Why I gave up martial art

I used to be a student of martial art, a fervent one. During my worst days, that was my only companion--it was only during those hours when I practice martial art that I could focus and not distracted by painful thoughts. I seriously thought I would take it as a life-long pursuit.

But I gave it up in college. Williams is not to be blamed. It is true we do not have such a professional martial art club, but I gave it up more because I wanted to.

My first encounter with Martial Art is Tai Chi, an ancient form of Chinese martial art.  The first day we did not learn forms, but about the philosophies. I remember very clearly what the master said: " The purpose of martial art is not violence, but is to stop violence. We learnt that our biggest enemy is never others people, but ourselves, our inner urge toward violence and brutality, and to master martial art, we need to master the art to curb such aggression. （克己） This is not an idealistic romantic tenet of some ancient Chinese philosophers, but a very wise idea---you can be very strong, as strong as you can, but if you cannot curb your urge to violence and aggression, soon it will backfire when you upset enough people and/or strong enough people. We will turn old and weak, and none of us can stay on the top, aggression and violence will turn back toward us if we do not curb them in the first place. Respect (礼）and benevolence (任）are always stressed. As these guide the previous principle, which literally means hold back yourself from you should not do. Even in Japan, the tenet of Bushido includes respect and benevolence, but they over-stressed loyalty and honor, and when being loyal to the wrong thing, and taking honor in the wrong thing, things get bad. What happened in WWII is only a sick and disgusting deviation from the true spirit, not the orthodox martial art philosophy. In the movie Yip Man, Yip Man said rightly: " You Japanese invaders are unworthy of martial art".

That is all good and beautiful. Later I realized however, mastering martial art will not help stop violence. In this age, violence never takes the form of bare-fist fight between individuals, but are staged by countries, organizations, and using deadly weapons that easily out-power the most skillful martial artist. In the movie Yip Man, Yip Man felt the same futility when he saw Japanese invaders did horrible things, and killed people but he could do nothing though he is the best martial artist of the time. What is more, I realized I began to develop knee problems from martial art practice. The purpose of martial art is to protect others from violence, and not only is that impossible, but also, instead of protecting ourselves, we are hurting ourselves. That was the last straw.

In this world, when the media continuously distort the truth, we do not even know what is right and what is wrong, then what is the use of power?

A puzzle and my critique

Foreword: I started the blog with the intention to write only two paragraphs with the title "A puzzle or not". Fortunately for me, and unfortunately for the reluctant readers, many related ideas came to me when I wrote this, and before I know it, this blog contains a hodgepodge of ideas.

In Economics, there are often "puzzles". These puzzles refer to the  situations that the observed behavior deviates from the optimal one. For example, the famous equity premium puzzle refers to the fact that "mysteriously" people are under-investing in equity, given the high equity premium. There are numerous such puzzles in game theory, when numerous experiments confirmed that people are not behaving optimally on average.

Are these puzzles?

Many economists say "yes". Their argument is this, while we do not expect complete individual rationality  there is no reason to expect people's behavior to systematically deviate from the optimal. In other words, people's deviation from the optimal should cancel each out! Since many earlier famous economists are trained in Physics, they might even draw an analogy with Physics (I am not aware if anyone did indeed draw such an analogy, but I imagine some would), when there is a voltage difference, the electrons will on average predictably flow in one direction, even individual electron might deviate from the predicted flow. More philosophically, local disorder does not preclude global order. This is indeed such a powerful idea, upon which many sciences, physical or social rest upon. I personally am obsessed with this idea, and I think if I can only remember one idea, this will be the one. Nevertheless, this idea has its bounds.

While local disorder does not preclude global order, it does not GUARANTEE global order either. While we do not expect people's behavior to systematically deviate from the optimal, we do not have any reason to expect that the average behavior will converge either! Then what is this average behavior then? Let me first divert you to a story the mighty Richard Feynman told:


Nobody was permitted to see the Emperor of China, and the question was, What is the length
of the Emperor of China’s nose? To find out, you go all over the country asking people what
they think the length of the Emperor of China’s nose is, and you average it. And that would
be very “accurate” because you averaged so many people. But it’s no way to find anything out;
when you have a very wide range of people who contribute without looking carefully at it, you
don’t improve your knowledge of the situation by averaging.

That's the point! When we are confronted with a very complicated economic decision (it does not have to be really complicated, it could be as simple as a game of flipping coins), many of us the laypeople are confused and have no idea what is optimal. When the welfare consequences are not that high, we basically just choose one action that looks right to us, and there is no guarantee what looks right to us will average out to be optimal. Yeah, you are right, we have some sense of what could be optimal and what could not. But even in the story of the nose length, the people have some sense. They know 100 inch is unlikely, neither is 0.005 inch.  It will be obvious to people that some options are bad, but that's it.

Why I bother to write this blog? For one thing, I like to test out my ideas on the internet and see if there are loopholes or counter-arguments obvious to other readers. But I actually think this is an important idea (no claim of originality here, as Feynman definitely saw this): semi-optimization (eliminating obviously bad choices) or bounded rationality will not lead us to optimal behavior on average. This calls into question lots of the work we do in Economics. When we run regression to estimate parameters like elasticity, many of the implicit assumption is that the average behavior we observe is optimal. This assumption actually does not need to hold, and when that's the case, the fancy regression some people do might be of the same quality as the estimation of the emperor's nose length.

One challenge facing social scientists is causality. For example, when we try to estimate the marginal value of education, we worry about omitted variable bias. We worry that one's education level might be correlated with the person's innate ability, which might again correlate with his earnings. Thus what some people do is to construct a model where the person choose the level of education optimally based on his innate ability. From that model, they design some statistical inference procedure. If only the average behavior is optimal.

Causality is indeed a huge challenge confronting social scientists. However, there are other challenges. The fact that the objects social scientists study (us!) do not fully optimize is a serious challenge. If we do not optimize at all, it is easy to deal with. If we fully optimize, it is slightly more complicated, but handleable. But semi-optimization is tough to deal with. We need to keep in mind people look to social science to guide their optimization--we might choose whether we want to continue education based on economists' estimates of marginal value of education, and it will be pretty funny to know that the very estimates economists come up with is based on the assumption that people have on average optimized.

What is the right attitude to do science? It is often tempting to make some assumptions so that things are tractable. If those are innocuous assumptions, then go ahead, and I think it is great! However, when those assumptions might invalidate the results we get, I would suggest caution. We do not do science because we want to be able to say something about it, but because we want to say something right! I do not mean, however, that we should stop, we might still benefit from a model with dubious assumption as that model might act as a benchmark. Nevertheless, we need to be aware of the model's limit. To act or implement policy assuming the model is correct is a "pretense of knowledge".  Austrian school distrust econometrics, for a reason---so many things could go wrong. Mainstream economists dislike them, and I think part of the reason is that they will not be able to do much with the data under the Austrian critique.  While I believe we could still do thoughtful empirical work, I have to admit the market is flooded with mindless regressions with no value what so ever!

Decision

First let me quote from The Art of Choosing,

the more choice you have, the greater the number of appealing options, no matter how discriminating your tastes...So you'll have to make some sacrifices, and each of these carries a psychological cost. Your enjoyment of the chosen will be diminished by your regret over what you had to give up. In fact, the sum total of the regret over all the "lost" options may end up being greater than your joy over your chosen options, leaving you less satisfied than you would have been if you had had less choice to begin with.

I read the book when I felt I could not deal with all the tough choices anymore, I chose to study the very process of choosing. As it turns out, theory enlightens but does not solve everything. In the end, I had to face the tough problem head-on.

It was tough. Actually no. It was tormenting. Lots of people made it very hard, but I do not mean it in a bad way---I loved those people and really wish I could hang out with them in the next five years. I care about the feelings of lots of people--scoff at as you may, but that is part of my upbringing.

 In the words o Harry Triandis, they are "primarily motivated by the norms of, and duties imposed by, those collectives" and "are willing to give priority to the goals of these collectives over their personal goals," emphasizing above all else "their connectedness to members of these collectives"...it's believed that individuals can be happy only when the needs of the group as a whole are met.

The above quote from The Art of Choosing serves to illustrate the very different mode of thinking that those brought up in the Western world is unfamiliar with. I am not trying to explain my decisions, I just wish to say because of my mindset, it is just tougher.

Chuan, Nick and Jenny, I really wish to join you all for the greater Williams community in Bay area, I am sorry I cannot. Jessy, Kelly and all the other friends I have or I have made in Stanford, how I wish to be able to hang out with you during the next five years. I am really sorry. Fate is relentless---I won't get it all. I hope it will somehow bring us back together sometime in the future.

I wish to say no more about the decision. I wish to explain it no more. However I made the decision is no longer important. The important thing is that I will live with it for the rest of my life. I will not regret. I will do my best.

I am really exhausted. I long for a cup of nicely marked caffe machiatto.

Let the data speak!

I am against the trend that we let data, and only data to speak for themselves. But I do have some thoughts on what they should speak. Namely, questions!

Asking the right question is an important, important skill. What is a good question? It is relevant, and we have a good attack! In statistical science, the second point means we have the right data! If we only have like 10 data points and you wish to estimate the parameters for a super-complicated models involving 10 parameters, I wish you good luck.

When I took Econometrics, I was cynical. I am unhappy with linear models. As far as I see, the relation we try to estimate could be quite non-linear.  However, there is a point, that I just begin to see. For a long time, (still in many areas today), data are scarce. It will be unrealistic to do a highly structural estimation, and it makes perfect sense for us to restrict us to linear models. At least, we recover correlations. The caveat many miss is that, once the model is ill-specified, the coefficients we get might not be interpretable, or requires more thinking, and quantifiers.

If I indeed get lots of observations for each possible vector of independent variable, I could impose no structure  I could simply estimate the mean of y_i for each possible vector of independent variable, and here we go.  I am not saying that's the right way to do it, but it will be ok.

A related talk I heard last semester is on spatial statistics. It talks about estimating earthquake frequency. The talk discusses how fine the grid should be. The solution is let the data decide! If you happen to have lots of observations, you can have finer grids...duh.

My view is that there is no physical probability! The world is deterministic. (For example, the coin flip is not random! At Persi can toss it however he wants) There is only belief. Lots of things we observe in life are just very complicated, and obtaining enough data to recover the deterministic relation becomes a bad bad question (because it is impossible). What is our job? We try our best to collect data, and based on the available data, we try to come up with the right question! The questions involves the model with the parameters to be estimated. The complexity of the model should match the data. What we could not be incorporated, we take them as "noise". It is our discretion to decide what is noise (the log term, or quadratic term, or that variable). This is where reasoning comes in. From research in the corresponding fields, we get a sense of what might be important and what might be negligible, and we make our assumptions accordingly. Data and assumptions are complementary not substitutable!

We are in the era of big data. There is no deny. But instead of being lazy and striving to make as few assumptions as we could, the availability of new data grants us the opportunity to ask questions that could not be asked before! Ask yourself not, what I can leave the data to do, ask yourself, what can I do with the data!

To follow or not to follow?

There are such a group of people, and they are considered the giants.

Sometimes they talk about their experience:

I am not interested in doing research and I never have been. I'm interested in understanding, which is quite a different thing--David Blackwell

Or Feynman discussed when he felt burned out in Cornell. Those discussions I can identify so well.  yet I am not sure if I should follow the steps of those giants. The problem is we are not sure if those people are giants because they take those steps, or if they can afford to take the route because they are giants.

Conditioning is a tricky thing. When conditioning on them being giants, those steps lead to success. Hardly a surprise. That's all the data we observe. The question interesting for me is conditioning on us ordinary people, what will the results be?

-----------------------------------------------------------------------------------------------------------------------

More relevant.

I am thinking about grad school. I ask myself, what is the interesting questions I am really interested in. I list tons of them, both in Econ and in Stats. But they share one thing, they tend to be foundational questions that many giants have worked on.  Should I work on those questions during my grad school years? The impression I got is probably not. Many students told me these are extremely risky things, and I might very well spend five years without getting anywhere. Then I might have to find a boring job to support myself, having very little time if at all, to think about those questions.

yeah, I know, follow my heart. yeah, I know, Einstein discovered relativity while working as a clerk. But I am not Einstein. If I were, I would be care-free. I would just go to any program, work on things I am interested in, whether it is in stats or in econ, or in physics, psychology or medicine. The education will no longer be a confining factor.
-----------------------------------------------------------------------------------------------------------------------

I will continue to read about those giants. But there will always be a sense of distance and skeptisism. Last term, i took a poetry class. In that class, when we analyse one poem, we see the poet's unbounded admiration of a master before him and envision himself being like the master, in aptitude and in attitude towards life. The poem ends in unpleasant realization that he is not that master.

A little bit of thoughts from school visit

First, I need to make it clear that these thoughts developed from my current school visit to Harvard Stats department, but it has nothing to do with the school choice I am to make now. This blog contains lots of mere speculations that came to me, and I found them to be interesting. I am jotting them down, not because I think I am getting at something, but rather, I want to keep those thoughts (naive as they are) and look back at them when I have time.

When I was talking to Joe, he mentioned that he is skeptical of the claims machine learning people are making these days. They tend to claim that big data will solve everything, and that the kind of machine learning algorithm makes no assumption.  If that's true, that would be almost a miracle. He commented: it seems that there is always a trade-off.

I have been a skeptic as well. Coming from an econ background, I am always suspicious of claims like this, which is too good to be true. The problem is I know too little, and many machine learning algorithm is quite opaque to me, and I have minimal intuition. It would be nice if one day, I can understand them and make it precise what kind of implicit assumption they make.  To me, one CANNOT make any inference without making any assumption. (this is no original idea) There is always a efficiency-robustness trade-off. Somehow through machine learning, we can break that, that seems implausible.

For me, inference is an iterative process. A naive and simplistic description would be: We start with a problem. We think about the problem. We decide on what assumptions we gonna make about the problem using our judgement. We start with these assumptions (models) and look at how well the data fit. When there is enough evidence suggesting the insufficiency of the models. We think hard and use a different set of models and do the inference...until we think we did a good job. There is a wonderful, wonderful quote from a paper by Blyth:

Dempster (1998) contrasted the ‘logicist’ and ‘proceduralist’ approaches to statistical modelling and inference. The logicist paradigm is concerned with reasoning about a specific situation under analysis, as opposed to the rote application and simple
reporting of defined procedures...The logicist approach requires choices – necessarily subjective, driven by the judgement of the investigator – about which objective features to include or omit in the modelling formulation. Thus, careful assessment is required to determine which features should be included in any formal [] model.

My hunch is that the logicist's judgement could not be proceduralized. (This is of course a very philosophical question, I have not yet had a very solid back-up, but that will be my guess if you point a gun at me and demand an answer).

One related thing we do is that, we want to have a "non-informative" prior in Bayesian analysis. I think this is both hopeless and pointless.  The difficulty is well-known for students of statistics--reparametrization mess things up (with some thinking it is actually not that surprising). I mean if you are a Bayesian, why shy away from prior? A more fruitful question is to investigate how sensitive results are to prior. or actually trying to find a good prior is helpful.

The thing is that, philosophically, there is no such state as non-informative prior and we observe data and update our prior. Priors have to be developed via ingredients other than data, and our mind is very good at doing that.  This cannot (or is very hard) be proceduralized.

On a certain level, the process of making higher-order assumptions is like developing priors. The difference is that we have more confidence in those assumptions, and for simplicity, we act as if they are the truth, so there are fewer layers in our inference structure. I think our mind and hunch has a comparative advantage in doing that. (I am actually interested to read up on Godel's incompleteness theorem to see if there are some insights from there).

Two trivially related comments:
1. I do not think highly of using computability and computational complexity from CS to study bounded rationality though it is in the fad. The complexity of the same problem is different for the brain and the computer. If we do, the best chance comes from psychology, where we can use insights from there study to define a different kind of complexity.

2. A never-changing financial model is doomed. There is a lot of judgement that came to each model, and those judgements have to be reevaluated and tinkered constantly. For some history, see More Money Than God. I thus think physics and philosophy (on the other extreme) is much better preparation than CS for those who work in finance.

A battle between Mars and Facebook

You Promised Me Mars Colonies,” warns astronaut Buzz Aldrin on the cover of the MIT Technology Review, “Instead, I Got Facebook,” ---“Why We Can’t Solve Big Problems.”

This is such a remarkable comment that it is worth translating in Chinese

“数十年前我们尚有殖民火星之壮志，如今却只会把弄facebook”。

Sadly, we choose not so solve big questions, because of distorted incentives and fear.

I wish to comment no more.