Free Will

The November 2006 issue of New Scientist carried a series of articles entitled “The Big Questions”. One of the articles was titled “Do We Have Free Will?“. The same question was asked in a New York Times science section article on 2 Jan, 2007 entitled “Free Will: Now You Have It, Now You Don’t“. So, why are people asking the question? Isn’t it obvious that free will exists?

The question arises because all humans are, after all, collections of molecules obeying physical laws. In that sense, anything and everything we do is simply pre-determined by the laws of physics. We cannot have free will because we are bound by the physical laws governing our molecules. There is nothing “free” about our will. There is no such thing as choice, and consequently, no such thing as free will.

The New Scientist article cites the example of a person who was turned into a deviant by a brain tumour. When the tumour was removed, he became normal again. When the tumour later re-grew because a portion of it was missed out, the man exhibited the same deviant behaviour again. The man did not choose to bad things; he was simply a slave to the physical processes leading to his deviant behaviour.

Why should we care? How does the question of whether we have free will affect our everyday life? To borrow one clear example from the New Scientist article, in a situation where a disease results in deviant behaviour, should the person be punished? Most legal systems are based on an assumption of free will. A perpetrator is punished because he or she is responsible for the crime in the sense that that he or she willfully committed the crime. This entails an exercise of free will. Thus, those who can demonstrate an inability to exercise free will at the time of perpetration of a crime are those who are sentenced leniently or even let off unpunished. Now consider what would happen if everyone has an inability to exercise free will. Would no one be culpable for any crime in that case?

I think free will exists only as an illusion. We don’t really have free will, and we are in fact slaves to physical laws. When we think we are making a decision, we are in fact only obeying the dictates of the laws of physics.

However, the illusion of free will is both useful and consistent. It is consistent because we cannot predict in advance what will happen. It is useful because we can use it to make sense of the way human societies organize themselves. This needs some elaboration. Maybe in a later post.

Free Will is Really a Question of Epistemology

Free will may have more to do with epistemology than physics.  Suppose the universe is indeed deterministic in the collection of rules sense.  That is, there is a set of transition functions that tell us how to calculate the next state of the universe given the current state of the universe.  However, we still lack complete knowledge of the future because we don’t have access to these transition functions.  Besides, we may not be able to apply the transition function.

First, we don’t know the entire current state of the universe, which is required as an input to the transition functions.

Second, suppose we grant that the first point is not an obstacle.  To answer a particular question maybe we only need a partial state of the universe which we actually know.  However, applying the transition function to calculate the next state may not be in the causal sequence for us.  That is, the transition functions themselves may not predict that we will apply them and find out the future.

So that’s why we don’t know the future.  Now the crux of my argument is this: that what we term “Free Will” is simply a statement about our state of knowledge.  When we are faced with two choices A and B, and we say “I made choice A out of my own Free Will at time 2″, what we are really saying is “At time 1 I didn’t have the knowledge/computational resources/ability to know for sure that I was restricted to choice A at time 2″. Since we don’t have knowledge of the future’s certainty, we don’t feel it is certain.  We feel that we have made a choice.

In this sense, Free Will is an illusion.  It is not that we could have made choice B; it is just that we feel we could have made choice B.  The feeling is Free Will, and it arises from the fact that, as part of the universe, we cannot calculate at time 1 what the choice at time 2 will be, or even see that the choice is fixed (since we are not intuitively aware of the transition functions).  Applying intuition, since we cannot calculate the choice or even perceive the transition functions, we assume that “we could have made” another choice.

Milk

Here’s an interesting table on lactose intolerance by ethnicity:

Table 1 % Hypolactasia (lactose intolerance)*
Race, Ethnicity, Country of Origin	Hypolactasia
Southeast Asians	98%
Asian Americans	90%
Alaskan Eskimo	80%
African-American Adults	79%
Mexicans (rural communities)	74%
North American Jews	69%
Greek Cypriots	66%
Cretans	56%
Mexican American Males	55%
Indian Adults	50%
African American Children	45%
Indian Children	20%
Descendents of N. Europeans	5%
* Assembeled by R. Rodriguez from various sources

It was taken from this source: http://nutrigenomics.ucdavis.edu/nutrigenomics/index.cfm?objectid=968814F6-65B3-C1E7-0C7007B71CC9959A

Interesting is that India is the largest milk producer in the world, yet almost 50% of Indians are lactose intolerant.

Causality and Karl Popper

I learned today of some absolutely fascinating interactions between Popperian critical rationalism and the theory of causality.  The counterfactual theory of causality is to scientists probably the most useful of the causal theories.  The way in which Popperian philosophy enters is in the meaning of counterfactuals and whether they are related by a so-called Structural Equation Model (SEM).

Counterfactuals

To illustrate, suppose we observe and are interested in three variables, . We know that comes before and chronologically, and comes before . Let’s talk about counterfactuals first. We observe , but suppose we now ask ourselves what would have happened to if, instead of letting nature calculate , we intervened to set it to some value such as . We denote this new, imagined variable by . We might also be interested in the counterfactual variable , which is the new variable that “would result” if we could intervene to set to 0. Counterfactual theories assume that variables such as “exist” and are “available to nature”, and that if actually happens, then nature responds by producing this version of . If, instead, occurs, then nature produces the entirely different variable .

Structural Equations

Let us try to reconcile the existence of such counterfactual variables with common views of determinism. If we tried to imagine a process by which nature “calculates” the variables , we’d be tempted to come up with something like this: . Here are three independent random variables (often called “noise”). So nature first calculates from some noise variable using a secret process (just a function, really, but unknown to us). Then it calculates from the previously calculated value of and the noise variable using the function , and finally calculates from using .

Such SEMs are very useful. They can be represented graphically and analyzed mathematically to answer a great many questions in causality, leading to a rich theory developed by Judea Pearl, among many others. An additional bonus is these models account for counterfactual variables in a very natural way. Suppose, for example, that we are interested in the counterfactual , that is the version of that results if someone intervened and set the variable to . (The mechanism by which this might be done is not relevant here.) Nature then simply computes the function . Another example is the counterfactual , which means that is first computed as , and then . The counterfactual is naturally defined as . Thus counterfactuals have very natural semantics in the SEM setting.

The SEM is also a very natural model to humans. Much of what we perceive as Newtonian physics and determinism works this way. Event happens, this influences event (but doesn’t determine it perfectly, which is why is necessary), and so on. Indeed, when I ask myself what other models of the universe might exist (and this question excludes quantum uncertainty and other similar weirdness), I am unable to conceive of a process which doesn’t boil down to an SEM of the type shown above. Most people, when asked to imagine a process by which the universe “creates” events, will probably come up with an SEM.

Perhaps unsurprisingly, this kind of model is inadmissible in the Popperian view, since it uses an underlying justificiation. Intuitively, the structural equations justify the counterfactuals. Delving into things a little more deeply, it turns out that this simple model makes a large number of assumptions that are not verifiable, and so are inadmissible in the Popperian view. But we need a specific example.

A Weird Counterfactual

Specifically, consider the “cross-world counterfactual” . Mathematically, there is no problem with this definition; the function is evaluated at which are themselves well-defined constants or random variables. The problem is with interpretation and observability. Any of the previous counterfactuals could be obtained in a natural way. To observe , set to 0, let nature determine and observe the resulting . To observe , set both to and to and observe the corresponding . But the new quantity is fundamentally different; it involves both (the first argument of ) and needed to observe . This means what we’re trying to do is the following complicated procedure: first intervene and set , obtain the random variable , and then turn back the clock, and now intervene to set as well as set , using the observed before turning back the clock.

Why Critical Rationalism Excludes SEMs

But of course, we can’t really turn back clocks. Thus the weird counterfactual above is unobservable; there should be no way for us to evaluate it under Popperian critical rationalism. If we can evaluate it, it means we are using a rich justification with implications that cannot be verified experimentally. Now, under the SEM it can be shown that

Since all of the quantities on the right hand side are based on observed variables, it means this cross-world counterfactual, which we “couldn’t possibly identify” without turning back the clock, is actually identifiable — a paradox!

What’s the resolution to this paradox? Simply that the SEM makes so many hidden assumptions that we can actually identify it. This explains why SEMs don’t conform to Popperian thought, and why a lot of work focuses on causality and counterfactuals without structural equations.

ANAND!!!

The whole game

There were a lot of interesting points that came out of this match.

One of them was the effect of age on performance.  A quick look at the Live Top List shows that Anand is among the 3 oldest in the top 35.  Only Gelfand and Ivanchuk are older, by less than 2 years.  An overwhelming proportion is still in their 20s.  Topalov is about 5 years younger than Anand; IGMs everywhere were of mixed opinions whether this improved Topalov’s chances significantly.  There were some slight indications that fatigue was a bigger factor for Anand.

Age is also a factor in how easy it is to find an opponent when you’re young and learning.  Anand used his first computer for chess in 1988, at age 19.  Certainly today’s players start using computers much younger.  This probably has some impact on their playing style.  There’s never a case where you can’t find an opponent for practice.  Anand is possibly the last world champion to learn chess without a computer.

It’s also interesting to note that the age at which people attain their grandmaster title has become much lower.  This may be because of computers, because the sport is more popular, because the grandmaster norms are easier, or a combination of all these.

Another interesting thing is that a tournament never quite seems to have the same drama as a one-on-one match.  There are various arguments against matches, and the ability to hold on to the title for several years and then remain champion in case of a draw.  Many IGMs think (and I agree) that this loads the game heavily in favour of the reigning champion, since the champ would prefer calm more even positions while the challenger must play riskier chess.  The rapid and blitz playoffs in Sofia might have been designed to mitigate this.  But while there may be some valid arguments for tournaments to determine the world champion, there’s a certain drama, a spotlight on personalities, and an intensity in matches that is missing from tournament formats.

I can haz lolcatz?

Ha ha.

Related memes: lolcat, 4chan.