Learning, A Physical Metaphor And An Economic One

One can say honestly that the vast majority of learning is linear or nearly so. But there are also points, one might call them "phase transitions", where suddenly progress becomes suddenly easier - or suddenly much harder. I remember reading a story about a jazz musician (I don't care to look up the source so I will not give his name, even though it is Charles Mingus) who was learning to improvise for the first time. It was himself on a cello and his sister with a piano playing a song of his own composition. His part was a single note - a pedal point. Suddenly, at the end of the song he had a break and played notes and notes that had never been written. His mind was empty except for the sound of the notes he played. It was hours of work - not hours but days and weeks - to culminate in what was probably thirty seconds of improv. But it was a phase transition, he was a different being afterward.

Learning is multidimensional, of course. At some points, altering in one dimension is pointless. In the above graph, one can see that at 1000 K, plutonium will not change phase at any reasonable pressure. Even in common sense you can see that if the temperatures is low enough, ice will not melt or sublimate whatever the pressure is. Moving constantly in the same direction can be a trap.

So it is with learning. After "phase changes" one finds that practice in one sense no longer might help. A beginning artist might learn much from copying other artists - even tracing them. Albert Ayler was called "Little Bird" because he was constantly practicing Charlie Parker solos. He got to know them so well that he could literally play them backwards. This was probably good practice for the young Ayler, but I doubt he was doing it in 1964.

Friedman-Savage Utility

Milton Friedman was originally interested in micro-economics. He, and the great Bayesian Jimmie Savage, tried to solve two economic problems with one stone. They worked together a great deal and wrote this classic paper. First was the question "Why do people buy insurance and lotteries?", the second was related to the distribution of wealth in society. This is a brilliant paper that everyone capable of understanding it should read.

Friedman and Savage proposed that the level of risk tolerance is dependent on wealth in a non-monotonic way. There were to be two inflection points - "phase changes" one might say. The poor would be risk-averse in order to sustain their lives, the wealthy would be risk averse out of lack of need to be otherwise. The middle class would be risk loving, perhaps out of a desire to get up to the upper class. This is only the simplest of possible Friedman-Savage functions, one can drop unlimitedly many phase changes in order to create as lower, upper and even middle income traps as desired.

There is an obvious similarity between this and learning. Wealth is perhaps practice time, Utility perhaps skill. In Silver Screen Fiend, Patton Oswalt describes stand-ups that remained in Virginia, telling the same stale jokes every week. It's a low skill-level trap. They were too risk-averse to take a bet that might make them mediocre - or perhaps even great. George Starosin - as clear eyed about old pop music as any man should want to be - defending, while defining his utility function, the idea that no great band would make a truly bad album. He is defending the idea of a high skill trap - if such a thing is a "trap" (don't the romantics tell us it is the more painful one?).

These are two metaphors for learning. I want to develop the ideas more carefully, maybe make some testable proposals. But it is nice to say it out loud and write it down - even if just as a check against madness...

Cowboy Bebop Review #4: Gateway Shuffle

Earlier I made reference to the famous anonymous quote "Writing about music is like dancing about architecture.". This excellent episode presents this dilemma at an even higher level. Sure, it features a couple obviously writerly elements - the Ganymede Sea Rat as an SF parallel to whale hunting - but what really makes it interesting is its directing. It was unit directed & storyboarded by Yoshiyuki Takei, a utility infielder for Watanabe (and Sunrise more generally). He delivered an episode that is simply a masterpiece of controlled montage. He uses a lot montage and wacky angles, but never loses control of those most important questions: "Whose perspective are we looking from?" and "What are we looking at?".

This episode also features tons of great acting from the subtle reserve of Spike, to the pants-on-her-head insanity of this week's bounty "Twinkle" Maria Murdock. Further, it contains a healthy dollop of interesting writing from the perspective of having witty lines and from the perspective of having an interesting plot. This week's session introduces important wider plot elements, such as the explaining more about the gates and - this bit is important - bringing Faye Valentine in as a permanent member of the crew.

And it does all this while keeping a slick, carefully controlled pace!

Today's adventure begins with the luckless but wily Faye Valentine out of gas, drifting around Jupiter. It's funny that she should be out of gas. It's almost like she isn't used to spaceships or something...

Anyway, a spaceship flies past, and then is destroyed. This gives us our first chance to see the monosystem that makes the core of small spaceships in Bebop. A dying man gives her a mysterious package inside. Of course, the best use of this plot device was The Good, The Bad And The Ugly, but it was old even then. It's funny how Faye lies to herself even when there's no one else around to hear her.

Meanwhile, Spike & Jet have tracked a bounty into a fancy restaurant. He's wining and dining a harem of young women and he orders "Ganymede Sea Rat". Jet describes it as disgusting, barely edible meat that is "enjoying" a spurt of popularity as a pseudo-delicacy. The obvious parallel is, as mentioned before, whale meat. Not particularly suited for Japanese tastes, whale meat was once only consumed by desperate fishing villages. Someone had the bright idea of claiming it was fancy solely on the grounds of it being old, and now Japan still hunts whale. There is really no logical reason to keep hunting these sea rats, gaudy rich people will move on to a new delicacy soon anyway.

Maria Murdock is so old she has lines on her neck

But just because a position is logical (whatever that means in politics) doesn't mean its espousers are. And that's how we meet the cult of "Twinkle" Maria Murdock. Ms Murdock introduces a new kind of bounty-of-the-week. Asimov was a simple-minded thug, Abdul Hakim was a tough-as-nails pet thief and Faye Valentine was a slinky con-woman. They were all very different, sure, but importantly they all had the same motivation - money and its promise of freedom. Asimov - and more importantly Katerina - was going to use the money to escape Tijuana. Abdul Hakim was in a tense, difficult place with his fence and therefore probably many people. Faye has massive debts that brutal, corrupt, not-exactly-boundary-respecting casino owners can use to control her. Well, Murdock isn't like that.

Also, it probably ought to be said that Bebop sure has plenty roles for women! There's been important female roles in all episodes and not one has been similar to another: desperate dreamer Katerina, the matronly pet shop owner, the devious Faye Valentine and now Maria Murdock. Basically no similarities in design, character traits or plot role. Pretty interesting! Having a female head writer probably helped in this department. There will be more good roles for women and girls as time goes by.

So, "Twinkle" Maria Murdock's cult/environmental terrorist group goes absolutely apeshit on the guy for ordering Ganymede Sea Rat. This is told in a montage of guns firing, people dying and Murdock dancing around maniacally. Spike captures Murdock, who - uniquely - doesn't put up a fight. This scene is also very well designed, as you can see above. This is just a good shot, it answers those two basic questions and still looks cool. In a lesser show we might see this scene from Spike's perspective - isn't he the main character? Here Spike is to the side and in the background, a mysterious and dominant figure. Murdock isn't reacting to his presence, she's standing straight up and down. She's got steel in her spine, you have to give her that. And you gotta love how much depth is in this composition - the closest cultist is on the camera man's foot, Spike & Murdock are halfway into the background.

"We like PORK!"

So, Murdock is on The Bebop and Jet goes over her background. In the establishing shot of The Bebop, it moves from the top of frame to the bottom, instead of left to right as Star Trek taught us. Just a little extra effort to keep the episode visually interesting. The thing that makes Bebop great is making sure these extra moments are always there.

The Sea Warriors used to be a fairly mainstream, though sometimes tactically pushy environmental group that opposed overfishing the Ganymede Sea Rat, industrial pollution, etc. They even ate pork! But their tactics got more and more extreme and Murdock began taking over, leading to an exodus of sane members. This left Murdock with a solid core of True Believers, but not much else. Why is she so confident that Spike & Jet won't be collecting the sizable bounty on her head?

Carbonation humor, never fails

As it turns out the government of Ganymede is run by complete pussies who cave to Murdock's terroristic demands. But Murdock is no mad dog killer, she is after something. What does she have on the Ganymede government that makes her so invincible?

Perhaps it is related to that doodad that Faye got from that guy? No points if you guess this one. So Faye bumps her head

Why should she be so awkward in spaceships?

and comes aboard the Bebop, where she is welcomed with customary grace.

More really good staging here.

The scene where Faye asks for help really reminds me of Fujiko from Lupin III. For those that don't know, Lupin III is a very long running series about a clowning super thief who is the grandson of Arsène Lupin (a character from French media very popular in the 30's). Lupin III was obviously a huge influence on Cowboy Bebop, but more on the edges than directly. Spike is vaguely like Lupin himself, in that they are both beanpoles with sticky fingers. But where Spike is mature and emotionally guarded, Lupin is completely immature and wacky. Jet is like Jigen - but where Jigen is a bushy haired ex-con, Jet is a bald ex-cop. Faye here is actually very similar to Fujiko, but we'll learn about how different they are in the fullness of time. I don't want to exaggerate, Bebop isn't reducible to Lupin in any sense. For one, there's a lot more variety in Bebop. In the original comics, naming all the women "Fujiko" was a running gag based on artist Monkey Punch's inability to draw more than one sexy-female body shape. In fact, in the latest Lupin series, The Woman Called Fujiko Mine (directed by Watanabe protege Sayo Yamamoto), it's come to the point that Spike is a bigger influence on Lupin than Lupin ever was on Spike.

Thinking about it, there seems to be no parallel to Goemon. Did you know in the original comics Goemon and Lupin were enemies? I wonder if this will come up later...

So, the plot. Jet ascertains that there will be no bounty from his friend Bob, a vaguely corrupt police friend of his. As Jet argues with Bob, Spike tries to break open Faye's doodad. This is a great sequence as Jet and Spike get more and more frustrated. The camera cuts around, following Murdock's increasingly worried eyes as tries to maintain a blank expression. The acting is really good in this scene and the montage approach highlights it.

With no bounty on their way Spike & Jet decide to let Murdock go. But what's odd about this scene is that the way its composed is focused on Spike. And not in the sense that we're looking from Spike's perspective at Murdock, its more like we're supposed to be looking at Spike. And he's got this oddly ambivalent look on his face. Is he up to something?

While Spike & Jet monitor Murdock leaving The Bebop, Faye manages to escape on her own. She is a crafty one. This scene sets up Faye & Ein's odd relationship. Faye's relationship with Ein mirrors her relationship with the rest of the Bebop crew. For the next few episodes, Ein and Faye are the only female members of the crew (admittedly, that makes the crew half female).

Well, the government is shocked to discover that the mass murdering terrorist is not 100% on the level, but not so shocked that she is moving around without a hefty military tale. Anticipating this, Murdock totally Han Solos the ISSP, first moving in one direction, then drifting out in emergency pods through chaff she laid down to a net she had laid in advance. After a bit of waiting, she and her cult move take off, able to carry out their plans hassle-free. In addition to being a cool sequence in its own right, this sets up the reason that only Spike & Jet are in the vicinity to stop them.

This sets off a cool sequence where we get to see Spike's ship - the Swordfish II - use its beam weapon for the first time. Spike's ship's design is based on a WWII torpedo ship, this is the equivalent to its torpedo. Faye comes in to save the day, snagging a sweet deal to 60% of Murdock's bounty. The government decides to seal up the Murdock cult in hyperspace, leading to an epic race to escape before they get sealed in. Spike and Faye get out.

If I didn't do all this hint dropping, it really wouldn't be obvious that this scene was more than an infodump excuse/joke.

This was a very good episode, featuring excellent writing, great performances and terrific direction. I had to leave out many of the smaller things that I noticed in order to keep the length under control. This is the kind of episode that helped create the Bebop legend. It was the first episode to let Spike fade into the background, hinting that Bebop would be much more than The Spike Spiegel Show. It's amazing to think that something this good could be one of the smaller, not particularly well remembered episodes. And the next episode, well, let me tell you, that isn't one of the smaller episodes. But that's a bridge we'll have to cross later. For now,

Two Recent Deaths

We recently saw the deaths of two men whose impact on 20th century thought has been profound but relatively unsung. Philosopher and mathematician Hilary Putnam and mathematician/economist Lloyd Shapely were men whose penetrating and patient analysis provided the solution for many deep problems.

Hilary Putnam

Hilary Putnam was a student of the logical positivist Hans Reichenbach and from him brought many of the subjectivist, syntactical tools beloved of the Vienna Circle. However, his great mentor was the American philosopher Willard Quine. Like Quine, Putnam sought to use "pragmatism" to escape the subjectivist straight-jacket of the logical positivists. Pragmatism, in Putnam's sense, means that we commit ourselves to believe in the objects we talk about. Even if there is, in some "strictly physical" sense, only atoms & void/quantum fields/strings, this is only a factoid about some wacky definition of existence, not a deep fact about the world. In fact, we act as if we believe in tables, chairs, brains, minds, money and perhaps even justice. To a pragmatist, this "acting as if" is more real belief than philosophical handwaving. Putnam's great contribution in this area was also getting out of Quine's behaviorist straight-jacket. We act as if minds exist, so we ought to believe they do. Putnam argued that the mind could be understood as a cluster of machines in various states with complicated functions, and therefore could happily be allowed into a sensible world-view without inviting in spooks.

Through his interest in pragmatism, Putnam became very interested in forms of philosophy beyond the small analytical circle he was raised in/helped raise. The logical positivists were after an austere world view, a small number of subjective percepts could be held to exist and everything else was metaphysical. The American Pragmatists provided Putnam a way into a richer world. Through enriched world view, Putnam hoped to communicate with philosophical traditions ignored by pure positivism, even including religious thought.

This richer world extended into his teaching. Putnam's relative friendlyness to so-called metaphysics certainly provided his student David Lewis with a friendly place to develop his formal approach to metaphysics. Putnam's other students include the great logician and logicist George Boolos, the potent structuralist Paul Benacerraf and the pugnacious Jerry Fodor.

Hilary Putnam believe that philosophy should not be a quiet academic exercise separate from the sciences and from real life, and as befitting a pragmatist, lived out that belief. He was active in politics, played a key role in proving Hilbert's 10th problem undecidable and co-developed the logic checking album that was used to design the very computer you are reading this on.

Lloyd Shapely

The brilliant mathematician Lloyd Shapely was one of the fathers of cooperative game theory. In a cooperative game, groups of players can work together or against one another. In the board game Key To The Kingdom, the goal is to get the key and go to a specific square. All the players can cooperate to harry the player with the key - but such cooperation only works until one of them successfully steals the key...

It doesn't take much thought to realize that many situations are equivalent to cooperative games. Rousseau believed all of society was based on cooperative games. He asked us to imagine that we were a pack of men, women and/or wolves out to hunt meat. We could all eat hares separately and sleep with stomachs half empty. Or we could all work together and take down a stag and eat like kings. Akela, the wise wolf, wants his pack to be healthy and strong. How can he analyze this problem?

What he needs is a function from coalitions onto reward. Let's say that there are four wolves: Mom, Dad, Son, Daughter. We'll call this the set of players \( P \). Then the possible coalitions are:

$$ \emptyset \textrm{ - nobody}\\
\{ Mom \}, \{ Dad \}, \{ Son \}, \{ Daughter \} \textrm{one member}\\
\{ Mom, Dad \}, \{ Mom, Son \}, \{ Mom, Daughter \}, \{ Dad, Son \}, \{ Dad, Daughter \}, \{ Son, Daughter \} \textrm{two members}\\
 \{ Dad, Daughter, Son \}, \{ Mom, Son, Daughter \}, \{ Mom, Dad, Daughter \}, \{ Mom, Dad, Son \} \textrm{three members}\\
\{ Mom, Dad, Son, Daughter \} \textrm{four members} $$

This set is traditionally called \( 2^P \), or the power set of \( P \). The amount of delicious venison we eat is a function \( v: 2^P \mapsto \mathbb{R} \). This is called the Shapley Value Function. Analysis of this function allows Akela to organize the pack by - for instance - offering extra meat to those who contribute more, etc. With his infinite wisdom, Akela always finds a stable distribution. Note that these equilibrium distributions can obviously be unequal, as discussed before. For instance, if Father Wolf is strong and Mother Wolf is stealthy, Akela may deem it unnecessary to allocate extra meat to Daughter and Son Wolf.

The Shapley Value Function is very general. On the Wikipedia page linked above, it is used to construct a crude model of a firm. It can also be used to model a general market. The function can even be extended to when the set of players is very large so that no individual player has an effect on the whole game. This is modeled by making the set of players continuous. Integration theory then gives the fascinating result that the cooperative game optima are exactly the market optima! But this isn't just another way of writing Adam Smith's invisible hand. Combining continuous workers with discrete employers can become a model of oligopoly in hiring and much more besides. Such models are used by, for instance, Krugman & Fujita to model the spatial development of economies.

The fact that venison/utility can be easily reallocated between the wolves makes this game one of "transferable utility". Shapely also did foundational work in cases where "utility" cannot be transferred. Shapely famously this particular great contribution to economics on an afternoon dare. His colleague David Gale asked him if there was a way of marrying a number of men and women given their preferences and that the marriages had to be "stable" - no (man,woman) pair would divorce to get one another. Gale expected that if the number of men & women was large, then there would be no solution. After an afternoon's thought, Shapely showed that there always were completely stable patterns and gave an efficient algorithm for finding them! (allowing gay marriage makes the algorithm slightly more complex, but the result is the same)

Though stated in a silly way, this problem is very deep. Your computer bandwidth right now is allocated using this algorithm. The Gale-Shapely Algorithm brought Shapely into the world of "Mechanism Design", the development of markets and other methods for distributing in a stable way. This research would eventually net Shapely a Nobel Memorial Prize in Economics!

Anybody's death is a loss to humanity, but a part of them can live in our minds and our hearts. I hope that these men will be among those who will live in your mind forever.

Steven Universe Segments 9 and 10: The Cats Meow

These segments both sort of involve cats, but not the kind that meow.

The first segment is "Tiger Millionaire", a pro-wrestling spoof. The plot is very basic. Amethyst feels oppressed so she takes it out in secret underground pro wrestling. In the end everyone reconciles and feels better. It's not readily apparent that anyone on the production team "knows a wristlock from a wristwatch" as the old saying goes. This illegal underground wrestling organization is so cheap that they can't even afford two announcers. I say it's illegal because it is taking place in an abandoned factory, but is it? Why would Sadie attend an illegal bloodsport? If it isn't illegal, why isn't it somewhere normal, like a gym or a high school?

Steven's wrestling persona is Tiger Millionaire, who is sort of a fusion of Tiger Mask and the Million Dollar Man. Well, mostly he's an under-the-top version of The Million Dollar Man (wrestling doesn't do the subtlety thing). Amethyst is the Purple Puma, who has no personality whatsoever (which is ironic). The majority of the episodes run time is spent with Steven and Amethyst pursuing the tag team belt, which is a mistake since Amethyst is omnipotent and invincible so there's not exactly much of a build up. Why should we root for them, aren't they gods taking advantage of mortals? We can't even root against them because the Purple Puma has no meaningful rivals!

Also, Steven isn't a tag team partner, as he's never tagged in. Tiger Millionaire is actually an interfering heel manager. Also, I hate to spoil the episode too much, but I couldn't get over the fact that it ends with 1) A speech referencing backstage events that the audience couldn't expect to understand, 2) faces and heels losing all definition and working to give an overpushed wrestler the belt and 3) getting the belt off of a ladder. This plot works for the viewer, but imagine all you were in the audience, you'd be totally confused. There's actually a wrestling booker named Vince Russo who used to be infamous for having matches a lot like that. It's kind of amusing if you think about it.

He did this twice a week for his adult life

The fight choreography is lackluster for an episode that is all about ridiculous fighting. Amethyst/Purple Puma's style never goes beyond striking except exactly once (she bear hugs somebody) and Tiger Millionaire never wrestles at all. Nobody has any fancy finishing moves, and considering the work Steven puts on making his character that's kind of surprising. I mean, look at Tiger Mask or The Million Dollar Man's finishers. Wouldn't it have been cool to see Amethyst do something like that. One of the beautiful things about animation is that you don't have to worry about safety or reality, isn't it? You could do spots that would make Sabu look like a wimp. Not only would it have been cool to see Amethyst or Steven do a Phoenix Splash, but also seeing Amethyst no sell someone's finisher would have been a good point to make on the whole emotional arc.

Dainty Step~

Maybe the fight choreography would be more impressive if I wasn't also watching Cowboy Bebop, one of the most impressive series of any kind in the field of fighting, but I digress. There actually is a lot of good, funny animation in this episode. Most of it involves Pearl being a drama queen. Above Pearl and Garnet are stepping onto a platform and Pearl does this goofy, exaggeratedly dainty step. It makes me laugh, but it's hard to describe in a screenshot.

The episode's biggest laugh come at the end after Pearl and Garnet find out about the wrestling thing (if you can't see that coming, I would recommend an eye exam). At one point Pearl makes the really exaggerated stance pictured above. It's hard to explain with stills why this is so funny. Reviewing animation reminds me of the old joke of "dancing about architecture".

This episode doesn't have the rushed feeling of the others, but it also feels like more of an idea for an episode than an actual episode. It hits all the emotional buttons, but it is obvious nobody really cared about the path between them. Fun but disposable.

"Steven's Lion" is the second segment in this episode and Steven gets a lion. So many of the characters of Steven Universe are drama queens (Pearl, Steven, etc) that it makes you remember how funny deadpan can be. Steven's lion is a good reminder of that. The lion often seems actively annoyed at his and The Gem's sillyness.

This has nothing to do with the review, but my screenshots all came out weird, so I can't illustrate this segment really well. Just imagine there's a picture of a desert here.

At the beginning, Steven & The Gems go to the desert to do a mission. The Gems leave Steven at a small dune in the shape of a semisphere, which is impossible but not important. More important is why do The Gems leave him halfway between home and the mission. Garnet says he is safe where he is, but he could be safe anywhere in the damn world!

So anyway, here Steven meets a giant pink lion. From what I have heard, with desertification there are actually lions in the desert now, which is sad. The Gems come back having captured a gem that made a sort of temple in the desert. Apparently this is a Bad Thing, but nobody explains why this is. We just have to rely on instinct. The sandstone objects it creates remind me of the desert stage in Mario 64, and that was bad guy stuff. So we know this thing is bad. They're kind of surprised to see Steven with a giant pink lion in the desert, but they're also magical alien gems, so what you gonna do? However, the Gems note that the lion is a wild animal and therefore cannot be domesticated. But, in a twist that forever changed A Boy And His Pet fiction, the lion ... followed him home!

If the thing was working, you would see a picture of Steven and his lion in front of his house. The "some kid selling auto insurance line" was funny.

So anyway, it turns out that Amethyst didn't protect the gem they collected and Steven moronically and melodramatically throws it on sand despite having been told that is a bad thing. Nobody even mentions that Steven is being a complete idiot here, but he wouldn't be able to if Amethyst arbitrarily decided to also be stupid. Amethyst is a complete plot device in this episode. She's so mentally checked out that it's like the firebrand punk of the last episode was replaced by Jeffery "The Dude" Lebowski. Despite the fact that they defeated the gem by themselves just fine earlier, The Gems can't defeat it now. It's up to Steven and his lion to save the day!

Here there would have been a picture of Onion being really mad. This is a transition to the next paragraph.

I skipped over the time Steven goes to the pizza place because it is pointless and only serves to introduce the fact that there exists a pizza place. The funniest thing in the episode is Onion's over-the-top reaction when he thinks Steven lied to him in the pizza place scene, but it could have been cut to make room for a better reason for Amethyst to not demonstrate basic competence.

This episode is more like the previous one in having a lot of notes to hit. It hits three separate metaplot notes loud as it can: 1) there exists a pizza place whose owners are friends with Steven 2) Steven is gonna totally gonna have a lion and 3) Amethyst is "adopted" (I don't know in what sense, but it's really obvious). Unfortunately, this overreach causes the writing to squish the characters into plot devices. The episode is really carried by the lion, who provides all the best comic and action sequences. Unfortunately, he can't carry the plot and the more you think about it, the less sense it makes.

These are the main composers for Steven Universe.

I haven't been mentioning it, but there's a lot of really good music in this series. Not to the level of Bebop, but still very good. One of the songs in one of the segments was a really cool drum thing, sort of like what they did with Birdman, or M'Boom. You can hear it here. I'm glad the creator of this show decided to give music an important part. See you next episode!