Tuesday, July 20, 2010

Is Chris Nolan The Best Director Of All Time?

The short answer is, quite possibly. 

For the longer answer, you'll have to indulge me with a bit of stats. You see, there's this website called imdb, (you may have heard of it), and one interesting fact about it is that it has the largest depository of user-generated ratings in recorded history.

So, after aggregating all of the movies that somebody has directed, it is easy to calculate his average rating on imdb. In order to see whether Chris Nolan really is the best director of all time, I did this for anyone who had seemed to have a reasonable chance of winning.

To be fair, I didn't count early movies that the director probably didn't have much funding for, movies that he wasn't the main director of, and documentaries, because they tend to be lame.

Once I did this, I realized that I had meandered into a dilemma. You see, the best directors had only directed one movie each! At the tops of the list were Florian Henckel von Donnersmarck, who directed The Lives of Others (an 8.5), and Tony Kaye, who directed American History X (an 8.6).

To appropriately punish these slackers for their limited sample sizes, I had an excuse to employ a fancy Bayesian estimator. This sounds much more complicated than it is.

Basically, I calculated the total number of movies each person had directed, inputted the average rating of a movie on imdb (6.9), and set an arbitrary variable, m, to be some value between like 0.001 and 1000. Then, I put each director's average rating and total number of movies through this equation, and viola: it spit out rankings that took into account the fact that von Donnersmarck and Kaye had only directed one movie each.

Now, determining which value to use for the variable m is an open and interesting question. It depends on your values: do you prefer a director that has made a whole lot of good movies, or one who has made just a few great movies? It'd be hard to answer this objectively.

If you prefer quality over quantity, then you should set your m low, so you don't punish low sample sizes as much. If you think that a director has to be somewhat prolific to be even included in the discussion, then you should set your m high. I set m to three different values to be fair to each of these reasonable positions.

When m = 20, the top 5 directors are:

1) Akira Kurosawa, score = 7.40 (weighted), directed 25 movies. Highlights: Seven Samurai, Yojimbo.
2) Stanley Kubrick, score = 7.36, directed 11 movies. Highlights: Paths of Glory, Dr. Strangelove.
3) William Wyler, score = 7.34, directed 26 movies. Highlights: Dodsworth, Ben-Hur.
4) Ingmar Bergmann, score = 7.34, directed 30 movies. Highlights: The Seventh Seal, Wild Strawberries.
5) Luis Buñuel, score = 7.29, directed 32 movies. Highlights: Viridiana, The Discreet Charm of the Bourgeoisie.

When m = 10, the top 5 directors are:

1) Stanley Kubrick, score = 7.58 (weighted).
2) Akira Kurosawa, score = 7.54.
3) Chris Nolan, score = 7.50, directed 7 movies. Highlights: Memento, The Prestige.
4) William Wyler, score = 7.46.
5) Hayao Miyazaki, score = 7.45, directed 9 movies. Highlights: Spirited Away, Princess Mononoke.

When m = 3, the top 5 directors are:

1) Chris Nolan, score = 7.93 (weighted).
2) Stanley Kubrick, score = 7.92.
3) Sergio Leone, score = 7.88, directed 6 movies. Highlights: The Good, The Bad, and The Ugly, Once Upon a Time in America.
4) Quentin Tarantino, score = 7.80, directed 7 movies. Highlights: Pulp Fiction, Inglourious Basterds.
5) Hayao Miyazaki, score = 7.78.

Another sort of difficult thing to choose is how to count Pixar's movies. Most of the movies list different directors, but really, who actually knows what goes on in that forsaken place? If you consider the Pixar movie making team as its own distinct entity, then that entity would end up at 5th, 3rd, and 5th on the above lists.

If you'd like to check my raw data, feel free to peruse this google document at your leisure.

So there you have it. Chris Nolan is the best director of all time... under certain assumptions. Finally, implicit in this post is the recommendation that if you haven't seen Nolan's Inception yet, you need to get your act together.

Sunday, July 18, 2010

Trade Off #5: Loyalty vs Universality

Contra some arm chair philosophers, most people are not selfish, and want to help others.

Typically, inertia pushes us to help a small group of people. Usually these are those who share easily identifiable traits with us and with whom we often interact directly. However, certain rules can push us to favor larger groups, and even much larger groups, such as the set of all present and future sentient beings in all possible universes.

The advantage of helping smaller groups is that it is easier to see the benefits of one's efforts and feel like part of a community. The advantage of helping larger groups is that one will be less influenced by randomness or bias. There are a number of ways to think about and describe this trade off, such as:
  • In psychology, the amount of money people are willing to not receive in order to give $75 to someone else decreases as the perceived social distance increases between them. So, we tend to only be loyal to a fairly limited number of people. (see graph below and here for more)
  • In ethics, one theory posits that you must consider social justice principles from behind a "veil of ignorance" that obscures your own particular situation. This line of thinking is designed to shift people along the spectrum towards universalism. (see here)
  • In evolutionary psychology, kin selection explains how selfish genes can promote animals to help others if those others are highly similar genetically. But, if kin selection is generalized to altruistic tendencies towards others in general, one can easily shift from loyalty to universality. (see here)
  • In every day life, every dollar that you spend on yourself or your amigos is a dollar that you could be giving to charity to help others. Give Well estimates that you can probabilistically save a life with ~ $1000, to give some perspective. (see here for their calculations)
To me, this trade off is brutal. I either have to admit that I don't care about a random stranger living in Mongolia as much as I could, or I have to admit that I don't especially care about one of my own family members. But the idea that you can be both fully loyal and universalistic is merely a pretty lie. And these can curry no favor in the quest to index the canonical trade offs.

(Above photo credit goes entirely to flickr user extraordinaire lastbeats)

Friday, July 16, 2010

Trade Off #4: Sure Bet vs Shot In The Dark

"What are my chances?"
"Not good."
"You mean, not good like one out of a hundred?"
"I'd say more like one out of a million."
"So... you're telling me there's a chance."

Whenever we have more than one option to choose between, we have to consider not only the relative value of each option but also the likelihood that we will be able to attain that option if we commit. Now, it makes no sense to choose something that is lower in both prob and value. But, if one option has a higher prob and a lower value, or vice versa, then we will have to rely on our values in deciding between them. Examples:
  • In psychology, research describing how people choose based on the relative probability and value of an outcome is extensive. One theory says we are especially risk averse for moderate probability / low value gains and small probability / high value losses. (see here)
  • In mate preference, choosing someone who is stable and dependable (sure bet) or someone with better looks and health (shot in the dark) is one of the universal trade offs across cultures. (see here)
  • In finance, models of investors trade off between minimizing the variance of their stocks and maximizing their average return. Since individuals have a diminishing marginal return to each add'l dollar, they are risk averse and willing to give up expected returns to take the sure bet over the shot in the dark. (however see here for a critique on the risk premium when people benchmark relatively)
This trade off is deeply ingrained in our thinking. Indeed, in competitive landscapes we often assume an efficient market and use reverse inference to conclude that if something is more difficult to attain then it must be higher quality. Surely no aggregation of trade offs could be complete without this one.

(Above photo and quote from the classic Dumb and Dumber scene)

Wednesday, July 14, 2010

Trade Off #3: Switching Costs vs Change Gains

Contrary to the myth of The Great Idea, we humans typically have an ample supply of promising ideas. The tricky part is in deciding which of these notions are most worth our finite resources to actually implement. Thus we come to the trade-off: do the costs of switching justify how much we would benefit from this new idea? Examples:
  • In genomics, replication errors can be useful when they lead to beneficial mutations and in fact that is how species evolve. But you have to factor in the costs of a harmful mutation as well, which is more likely, and which we can think of as the "switching cost" that keeps the rate of beneficial mutations low. (see here)
  • In psychology, keeping your identity small is useful so you minimize the costs of switching your beliefs when something else proves more true, or switching your strategies when something else proves more useful. (see here)
  • In behavior analysis, increasing the change over delay time between two reward schedules decreases the probability that pigeons will switch between them. (see here)
  • In business, upgrading to the next version of software might not be worth it, given all the work customers have to do to learn the new system. (see here)
Broadly, switching costs can come in the form of time, money, ATP, status within an in-group, psychological energy, and the possibility of messing up the transition. This balancing act is in my mind under-prioritized, and deserves its prominent place in the inventory of axiomatic trade offs.

(Above photo credit goes to SantiMB. Have any suggestions or ideas for the trade off series? Holla acha boy, amckenz at g mail)

Monday, July 12, 2010

Trade Off #2: Offense vs. Defense

This trade off will come about whenever time is limited, there is competition between agents who are all potentially vulnerable to attack, the same resources each agent uses for offense could also be used for defense, and the primary goal of each is to win. There are many examples:
  • In botany, plants grow their cells larger in number and size to maximize their exposure to the limited supply of sunlight. But plants also want their cells to be mature and specialized to protect against herbivores and pathogens. Growth (offense) and maturation (defense) rely on the same metabolism, so plants must choose between them. (see here)
  • In soccer, Donovan's beautiful late goal against Algeria was not so so surprising, given that Algeria themselves had an incentive to score. This necessarily lowered their defenses, and allowed the US to capitalize with a glorious counter attack.
  • In immunology, testosterone both develops sexual characteristics and hinders one's immune system. If you think of reproduction as offense and survival as defense, it is clear why you should be wary of macho guys come flu season. (see here)
  • In national politics, war becomes more likely when conquest is easier. Nation states are well aware that by attacking weaker opponents they will still have enough resources available to defend themselves. (see here)
This is a solid and deserving member of the growing trade off canon.

(Above photo credit goes to Lorianne DiSabato.)

Saturday, July 10, 2010

Trade Off #1: Efficiency vs Predictability

Efficiency is quite nice when you have no competitors, but when you do it comes with the nasty downside of predictability. If you always make the most efficient choice given your options, then your opponents will be able to predict your choices and wreck you easily. So, agents typically choose to sacrifice some efficiency in return for some much needed unpredictability. Examples:
  • In predator-prey interactions, escaping prey typically add random noise to their movements, zigzagging, looping, and bouncing away. Although this is less efficient, it prevents predators from learning a systematic rule to predict exactly how prey will escape. (see here)
  • In primate courtship, individuals may have evolved to add random variability to their thoughts and behaviors so as to avoid having their minds read by fellow apes using theory of mind. (see pdf here)
  • In game theory, nearly every solution to interesting multi-person games has a mixed rather than pure solution. For example, in the iterated prisoner's dilemma the algorithm "generous tit for tat" cooperates sometimes even after an opponent's defection, but only randomly. Thus it is impossible to exploit, but avoids the infinite cycles of defection you get from pure tit for tat. (see here)
Regarding the necessity of competition, note that a single institution or individual can usually be profitably modeled as the sum of various competing desires. So, even when you are analyzing the actions of only one person in isolation, you should expect to find trade offs between efficiency and predictability.

(I'm hoping to compile a list of all the canonical trade offs, which should be fun for the whole family. Above photo of peregrine falcon chasing a cormorant comes courtesy of flick user Nick Chill.)

Sunday, July 4, 2010

Emulating Boyden

It's an open question whether you should listen preferentially to advice from those who are successful. The upside is that they are more likely to employ useful hacks, but the downside is that they might not be especially self-aware.

If you do buy the star emulation approach, then the 30 year old neurobiologist Ed Boyden is someone to listen to, as his resume suggests. So, here is a transcript of a June interview of his, and below are three quotes.

First, on advice:
I have received a lot of good advice over the years, but the best was to figure out how I think and feel when going about solving difficult problems, so that I can approach problems in a fashion that is optimal for the way my mind works, in order to maximize my positive impact on the world.
Second, on our small slice of infinity:
Since there is always an infinite amount of information that we don't know, and an infinite number of things that we don't fully comprehend, there is therefore an infinite number of possible important scientific projects. Since we can only do a finite number of things in our lives, the human act of doing science is obligately an aesthetically-driven act. I spend a lot of time thinking about not just the impact, but about the beauty of what we're doing. A good scientific story has cliffhangers, surprise endings and drama.
Third, on music:
I listen to a lot of Bach and Mozart when my mind is operating in a logical or imaginative fashion, and electronic music or techno when it's time to crank out results.
I'm not surprised that he listens to non-lyrical music, which is awesome for boosting concentration. I am also not surprised to hear that he has a strong utilitarian drive, in his aim to "maximize my positive impact on the world."

I am surprised, however, that he admits to using a narrative approach to science. Maybe thinking about the "plot" of an experiment helps to drive him while remaining willing to change his mind.

You may recall Boyden's excellent (2007) advice on how to manage brain resources in an era of complexity. Contra to the current technophobic haterade movement, Boyden embraces lots of tech-based solutions, even calling his laptop his "brain co-processor." And yes, he is on Twitter, although he only updates seldomly.

Thursday, July 1, 2010

Heyman On Alcoholics Anonymous

Brendan Koerner's article on why AA works has kindled a spirited convo in the 'sphere. If you are interested in this discussion, I'd recommend Gene Heyman's thorough 2009 book Addiction: A Disorder Of Choice, which discusses many relevant ideas.

One of his insights, that could answer the question posed by the article, is that choice-oriented rehab programs, like AA, "produce positive outcomes by enhancing the value of activities that compete with drug use and have developed effective techniques for encouraging hope in a brighter future."

To Heyman, one of the key distinguishing features of addicting substances is that using them makes other activities less rewarding. So, initial use leads to an increased preference for repeated use, in a downward cycle.

AA works because "just as heavy drug use initiates a downward spiral of increasingly negative consequences and decreasing options, healthy alternative activities can set in motion an upward spiral of increasingly positive consequences and increasing options."

Heyman also offers one of the most coherent explanations of voluntary behavior I have seen. His three principles for voluntary behavior are that 1) Preferences are dynamic, so that current choices alter the values of future outcomes, 2) Agents can choose between options one at a time or turn one-shot choices into sequences and choose among those (i.e., there are local or global choices), and 3) Individuals choose the best option.

Note that within this theory, certain voluntary choices can be quite self-destructive, as the best option in the short run (local) could be rather hazardous in the long run (global).

The theory has broad explanatory power. For example, consider the common tendency to justify drug use as the "last time." This makes sense because, as Heyman notes, "from a local perspective, the drug is the best choice; but from a global perspective, abstinence is the best choice. The ideal solution is to somehow do both.... If the situation can be framed as the "last time", then the dilemma dissolves. The same reasoning applies to "special occasions.""

Of course this choice theory can't explain all of the individual variance in outcomes, and its explanations break down particularly often when there is co-morbidity with other mental illnesses. But for choice to not get any play in an article like Koerner's is, to me, ridiculous.

If you don't feel like shelling out the $21.56 + S&H for Heyman's book, you might consider perusing an article of his (pdf) that touches on many of the same points, including the crucial local vs. global distinction (figure 4, p 113). But do also consider the book, which Ryan Holiday called "fascinating" and which Tyler Cowen said he "couldn't put down!", although they both ultimately hedged, for reasons which it is their voluntary choice to withhold.