Stimulated Annealing

January 15, 2011

Promoting Stimulated Annealing

Three friends separately forwarded me an article in the Wall Street Journal in which the author, a professor at Yale Law School, argues why what she calls “Chinese mothers” are better than “Western” ones. The article was a bit silly: not only did the author adopt an intentionally confrontational, somewhat petulant tone, but she also committed a basic statistical fallacy:

Chinese parents demand perfect grades because they believe that their child can get them. If their child doesn’t get them, the Chinese parent assumes it’s because the child didn’t work hard enough. That’s why the solution to substandard performance is always to excoriate, punish and shame the child.

Actually, if a child does worse than normal on a test, he or she is more likely to do better on the next test purely because of regression toward the mean. To attribute this improvement to “sham[ing]” the child is to confuse correlation with causation. The psychologists Daniel Kahneman and Amos Tversky noted this fallacy in their 1974 paper Judgment under Uncertainty: Heuristics and Biases:

In a discussion of flight training, experienced instructors noted that praise for an exceptionally smooth landing is typically followed by a poorer landing on the next try, while harsh criticism after a rough landing is usually followed by an improvement on the next try. The instructors concluded that verbal rewards are detrimental to learning, while verbal punishments are beneficial, contrary to accepted psychological doctrine. This conclusion is unwarranted because of the presence of regression toward the mean… Thus, the failure to understand the effect of regression leads one to overestimate the effectiveness of punishment and to underestimate the effectiveness of reward.

Of course, punishment might work in certain cases. But especially for the “stereotypically successful [Chinese] kids” the author describes, regression toward the mean is likely to explain much of the supposed imprvement following a poor grade. Perhaps the author did not ace an intro-level statistics or economics class?

However, my goal for this post is not to discuss statistical fallacies but rather how to explore how parents can foster both creativity and achievement in their children. (Normally I write about topics nobody else cares about, but I thought I would make an exception here since this goal is in line with the blog’s overall purpose.) First, one point that stood out from the WSJ article is that “Chinese mothers” want their children to be well-rounded, at least within academics and music, in that they have separate achievements in many different areas. However, true well-roundedness is about tying those achievements into something coherent and directly leveraging achievements in one area to do even better in another.

If parents view the development of well-roundedness in a disjointed way, I think their kids are not just less likely to make connections between different interests, but also less likely to gain much depth of knowledge in any individual interest. Take the example of spelling bees, popular among Indian Americans (many of whom probably have mothers who qualify as “Chinese”): if you view the spelling bee as a competition, without placing it in any broader context, then the most natural approach is to just spend hours memorizing spellings. If you’re diligent about this, you’ll probably do reasonably well. But I do not actually think anyone finds memorizing long lists of words that much fun, so once the spelling bee is over, you’re probably not going to continue with any interests related to spelling…because you never really developed any. On the other hand, if you relate the spelling bee to, say, a broader interest in linguistics, ethnic studies (consider the politicization of the Hindi versus Urdu divide, Dravidian linguistic nationalism, or Francization), or Old English literature, then it is way more likely that the spelling bee will enhance and bridge together your existing interests. Ironically, this approach is probably better for your immediate goal of winning the competition as well, since you are far more likely to retain new facts if you relate them to ones you already know.

So instead of forcing well-roundedness, I would try introducing someone to a lot of different areas and seeing what sticks. There are many ways to do this:

  • Picking toys that encourage creativity and different ways of thinking. I think wooden blocks are the best toys ever, especially if you have so many that you almost have to work with other people. Legos can also be good, as long as you get a random assortment of pieces and not the special sets where you have to follow a bunch of instructions.
  • Going to a school with a really wide range of people, from different ethnic and socioeconomic backgrounds and where the parents are in all kinds of professions. Inviting people to your home and going to other people’s homes is very important too. Growing up in a big city makes this much easier.
  • Visiting all kinds of museums: science museums, art museums, non-traditional museums like this, etc. Museums are a great way to explore a lot of areas very efficiently, so I think visiting a museum maximizes the chance that you will find something interesting and then pursue it.
  • Encouraging applications. For example, if you take your kid to a science museum or read some Magic School Bus books together, you should have actual experiments prepared as a follow-up.

When doing the above, a few points are important to keep in mind:

  • You should view your role, for the most part, as an enabler. You’re hoping to get your kid addicted to something, and then you just keep supplying the drugs. Occasionally an obsession can become unhealthy, but I think it’s important not to kill interests for the sake of making your kid more well-rounded.
  • Your kid might become somewhat lopsided. I don’t think this is necessarily a problem, but you should view that lopsided part as providing the base for expansion into future interests. For example, your kid might be really into maps, which is great but not especially useful. Therefore, you can buy atlases that include all those nice colorful sidebars about economies and governments and cultures. There’s a good chance that your kid will branch out into at least one of these areas. In my view, this is the best way to build true well-roundedness, since new interests naturally develop from existing ones.
  • All this creative stuff should not take the place of rote memorization. I actually think there has been way too much of a backlash against rote memorization and in favor of “new ways of thinking”. You can explore all the new ways of thinking you want, but if there aren’t any facts to work off of, you won’t get anywhere. It is important to keep in mind all levels of Bloom’s taxonomy. So things like memorizing spellings, multiplication tables, or really anything will always be important, no matter how much people rely on calculators or Google or Wikipedia.
  • Going off of the last point, there should be some kind of constant evaluation. After you go to a museum, you should be making sure that your kid did actually learn something, and if not, find out why. For example, maybe the museum didn’t have enough interactive exhibits and next time you need to build up interest by doing some science experiments before going to the museum. Passively thinking that your kid will always absorb stuff on his or her own is a terrible idea.

Finally, I do not think it is useful to make distinctions between ethnic groups or use terms like “Chinese mother” and “Western mother”. I am not entirely convinced that there are any meaningful differences between parents from different ethnic groups, once you control for factors like socioeconomic background and parents’ education. But more importantly, even if there were, what would we actually do with this result? Our goal should be to identify the strongest elements of different parenting models. Whether those elements are Chinese or Western or Burusho is uninformative and distracts from the most useful information.

November 21, 2010

The Parsi Genealogy Project

Filed under: Finance, History, Religion — Tags: , , , , , , , , — stimulatedannealing @ 7:16 PM
The Parsis in Bombay

The Parsis in Bombay

When I was in Bombay a few months ago, I asked every Parsi I met a single question: what about Zoroastrianism has made, and continues to make, the Parsis such a successful community? One of the most illuminating responses I received was this: “None of the rituals, texts, or commentaries are essential. When you reduce Zoroastrianism to the core, it is nothing more than Good Thoughts, Good Words, Good Deeds.” But how does this tell us anything about Parsi achievement? The photographer Sooni Taraporevala offers us a clue in her book Parsis: A Photographic Journey:

Zarathustra’s religion was radically different to anything mankind had ever dreamt of thus far. Instead of a religion based on fear, on propitiating and appeasing several Gods, Zarathustra’s religion put a free, thinking, rational mind on centre stage… According to Zarathustra, salvation for the individual depends on the sum of his/her thoughts, words, and deeds, and there can be no intervention by any divine being to alter this.

Therefore, Zoroastrianism places the burden of choice on the individual, and the individual alone. With choices comes responsibility, for if we alone make our choices, we alone are responsible for their consequences. (Check out R. C. Zaehner‘s articles here and here for more on Zoroastrianism and free will.) This way of thinking necessarily leads to rationality and to active engagement with the rest of the world. Rationality is the only means by which Zarathustra would have us make our choices: in the brilliantly simple Zoroastrian moral order, where Good Thoughts, Good Words, and Good Deeds are all that matter, what other means do we have? And in a world where the burden of choice is ours alone, how could we not engage with the rest of the world through right action? To withdraw inward would be to turn aside from the burden of choice, abnegating the responsibility that burden confers on us. In a strong echo of Max Weber’s thesis of the Protestant Ethic, T. M. Luhrmann goes so far as to claim that “Zoroastrianism was equated by many…with an ethical system alone: God exists, but He is worshiped through the doing of good deeds.”

So the Zoroastrians did not withdraw inward, and instead contributed to the world far out of proportion to their numbers. They founded an empire that surpassed anything the world had known before, not just in landmass and administrative efficiency but also in religious tolerance. Some centuries after that empire fell, they founded another, one whose cultural contributions reached as far afield as Japan, where their aesthetics influenced the design of the masks used in Noh drama. (See this post for a “history” of pre-Islamic Iran in four lines.) And when that empire fell, fleeing religious persecution, some Zoroastrians came to India.

The story of how the Zoroastrian refugees landed at Sanjan in Gujarat is well-known, but my favorite version, from Boman Desai‘s The Memory of Elephants, is below:

A month after their arrival, the rajah was finally meeting the Iranis officially… He raised his hand: the Iranis were brought to the center of the assembly and invited to tell their story. The seniormost of the dasturs, the priests, each of whom wore a white turban and robe, had been elected spokesman. Jadhav Rana sympathized with the Iranis, but was uncomfortable with their warlike appearance. “This is a sad story,” he said, when the dastur was finished. “What you wish — a place to stay where you may worship freely, where you may cultivate the soil so that you are not burdensome to others — is fine and honorable, but it is not that simple. Let me show you how it is.

He clapped his hands twice and a jug of milk, filled to the brim, was brought out. “Sanjan is like this jar of milk,” he said. “There is no room for more.”

The old dastur brought a coin out of his robe. “Your Highness,” he said, holding up the coin. “If I may be so bold.”

Jadhav Rana frowned, puzzled, but nodded giving his permission.

The dastur slipped the coin carefully into the jug without spilling a drop. “Your Highness, we Iranis will be as the coin is in the milk. You will not even know that we are here.”

The crowd applauded the dastur, but Jadhav Rana didn’t smile. “This is well,” he said, “but a coin is tribute, and the hospitality which can be bought with a coin is not the hospitality of Sanjan. How will you repay our hospitality?”

The dastur dropped a pinch of sugar into the milk, taking care once more not to spill a drop. “Your Highness,” he said, “as the sugar sweetens the milk so shall we endeavor to sweeten your lives with our industry.”

Members of the crowd jumped as they cheered…

Jadhav Rana, and the teachings of Zarathustra, demanded nothing less than active engagement with their new world from the very first Parsis.

While reading about the Parsis, one of the patterns that quickly emerged was not just the community’s accomplishment across diverse fields, but also its supportiveness and interconnectedness. When Homi Jehangir Bhabha wanted to set up an institute devoted to fundamental research in theoretical physics, he could rely on the financial support of a trust founded by a fellow Parsi, his uncle Sir Dorabji Tata, and the moral support of his uncle’s second cousin, J. R. D. Tata. Somewhat ironically, Bhabha, who later became the father of India’s nuclear bomb, could claim as his second cousin Rattanbai Petit, the wife of Muhammad Ali Jinnah. Jinnah’s only grandson, Nusli Wadia, could claim direct descent from nearly every leading Parsi industrialist of the nineteenth century, from Sir Jamsetjee Jejeebhoy to Sir Dinshaw Petit to Naoroji Nusserwanji Wadia, his great-grandfather. N. N. Wadia’s own grandfather, Ardeshir Cursetji Wadia, was the first Indian Fellow of the Royal Society (an honor Homi Bhabha was to earn almost exactly a century later) and the first Parsi to visit the United States. Ardeshir Wadia’s great-grandfather and the first Master Builder of the Bombay dockyards, Lowji Nusserwanji Wadia, brought with him from Surat Parsis like Kavasji Kamaji, who founded the Cama family, known equally for entrepreneurship and scholarship. It was one of these Camas, Merwanji Mancherji Cama, who gave the lawyer-turned-inventor Ardeshir Godrej his startup capital.

Another pattern that emerges is how this network allowed the Parsis to become one of the most dynamic communities in the world. The Wadias offer just one example: Lowji Wadia began as a shipbuilder, which gave his family a direct view of the booming trade across the Indian Ocean. Seizing the opportunity, his grandsons Pestonji Bomanji Wadia and Hormusji Bomanji Wadia decided to enter trade themselves. But this trade needed financing, so Pestonji’s adopted son Dadabhai Pestonji Wadia became the preeminent banker of his time, at one point owning 37.5% of the capital in the Bank of Western India. Then as cotton became enormously profitable, aided in part by shortages during the American Civil War, N. N. Wadia founded Bombay Dyeing – following Cowasji Davar and his former employer, Sir Dinshaw Petit, in his entry into the cotton industry. Nusli Wadia too has shown his ability to adapt: while the Wadia Group still owns Bombay Dyeing, the majority of its profits now come from Britannia Industries, one of India’s largest biscuit manufacturers. And at every stage, we see Parsi entrepreneurs relying on the most advanced technology of their time: Ardeshir Wadia studying the most modern shipbuilding techniques in the United Kingdom and bringing gas lighting to Bombay; J. N. Tata traveling to Europe and the United States to study the latest methods of steel production, eventually bringing the American engineer Charles Page Perin back with him to Jamshedpur; Ardeshir Godrej and his brother Pirojsha inventing the world’s first springless lock, and as a more recent example, Tata Motors under Ratan Tata developing the “one-lakh car”, the Tata Nano.

To trace these networks of mutual support and innovation, I began to create a family tree that would link together all the Parsis about whom I had read so much. While I began with the Wadias, slowly I began to add other families: the Tatas, the Camas, the Jejeebhoys, the Petits, and so many more. I relied mostly on old books about Parsis, many of which are now in the public domain, as well as numerous scholarly articles. (Interestingly, one of the most valuable repositories was the Digital Library of India at the Indian Institute of Science, founded with the financial support of none other than J. N. Tata.) The tree now spans 13 generations and nearly 200 individuals, including many of the most famous Parsi businessmen.

But it is nowhere near complete. My goal is to include every Parsi I can in this project. So if you have any information that would be useful — corrections to this tree, your own trees, interesting documents, contacts of people who would have the information I need — please contact me. The more people this project includes, the better we will be able to see how the Parsis continue to actively engage with the world, following the teachings of Zarathustra and “sweetening lives with their industry” as they promised Jadhav Rana they would.

Technical notes: To create the family tree, I created two CSV files. The first contains node data, with one line per individual, while the second contains edge data, with one line per family (father, mother, children). I then wrote a quick Python script to process these files into a DOT file. The result is a bit messy, both because of limitations in DOT and because the tree is so closely interconnected. If you have a better solution, please let me know. Finally, some of the spellings are inconsistent (e.g. Jamsetji vs Jamsetjee vs Jamshedji) — this is intentional. Rather than choose one spelling for every person’s name, I chose the spelling that I saw most frequently for that person.

February 28, 2010

Static vs Dynamic in Visual Art

Filed under: Art — Tags: , — stimulatedannealing @ 9:43 PM

A friend just sent me an article (PDF) in Tuesday Magazine called “Physics, Art, and AI”. In the article, the author “utilizes concepts taken from electrodynamics to generate aesthetically balanced images”. While the author’s attempt to apply physics to aesthetics is quite interesting, I disagree with his premise. The author wants to say that “aesthetically balanced images” are more pleasing, which I mostly agree with, but he then tries to define a balanced image as one “in which the eye moves across the whole region without resting at any specific point, unless that point is crucial to the content of the work (emphasis added)”. This definition has two major problems. First, the definition is too restrictive: its “unless” rules out so many of the greatest pieces of art, where the artist intentionally draws our attention to a single point. Second, ensuring that the eye moves across the “whole region” is not a necessary condition for creating aesthetic balance. My goal for this post is to illustrate these two problems more clearly and show how they point to a tendency to view visual art as static, rather than dynamic, when in fact the dynamic aspect of visual art is what transforms a good piece into a great one.

Consider Escher’s famous lithograph “Ascending and Descending” [1960]:

Escher, " Ascending and Descending" (1960)

Escher, Ascending and Descending (1960)

As well as Escher captures the architectural details of the building, most people’s eyes are immediately drawn to the impossible staircase. That staircase is what transforms the piece from a pretty picture of some building you might find in the Low Countries to the iconic picture most people, if not everyone, reading this will recognize. If we limit our discussion of art to works where drawing the eye to a specific point is not “crucial to the content of the work”, we lose not just this piece, but also Hokusai’s “The Great Wave off Kanagawa” [1832] (where we are drawn first to the spray of the wave and then to its target, Mount Fuji)…

Hokusai, " The Great Wave off Kanagawa" from 36 Views of Mount Fuji (1832)

Hokusai, The Great Wave off Kanagawa from 36 Views of Mount Fuji (1832)

…this cell by Hergé from The Crab with the Golden Claws [1940-41] (where we are drawn to Captain Haddock’s exploding bottle)…

Hergé (Georges Remi), The Crab with the Golden Claws (1940-41)

Hergé (Georges Remi), The Crab with the Golden Claws (1940-41)

…and the Pakistani modern artist Tazeen Qayyum’s “Exposure” [2008] (where we – and the sinister green orb – are drawn to the cricket that will soon be just an outline).

Tazeen Qayyum, " Exposure" (2008)

Tazeen Qayyum, Exposure (2008)

If these were just random nice pictures that I’m picking out, then maybe the author’s definition of aesthetic balance would be fine. But they aren’t random nice pictures. The ability to draw a viewer’s attention to one point is so important because that one point is what makes the whole piece interesting. One of the things I noticed about the Tuesday Magazine article is that the human-generated pieces of modern art to which he compares his computer-generated images are…boring. It’s not really that surprising that that people should find the latter more pleasing: if you compare them to the human-generated images, you will see that the computer-generated ones have far more irregularities than the human-generated ones, from jagged lines to odd shapes to non-complementary colors. Therefore, while both the computer- and human-generated images satisfy the author’s standard of not drawing the eye to “any specific point”, the former at least draw us to several points, while the latter draw us to none at all. Of course, this is not even enough to make the computer-generated images “great art”; it just makes them a bit better than their human-generated counterparts.

So the author’s definition of aesthetic balance is not just restrictive – it’s actually wrong. In viewing all of the pieces above, our eyes rest on individual points, yet they are still balanced. The Escher piece draws us to the ever-rising staircase and creates an improbable balance as our eyes perpetually circle around it. The Hokusai piece draws us to the wave and creates balance by taking us to the natural culmination of the wave crashing over Mount Fuji. The Hergé piece draws us to the exploding bottle and creates balance as we follow Tintin’s inquiring gaze to the left across the desert and finally to the shots coming from the horizon. The Qayyum piece draws us to the cricket under the green orb and creates balance by showing us what the destruction that came before.

These observations do allow us to rescue the author’s definition of aesthetic balance. His main error is to set up a contrast between guiding the eye across the whole expanse of the image and allowing the eye to dwell on a single spot. This is actually quite an interesting contrast, and probably a common one for people to make, because it points to our tendency to view visual art as static: the assumption is that when we look at an image, we either see a part or the whole without any possibility of our perception evolving from one to the other over time. The best artists mean for us to view their pictures dynamically, like music. We might focus on one part, taking it in before we shift to another, allowing the picture to reveal itself a little bit at a time. The painter, just like the composer, creates balance by inducing us to form expectations about how the art will evolve and then systematically fulfilling or violating our expectations. Will Tintin trace the bullets that has just shattered Captain Haddock’s ever-present whisky bottle back to the guns that we, the viewers, can see poking out from behind that dune? Will Beethoven break through the claustrophobia he has created at the end of the third movement of the Fifth Symphony and achieve the climactic triumph that we, the audience, could see prefigured in the hopeful tension of the last five minutes? We have to wait to find out – but the waiting will be worth it, and that is what makes Hergé and Beethoven’s art great.

January 12, 2010

Kolmogorov Complexity, Autism, and Music

Filed under: Art, Psychology, Statistics — Tags: , , , — stimulatedannealing @ 5:37 PM

I think algorithmic information theory is one of the most interesting subfields of information theory and computer science. Much of my interest comes from the fact that algorithmic information theory is an interdisciplinary subject: Gregory Chaitin described it as “the result of putting Shannon’s information theory and Turing’s computability theory into a cocktail shaker and shaking vigorously”. Information theory itself is an interdisciplinary subject, combining ideas from:

(If this list interests you, check out David MacKay’s free textbook Information Theory, Inference, and Learning Algorithms or Tom Cover and Joy Thomas’s Elements of Information Theory.) I enjoy interdisciplinary subjects since they are especially good at helping me develop intuition through lateral thinking. If I have a reasonably good grounding in one field, an interdisciplinary subject might allow me to use what I know in that field to enter another one.

The other reason I like algorithmic information theory, and information theory in general, is because it provides me with some interesting ways of thinking about problem solving. My goals for this post are:

  1. to explain how Kolmogorov complexity, the central concept in algorithmic information theory, might help us think about how we solve problems
  2. how this simple model of problem-solving accounts for common symptoms of autism spectrum disorders
  3. most practically, how this model suggests that certain types of music can help us increase our problem-solving ability

Kolmogorov complexity defines the algorithmic complexity of an object as the length of the shortest binary computer program needed to specify that object. For example, the Mandelbrot set looks quite complicated, but it has near-zero Kolmogorov complexity because the length of a program needed to compute the Mandelbrot set is so small. The “objects” considered in complexity theory are usually bitstrings (unsurprisingly, given how strongly the field has been influenced by, and also influenced, computer science). Now imagine that I ask you to gamble on the bits in a bitstring x of length l(x), where I offer you even odds on each bit and you do not know the origin of the string. If you follow a universal gambling scheme, betting 2^{-K(x)} on the string where K(x) is the string’s Kolmogorov complexity, then the wealth S(x) you gain from betting on the string satisfies

\log S(x) + K(x) \geq l(x)

(Theorem 14.9.1 in Cover and Thomas). Essentially, your log wealth is lower-bounded by the length of the string minus the complexity of the string. The above equation is interesting because it shows a direct connection between complexity, predictability, and “profitability”: the more we can reduce the complexity of a system, the more predictable it becomes to us, and therefore the more we can “profit” from it.

I think a good definition of intelligence is: the ability to reduce a complex system into something simpler. The better-structured a system is, the greater our ability to “compress” the information we have about a system — and therefore, the greater our knowledge of that system. Algorithmic complexity theory offers a way of making this definition more concrete. In the scheme described above, x is no longer a bitstring but a system, l(x) is how much data you have on the system, and K(x) is the complexity of the system. Then l(x) - K(x) measures how much you have “compressed” the system, that is, how much structure you have been able to extract from your data, thereby lowering the complexity of your initial dataset. This makes S(x) a measure of how much we “understand” the system: compression becomes knowledge.

Therefore, every problem we face is an issue of reducing the complexity of / extracting structure from / compressing a system. At any time, we are going to be trying to solve several different problems at once. Only one or two problems might occupy our conscious attention, but because we do not really use our minds to their full capacity, we carry around excess capacity that the brain unconsciously allocates to other problems. For example, you might be working on a problem set, but subconsciously your mind is then you’ll find that part of your mind is thinking about some roommate issue. My theory is that this unconscious allocation follows something like

R(x_i) \propto (l(x_i) - K(x_i))^{-p},

where x_i is the system with which problem i is concerned, R(x_i) are the resources allocated to solving that problem, and p is positive real number. The difference l(x_i) - K(x_i) measures how “easy” a problem is: either we have a lot of data about the system (high l(x_i)) or the system is relatively simple (low K(x_i)). Then harder a system is, the larger the quantity on the right will be. The parameter p controls how much larger: if p is very large, the brain will attack hard problems with far more resources.

For some people, the brain is relatively good at efficiently diverting excess capacity to other problems and then working on those problems in the background. These people are the ones who are good at multitasking, or the ones who might make sudden breakthroughs on a math problem even when they don’t think they are actively thinking about that problem. However, for others, the brain is not that great at diverting excess capacity. Specifically, if p is too high, the most complex problem will just suck up all of your resources — and then you not only lack excess capacity, but you also lack the capacity to solve the problems you were originally trying to solve.

In this simple framework, someone with autism would have a p that is too high. I think this explains why people with autism spectrum disorders can become paralyzed in social environments. Social environments require the solution of several problems at once, but if one is particularly complex, a person with autism will focus only on that one problem to the detriment of all others. Furthermore, people with autism might resort to repetitive behavior as a means of coping with very high values of p: compulsive and ritualistic behaviors are ways of reducing the complexity of tasks that might otherwise prove overwhelming. On the other hand, autistic savants are examples of the extraordinary achievements possible when an especially high proportion of mental capacity is devoted to a single problem, but it is important to remember that savants are extremely rare.

My guess is that some people with autism find music helpful because listening to it soaks up excess capacity without posing the potential to use up all of their mental resources. Music has to be interesting / complex / unpredictable enough that it can attract our attention and lodge itself in the brain in the first place, but it also has to be boring / simple / predictable enough that once it has taken root, it does not become parasitic and overload the minds of people who have very high values of p.

This might be especially true for autistic people, but it is true of others as well. Therefore, when I select music, I try to find pieces with three properties:

  1. strong rhythm (or more correctly, strong meter
  2. strong melody
  3. textural “depth”

The first two properties give a piece its structure and are I think relatively well-understood. Structure induces us to form expectations of what will happen next while we listen to the piece: the composer will occasionally violate our expectations, keeping the piece complex and unpredictable enough to attract our attention, but he or she will probably satisfy our expectations most of the time, ensuring that the piece is simple and predictable enough so that it does not use too many mental resources. The third property is not as well-understood but plays a critical role in helping a composer balance complexity and simplicity. By depth, I mean a particular form of complexity in which a composer will overlay at least three different patterns. The most obvious one will be the melody, then there might be a harmony (this can be weak), and finally there will be a base rhythm. One of the interesting things about A. R. Rahman‘s music is that his harmonies often blur the line between harmony and rhythm. This is very useful because at first the harmony-rhythm sounds more like a harmony, which provides just enough complexity to absorb the excess mental capacity of a listener. However, because the harmony is really more like a rhythm, the harmony-rhythm makes the structure of the piece far more apparent, thus leading to a massive reduction in complexity as early as on the third listening. Essentially, “false complexity” allows the piece to take root in the mind and soak up excess capacity, but the piece doesn’t become parasitic because all the false complexity soon falls away. By that time, though, the piece has already inserted itself and can help focus your mind.

Here are some examples of pieces by A. R. Rahman that meet the criteria above:

  • “Tere Bina” (SONGS.PK link) from Guru also has a strong, easy-to-remember melody; a harmony-rhythm; and an actual rhythm on the tabla. The rhythm on the tabla is interesting enough that a harmony-rhythm isn’t really that necessary, though you can still hear one during the chorus.
  • “Khawaja Mere Khawaja” (SONGS.PK link) from Jodhaa Akbar is similar, though I don’t think it has quite as obviously well-defined a structure as the other two pieces (this does make it a bit more interesting, though).
  • “In Lamhon ke Daaman Mein” (SONGS.PK link) from Jodhaa Akbar has a very strong, easy-to-remember melody; a harmony-rhythm on what I think is a santoor; and then an actual rhythm on the drums.

The instrumental passages in all of these pieces also showcase the harmony-rhythms. All of these songs are good on both the structure side and the depth side, but “Tere Bina” focuses more on structure while the Jodhaa Akbar songs focus more on depth.

Finally, for all of this to form a serious (i.e. scientific, rather than pseudoscientific) theory, I need to be able to formulate some testable hypotheses. I can borrow ideas from information theory to measure how structured or complex a piece of music is, but I do not know how to measure a person’s attentiveness. Do any readers know how to do this?

January 8, 2010

The Fall of the Shah

Filed under: History, Psychology, Religion — Tags: , , , — stimulatedannealing @ 5:38 AM

The Shahnameh, or Book of Kings, is Iran’s national epic. Written by the poet Ferdowsi around 1000 C.E., it retells Iran’s history from the mythical first ruler Kayomars to the last Sassanian monarch Yazdegerd III, who died in 651 C.E. An integral part of Iranian culture, the Shahnameh has been credited with preserving the classical Persian language and protecting much of Iran’s unique national identity. You can read a partial English translation of the Shahnameh here.

The following poem is meant to be an additional (short) chapter of the Shahnameh recounting the fall of Muhammad Reza Shah Pahlavi, the last Shah of Iran. My goal was to see how much information I could cram into one poem, so I hope you learn something about Iranian mythology and history. For example, the first two lines of the poem are paraphrased from the Shahnameh itself; the first verse takes the reader through 25 centuries of Iranian monarchy, while the rest summarize Muhammad Reza Shah’s rule; and I use the story of Jamshid, the mythical fourth Shah of Iran, to foreshadow Muhammad Reza’s fall. If you find the psychological elements of the poem interesting, like the Shah’s reaction to the first assassination attempt against him, you might be interested in reading Marvin Zonis’s book Majestic Failure, my source for most psychological details.

How can man escape fortune preordained,
To which his actions are fatefully chained?
Why should he strive for anything at all
When all that is certain is his downfall?

Justice He bids me do, as judge will He
All that lies behind and ahead of me.
Before ancient kings and the eyes of God,
I stand awaiting history’s last nod.
Proud Jamshid and valiant Manuchehr,
To one-tenth your deeds I hoped to compare!
Judicious sovereign, Cyrus the Great,
If only I could have followed your fate!
Sassanian Shahpur and Ardeshir,
To your brilliance I might have come near.
Safavid Tahmasp and Abbas most wise,
Plans akin to yours I tried to devise.
Twenty-five centuries of kings divine
Have guided Iran by worthy design.
After twenty-five, in not more than one,
The age of monarchy is all but done.

Nearly four decades ago I was crowned
With war and chaos raging all around.
My father deposed by British intrigue,
I found myself rather out of my league.
When Azerbaijan was pressed to secede,
I could do nothing for those in great need.
Only the aid of the United States
Could help Iran steer through perilous straits.
Then two years later, God proclaimed to me
Instructions set forth by divine decree.
An assassin sent five shots at my head,
But hardly a drop of my blood was shed.
My mission became evident that day:
I would guide Iran on its noble way.
No earthly power could obstruct my path
For fear of receiving heavenly wrath.

One man dared to challenge my iron will,
Rousing the masses with words false and shrill.
Our oil, he declared, should be ours alone;
What is found in Iran, Iran must own.
With Marxists and radical Muslim friends,
He fought only to achieve his own ends.
When I demanded his resignation,
He cheekily said to leave the nation.
I left knowing that I would return soon
To mock that impudent, treasonous loon.
With help from America and Britain,
That fool’s fall was decisively written.
But a king is not made by foreign force;
Inner might must be the prevailing source.
Iran most keenly called for my return;
For their dearest Shah they would always yearn.

My restoration confirmed my mission,
As I broke with outdated tradition.
I redistributed lands to peasants,
Who accepted them as royal presents.
More literate people I strove to make,
So Iranian commerce might awake.
Our infrastructure I sought to rebuild
For Iran’s potential to be fulfilled.
Just the riots of nineteen sixty-three
Interrupted my unshakeable glee.
Reactionary mullahs could not know
What wealth was being sown by their sworn foe.
Behind the shield of Providence once more,
I quelled dissenters I had seen before.
My White Revolution would soon prevail
Over the insurgents’ tiresome wail.

Like the charmed cup of immortal Jamshid
Oil ensured my policies would succeed.
My finance minister doubled the price
Of Iranian crude not once, but twice.
With petrodollars I began to buy
All the weapons I could from my ally.
America could not care any less
About Iran’s military excess.
I met with foreign business directors
To develop Iran’s other sectors.
Within just twenty years, I guarantee,
Iran will have Asia’s top GDP.
Surely my people ought to understand
The generous motives of my command.
Those who sneer mockingly at my goodwill
I shall let the law clandestinely kill.

And then to my Jamshid came cruel Zohhak
From off my head the ancient crown he struck.
All were against me, those whom I had served;
For me their deepest loathing they reserved.
Despite our triumphs, they all only yearned
For all I made to be thoroughly burned.
With my concessions scornfully rebuffed,
The mob could hardly wait to cry, Shah raft!”
Filled with inexpressibly bleak concern,
I left the country, never to return.
The last of the Shahs, forsaken am I,
Exiled from Iran and left to die.
Justice He bids us do, as judge will He
All our deeds that His omniscient eyes see.
Before its own people, the world, and God,
Iran now receives no propitious nod.

S(t)imulated Annealing

Filed under: Psychology, Statistics — Tags: , — stimulatedannealing @ 5:36 AM

Simulated annealing is a popular method for finding an approximate global minimum of a function when the search space is large. Imagine we want to find the lowest point in a valley. We can throw a very hot ball into the valley: at first, the ball will jump around quickly, exploring several parts of the terrain, but as the ball cools down, it will not be able to jump as high and will therefore, on average, settle into one of the lowest points of the valley. Choosing the cooling schedule for the ball is important, since if the ball cools down too quickly, we might find an especially suboptimal minimum, while if the ball cools down too slowly, our method will be inefficient. For example, if this valley is a cost function (think of it as a negative utility function) over all possible actions that we can take in life, and the points the ball visits represent the actions that we choose, curiosity and discipline are what control our cooling schedule. Curiosity is what makes us open to interesting opportunities, while discipline is what enables us to focus on only those opportunities that are consistent with our long-term goals.

Of course, simulated annealing assumes that the terrain of the valley does not change over the cooling period; in particular, it assumes that the ball’s movements do not affect the terrain. This assumption clearly does not hold in our utility maximization example since 1) the options available to us in the future depend on our current actions (the neighbor set is dependent on the current state) and 2) the shape of the utility function depends on the actions we have taken so far (the cost function is dependent on the path of previous states). In this case, we can no longer say that the ball has a good chance of reaching the bottom of the valley. Therefore, we may need to choose more complex cooling schedules: i.e. instead of allowing the ball to cool monotonically, like the standard T(t) = \frac{d}{\log t}, where t is time, d is a constant, and T(t) is the temperature at time t, we will probably need to stimulate it with quick bursts of heat. In our utility maximization example, this means we will need sudden spurts of curiosity to stimulate our minds, allowing ourselves to adapt to a dynamic utility function.

My goal is for this blog to help provide those quick bursts, both for myself and potentially for you.

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