QC as an excuse to revisit a metaphysical issue

or On talking about the ``Laws of Nature''

by Oded Goldreich

[Nov. 2011]

In my first objection to the thesis of QC believers, I wrote that the Laws of QM are merely a refutable model (or assumption) about the real world, they are not the reality itself nor can they ever be proved to provide a full description of reality. In the current post, I wish to elaborate on this. Specifically, I will argue that any claim of familiarity with the ``Laws of Nature'' is highly inappropriate and unsound.

I am going to assume a dichotomy between the world (or ``nature'') and any possible cognition. This dichotomy is a starting point of almost all philosophical traditions, which differ in their view of how the corresponding gap is and/or can be bridged.

I subscribe to the critical tradition that is associated with Kant's Critique of Pure Reason, which in turn can be traced back to Aristotle. This tradition asserts that our ``view of the world'' is determined, to a large extent, by our a priori conceptual framework, which in turn ``filters'' and/or ``structures'' the a posteriori sensory data obtained from the world. An archetypical example is the concept of causality, which (according to this position) cannot be deduced from the world, but rather predetermines the way we understand the world. According to this position, we have no direct access to the world per se, but rather access it indirectly through our ``ways of viewing it'' (which may be thought of as glasses and/or filters).

Applied to the scientific study of the world, the foregoing means that ``the laws of nature'' that scientists ``discover'' cannot be claimed to be the very laws governing the world, but are rather a good model of the world, where a good model is one that provides correct predictions and simple a posteriori explanations. Needless to say, from this perspective, it is quite naive to think that the current model, which is merely a model that is currently deemed good, just happens to reflect the ``ultimate law of nature'' (to which we can never have direct access).

Indeed, the foregoing position is not the only one existing in the philosophical tradition: One prominent alternative position (traced to Plato) maintains that cognition reflects the world. How such a reflection is guaranteed is a different story, but I wish to stress that also under this tradition the current (historical) perception of the world is never identical to the world, it is just an approximation of it. The impossibility of identity (between the world and its perception) will be discussed below, but at this point I wish to drive home an important conclusion: Also according to this philosophical tradition, during the course of human history, one can never prove that the current perception of the world is equivalent to the world, putting aside the probability that this will ever be the case.

According to both philosophical traditions, the quest of science is to improve the model of the world, which provides an approximation of it, and the history of science shows a march of progress towards this goal. The difference between the traditions amount to whether this model is constructed subject to the structure of rational thinking (i.e., the Aristotle/Kant tradition) or reflects the actual structure of the world (i.e., Plato's tradition). But none of these traditions dare suggest that the current cognitive model is equivalent to the real world, let alone that such an assertion can be proved.

The foregoing account hides problematic issues w.r.t the notions of approximation and progress. These issues are irrelevant to the point I made, but are of great interest. Firstly, accepting the dichotomy of world and perception, one cannot expect the cognitive perception of the world to be identical to the world, because they are fundamentally different things. Thus, one can only expect an equivalence, which is to be understood in terms of functional equivalence. But, as we (in TOC) know, even when given the explicit description of two evolution rules, it is impossible to determine whether or not they are equivalent. (An analogue assertion with respect to efficient evolution rules relies on the assumption that P is not equal to NP.) When one of these rules is only implicitly given (via oracle access), impossibility of testing equality arises even for efficient evolution rules. Lastly, regarding approximation, we (in TOC) have good notions of approximation between functions, but these notions refer to an input distribution. But a new model of the world usually triggers new type of experiments, which should be conceptualized as new input distributions. Thus, a better approximation of the world means not only a greater fitting on the sample used by the previous model (e.g., a perfect fitting of the old sample, which may have contained points that the old model failed to fit, which in turn caused the search for a new model), but also perfectly fitting a bigger sample (which transcended the sample ever considered for the old model).

Returning to my main point, let me stress that no model is ever tested for fitting all possible instances, and one can never be sure of such a perfect fit. Every model is an extrapolation that extends far beyond the existing experimental data, and such an extrapolation is always speculative. One can hope that the model is the simplest one that explains the existing experimental data, but this does not rule out the possibility that the model is wrong and that this can be demonstrated by experimental data that is currently unavailable.

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