Different types of chance

Jacques Monod

When we don’t know why something happens, we usually say that it is due to chance. But this statement is ambiguous, because there are two different types of chance:

• Epistemological chance, where the cause of what’s happening is well-known, but so complex that it remains outside the scope of our knowledge. Almost all games of chance (dice, roulette, lottery jackpot) are examples of this type of chance. Rolling dice conforms to the laws of mechanics, but the conditions are so complex that we cannot predict the result of each roll. This type of chance is what Jacques Monod called operational uncertainty in his book Chance and Necessity (1970):

This term is used... in relation to the game of dice, or roulette, and the calculation of probabilities is used to predict the result of a play. But these purely mechanical and macroscopic games are not "the result of chance" except because of the practical impossibility of controlling the throwing of the dice or the ball with sufficient precision. It is evident that a very high precision launching mechanism is conceivable, and would make it possible to largely eliminate the uncertainty of the result... The same thing happens, as will be easily seen, in... many phenomena where the notion of chance and the calculation of probabilities are applied for purely methodological reasons. (My translation into English).

• Ontological chance or physical chance, which is not due to our ignorance, but corresponds to a true indeterminism. Monod calls it essential uncertainty, and describes it thus:

This is the case, for example, of what can be called "absolute coincidences", which result from the intersection of two mutually independent causal chains. Suppose, for example, that Dr. Dupont is called urgently to visit a sick person, while the plumber Dubois works on urgent repairs to the roof of a neighboring building. Just when Dr. Dupont passes under the eaves of the building, the plumber inadvertently drops his hammer, whose (deterministic) trajectory is intercepted by that of the doctor, who dies with a broken skull. We say no luck. What other term can be used for such an event, unpredictable by its very nature? Chance here must evidently be considered essential, inherent in the total independence of the two series of events whose meeting produced the accident.

According to the Copenhagen interpretation of quantum mechanics, due mainly to Niels Bohr, the physics of elementary particles is not deterministic, but random, with physical indeterminism. If this is true (all attempts to discover hidden variables that would convert physical into epistemological indeterminism have failed), the cosmos appears to be intrinsically probabilistic, and its evolution can only be followed statistically.

Werner Heisenberg

Heisenberg’s uncertainty principle gives us an additional possible source of chance, by pointing out that it is impossible to know two properties of matter (energy-time; position-momentum) with absolute precision. Knowing one of them with huge precision makes the other escape our control automatically. But this means that chaotic systems, although they may be deterministic, are automatically subject to chance. Let us see how.

The evolution of a chaotic system, from two almost identical initial conditions, makes it move, after a certain time, to two quite different states. I explained it in this post. It turns out that many of the physical laws we know give rise to chaotic behavior. Therefore, if in one of these systems we start from two different initial conditions, which differ by less than the limit established by the uncertainty principle, we won’t be able to predict the final state of the system after a certain time. Is this chance? And if it is, is it epistemological chance, or physical chance?

Some think it is a form of epistemological chance, since we do not know how to predict the outcome. But others think that it is physical chance, because contrary to what Monod explains when talking about epistemological chance, the impossibility is not practical, but theoretical.

In previous posts I have pointed out that chance might not exist, or at least be compatible with design. In this case, the word chance usually refers to what we have called ontological chance, physical chance, or essential uncertainty. As I indicated above, epistemological chance is not true chance, but rather makes reference to our ignorance. In the next post I will elaborate on this idea.

The same post in Spanish

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Manuel Alfonseca