....And Back from Matter to Mind: A Strange Loop of Fundamentality

There is something deeply puzzling about the above: if the mind is more fundamental than the world, then what about our familiar notion of causality? For example, don’t we have a coherent explanation for the kind of technical, information-theoretic con­tent of our brain as a result of the laws of physics? The formation of the solar system, the genesis of the first life forms (despite our missing knowledge about the details of this event), and the subsequent process of Darwinian evolution are explanatory tri­umphs of science that allow us to understand perfectly well why there are functional brains in the first place, and why they roughly have the informational structure they do.

The answer is a clear “no”—this standard explanation is still available and per­fectly valid. The catch is that there are now two possible and mutually compatible perspectives to take. This can be seen by example of Fig. 2: on the one hand, we can argue directly via an observer’s state, as on the left-hand side. Postulate 1 tells us that algorithmic probability determines what happens to an observer, and the right-hand side can be seen as a consequence of this: the properties of algorithmic probability imply that some notion of external world emerges. But, by the very definition of what this means, this emergent external world gives an excellent description of what happens to the observer state, since its output configuration evolves under the same probabilities as that state. For example, if (on the right-hand side) a glider collides with the observer’s part of the grid, then (on the left-hand side) there will be a cor­responding state change of the observer. It is therefore consistent, for all (not only practical) purposes, to regard the collision with the glider as the cause of that state change.

In other words, since this emergent world corresponds to a simple algorithm which represents an excellent compression of the observer’s probabilistic state changes, we can regard its functioning as the background ontological structure that gives rise to what the observer sees. Thus, we can use it to obtain algorithmic, causal, or “mech­anistic” explanations for the observer’s states (including evolutionary explanations), but we may want to keep in mind that this background algorithm is ultimately itself not fundamental.

Given these two possible perspectives, it becomes somewhat unclear how we should “draw the arrow” in Fig. 1c: in some sense, we have “reversed the arrow” by declaring the first-person perspective to be more fundamental than the physical world. On the other hand, in the resulting worldview, the emergent external world can nevertheless consistently be viewed as the sole mechanistic basis, and thus cause in a physical sense, of that first-person perspective. In the end, we arrive at a picture (Fig. 3) that was first conceived by John A. Wheeler: a “strange loop” of mind and matter, subsequently giving rise to each other, and supervening on the respective other, in conceptually slightly different ways.

In summary, we learn from this approach that an ultimate notion of fundamentality may have a very subtle structure. On the one hand, “reversing the arrow”, i.e. turning

Fig. 3 “ ‘Wheeler’s eye”, redrawn according to [19]

our idea of the direction of supervenience upside down, can lead to novel insights that are not otherwise available, as the examples of noncommutative geometry and the approach sketched above have shown. On the other hand, the resulting worldview can exhibit surprising features that undermine our intuitive ideas about fundamentality, including a disidentification with causality, perhaps confirming views like Bertrand Russell’s skepticism towards the latter. These surprises may well be relevant for approaching some notorious open questions in the foundations of physics.

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