Sunday, September 11, 2011

History Lesson


Earl Hines made this a great historical/musicological monologue for Ralph Gleason's Jazz Casual, a series that ran from 1961-1968. As far as I can tell Hines doesn't embellish anything. In fact, he comes off as being quite humble and appreciative of his influences in the episode. The influence of the great bebop performers on Hines is particularly interesting to me (though I'd also be interested in the reverse relationship, especially on Monk). Hines's lack of ego is shown by his willingness to listen to the Bop players. Though it wasn't true by the 1960's it's place in Jazz music when it began was controversial, some condemning it for the same reason Hines praised it (bringing in more sophisticated harmony). Hines and Billy Eckstine were important bridges between Armstrong and Gillespie.

Part 1
Part 2
Part 3

Friday, August 19, 2011

That I've Been Doing When I've Been Not Posting

Many apologies for not posting anything in months. After a change in jobs and home, I simply forgot that I had or ever wanted to blog. It would be interesting to know the role environment plays in life, since there is no obvious reason that physically moving should change my writing habits.

Well, since then I have found many things that are new to me. One of the best blogs online is Terence Tao's. It's neat to see the web of mathematics tied. In addition to wonderful expository notes, interesting alternative proofs and statements of open questions from all over mathematics, the simple shorthand created by being able to linking to Wikipedia to have explanations of a concept tangential to the author's point can turn a post into something the equal of a textbook. The broad range of topics covered by Tao also gives much to recommend.
If one wants a little more time wasting fun to math, then the Stanford Encyclopedia of Philosophy has some great articles. Popper has always interested me when I think about my physicist hat. There is good criticism to make about details of his approach. Namely, that Popper left out the importance of error analysis in both The Logic of Scientific Discovery and Realism and The Aim of Science and led poor Lakatos completely in the wrong direction. Take the following critique:

"Popper himself is fond of citing ... the anomalous orbit of Uranus posed for nineteenth century astronomers. ... [A]ssuming Newtonian mechanics to be precisely correct, the observed divergence in the elliptical orbit of Uranus could be explained if the existence of a seventh, as yet unobserved outer planet was posited. Further, they were able, again within the framework of Newtonian mechanics, to calculate the precise position of the ‘new’ planet. Thus when subsequent research by Galle at the Berlin observatory revealed that such a planet (Neptune) did in fact exist, and was situated precisely where Adams and Leverrier had calculated, this was hailed as by all and sundry as a magnificent triumph for Newtonian physics: in Popperian terms, Newton's theory had been subjected to a critical test, and had passed with flying colours. Popper himself refers to this strong corroboration of Newtonian physics as ‘the most startling and convincing success of any human intellectual achievement’. Yet Lakatos flatly denies that there are critical tests, in the Popperian sense, in science, and argues the point convincingly by turning the above example of an alleged critical test on its head. What, he asks, would have happened if Galle had not found the planet Neptune? Would Newtonian physics have been abandoned, or would Newton's theory have been falsified? The answer is clearly not, for Galle's failure could have been attributed to any number of causes other than the falsity of Newtonian physics (e.g., the interference of the earth's atmosphere with the telescope, the existence of an asteroid belt which hides the new planet from the earth, etc)."

Now, if this critique worked, it would be pretty devastating for the practicality of Popper's program - and Popper always emphasized this practicality (rediscovering and using the Pragmatic theory of truth? I kind of doubt it). But Lakatos's argument hinges on something that should not just be accepted as plain truth that "(e.g., the interference of the earth's atmosphere with the telescope, the existence of an asteroid belt which hides the new planet from the earth, etc)" would have been accepted. First of all, it requires proof that Galle could not control for deviations in the Earth's atmosphere (that is, a proof of his incapability of error analysis). The existence of an asteroid belt is not a neutral position at all, but a rival theory. Not only must it be tested but it must be tested in the same way!

In addition, Lakatos seems to be assuming that an ontological commitment to Newton's Laws is stronger than a practical commitment to empirical standards. Would the experimentalists give up a method to please us theorists? An interesting historical case for philosophers is the question of the existence of atoms. Chemists (playing the role of experimentalists) have believed in them since Dalton in 1803, while some physicists hoped they could be eliminated as mere intuition enhancing artifacts as late as 1908! This 105 year controversy should give an aspiring philosopher a good playground for testing proposals of standards.

Popper is also responsible for modernizing the idea of pseudoscience. Bad science is responsible for a lot of pain, like what Lysenkoism did to genetics and agriculture under the Soviets. However, I don't think it's as all-fired important as Popper does. Lysenkoism was bad because it was wrong, not because it was pseudoscientific. Isn't that enough? A more thorough study might look at how the Soviet structure supported Lysenkosim (or how the Catholic Church supported Ptolemyism or how Freudianism was supported by 50's corporate culture), but it would not be much help to a practicing scientist.

Oh, I haven't yet mentioned Popper's interesting work in the foundations of the social sciences (in his book The Poverty of Historicism), demonstrating the impossibility of genuine general social prediction, and by extension showing that this cannot be the goal for a social science. This part of his theory makes hogwash of many older ideas of history and has never been successfully rebutted. His books The Open Society and Its Enemies are nice books about social philosophy, making the novel argument that democracy's superiority over, say, a Voltaire-ian enlightened dictatorship is democracy's ability to do and un-do without violence. It would be interesting to test his ideas using theories of decentralized control (I cannot give a real analysis because I lack real knowledge of that area). Is the complexity of changing a democratic system a greater difficulty than regulating an country with the extreme information poverty that a dictator must be in? Is the question identical for centrally planned (i.e. Soviet) and decentrally planned (i.e. capitalist) economies? Popper thought so, though his friend Frederich Hayek believed that centrally planned governments with decentrally planned economies were superior.

Phew! That's enough damn Popper.

I've discovered that many of the old Charlie Chan movies are on YouTube! Charlie Chan at The Olympics, Charlie Chan in Egypt and Charlie Chan at Monte Carlo are all very fun. Some people think that Chan's sedentary and unassuming nature are a bit of a stereotype, but I disagree. In any case, you might notice that the actually Asian man in these movies - Keye Luke as Lee Chan - is vigorous and athletic.

This beautiful song by Billy Strayhorn is given an amazing performance by Johnny Hodges and a characteristically astounding arrangement by Strayhorn's great mentor Ellington. The world is full of wonderful music, and we moderns have more access to it than anyone in all history. Take this obscure piece by Mozart that must be performed on an instrument that went out of fashion shortly after his death. ~7,000 people have heard this one version. Do you think that anyone ever heard it in the century after his death? How many do you think heard it in his life?

Well, hopefully I'll get myself to post more regularly now.

Saturday, September 11, 2010

David Kellogg Lewis's Convention

American Analytic philosopher David K. Lewis wrote the book on convention. By considering the meaning of convention, Dr. Lewis brings insight into several important areas with particular interest paid to language. The book was inspired by a spirited attack on the idea that language is ruled by convention by Lewis's teacher WVO Quine. Quine's questions can be paraphrased: "If language is ruled by convention, what language was the convention in? If convention is not literal, what is meant by it? If this is a vauge metaphor, what makes us think it's the right one?". Lewis was also inspired by economist Thomas Schelling's analysis of Coordination Problems.
I do not envy the person who had to come up with a cover to a book titled Convention, but I cannot praise their total lack of effort.
The model that the remaining definitions is - unless stated otherwise - the Normal-Form Game of Von Neumann and Morgenstern. A normal form game can be characterized by it's demonstration of payoffs for different options. It represents each player as a dimension and each option as a row, column or higher dimensional axis. One of the classics is it's representation of the Prisoner's Dilemma:An alternate way of characterizing Normal-Form games is as functions. The set (lets say of size n) of players puts their choice into a n-tuple, which is then fed into the function. The function maps the decisions (which are integers) onto payouts (which can be real). In the case of the above game P(<"Player One","Player Two">) = <"bottom number","top number">. So to completely characterize this function P: P(<1,1>) = <3,3>; P(<1,2>) = <5,0>; P(<2,1>) = <0,5>; and P(<1,1>) = <2,2>.

Most of the mathematical details are inessential to the analysis - Lewis goes as far as to say that he could remove it entirely without substantially weakening his position. Lewis mainly uses Equilibria as his tool for insight, allowing for strong conclusions and good generality. Following Schelling, Lewis distinguishes a continuum between games of pure coordination - games in which the player's payoffs are equal in every square - and games of pure competition - games in which the player's payoffs are opposites in every square. Again, inspired by the work of Schelling Lewis restricts himself to games closer to cooperation.

An equilibrium is when each player has made the best choice given everyone else's choice. In other words, they could not have improved things by altering their and only their choice. In the Prisoner's Dilemma above, for example, Player One's payouts are either 3 or 0 if he chooses column one, and either 5 or 2 if he chooses column two. Thus column two is the better option no matter what Player Two does. Similarly, row two is better for Player Two no matter what Player One does. Thus <2,2> is the equilibrium.

Lewis is particularly interested in a subset of equilibria: coordination equilibria. A coordinition equilibrium is when each player would not have been better off if any player acted differently. That equilibria and coordinition equilibria are different may not be immeadiately apparent. In fact, in games of pure coordination they are identical (this is shown easily). However, they can be distinguished in games like the following example:In this game <1,1>, <1,2>, <2,1>, and <2,2> are all the possible moves. <1,1> is a equilibrium - Player One prefers to could not improve by altering their choice, neither could Player Two improve by altering their choice - and a coordination equilibrium - Neither Player would be better off if any player changed. <1,2> and <2,1> are not equilibria - in both cases, one of the players (Player One in the case of <1,2> and Player Two in the case of <2,1>) would have been better off had they chosen differently. Thus neither are they coordination equilibrium. <2,2> is different. <2,2> is an equilibrium: Player One could not have made their lot better by changing to <1,2> and Player Two could not have made their lot better by changing to <2,1>. However, it is not a coordination equilibrium: Player One would be better off if Player 2 changed their decision (i.e. at <2,1>), and Player Two would be better off if Player One changed their decision (i.e. at <1,2>).

After some interesting analysis, Lewis proposes that "We may achieve coordination [equilibrium] by acting on concordant expectations about each other's action." (p. 27).

The next concept is that of a Regularity. A regularity is a pattern of behavior, a repetition of a decision. For instance, Player One (a population of size 1) might have an arbitrary preference in repeated Normal Form Games to choose option 1. A regularity can be in an individual or in a population. Regularities are relative to Situations. A Situation is anytime a choice must be made - we are describing these in terms of Normal Form Games.

A regularity in a population is a Convention if and only if 1) everyone in a population exhibits the regularity, 2) everyone expects everyone else in a population to exhibit the regularity, 3) everyone has approximately the same preferences in options (in other words, the situation is more cooperative than competitive), 4) everyone in the population prefers to exhibit the regularity on the condition that at least all but one person in the population also exhibits the regularity, and 5) there exists another possible regularity that matches rule 4 and it is impossible for one to follow both regularities at the same time.

To return to our second example, "Choose row/column one" might be a convention. Player One will choose column one. Player One thinks that Player Two will choose the row with the highest number for their payout, and thus have reason to expect Player Two will choose row one. Both want the highest payout. Both would prefer to choose row/column two if the other chose column/row two. Player One prefers to choose row one in any situation (payoffs are 1 or 0, which is better than .5 or .2) and the same with Player Two - thus they prefer to choose row/column one if at least all but one person in the population also chooses row/column one. Thus if Player Two chooses column one, the players have formed a convention - and without communication!

This is Lewis's definition of convention. I'm working on a defence/critique of it, but it's more involved than my usual posts, so I'm going to separate it into a new post. Stand by, it might be done before the day is out!

Saturday, May 22, 2010

Slogans

Well, my boss is out of town and I finally thought of something worth writing about.

"How small a thought it takes to fill a whole life!"
-Wittgenstein

What is a slogan? What is sloganeering?

I am not interested in advertising slogans.

One definition of a slogan is "thought stopping cliche". Like most attempts to define words with other words, this is both a failure and misleading. It is a failure as it gives no insight into the nature of slogans than Euclid's definition of a line as "breadthless length" gives us insight into the nature of the line.

But it is the misleadingness of the definition that makes it worthy of contempt. The idea that people who are our opponents do not think is noxious to our own thought. The idea that even those who have been duped by cults and other such things so not think is outright dangerous. The problem comes that when we are ourselves duped we can fool ourself further by noting that we continue thought. Surely this means we are not sloganeering?

A slogan must be a sentence like any other, capable of being evaluated. If a slogan is untrue, then it is bad because it is wrong, not because it is a slogan (e.g. "Slogans are thought stopping cliches"). If a slogan is true, then we can have no problem with it. A good example comes from Richard Feynman.Dr. Feynman was asked to see the work of Uri Geller. Mr Geller claimed to be able to manipulate matter without using matter, called "psychic power". His demonstration of spoon bending was particularly disseminated. The trivial use of what would be an astounding discovery suggested to many that what was happening was no more than a parlor trick. Feynman enjoyed the spotlight and acquiesced. When Mr Geller bent a spoon, Feynman was unimpressed. When asked to explain it he said "I'm smart enough to know I'm dumb".

This certainly is a slogan. Though Feynman was quite a free thinker, he did not explain Geller's spoon bending. This was an important decision, as if he had held out various hypothesis he could have fooled himself into thinking that there was no alternate hypothesis, which (since it is well known that anything true can be proven infinitely many ways) is almost always false. In fact, Dr Feynman's slogan is not quite correct. A talented - if amateur - magician, Dr Feynman was able to figure out how he did it and provided evidence of its truth. Feynman's explanation was that he was using prestidigitation to hide that he was bending the key with his fingers. When asked to bend a hard metal key, Mr Geller could not perform.

Still, Dr Feynman's slogan is obviously true if parsed correctly. We cannot fool ourselves into thinking we can out-think charlatans, for nothing plays better into their hands than hubris. I do not think that anyone can accuse our desire not to fool ourselves with the end of thought.

Some slogans, like some sentences, are vague. The slogan "Live for nothing or die for something" used by Burmese freedom fighters might express a truth, but it must be a vague one. "something" could mean anything from freedom to the love of a dictator. In it's original formulation it is a question, the information it wishes to gather is if the questioned prefers a meaningless life of oppression and poverty or a the danger of a life with meaning (and, admittedly, still poverty) casting off the oppression. In this case, it is still a slogan but it is not a vague one. "Is certain painful meaninglessness life worse than the risk of a painful death?" is not a question that has easy answers, but it is a valid inquiry.

I think that those examples suggest a generalization. The properties that they share are striking, despite the differences in formulation.

A slogan is a sentence, to be sure. It must be a pithy sentence. A slogan only exists in a general context - it must relay an aspect of a philosophy that is parsable within the philosophy. Both of the slogan's examples used contradictory imagery to convey a point, though I think it would be too hasty to claim that was a general property.

Further empirical study of this, even one equally amateurish as my own, could yield insight.I think that it is impossible to consider the manipulative powers of slogans without conjuring Geroge Orwell. Orwell's short novel 1984 asked us to consider a nightmarish world where an omnipotent government was able to control the sense of reality of it's people through propaganda, continuous warfare and even torture. Central to the government's plan is "Newspeak", a language in which criticizing the government is grammatically impossible. The value of the novel was our drawing of parallels between it's idealized totalitarian state and real states. But if sloganeering isn't formulated as "thought stopping cliche", then does the rest of his analysis hold?

The ultimate chapters of the book are a direct confrontation with a horrific terror, the concept that a person can hold ideas that they do not even believe - a constant self-induced rewriting of one's perceptions of reality until it matches what the government desires. As terrifying as this still is, I must admit that age seems to soften the blow. I simply cannot realistically believe that an actual dictatorship requires or even encourages this behavior. It is the case that people who are fooled are truly fooled.The servants of Kim Jong-Il truly believe in him. Doublethink is absent. Doublethink, which requires knowledge of his baseness, is illegal.

When we look at the behavior of the manipulative in the real world, we see that they often come up with world views that are self-supporting. Even if we do not think they believe it (irrelevant to it's truth as it is), we cannot prove this. Trying is a honeyed trap.

Though it is repetitive, I must remind you of the misleading nature of believing that a slogan is a thought stopping cliche. It turns a word into a barb, one's enemies are unthinking sloganeers that believe something patently untrue. It is almost impossible to apply this to oneself. But it is actually true that any mildly eloquent person speaks in slogans, because a good slogan says a true thing in an efficient way. We reduce other people to a word - "hypocrite" - and leave them. Is it not obvious that much is lost in this lonely path? Must we proclaim our own sanity so loud that we call the world mad?

Friday, March 5, 2010

Heaviside


I noted this with interest recently, a short biographical essay of Heaviside by a descendant of his. Heaviside's primary contribution to science was simplifying the formalism describing electromagnetism developed by James Maxwell - Heaviside even popularized the term Maxwell's Equations.

Surprisingly to me, Heaviside was a controversial man in his day. His simpler, more beautiful formulation was attacked as being lobotomizing Maxwell. Heaviside was an accomplished engineer before, during and after doing his scientific work and indeed much of his work could be thought of as improving the efficiency of Maxwell's equations to the point that they became useful.

I suppose I should mention what these equations are, and though I am a mathematician I will try to use words in order to increase my audience.

Two of the laws are called both called Gauss's Law, after the genius Carl Gauss. Gauss (and unknown to Gauss, before him Lagrange) showed that the flow going out of a volume is equal to the flow leaving the inside. Gauss's 1st law says that the flow of electricity out of a closed surface is the electric charge inside. Gauss's 2nd law says that magnetism does not flow out of a closed surface.

A few things: 1) if there exist electric monopoles (northern compasses with no south, or vice versa) then Gauss's 2nd law would have to be amended slightly, 2) Gauss's Law is equivalent to Coulomb's inverse square law for electric force even without the other laws and 3) nobody likes that these laws are both called Gauss's Law but nobody does anything about it.

Another of Maxwell's laws is known as Faraday's Law, this time after it's discoverer. It states that electromotive force in a circuit is fixed by the rate of magnetic flow through the circuit. This law was discovered empirically by Michael Faraday who - in addition to being one of the greatest experimentalists of all time - was sufficiently handsome in his younger days to warrant his picture here.The final of the four canonical Maxwell's law's is Ampère's Law, which states that a magnetic field can be electrical current or by a changing magnetic field. This second fact was discovered by Maxwell, who used it to show that 1) electricity and magnetism are related and 2) light can be modeled as an electromagnetic wave.

It is too bad that figures as important and stolid as Heaviside are now more obscure than flashier figures such as Tesla. The life of science of their days was a deeply vibrant, if one is interested in such narratives. Faraday, for instance, was a fascinating and practical man, the image of the good scientist in the imagination of the time. His Christmas lectures aimed at young people show his astounding plainness of thought (I mean this as a high compliment, after all is it not often said to seek simplicity in all things?) and his respect for his countrymen.

Saturday, October 31, 2009

Vicipeadia

There's something about Latin. It has, to me, a distancing effect. There's not a joke on the page on the Iraq War, but I can't help laughing. Latin is so distant and dead, but here it is pretending it is contemporary. It's hysterical!

You know, I suppose this may seem like a good time to write about the wiki concept. The contrast between the dynamic modern idea of a wiki seems to contrast the old language. The fact is that the Library of Alexandria was smaller and held more errors, but we are allowed to celebrate it. Some people find it astonishing that there exist imperfect sources of information - it would be more rational to remember that there occasionally exist good sources of information. If Wikipedia is less reliable that, say, Encyclopedia Brittanica it must be remembered that the wiki dwarfs the print work. The Wikimedia community is an enormous source of information, and not just encyclopedia articles. Paintings, pictures of animals, court documents, plays, recorded music, and much more. If used in a mature way, Wikipedia is even better than good, it is useful.

It is pleasant to live in a world where there is such access to information that we can afford to be snobbish about sources. Could you imagine the reaction of Diderot to the French Wikipedia?

Saturday, October 24, 2009

Limericks

I've been addicted to limericks these past few days. They are simple fun, so I can write three in a lunchbreak! Because I'm not compelled by any standard of quality, here are a few of my pieces. Special thanks to Aaron Philby and The Medicated Cartoonist for their excellent work.

The mathematician Euler
was near blind far-sighted toiler.
He wrote with great haste,
but without making waste,
his mind as hot as a broiler!

alternate poem for english speakers:

Sitting the with his ruler
is the mathematician Euler.
Invisible to his eye
are gamma, sigma, and pi,
but to me there isn't anything cooler!
Euler's Student Lagrange,
Also covered a range.
His work in mechanics
cleaned up the antics
of many a model most strangeRichard Phillips Feynman,
liked to wine and dine them.
He'd meet a nice girl,
they'd go for a twirl,
digging those intellectual mines inMurray Gell-Mann discovered the quark,
Using the time honored method "hard work".
He now studies complexity
and adaptivity-
He certainly has made his mark!

I've fallen into a rut;
my poems just don't make the cut.
I start with a name
then play a game,
and never do anything butThere lives a man named Eddie Fizgerald,
a cartoonist/philosopher/actor/and/herald.
Well maybe he's never acted in a movie,
but he's done something equally groovy:
he's always been Eddie FitzgeraldIn Britain, on medication,
lives a maker of animation
He draws a cartoon
as he stares at the moon,
and thinks about emigration

This next poem was a tough one.
But pi is just way too much fun!
The number is gentle,
but quite trancendental
and the rhyming's a son of a gun.

The π sits a mite amazingly,
on adders shock and typey.
Ignoring beginners,
for to see againers
find novels of brains idly

I bid my readers adieu,
though I'll soon get back to you.
I have no gift for rhyme
and even less time!
And I'm trying to start posts anew!