Abstract
A perplexing problem in understanding physical reality is why the universe seems comprehensible, and correspondingly why there should exist physical systems capable of comprehending it. In this essay I explore the possibility that rather than being an odd coincidence arising due to our strange position as passive (and even more strangely, conscious) observers in the cosmos, these two problems might be related and could be explainable in terms of fundamental physics. The perspective presented suggests a potential unified framework where, when taken together, comprehenders and comprehensibility are part of causal structure of physical reality, which is considered as a causal graph (network) connecting states that are physically possible. I argue that in some local regions, the most probable states are those that include physical systems which contain information encodings—such as mathematics, language and art—because these are the most highly connected to other possible states in this causal graph. Such physical systems include life and—of particular interest for the discussion of the place of math in physical reality—comprehenders able to make mathematical sense of the world. Within this framework, the descent of math is an undirected outcome of the evolution of the universe, which will tend toward states that are increasingly connected to other possible states of the universe, a process greatly facilitated if some physical systems know the rules of the game. I therefore conclude that our ability to use mathematics to describe, and more importantly manipulate, the natural world may not be an anomaly or trick, but instead could provide clues to the underlying causal structure of physical reality.
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Notes
- 1.
This may be a point of contention for some, as one might argue that Germany won due to physical superiority, but that is a different sort of physical argument than the one being put forth here.
- 2.
This constraint imposes all possible states of the world to have a one-to-one deterministic mapping connecting each state to at most two other states per time step.
- 3.
This last point is most obvious for the case of one-to-one mapping where no information about past states is lost in the mapping.
- 4.
To be perfectly accurate I should include general relativity in this argument, but the argument stands the same regardless of what our current theories to describe reality are, so long as they permit new states of the world to be realized that could not be realized in the absence of such knowledge.
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Acknowledgments
The author wishes to thank Paul Davies and Chiara Marletto for comments, and in particular to thank Chiara Marletto for the terminology of “explanatory graph” to describe the network of reality containing comprehenders and the insight that heritable connectivity is essential to its formulation. Additional thanks to the FQXi community for the lively discussion and insightful comments on this essay
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Walker, S.I. (2016). The Descent of Math. In: Aguirre, A., Foster, B., Merali, Z. (eds) Trick or Truth?. The Frontiers Collection. Springer, Cham. https://doi.org/10.1007/978-3-319-27495-9_16
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