Idealism and Modern Science

 "...[T]he Universe begins to look more like a great thought than like a great machine"
- James Jeans, The Mysterious Universe

I don't think it is unfair to say that most physicists are in some sense physicalists, that they believe that all that exists are physical objects. It would be foolish to say that they are dogmatic in this kind of materialism, a physicist would admit that there are fluids and gases in addition to atoms, fields and void - not to mention chairs, computers, brains and maybe even minds and social forces. Even if they say they do not believe in social forces, they would still act as if they exist. James Jeans - one of the cofounders of physical cosmology and major figure in early quantum mechanics - is an exception, possibly the only major physicist to endorse subjective idealism. I'd like to think "What is the best argument one could make for idealism using modern science as a guide?". This is just my first pass, and it will be a little thick with the philosophy - since I understand it less than the physics I feel the need to explain it more.

Immanuel Kant

First, a bit of background. Idealism was created by the German philosopher Immanuel Kant. His goal was to make the world safe for objective science in the light of what he understood to be David Hume's subjective attack. It was later amended and extended by Schopenhauer and others.

An example will make this attack clear. Imagine you see a baseball flying through the air. A moment later, the same baseball is soaring in the opposite direction. I ask you how this happened. You point out that there is a baseball game going on and the batter most likely hit it. How do you know  that? The answer is simple, but pregnant with complexity. You learned that baseball bats cause baseballs to change their course. More generally, Hume observed, you have never seen anything cause anything else, but have only learned to think of it that way. The answer for of how the baseball knew what course to take is more difficult, and I'll return to it later. Another example: in modern psychology we have learned why honey is sweet - it is sweet because we like it. The way that we project our liking of honey onto the world is denoted in the English Language as "sweet". These two behaviors, projecting an inner feeling onto the world, are found throughout human nature.

David Hume

This creates a trap. If so many of our notions are subjective, then how can we examine the world in an objective way? In his most complete work, Treatise On Human Nature, Hume escaped this trap by appealing to the notion of equilibrium. We may start out by false beliefs, but they cannot be stable against sufficient reflection, experiment and experience. This is a cheerful way of viewing the world. It is also erupting with implications and uses. Hume and his informal student Adam Smith used the concepts to develop psychology and economics. Unfortunately, Kant never saw this book or its solution. He only read Hume's An Enquiry Concerning Human Understanding, which contained the criticism but not the escape hatch. Kant was troubled, conflicted. He held the incredible success of the new Newtonian Physics in the one hand and a devastating criticism of the concept of objective science in the other.

Kant's solution is very complex. He had many disadvantages that we do not. In his time: Formal logic was in a pathetic state, psychology and anthropology simply did not exist, field theory did not exist in any form, the concept of biological evolution was a century off and even the classical mechanics and mathematics the informed him was frequently informal and its implications often deeply unclear. In view of this, Kant's achievements are very great. Today, we can afford to coast over what was very difficult for him.

The Dang-An-Sich

We start with a division between the particles, strings, fields and void that make up the world. This is the world as it exists without organization. Kant called the particles, strings, fields and void that make up an object the "Dang-An-Sich" (the "thing in itself"), but this is incomplete. As Schopenhauer pointed out, the distinctions between interacting objects are not in themselves "real" in the sense Kant wants (Why? Schopenhauer would say correctly, "Because energy is only conserved for the whole system.". Schopenhauer's exposition in general benefits from the enormous progress in the understanding of classical mechanics between their lifetimes). The universe as a whole must make up one ball of particles/strings/fields/voids. Schopenhauer called the big ball the Great Will. I will call it The Dang-An-Sich, the definite article. Very little of what we think of exists at this micro-macro-mega-meso-perspective. There are no tables, no chairs, no phases of matter, no minds, no social forces, no words, none of that. The Dang-An-Sich is an awesome object, but empty of content.

It is now possible to return to the question of how the baseball knew there was a game going on. Obviously. the baseball didn't, the system merely evolved in the way it did. From the point of view of the particles/strings/fields/voids in the field, the forces merely redistributed themselves according to fixed rules (the principle of least action, path-integral, etc.). The internal dynamics of The Dang-An-Sich are completely objective, but not terribly useful. The movements of a water molecule are from a purely local perspective, just what they are. They are ignorant of the fact the phase of the system as a whole.

It is only once we "choose" to think of The Dang-An-Sich as having temperature, pressure and other macro-properties that we get those properties back. This is called in physics "coarse graining". These higher level variables are the statistics of The Dang-An-Sich. The choice of statistical functions is not wholly arbitrary. Some objects are forced into it, the so-called necessary statistics. The best "choices" of partitions of The Dang-An-Sich into macro-states is done in such a way that knowledge of The Dang-An-Sich would not improve predictions of the evolution of the chosen macro-variables. They are termed "sufficient statistics". The basic thermodynamic functions take this form. You can read more here and here.

This new world has many new objects in it. These objects depend on our representations of The Dang-An-Sich. Not all representations are the same. One person may think in terms in temperature, another in inverse temperature. However, once a representation is chosen, the evolution of the chosen statistics is objective. We can do as we will, but we cannot will as we will. Still, this level of description is far richer than The Dang-An-Sich. We can now distinguish ice and water, a crystal from the air that surrounds it, and much more besides. However, this does not quite bring us to the world of experience. Schopenhauer might have called this world, "My Physical Representation" (if he were interested in it).

Daniel Dennett

There is still much distance to go until we get to idealism proper. Philosopher Daniel Dennett gives a sketch of how to extend the logic of partitioning The Dang-An-Sich into My Physical Representaion to include tables, chairs, minds, sweetness and social forces. He follows von Uexküll and James Gibson in developing this sketch into testable theories. Tables and chairs are defined in our minds not by their physical properties, but how they can be used. This new method of distinguishing objects are called the objects "affordances". This now expanded version of My Physical Representation was called by Schopenhauer "My Representation". My Representation is not objective given the evolution of The Dang-An-Sich. I can, by piling things on a chair often enough, come to think of it as a table. Schopenhauer was particularly interested in mystical practices, which he thought could give one conscious control over how one partitioned the world by affordances.

To recapitulate: in The Dang-An-Sich there were atoms/etc, but nothing that could be called a table. In My Physical Representation, there could be a solid with such and such mass and such and such composition. Now, in My Representation, there are finally tables which I recognize by the affordances it gives me. This is world is enormously more rich than the previous. As Jeans might have said better: "The Universe looks more like my thoughts than like a great, independent machine.".

Arthur Schopenhauer

Schopenhauer's pessimism can be understood best in this context. In "The Sad World", as Brouwer put it, the only thing that cares about living things are other living things. Many people caricature and misunderstand Dawkins's The Selfish Gene as implying that individuals are selfish. Far from it! The point of the title is that genes, like all other non-living things, do not care about us. They, after all, gave us finite lifespans just to avoid competing with themselves. The sun doesn't care whether we freeze or burn. To The Ding-An-Sich, there is no I to burn, nor even any burning. Occasionally oxygen atoms are moved by the rules closer to some non-oxygen atoms, but even this may be too high a level of description for The Dang-An-Sich. To Schopenhauer, the indifference of all things implied that the highest spiritual act is to expand one's mind to consciousness of The Dan-An-Sich - which is to say into nothingness. To hedge his bet he allowed that there might be something beyond The Dang-An-Sich only accessible to mystics, but this is not supported by his general system. I do not agree with this nihilism. I think that the neutrality of The Dang-An-Sich heightens the importance, uniqueness and scarcity of kindness for humans and animals.

What about the counter arguments to idealism? Daniel Dennett is not an Idealist, but I don't think he would object to nothing in my presentation here. I think he would note that if this was what Idealists meant, then one could be an Idealist Physicalist. He would be right - by my lights you could be an Subjective Idealist/Objective Physicalist and which you call yourself depends more on mood than principle. I would say that The Dang-An-Sich and My Representation are just old ways of distinguishing the scientific and the manifest world-views. If he wanted to insist on not being an Idealist even then, he could then respond that the grammar of idealism isn't an optimal partition of the space of ideas, that it may even be an impediment to research. (And Jeans's distinction between machines and thoughts is unclear at best.) He may have a point, but it is much weaker than a genuine, hardcore physicalist would hope.

L E J Brouwer

This post was inspired by reading Life, Art And Mysticism by L E J Brouwer. It's a weird book.

Today in deliberate misreadings: Politics And The English Language

 George "The Animal Steele" Orwell

Everyone knows George Orwell wrote a great essay on political language. Hipsters (edit: I don't mean to attack this person specifically. The was inspired by someone I know personally) know that the essay is bunk, claiming stupidly that we should all write beige, colorless prose and always avoid the passive voice. The fact that I called them hipsters tells you where I stand. Yes, it is strange that Orwell should make us want to write as dully as ... The King James Bible. Gosh, it's almost like such a reading doesn't make sense when you think of it like that. Well, that's because it doesn't! One would think that linguists would understand the idea of qualifying phrases! Imagine if I wrote such trash about fluid mechanics:

 I've always been fascinated by vortex dynamics

"How stupid is Helmholtz's essay on vortex dynamics? If he were right, wingtip vorticies couldn't end in a fluid, so they'd have to extend all the way back to where the plane started at the beginning of time. That's ridiculous. I can't imagine the damage done to fluid mechanics by this illogical essay."

All I have to do is ignore that Helmholtz ever said "velocity potential" and I make him sound ridiculous. Yes, it's easy to sound smart when you cut out half the sentence ("Never use the passive ..." rather than "Never use the passive where you can use the active."). Plus, it lets you get out of having to use real data! Since you've created a totally artificial theory that nobody ever proposed, nobody will call you on it if you reject it badly after all. Heck, why not go further? Let's claim Maxwell never discovered Maxwell's correction to Ampere's Law, just by leaving out those parts of his books! It's fun!

In ur noospapers, writin' ur propaganda

Okay, now they've got me doing it. These kinds of arguments are well documented in Schopenhauer, and it is more fun to attack hipsters and George Orwell than it is to sit around in your underwear. I should have a sense of humor about things. If you do something as simple as read the essay, you'll notice that Orwell's praise is always toward the visual and metaphorical and away from the beige and standard. Orwell didn't say "When there is a gap between one's real and one's declared aims, one turns as it were instinctively to long words and exhausted idioms." but rather "When there is a gap between one's real and one's declared aims, one turns as it were instinctively to long words and exhausted idioms, like a cuttlefish spurting out ink.". Read those two sentences and tell me there's no difference. Or how about this dull, image-less prose taken from something Orwell himself thinks is worth publishing:

"When one watches some tired hack on the platform mechanically repeating the familiar phrases ... one often has a curious feeling that one is not watching a live human being but some kind of dummy: a feeling which suddenly becomes stronger at moments when the light catches the speaker's spectacles and turns them into blank discs which seem to have no eyes behind them."

What's that from? Oh right, that's from the very essay you just read! Orwell is throughout the entire essay calling for more colorful, more illustrated, more metaphorical/simile-heavy prose. He uses images constantly throughout the essay, and indeed throughout his writing. I wouldn't go as far as to say Orwell was a frustrated artist, writing because he couldn't draw political cartoons. That's G.K. Chesterton you're thinking of. But Orwell always had his eye fixed on creating an image in the reader's mind.

I didn't say anything about Orwell's deeper concern that avoiding metaphor and imagery allows one to deflect from what one is really writing about. I don't know that if Laski had to write about the Soviet in the way Orwell said that it would force Laski to think about what the Soviet was really doing and he would find it in himself to criticize them before Czechoslovakia. I'd guess that Orwell has a point but the psychological issue needs to be studied empirically. Do such studies exist?

"Weird" Al Yankovic Is A Much Loved National Treasure

Well, that's the truth. Nobody would have guessed that thirty years ago.

If I Have Mine and You Have Yours, Do We Have Ours?

Let's play pretend. Let's say you're an earnest young music producer and you're going to make a star out of an earnest young talent. She's really good, Joni Mitchell or Kate Bush level. How do you capture her genius? Do you hire strings, really go balls out? Or is it more beautiful to capture her pure and unrestrained? Well, here's one piece of advice:



That's not helpful is it? Alright, well, here's what we think mathematically. This is a problem of "Multi-Objective Programming".

Single objective programming, or simple optimization, is pretty simple to understand (though in practice it can become quite difficult). You want to do ... something and you want to do your best. You wanna make the most money, or move the most people, or be the purest, or rock the hardest, or be the funniest, etc., etc. It was recognized by Newton that for smooth payoff functions, finding maximums and minimums was equivalent to finding the roots of derivatives (he wouldn't have phrased it like this). So all you have to do is have a root-finding technique, and there are very efficient ways of doing that. It's simple enough that reducing a design decision to an optimization problem is equivalent to solving it. I've actually done some work in this area, engineering stuff by optimization techniques.

Multi-Objective Programming is more complex. It's satire rather than just comedy - now you want to be as funny as possible and reach as many people as possible. Occasionally you're going to run into some trade-offs. How long are you willing to stray from the message for a laugh? How many laughs are you willing to sacrifice to get to the point? There's no longer any notion of a simple best, there's real trade-offs. How can we solve such a problem?

The notion of a "solution" to a problem with multiple objectives dates back to Hume, but has its first clear enunciation in the work of economist Vilfredo Pareto. Pareto was a very interesting person. He was at first a dedicated Free Market Liberal type and dedicated much of this part of his life to simplifying and extending the economic equilibrium theories of Leon Walras. He later decided that economic theories from Hume to himself left out the "irrational" aspects of human behavior. He believed that human nature was fundamentally non-logical, that political power was found in the vicious struggle of elites and that empirical study of sociology is what is best in life. By the end of his life, he was calling for releasing the hounds on anyone to the left of Mussolini - of whom he was very, very big fan. Hey, I said he was smart, not wise.

Well, Pareto's other beliefs aside, his proposal for the solution of multi-objective problems was very important innovation. A solution is called "Pareto" if improving in one aspect must mean detracting another. For the Joni Mitchell example, it would mean going beyond tasteful, jazzy backing to syrupy Mantovani backing (I don't hate Mantovani, just note that he'd be wrong for Mitchell). This isn't an optimum in the original sense -it can't be an optimum in the original sense. There's no longer a clear notion of best. It's a notion of stability of decisions. Imagine that Joni Mitchell had two producers, one who wanted bigness and the other honesty. Of course, much of what she does can please both producers - write a beautiful melody with lots of hooks and nice lyrics. But at some point, adding/subtracting some more strings will please one and not the other. Pareto's idea is not perfect. For instance, if Joni decides to completely listen to one producer and not the other, that idea is perfectly Pareto - even if it is wrong. To put it another way, let's say Mom bakes us a pie. If I take the whole pie, you can't get any without taking some from me. The distribution is Pareto - but not good.

The most important application of this idea, and Pareto's original application, was to the distribution of goods in a static economy. In this post, I discussed about how a highly unequal distribution of goods could develop from trade economy. Notice that at a Pareto stable point, trade effectively stops - Chamberlin stays the richest person. Nobody can make themselves better off without hurting someone (not necessarily Wilt, mind you). This has powerful implications. In fact, an economist named Francis Edgeworth developed a highly innovative iterative argument where trade people negotiate and renegotiate their contracts. Since only the set of Pareto equilbria are stable (this is a mathematical sticking point), they must land on one. This was, arguably, the first argument that an invisible hand could actually achieve a stable distribution, rather than the Walras/Pareto demonstration that one exists. Of course, this argument is also present in a purely verbal form in Hume. I've written about this before.

Well, I'm having trouble with my laptop battery, so we'll have to get into Pareto and dynamic economies some other time. See you then!

Uninteresting Note: I originally wanted to name this post "Economies Wobble But Do They Fall Down?" but that's about the stability of equilibria and not what an equilibrium is.

Solo Duke

Well, I wanted to write a wise post on some classic results about on (Pareto) stability of a growing economy (in short, cain't be done, son), but I couldn't think of anything to say that would be interesting. But then I saw this and of course anything I'd say would pale in comparison. I love that Duke starts with Fluerette Africain, a number he wrote (for Charles Mingus - Duke's best work was always specific) relatively recently to this recording. It shows Duke's influence from Monk, an influence that Duke thanked Monk for at every opportunity! (of course, Monk was deeply influenced by Duke as well - and first)

Coleman Hawkins & Duke Ellington

Well, I guess I should give my opinions on the essential Duke... nothing like judging great artists and great men. Well, I bend strongly toward the weird. Money Jungle - played by the trio of Duke Ellington, Charles Mingus and Max Roach - is definitely on the list. Music should have big personality, that was Duke's philosophy. Ellington At Newport is a better portrait of his general sound. Of course, one of his very best albums is his tribute to his long time music director and close friend Billy Strayhorn ... And His Mother Called Him Bill. But, of course, this doesn't feature Ellington's compositions. Billy Strayhorn's style is instantly distinguishable from Duke's, I don't consider myself a connoisseur and I've never once confused them in my life. Billy was better educated than Duke, and Strayhorn's style was ... educated, urbane melancholy. Ellington tended to break rules more innocently and with more dramatic effect. Of course, & John Coltrane and Meets Coleman Hawkins are great for post-bop enthusiasts like myself. Some might argue that Coleman Hawkins and pre-bop rather than post-bop. The use of "rather than" rather than "as well as" is their only mistake.

 I think this is the right orchestra...

 Once more modern albums have got you used to the Ellington genius, try The Blanton-Webster Band, which captures his 40's sound. People not used to 40's sound should not jump into the old material with both feet. Good recording technology is a blessing. Well, that's my attempt to give my favorite albums. Of course, there's collections galore, but I can't sort through all those.

I also wouldn't try to introduce someone to 40's music through Ellington - it was too innovative. It's a double whammy of intricate compositions and old fashioned sound. I'd try the great Louis Jordan, though it might trick people into thinking music in the 40's was any good. Good place to start, other than the earlier links, is his classic story of getting beat up and arrested at a raucous party.

Update

 So, if you accidentally read this blog, you might have noticed a couple posts ago I complained about being in between jobs. Well, almost as soon as I wrote that I got an offer to work at the Polish Academy of Sciences, and the expense and stress of moving (among other more private matters) made me forget that I had a blog. As always, it was remembering that I liked Steve Reads that reminded me that I had all this half written junk.

I've only now been in Warsaw for about a week, so I won't give any half digested first impression crap. Okay one: is there really a pho restaurant in every university district in the world? Clearly, this implies that college is the right place to go. I guess should count myself lucky.

W Sierpinski

So, Warsaw (and Poland more generally) has this massive history of mathematical excellence that I know a lot about, but writing it would be a lot of effort. Plus I'd have to describe what they were doing. The guy above gave the first course dedicated entirely to set theory anywhere in the world! He's kind of a big deal. The mathematical skill of the Poles was sufficient that they were the ones to actually crack ENIGMA (they actually have a lot of crypto courses at the University of Warsaw, but I somewhat doubt that is a tradition dating so far back). So, one day I will probably idly write a history of Polish mathematics, forget to publish it and move to Korea.

Anyway, hope you're all having fun out there while I'm stuck in the actually acceptably warm Warsaw. Perhaps I'll remember this blog more this weekend, where I have a nothing planned but endless paperwork.

Nozick, Roemer and Thou: Or, Only Equilibriums Equilibriate

So, this is my fluffy insubstantial post about the distribution of wealth, justice and injustice, and the only practical goals of all possible political philosophies. Soon I'll be free to write about deep issues like the flow between two rotating cylinders.

Anyway, who are the Roemer and Nozick of the title? I'll give 'em a lil' blurb.

Robert Nozick

Robert Nozick was a philosopher from New York who did most of his life's work at Princeton. I've read four of his books and enjoyed three. The one's I have read are Philosophical Explanations, The Examined Life (this is the one I didn't like), Socratic Puzzles and Invariances. I think the last one in particular got at something really neat, a good definition of objectivity. I'd like to state it like this. A statement is objective if it's meaning does not change under the kinds of permutations relevant to the discussion. He fleshes out this intuition well. Nozick considered epistemology to be his life's work - or at least that's what he says in all three books. His goal was to make a real, philosophically rich epistemology out of decision theory and possible world semantics. This was also David Kellogg Lewis's goal, but Lewis was rather more technically proficient and Nozick was more interested in the traditional philosophical side of things. Anyway, his first book was Anarchy, State, and Utopia, a book about political philosophy. His idea was to develop a novel defense of small state libertarianism. He argued that it could be justified even if it created, for instance, massive inequality. His basic idea was the idea that if every step on the path was good, then the destination is holy. I'll go over this in more detail in a bit.

John Roemer

John Roemer is an economist of the top rank - also, an Analytical Marxist. He's a fellow of the Econometric Society, the Guggenheim Foundation and the Russell Sage Foundation. He has written many important papers, three articles in Palgrave and several books, though I've only read one. The book I read was Free To Lose. He also once wrote a book about how we could replace corporations with co-ops and get all the upsides of market competition. He's rather more clever than Nozick, but that only gives Roemer the advantage if he is right. One of Roemer's accomplishments developing a simple model in which an unequal society where every member is given the same choices develops classes (and therefore further inequality) because of the initial inequality. In addition to the important advantage of making sense of the idea of class without reifying it like so many socialists do, this plays an important role in how we ought to think about inequality.

Wilt Chamberlin

So, the issue today is Robert Nozick's idea that inequality can be morally justified on the grounds that every action that leads to inequality might be justifiable (Nozick, who is very witty, calls these "capitalist acts between consenting adults"). He gives the following example. The people of Philadelphia are more than willing to give their money - of which they have little - to the Warriors organization - which has much - because they want to see Wilt Chamberlin's athletic feats. Clearly, we don't disapprove of actions just because they collectively result in inequality

Yes, that is Arnie in the middle there.

With a little fiction, the thought experiment can be made more clear and its importance will shine through. In this alternate Philidelphia, everyone has the same amount of money, let's say $1. Wilt Chamberlin decides to hold an expo. People pack in from miles around and give Wilt a token of their appreciation, let's say $.01. If 100,000 people see the expo, Wilt now has $1001 and is the richest man in Philadelphia. It would be ridiculous (and, in the end, require cruelty) to stop people from seeing Wilt. One can argue that the right thing to do here is to redistribute by taxes and transfers, and that one can do this without violating moral strictures too badly. But this misses the point. What is important about this example is not Wilt Chamberlin, but that the world gravitated to a place where there was a richest person, even though it started out with everyone being monetarily equal. The distribution of wealth that society aims for must be a stable equilibrium. If equality is not stable, then it will not happen. Was Pareto right to think that a power law distribution was the only possible outcome? I deeply doubt that, but the idea must be confronted.

Well, what does Roemer say? First of all, Roemer shows that equality is a stable distribution of wealth under capitalism if we presume that people are equal, so that the Wilt Chamberlin example can't work (why not? Because then everyone could hold an expo and Chamberlin couldn't stay the richest man in Philly). Second, Roemer shows that inequality can result from inequality of resources and limited menus for employment even if everyone is equal, so that there has to be at least two components to inequality, not just one's own personal qualities as Nozick's example suggests. .

This is a huge spoiler

It is clear that Larry Page and Sergei Brin are clever guys, but are they cleverer than, say, Terence Tao? Certainly they are much richer. If you put a gun to my head and told me to invent a search engine, it probably would have looked like PageRank even before I knew what that was. But the fact is, there is more than PageRank (and their brains being smart enough to conceive of PageRank) to their wealth. In otherwords, Page and Brin aren't rich just because of their Wilt Chamberlin-esque personal qualities. They are also able to parlay their wealth by taking advantage of more opportunities than a less rich person. They are rich - partly - because they are rich. More positive liberty has given them more negative liberty, and the negative liberty can be parlayed into positive liberty. That needs to be taken account of in any discussion of inequality and it is just ignored in Nozick's thought experiment.

Roemer even goes as far to call the Chamberlin example "socialist inequality" (which is unfair, since they didn't articulate it). You might notice this section was a lot drier than Nozick's. Romer's biggest problem is, I think, the fact that he has imbibed these models so deeply that he cannot write without them. Maybe I'll think of a way to illustrate this better.

Roemer ignores the extent to which inequality is created by market failures, at least analytically. Nozick argues that regulation leads to industry dominated regulatory bodies that make markets fail more, but he 1) only addresses old fashioned command and control regulation 2) fails to come to terms with copyrights, trademarks etc. which cause damage without being "regulatory bodies" and 3) says that these generally lead to a rise in price which is contrary to the facts (George Stigler and Milton Friedman could barely measure a rise in electricity prices and later analysis has suggested that there actually was a positive effect).

All of this means that inequality actually has at least three components: personal qualities, feedback from greater choices due to wealth and market failure. Nozick can sort of justify inequality source number one, but the other two are unjustifiable even on his account. Anyone who wants to morally justify inequality needs to justify all three at least.

Didn't Write LOL

Alright, you might have noticed that I didn't post twice yesterday and that this blog title is not the promised post on Fourier Analysis. Well, my life got in the way. I'm still going to post every day, but I'm not going to write a big substantive until next Tuesday.

If I post any more YouTube videos, this blog is going to become a Twitter feed. Maybe I should review something I've read? I haven't been reading like I was when I started this blog. I could do a review of the last thing I watched, but I don't think the internet likes The Rockford Files as much as me - though you should 'cause it's great. And I'm also at risk at becoming a Tumblr if I continue to lack content the way I do.

Alright, how about this: is there any correlation between money spent on a TV show and its quality? Here's a good list, kind of interesting to think about. I think modern sit-coms just look awful. Big empty fishbowls. Back in the old days, All In The Family and its ilk had a certain grittiness to their look, like an Angry Young Man play. Whether that is good or not is up to you. It's important though to compare apples to apples, sitcoms like Friends and The Big Bang Theory (shows I don't watch, but have friends that do) cost a fortune because the main actors are so popular that they can be paid ~$1 million an episode. That can't be compared to a cool looking show like It's Always Sunny in Philadelphia.

Great Promotional Bebop Art From Character Designer Toshiro Kawamoto.

Interesting fact: anime is dirt cheap to make. This is the real reason they can concentrate on the safe but small (and pretty horrible) "otaku" market (which wants - thinks it wants - nothing but more of the same, but more fetishized). Each episode of Bebop was made on a budget of ¥20 mil, which is about $230,000 (taking into account inflation). Each episode of a comparable American series in terms of looks, Avatar: The Last Airbender, cost $1 mil to make. Of course, there were other costs to make the series as a whole, but that's not going to change the overall story. Sequel series Avatar: The Legend of Korra costs $1.7 mil an episode.

In his book Starting Point, the great Hayao Miyazaki blames Osamu Tezuka for this (he says Tezuka was willing to work with low budgets because he conceived of animation as a side gig to comic books). But I wonder if people would be willing to make risky shows like Bebop if they had to pay full price. It's a great book, worth checking out. Miyazaki is a very interesting person, much more pessimistic (especially politically, as Miyazaki is an environmentalist and a pacifist) in person than on the screen. Reading his regrets, his triumphs, his frequent attacks on the lack of emotional depth in other Japanese animation and his ambitious plans for his movies is very impressive and interesting. He writes about his inability to understand his father until it was too late, his love of his crappy first car and his relationship with the industry in a very honest way. Highly recommended.

Hey, that's kind of a book review of the last thing I read! I guess this blog isn't totally content free!

What do you mean "finite", kemosabe?

There are a lot of alternatives to what mathematics is. Most of these approaches privilege certain sections of classical mathematics over others, the privileged sections are called "true" and the unprivileged "unproven". Some of them, like the varieties of constructivism or intuitionism, are respectable minority viewpoints. They have disadvantages - the theories aren't closed under as many operations. But they have advantages too, as a constructive proof allows one to actually calculate an answer. This is of great interest for an applied mathematician like myself. Then there are the finitists.

Ever heard of Archimedes, Newton, Cantor? Morons.

Well, it's difficult to talk about finitists, because the bold, bold declarations (Edward Nelson is gonna prove Peano inconsistent! Doubt it) and monster raving egomania (has to be read to be believed) make it hard to understand them. But let's set aside all the technical machinery that masks their real arguments. Let's focus on something so simple even finitist will have trouble corrupting it.

This version is much better than the Three Dog Night one

Is 1 a finite number? What makes you say so? Isn't it a real? Isn't it a limit of the sequence [.9, .99, .999, ...]? Isn't it an infinite amount of zeros, a 1 and decimal marker then another infinite sequence of zeros? Why do we privilege "-1" as a symbol for the number 2 less than one, and not the p-adic representation ...1111111111111? There is no answer. Indeed, in computers that run 2's complement arithmetic, the p-adic representation would be the natural extension, not the invention of this wholly new symbol "-". Whether an object is "finite" or "infinite" is dependent on representation. This is not good!

Right Isosceles Triangle

Draw a line, then another line of the same length at a right angle to that line (this is easy to do if you know a bit about geometry). An amazing thing is true. You can double, triple, quadruple the length of AC easily with just a straight-edge and a ruler. The same is true of BC. But, no matter how much you do so, the two endpoints will never both lie on a circle centered at C. Ever. Try it, it's fun! This means that the side is irrational, and in one representation - decimal - "infinite". As infinite as 1.00000000..! None of the prevarications of Zeilberg or any finitist will get a around that.

"What, my representations arbitrary?"

 
Look, one could try to argue until one is blue in the face, but finitists don't care about such things. They want there to be a distinction between the finite and the infinite, and they want to stay on this side of it. The only answer the preserves the intuition is that there must be a non-arbitrary representation. And perhaps there is - the representation in a Turing Machine for instance. What's representable in one ought be in another, na? Never you mind that nobody in the world thought like this before and nothing bad has ever come of it, that's pointless twibbling. The issue here is that one does not get finitism out of this line of thought, but rather a form of constructivism. Any alternative to mainstream math thinking is going to lead out of finitism eventually, because finitism is too arbitrary. I've discussed how Wittgenstein's ideas lead to a non-finitist criticism of mainstream bath before.

I missed yesterday, so I'm gonna try to get two posts in today. This blog is officially back in business!

Music of the Rectangles, Part One

A lute arrangement of Ravel's Pavane Pour Une Infante Defunte, probably by Yoko Kanno

So, Steve Laniel of SteveReads.com asked a very reasonable question about Fourier Series, Taylor Series and possibly a bunch of other series named after long dead men. I wanted to say about a million things in response, but what I ended up saying was unhelpful and vague, so I am gonna try and make up for it here.

So, consider the Dead Princess with the lute in the above video. She asks Space Dandy if he can hear her music. He can, and that's a very complex fact if you think about what is happening physically. Impulses course through her unfeeling fingers and the strings vibrate, which causes the air to vibrate and those vibrations propagate through the air in roughly spherical waves into your ears, in which a membrane vibrates and sends signals into your brain. What interests us here today is the vibrations in the air, the music in itself as it where. So, let's say that I graphed the pitch of some music over time. What would that look like? Maybe something like this:

No, this isn't from any signal analysis of music or anything. Just a random analytic signal.

Well, what about this? What does it tell us? We need to turn this into something we can handle. I only drew a little piece of a function here, I could have easily drawn one that represented hours of music. There are different ways of thinking of a melody. One is that we could think about what is going on locally, what you hear at each point in time. Now, you can't hear any complexity, any harmony or melody, at just one moment in time. This is the above collapsed to just one point in time:

Helpful. Also, thanks MATLAB for changing the background color for no reason

Now if we're allowed to hear a tiny snatch of music (a little temporal neighborhood) we can figure out a lot more. We can figure out maybe the key it is in right now and what kind of instrument is playing. Some composers, such as Jean Sibelius, pride themselves on the internal logic of their compositions.

Brook Taylor

This is the approach taken in the Taylor Series, invented (in generality, special cases are ancient) in secret by Issac Newton. Some things are well understood like this, we call the analytic. You can tear them into the smallest pieces and learn about the whole. Our intuition is that everything is like this, we assume our local experiences give us knowledge of larger experiences. Of course, that intuition is wrong, the experiences of others might be very different than our own. The same thing is true in physics, we expect that if when a metal is heated it expands then we expect it to continue to expand. This is reasonably close to true of iron, but not of plutonium, which makes it devilishly difficult to machine. Let me show you some approximations to the above musical score made with the Newton/Taylor/MacLaurin idea of listening carefully to a tiny passage at a particular time.

With Approximations.

The red is a low order approximation, the equivalent of assuming that a tone is going to increase because it is at the moment. The other approximations involve paying a little more attention to a very small fragment of music. The important thing is that the changes between pitch is "smooth", we can figure out from where we are the location where we are going. This is not the only or even the most interesting way to write music.

 Rather than infinitesimal steps

Other musicians, like Stravinsky or John Coltrane, are proud of their music's movement. You cannot, by listening to one moment, figure out what the next moment will sound like. This corresponds to a score more like this:

Again, this picture is suggestive, not literally from music.

 Consider the moment when changing from one pitch to the next in the above picture. What note are you playing at that moment? It seems - correctly seems - like a whole range of notes would be equally okay to play. What note are you hearing at that moment then? The answer is not defined. In order to understand a signal like this, we have to go from a local point of view to a global point of view? What does that mean? That's the point of view of Fourier Series...

Infante Defunte

The original version of this post bloated to gargantuan size, so I am going to cut this post off here. Tomorrow, I will post the  part of the explanation that is about Fourier series. I'm going to break things up though, tomorrow will be a post on finitists and why they are wrong.

Various And Sundry Personal Things

Current Theme Song

A lot has happened since I last posted on this blog. Most importantly, I've officially gone from being employed to being, shall we say, between jobs. Rather than drink and spend money like I had it, I'll go back to a nice cheap blogging habit.

Anne waits for her new family

Since I last blogged, I've purchased and watched every Isao Takahata movie (except Only Yesterday), and bought DVDs his TV series Anne of Green Gables. I can't praise his work highly enough. His film masterpieces are certainly The Tale of Princess Kaguya and Grave of the Fireflies. The Tale of Princess Kaguya is particularly amazing. It was made in another world, where they make films differently. Now that Space Dandy is over, I don't watch traditional TV anymore, relying on my massive collection of DVDs, books and the internet to entertain me. It's been pretty good for me, I think.

Better Than Average

I've been practicing drawing, but I'm still not good enough to post pictures here. Maybe soon these posts will be marred by my horrible cartoons as well as my horrible writing. If I'm mentioning this I must not have much to say about myself.

Severian

Oh, I've been reading Gene Wolfe's Book of the New Sun, but I keep forgetting about it and having to re-read sections I've already read. This is good to see Severian misinterpret the simple things around him, but bad when it comes to actually reading. It's a fun book, but I'm still at the beginning. It also obviously calls for being read twice. It reminds me of the old show, Neon Genesis Evangelion. I know they've both read and been influenced by Cordwainer Smith - one of my favorites - so it is probably just convergent evolution.

Well, with no job to encumber me it'll be daily blogging for a bit. Hopefully they won't all be this dull. If I can't spontaneously be interesting, then I'll restart the IITSTIAPW series and start a project systemically famous anime directors.