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.