Causality from outside
Openness as superstition
I have been invited to give a talk at the 17th Marcel Grossman meeting, to be held this week in Pescara, Italy. Even as I am writing this post, I still did not finalise my slides, and my talk is this Thursday. The topic I will cover is –of course- the application of causal discovery to astronomy. I just gave a talk about it at the annual meeting of EAS, the largest astronomy conference this side of the pond (this being now the European side). But this time the audience is different: it is going to be mostly theoretical physicists.
Why would a seemingly straightforward application of some relatively new mathematical machinery to astronomical data be of any interest to theoretical physicists? How is this different from, say, applying persistent homology to star clusters? Or Koopman theory in the form of dynamic mode decomposition to variable star light curves? These two are also a first in terms of application to astronomy and have been well received by the computer science community – the latter earned us a spotlight at the Scaling AI for Scientific Discovery workshop at ICML1- but theoretical physicists do not seem to care that much.
Causality touches deeper, more fundamental strings. One of these is the distinction between physical law and boundary –or initial- conditions. Let’s take PV = NkT as an example. This is a law that holds -approximately- for gases that are not too dense: for a given number N of molecules, the temperature T, the pressure P and the volume V are linked by this relation (with k being a constant). It would seem weird to interpret this law causally: while it is true that by setting T and P –by means of a piston that can bear an adjustable load, compressing the gas- the gas will end up occupying a volume V, it is also true that placing the same gas in a rigid contained with a given volume V and bringing the temperature to T will result in the gas’ pressure being P.
Expanding on this scenario, if we repeat our experiment many times, taking T and P from two independent statistical distributions, and we measure the corresponding V, a causal discovery algorithm will find T -> V <- P. But if we set T and V and measure P, it will find T -> P <- V. Causality is not in the law: it resides in the boundary conditions, and those are not determined by PV = NkT.
Now leave the lab and replace our box filled with gas with a galaxy: who sets the boundary conditions for galaxy scaling laws? Do our operational definitions of causal relation stay meaningful when scaled up to cosmological scales? Clearly there is no outside -hence no boundary- when the object under consideration is the whole Universe.
The very distinction between law and boundary conditions implies a kind of freedom which can effectively be achieved only in an open system: if boundary conditions could not be freely set from the outside, they would be just part of the law2.
Maybe this is just a kind of intellectual pareidolia, but this passage from The Tacit Dimension seems to be addressing precisely this point:
But how can a machine which, as an inanimate body, obeys the laws of physics and chemistry fail to be determined by these laws? How can it follow both the laws of nature and its own operational principles as a machine? How does the shaping of inanimate matter in a machine make it capable of success or failure? The answer lies in the word: shaping. Natural laws may mold inanimate matter into distinctive shapes, such as the spheres of the sun and the moon, and into such patterns as that of the solar system. Other shapes can be imposed on matter artificially, and yet without infringing on the laws of nature. The operational principles of machines are embodied in matter by such artificial shaping. These principles may be said to govern the boundary conditions of an inanimate system –a set of conditions that is explicitly left undetermined by the laws of nature. Engineering provides a determination of such boundary conditions. And this is how an inanimate system can be subject to a dual control on two levels: the operations of the upper level are artificially embodied in the boundaries of the lower level which is relied on to obey the laws of inanimate nature, i.e. physics and chemistry.
This brand of vitalism is tenable –at the cosmological scale- only if the universe is not a closed system, making the distinction between law and boundary conditions meaningful.
Interestingly, a similar paper we submitted to a similar workshop at ICML 2023 was rejected instead
This is the kind of openness that is implicitly posited by assuming the existence of a free self separated from the totality of perception: free will and causality have a similar metaphysical smell.