Category Archives: Wild Guesses

Before and After

I just came back from today’s concert by Chicago Symphony Orchestra. It was fabulous. I am really into symphonies (a switch from concertos) recently, and Brahms No.2 was just beyond words.

The following stream of thoughts came to me BEFORE the performance:
Art and science incredibly mirror each other, in that both involve a process of creating and defining a set of criteria. The criteria is for those who practice it, as well as for those who wish to admire them. Without knowing the standard, one may be able to tell the worst art or science from others, but cannot tell which one of the avant-garde is truly valuable. The standard is subtle, but not trivial. The value of art and science is known only to those who have learned them well enough.

Moreover, both art and science contain elements that are drastically different from “problem-solving” for engineers. They explore and experiment with the underlying structures of the problem, but not merely for the purpose of solving it. This is good and bad. On the bright side, they raise questions and reveal insights that are naturally ignored by the engineer. On the dark side, because the answer to “what is important” for art and science is soft and not known to anyone on earth, it is subject to those in possession of power. Unlike what Plato has envisioned in “The Republic”, those with power are not necessary who deserve the power. In fact, they are usually those who have the strongest desire and lust for power. Thus, this opens up space for the human lust for power to exercise and even rule. A danger, in a sense.

The following stream of thoughts came to me AFTER the performance:

Who cares? The sensational music rules!

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Democratizing Knowledge and Garbage

Democratizing Knowledge to valuable ideas is what \LaTeX is to good writing.

The relation implicit in both of the above two pairs is: there is no correlation.

If we are thinking garbage, democratizing knowledge merely mobilizes our garbage.
If we are writing garbage, \LaTeX merely visualizes our garbage.

Symptoms

I was seeing the doctor yesterday for my occasional headaches. Before going to the doctor, I suspected that I had slight migraine. Yet to avoid “self-fulfilling prophecy”, I refrained from googling the symptoms of migraine before talking to the doctor. It turns out that my self-reported symptoms (hopefully uncontaminated by any medical knowledge) was consistent with the doctor’s knowledge about symptoms of migraine. So I willingly took her diagnosis as relatively “scientific” and decides to store some pain-killers.

Talking about “symptoms”, this experience triggers some thoughts in me on the philosophy of scientific inquiries. My suspicion (or in fact a well-argued point) is that for the 20th and 21th century, the paradigms of physical and social science is under transformation from deductive-driven to inductive-driven. By this I mean that descriptions about how the physical and social world works is shifting from “explaining the underlying generating mechanism” to “describing the observed symptoms”. The word “symptom” is used here as a neutral word. For example, astronomy that used to work out a “perfectly predictable orbit of planets” in the universe has now paused, and recognized that the motion of planets in outer space is in fact much less predictable and more complex than textbooks used to teach us. Since the turn of last century, Newtonian theory has been realized as merely a mental short cut (which may even lead us to the wrong destination) to understand the physical world.

Same with social science. I take the economic approach as an extreme case of mental short cut at best. It is time that social scientist acknowledge to the world that what appeared to be “noise” may now turn out to be “symptoms of truth”.

The Evolution of Stupidity

The other day Y commented to me (quoting somebody else) that while technology of our age has advanced, so has our stupidity. Stupidity evolves pretty fast. It is even more difficult to stop man from thinking naively on a single dimension than to stop the technology to advance.

I think there is another side of the story. While technology advancement facilitates the solving of problems, it also raises the complexity of the problems. The nature of societal relations has entered the phase of complex interdependence, meaning that a minor decision can incur high-stakes. In the past, a stupid decision will imply bad consequence within a limited range, while in our age we will see a radiation in the wake of a stupid decision. Stupidity is augmented through the high-stakes associated with it.

Counterfactuals and Signaling: the Local and the Global

This is an interesting post on signaling v.s. human capital argument.

The post above mentioned asks a counterfactual question: Would you have achieved as much as today if you have failed all the courses the content of which you have almost completely forgotten today? By answering “no”, the blog author stands up for signaling theory as opposed to the human capital theory. (of course, assuming that he, as a top economist, is a winner of life.) If we follow human capital theory, the answer would be “yes”, because it makes no difference to the human capital stock.

But from a policy point of view it would be more interesting if we move from a “local” perspective to a “global” perspective: What if I frame the question in a different (and probably the opposite) way: Would you have achieved as much as today if all your cohort(including you) have failed all the courses the content of which only you, among your cohort, find very helpful in work today? If you following signaling theory, then probably the answer is still a “no”, because everyone failing means no differentiation, and no differentiation means that you cannot send out an effective signal.But you will achieve better than in the scenario of the original question, because no advantage means no disadvantage either. If you support the human capital theory, then the answer is “yes”, because it does not change the human capital stock.Under a signaling model, ability and skills are positional, while in human capital model they are not.

Why we should be careful about cross-group comparison of causal effect

I was sitting in a friend’s thesis defense the other day, and a statistics professor commented: You need to define clearly what is from data and what is from the science!

Here, the phrase “the science”, as I figured out, should be translated to “the theory” in social science. The dichotomy between “data” and “science” is pretty much close to the one between “measurement” and “theory”. A statistician may feel stunned when your interpretation of the data suddenly hits “the science”. A social scientist may feel less so, because it is all too easy to confound “theory” with “measurement”.

So does there exist an unbreakable distinction between “measurement” and “theory”? This is so grand a thesis that I do not venture to build through one blog. But let us take one most common example of a “causal effect”.

Consider this experiment (Experiment 1):
I have two kettles of water and they are identical in volume and temperature. The temperature for both of them is 50C. I heat Kettle A for 5 minutes and do nothing to Kettle B. The temperature of Kettle A rises to 70C while the other one remains unchanged.

This “experiment” leads us to believe the following statement of “causal effect” (Statement 1).
“The heating caused the temperature to rise by 20C.”

Next, consider a slightly different experiment (Experiment 2):
I have two kettles of water and they are identical in volume and temperature. The temperature for both of them is 70C. I heat Kettle A for 5 minutes and do nothing to Kettle B. The temperature of Kettle A rises to 90C while the other one remains unchanged.

Shall we arrive at the same conclusion as Statement 1? Yes it sounds right. The two experiments give identical causal effect of heating.

Note that it is implicitly assumed in Statement 1 that the causal effect is the absolute difference in a linear reduced-form.

Now let us change our definition of “causal effect” to “percentage change”. Let us make the following statement (Statement 2):
“In Experiment 1, the heating causes the temperature of water to rise by 40%; In Experiment 2, the heating causes the temperature of water to rise by 28.6%. The heating has a larger effect in Experiment 1 than Experiment 2.”

It is not difficult to note that the difference is due to the difference in baseline temperature. Defining causal effect in proportional change instead of absolute change not only changes the quantitative conclusion, but also the qualitative conclusion (moving from “the same effect” to “a larger effect in Experiment 1”).

This is not the end of the story. Now let us set a ceiling to the temperature. Suppose that the boiling point of plain water is 100C. It cannot go above 100C. Consider the following statement (Statement 3):

“In Experiment 1, the heating causes the difference between the temperature of water and its boiling point to decrease by 40%; In Experiment 2, the heating causes the difference between the temperature of water and its boiling point to decrease by 66.7%. The heating has a larger effect in Experiment 2 than Experiment 1.”

See- the qualitative conclusion changed again (moving from “a larger effect in Experiment 1” to “a larger effect in Experiment 2”). This change is due to my change of the definition of causal effect to “the distance between current stage and the ceiling”.

The readers may have noticed that I have, on purpose, set the baseline temperature of my two experiments to be different. In laboratory science, an experienced researcher might not be so stupid to design two experiments that have different baselines and then feel stunned at the “confusing” results. However, empirical researchers in social science never had the opportunity to set everything equal at baseline. I make up this example because I think this is a good instance that illustrates why comparing “causal effect” across groups in social studies should be executed with extreme caution. Here comes my love for philosophy: Causal effect, in a broad sense, is a “measurement” rather than a “theory” – or, as David Hume has alluded to, “theories” are constrained by the way our brain “measures” the empirical world.

Back to the practical world, Economists crazily invented “elasticity” to capture the percentage change, but my example shows that elasticity is just one of many possible measures that could give opposite conclusions. Sociologists are concerned much less with “effect size”, and even when they do, they sometimes do not articulate their measurement. Psychologists speaks up for “framing effect” a lot in human reasoning, but who says that scientists are not humans and will not be biased?


Oh Hume is the real inspiration!

Speaking of Blackout

Decades ago, MLK was fighting against people who said “Black, out!”

Today, Wiki, google, WordPress and even the “Marxist Internet Archive” are fighting against SOPA by a “blackout”.

Speaking of the freedom of “knowledge”, my feeling is actually mixed. I share with many of my friends a personal fondness of Wikipedia and an opposition towards SOPA-type acts, yet I will keep my critique against the democratization of knowledge. Democracy could be oppressive ideologically: It is way too easy for socially constructed knowledge to become norms and social pressure, and norms usually come at the cost of the enhancement of human creativity and real innovation. In particular, knowledge can become the soil of “mental shortcuts”, and thus prevent people from thinking from a novel angle. Thus I harbor more doubts against the wiki-style of thinking in real-life than most intellectual people do.

 

Update: an interesting point made by Qingqing in her comment:

SOPA may work in a way that is against your favor: as the wiki protesting webpage argues, SOPA harms small websites more cuz they are more unlikely to be able to afford monitoring cost. In your argument, I guess small sites stand on the side of creativity while big ones represent “norms”.

Avoiding Death by Avoiding Birth

In a class that I taught yesterday, my students were discussing “divorce” as a social issue. One of them suggested that since divorce is not desirable, why don’t we get rid of marriage entirely?

I cannot help but break into laughing. I responded: oh, this is like getting rid of death by getting rid of birth.

Hilarious as it is, this is not uncommon. In fact, the practice of may governments nowadays are no more than “avoiding divorce by avoiding marriage” or “avoiding death by avoiding birth”.

No! It is accident, not luck!

Social scientists nowadays characterize the unexplained as “luck”. It is believed that luck determines a significant portion of what we have.

Yet, for a moment today, I realize that “accident” might be an even better word than “luck”. It is through millions of “accidents” that we stand as who we are today. The dividing line is that, “accidents” can accumulate, one after another, yielding positive feedback – but the word “luck” sounds more like uncorrelated shocks.

In a stochastic sense, life is more of a “random walk” than being stationary.

The learnable and the unlearnable

Let’s start with the story of Wolfram|Alpha. Check out the webpage. It is the Wiki for geeks. I am a big fan of it.

Wolfram|Alpha is a web-based answer engine that is most powerful in providing answers for the user’s computational queries or inquiries about statistical facts. It has a very user-friendly interface and produces an easily-readable output. For example, if you are interested in the expression: x^2/(x^0.5+sin(x)), you can simply input the function, and it will return to you its plot, roots, series expansion, derivatives, etc..

In a word, Wolfram|Alpha is my computational Wiki. The server of Wolfram is essentially located at MATHEMATICA. I use it as a very handy browser-based mathematica on my PC and an App on my ipad. It enabled me to implement complicated functions the algorithm of which I may not be able to write.

Today, I heard a cold joke from an engineering friend: The password to their programmer forum is the 547345-th prime number. A well-trained programmer can easily work out the algorithm for obtaining this number within limited time, but a non-programmer is not supposed to do so. However, nowadays, a non-programmer can easily open Mathematica, and input Prime[547345]. The software will quickly respond with the answer.

While I don’t have Mathematica installed in my PC, I can easily type Prime[547345] in my Wolfram page, and remote server gives me the answer. The password is 8121067. I did this within 5 seconds, and I am a non-programmer, not knowing any good algorithm myself.

Here comes my point of telling the long Wolfram story.

Ours is a time of fast-learning and fast-learners. Two-by-two multiplication can be learned at school, cooking pasta can be learned from a recipe, the modern-world diplomatic politics can be learned at a cocktail party. “Nothing is hard once you put your heart into it!” – That is what I was repeatedly told when I was a kid. Even if we don’t want to spend time learning by ourselves, computer software enables us to compute complicated algorithms faster than a human brain. And in the event of me having no software installed on my PC, I still have my Wolfram webpage to easily perform my tasked on a remote server at the Mathematica company. In a world, this is a time of learning – human learning and machine learning alike.

In such a happy-learning world, are we worry-free? Is a fast-learner the world-saver? Unfortunately, democratizing knowledge does not guarantees the democratizing the ability to create the unlearnable. “Knowing-how” does not guarantee the invention of ideas and thoughts. The former is learnable, while the latter is not. A fast-learner may not be creative, and it is creativity that saves the world, not learning ability. Art is not totally learnable. Neither is science.

After all, the truth that keeps human race alive is that we, or at least some of us, aspire to go beyond learning. We train machines to perform some of our tasks, because we want to free ourselves and invent ideas and thoughts that can be learned by others. We spend some effort on self-control in learning the situation, because we want to better activate our intelligence in creating something new.

I am a fan of Wolfram, but not addicted to it. Wolfram computes the learnable, and I shall continue with the unlearnable.