Occam's Razor in Science and Chess

Somewhere along their education, most scientists learn about Occam's razor. This principal, attributed to the 14th century logician William of Ockham, is usually stated as the preference for a simpler theory over a more complex one (as long as both are supported by the facts). When formulated this way, it might also be called the law of parsimony or economy, or just the rule of simplicity.

Occam's razor does not only apply to the hard sciences. This rule has been applied, sometimes in a modified form, to many fields. Even chess players may utilize Occam's razor. After all, while scientists use experimentation to falsify competing hypotheses, chess players engage in a similar activity by evaluating competing moves through analysis (often with computer help). Just as two different hypotheses may explain the facts, two candidate moves may appear (at first blush) to be playable. In either case, experimentation or analysis is used to find the correct choice between the alternatives.

I would suspect, however, that many scientists  do not appreciate the rationale behind this razor, as well as it limitations. They may be in danger of over estimating the power of this principle. In fact, I'd wager that chess players are more aware of the proper use of Occam's razor. Some of the original justifications for the razor where aesthetic (simpler theories and more elegant moves must be better), but this rationale is quite simply irrational. There is no good reason to believe a priori that either the inner workings of the cell or the strategy on a chess board must be simple. Even if many successful theories rely on simplicity, this does not preclude a phenomenon (or a position) being studied that requires a complex explanation.

Select 'Read More' to see the complete article, in which I discuss the justifications for Occam's razor using examples, and exceptions, from the chess world. The law of simplicity is more of a guideline, a way of prioritizing experiments and guarding against circumstantial theories. 

As Sherlock Holmes might say, understanding Occam's Razor is "Simplicity itself!"

There are, in my opinion, two major justifications for Occam's razor. The first, and probably most important, is that certain theories may be easier to test than others. In most cases, the simpler theory will be easier and quicker to falsify. In this way, Occam's razor guides prioritization in science, but doesn't indicate which theory is more correct. 

Another justification is that more complex theories may be contingent, or ultimately require, many more experiments. Since the data from any particular experiment may be prone to human error or can be skewed due to noise, theories which rely on many experiments are more likely to be built upon faulty conclusions. In other words, since a chain is only as strong as its weakest link, it is likely that a very long chain is weaker than a short one (there are more opportunities for a weak link)

Both of these justifications are at work behind the calculations of an adept chess player. As I pointed out in my primer on chess tactics, it is often a good idea to calculate forcing variations first, even if none of the moves turn out to be good. This is the practical justification for Occam's razor; simple, forcing moves are looked at first because they are easier to analyze.

This prioritization of chess calculation is especially important when the clock is ticking. It often also allows unexpected sacrifices and attacking patterns to be spotted. However, sometimes these attacks, while forcing and easier to calculate, are outwardly not so simple! This highlights a problem with the practical justification of Occam's razor. Blindly following the principle of simplicity is counterproductive when it leads one to eschew a more complex, but easier to study, hypothesis. In science, there is an even greater potential for this disconnect between the principle of simplicity and the practical benefit of that principle. While in chess, the resources to analyze any particular move are similar (just time and brain power), in science one hypothesis may require much more expensive and laborious equipment to study than another. In such a case, the simpler theory has become the one that is more difficult to study and falsify, and therefore should not be the highest priority for allocation of scientific talent and resources.

Even when the simpler theory is easier to test, it does not mean that theory is more likely to be objectively correct. Again, this concept is familiar to chess players, and is illustrated in the following position, taken from Pdogaets vs. Dvorestky, USSR 1974. The position happens to be a great example of zugzwang.

In the above position, it is Black to move. Several moves are possible; using Occam's razor, one might first analyze all checks and captures (since they are the simplest to analyze, by virtue of the limited nature of the opponents replies)

1…Qh2+ and 1…Qh1+ fail to 2.Qxh2 and 2.Qxh1, respectively. Likewise, 1…Qxf2+ 2.Rxf2 Nxf2 3.Qg3 results in great material loss for Black. So there are no productive checks.

1…Rxf2 2.Rxf2 is similar to the line above with 1…Qxf2+, and leads to nothing but ruin for Black

1…Nxf2, the only other capture available in the position, also leads nowhere. For example, 2.Rxf2 Rxf2 3.Qxf2 Qxf2 4.Kxf2 leaves White with an extra piece for a pawn, and a winning advantage.

Here, all the most easily calculated (in some sense, the 'simplest') moves fail to give Black anything. In the actual game, Dvoretsky played 1…Kh6!! This move puts White in zugzwang; any move he makes (other than the pawn moves b3, b4 and bxc5) will lead to defeat. In order to know that this is the correct move, Dvoretsky undoubtedly calculated what would occur after almost every White reply.

2.Ra1 (or anywhere else) Rxf2 and mate with either …Qxf2 or Qh2 next move is unavoidable.

2.Qg3 Rxg3 3.fxg3 Qh2#

2.Qh2 Qxh2#

2.Qxf3 Qxh2#

2.b3 Kg7 3.b4 Kh6 4.bxc5 bxc5 (and White must make one of the above moves. This line is what actually occurred in the game, which ended here with White's resignation 0-1)

As you can see, the move 1…Kh6 required more calculation, covering more possible responses by White, than a move like 1…Qxh1+ In this case, the simpler move was not the better move.

The other justification for Occam's razor, the effort to minimize the number of potentially misleading observations the theory depends on, also has analogies in the chess world. When calculating a forcing line, it is easier to ensure that the calculations are correct (there are less variations in which error can be introduced).  Likewise, scientists are rightfully wary to support a theory that has many potential weak links. It is important to note, however, that this depends more on the quality of the links than the number; it is perfectly conceivable that a simpler theory is based upon more misleading data.

Consider for example, the position after Black's 23rd move from the famous game Kasparov vs. Topalov, Wijk aan Zee 1999

In this position, Kasparov played the stunning 1.Rxd4!, a move which requires the calculation of a very long and complicated series of variations after 1…cxd4. If, at any point in those calculations, Kasparov was mistaken, either Topalov or computer-equipped commentators would have proven 1.Rxd4 to be an inferior move. This greater risk for being incorrect, however, does not detract from the fact that the Rook sacrifice is one of the best, if not the best, moves for White in the position.

This position also serves as an example for the more common use of Occam's razor (particularly the principle of limiting the amount of data the theory relies upon). Instead of 1…cxd4, as Topalov played in the game, he should have played 1…Kb6, maintaining equality. Clearly, this is a case where the theory or move which requires more calculation of many different lines turned out to be the incorrect choice. Topalov must have overlooked something buried deep within one of the lines which led to his defeat.

At the chessboard, in the laboratory, and in many other aspects of life, it is important to keep Occam's razor in mind (Most simply put, "Keep it simple, stupid!"). In some cases, blindly following this rule will serve you well. However, it is equally important to be aware of why this principle exists in the first place, and to recognize instances in which a preference for simplicity would lead you astray. After all, a good chess player knows that rules of thumb are only useful some of the time, and Occam's razor is no exception.

What are some examples of, or exceptions to, Occam's razor that you have encountered in your own life?