Tuesday, February 22, 2022

The Two Ockham's

In reading the first chapter of Bostrom's Anthropic Bias: Observation Selection Effects in Science and Philosophy,[1] his overview dealing with multiple worlds makes me feel as if there are two ways in which Ockham's Razor[2] are being used in science. That is, the general maxim of reducing the number of "entities" to a minimum is applied in two opposing ways, one of which is evident in anthropic reasoning. One of these ways is to reduce the number of actual things that you suppose to exist and the other is to reduce the number of postulates required to make predictions with a theory.

How does that work?

Fine tuning is a modern sin in theoretical physics. A theory that has a large number of free parameters, but only a few of which could lead to observed consequences, needs to have additional assumptions about those parameters. If these are unexplained, then the theory is fine tuned. This is generally felt to be a flaw because it is surprising that an otherwise successful theory should require a large number of ancillary assumptions -- 31 in the case of particle astrophysics[3] -- to predict the existence of the universe. Although not strictly a error, taking an elegant and insightful theory and clothing it in hand-me-down experimental parameters is a bit gauche.

This is where the anthropic principle comes in. This principle, in this case, states that the universe has to be the kind of universe where you and me can exist. We're pretty sure that we do. This constrains overly loose theories, theories that require fine tuning, so that they can make predictions. This method was famously used by Steven Weinberg to predict the approximate magnitude of the cosmological constant. This has also recently been used to try to shore up string theory as it has become looser, parameter-wise, than once thought. Anthropic reasoning is an end around fine tuning.

The expansion of possible string theories from five to an infinite number has made anthropic arguments possible in that each particular universe that would be associated with a string theory[4] (with different parameters) exists, and the reason why we are in this universe with these fundamental constants is not because of any finely tuned assumptions that we have to make, but rather it is because of the existing universes, we have to be in a universe that supports our existence. This can be true with parallel universes, sequential universes, and so on, just as long as there is an infinite reservoir and the proportion of those universes is a subset of the same transfinite cardinality of the reservoir.

This is what brings me to Ockham's razor. This is usually stated as "entities must not be multiplied beyond necessity" or "plurality should not be posited without necessity." If there is no necessity to postulate a soul in order to understand consciousness, then don't postulate a soul. Normally, you would think that this would exclude a string theory landscape, that in order to explain the values of the universal constants that we measure, we need to postulate not just a soul, but an infinite number of souls.

But that's just one way to think about it. Another one is Aquinas' maxim, "It is superfluous to suppose that which can be accounted for by a few principles has been produced by many." In this case, the anthropic principle is supported by Ockham's razor. We have literally reduced the number of assumptions we need to make from 31 ad hoc interpretations of experiments to a single proven principle.

Both cases have a claim to be following the spirit of Ockham, and to me neither is obviously right. At least, neither seems to be the better argument in all cases. So, we have a situation where the same, admittedly somewhat subjective[5], principle would require us to take opposite approaches to the same problem. How do we decide which to follow?

[1] Anthropic Bias: Observation Selection Effects in Science and Philosophy, Nick Bostrom. [Amazon]

[2] I prefer the ckh over the cc. How can Occam's Razor be named for Isaac of Ockham?

[3] See for example Tegmark, Aguirre, Rees, and Wilczek's "Dimensionless Constants, Cosmology and Other Dark Matters." [arXiv] See also Physics Frontiers 55: Multiversality.

[4] Anthropic Landscape of String Theory, Leonard Susskind. Extrad Dimensions in Space and Time [Amazon], Bars and Terning, Multiversal Journeys Series. See also: Physics Frontiers 35: The String Theory Landscape.

[5] But Ockham's razor is no less subjective than the beauty of a physical theory, and a lot of people give that a lot of weight.

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