubt that reason/philosophy alone can make a political argument look good - logic shorn of evidence tells you nothing about reality.

What I find most interesting about Nozick is his last book, Invariances. In this book, Nozick develops a novel explanation of what is "objective". The usual philosophical gloss is that something is "objective" iff we could conceive of a completely physical description. This does not match what we usually mean by the word. When someone is pointing a gun at me, I would say they are objectively being a menace. I do not mean that there is some physical description of him being a menace. What I mean - according to Nozick - is that their being a menace is invariant over the variations relevant to the conversation. This ties down the notion of objectivity to Wittgenstein/Lewis idea of language games.

Nozick is interested in the implications for ethics - Could there be "objective ethics"? This is less interesting to me, but I'll go through it nonetheless. Nozick tries to build up from a libertarian state to a democratic state using the idea that some values (desired desires) can be better served by democracy/market mixture than a "pure" market. Rawls, another ethical/political philosopher, proposes his "veil of ignorance" argument as basically Nozickian objective ethics. I think that shows that there are, in fact, too many Nozickian objective ethical systems. These examples can be multiplied until and beyond one reaches the count of ethical philosophers. Nothing says that one definition of relevant variations is the right one.

My plan now is to do three more posts like this. One on Daniel Dennett, the philosopher who influenced me the most. Then a third post on classical and continental philosophers, who are important and deserve mentioning even if they haven't struck my fancy.

First color picture of the post

Also, you may or may not see a review today. I've been having internet troubles and am having a hard time watching videos.

Maxwell's Demon

In Theory of Heat, J C Maxwell - one of the greatest physicists of all time - attempted to illustrate the new theories of molecular flux and thermodynamics in a form as complete as the science allowed. He finished this section with a thought experiment that purported to show "Limitation of the Second Law of Thermodynamics". "Before I conclude, I wish to direct attention to an aspect of the molecular theory which deserves consideration". He introduced the idea we now call Maxwell's Demon, meant to illustrate the nature of Maxwell's thoughts on the Second Law. I'll let Maxwell illustrate:

"One of the best established facts in thermodynamics is that it is impossible in a system enclosed in an envelope which permits neither change of volume nor passage of heat, and in which both the temperature and the pressure are everywhere the same, to produce any inequality of temperature or of pressure without the expenditure of work. This is the second law of thermodynamics, and it is undoubtedly true as long as we can deal with bodies only in mass, and have no power of perceiving or handling the separate molecules of which they are made up. But if we conceive a being whose faculties are so sharpened that he can follow every molecule in its course, such a being, whose attributes are still as essentially finite as our own, would be able to do what is at present impossible to us. For we have seen that the molecules in a vessel full of air at uniform temperature are moving with velocities by no means uniform, though the mean velocity of any great number of them, arbitrarily selected, is almost exactly uniform. Now let us suppose that such a vessel is divided into two portions, A and B, by a division in which there is a small hole, and that a being, who can see the individual molecules, opens and closes this hole, so as to allow only the swifter molecules to pass from A to B, and only the slower ones to pass from B to A. He will thus, without expenditure of work, raise the temperature of B and lower that of A, in contradiction to the second law of thermodynamics."

The Wikipedia image is much better than the one I tried to make.

This brief thought experiment has given rise to a minor, but interesting, literature on whether Maxwell's reasoning is correct. Surprisingly, smart money says "No."! . The primary difficulty in Maxwell's thought experiment is his opinion that just because you can capture one fast particle that you can continue to capture more. In fact, this is a direct violation of the principle of detailed balance - if the door is open for any length of time, it is as likely to let a particle out as in (there are as many fast moving particles on one side of the door as the other after all!). Maxwell's reasoning is therefore circular, it assumes that if one could violate the second law, then he could. Another way of putting this is that he did not include the work done by the demon as a part of the system. If the demon is considered a rectifier or computing device, then the entropy of this device must be such that equilibrium will still be reached. This approach is demonstrated in a state of great excellence in this paper. Since the invariance of phase volume is a principle of mechanics, the circularity of reasoning described is revealed. This second approach - really the first approach in new clothing - was pioneered by Szilard and brought to a state of modernity by Landauer. In this paper, the Szilard-Landauer approach is given a simple model which is solved explicitly. They don't go into detail about the equivalence of these lines of thinking, in fact I don't know if anyone has bothered to do so. Incidentally, this literature has been tough for me to track down, even some of the most famous papers by Smoluchowski (as far as I know, Experimentally Verifiable Molecular Phenomena that Contradicts Ordinary Thermodynamics has never been translated!). Still, I can give examples of pieces of the literature. This literature is not pure theory, it also includes plentiful experimental and numerical examinations of these thought experiments. This excellent paper includes both a good summary of the issues and a formal model of the above trapdoor, showing precisely how it fails. This paper shows how well numerical experiments can clarify and elucidate, something near to my own heart.

Before I go, I should mention that I first became aware of this literature through the Feynman Lectures on Computation, which includes chapters on Quantum Computing, Reversible Computing and the physics of computation. His discussion of these issues probably influenced me a lot, but I don't want to dig it out of it's current location. Feynman also made a sizable contribution to this literature in his Lectures on Physics, where he introduced the Brownian Ratchet to illustrate the concepts above. This section is a very good example of how theory can be used to elucidate.

Much, much better than my attempts  

The two sides of the ratchet are in two boxes of gas, to the center a mass is tied. Randomly, the gas will push the blades in tank 1 (at temperature 1) left and the pawl in tank 2 (at temperature 2) stops the ratchet from moving right. This means that just like the Smoluchowski trap, the ratchet works as a rectifier. Feynman analyzes in detail why this fails - and it fails for the same reason that Maxwell's failed. There is a presumption that the pawl is not subject to the same random fluctuations, in other words that one need not worry about gas particles moving the other way. This whole chapter is worth reading (of course, the entire book is worth reading...) but I will only reprint his final words:

"If T2 were less than T1, [then] the ratchet would go forward, as anybody will believe. But what is hard to believe, at first sight, is the opposite. If T2 is greater than T1, the ratchet goes the opposite way! A dynamic ratchet with lots of heat in it runs itself backwards, because the ratchet pawl is always bouncing. If the pawl, for a moment, is on the incline somewhere, it pushes the inclined plane sideways. But it is [almost] always on an incline plane, because if it happens to lift up high enough to get past the point of a tooth, then the inclined plane slides by, and it comes down again on an inclined plane. So a hot ratchet in pawl is ideally built to go around in a direction exactly opposite to that for which it was originally designed!"

Exciting stuff!