Economics as bridge between math and science
Objects in our world sometimes organize around physical patterns pertaining to things like light and gravity and inertia and sometimes to non-physical patterns like the prime numbers. There is a tension here: why are the patterns we organize around sometimes physical and sometimes mathematical? How do they interact? How do physical processes induce mathematical patterns to show up? The answers to these questions may come from economics. This is because economics has properties of both math and science.
On the science side, economics typically classified as a science, and it gathers data and uses experiments to form models that make empirical predictions about the world. These are all clear signs of a science.
But economics also shares some properties with math. First, economics and math are both based around a kind of constraint concept that says, “You’re not allowed to get everything that you want.” In economics, this is scarcity, which says that you have to make tradeoffs, giving up one thing to get another, and in math, this is logical consistency—you can’t have a proposition and its negation unless you contradict yourself.
Second, both economics and math exhibit important patterns that are clearly used by organisms and other systems in the physical world. Periodical cicadas exploit the mathematical pattern of primes to determine when it’s optimal to emerge. Similarly, economic patterns are exploited by people to coordinate in settings as diverse as the economy and basketball games—people, and other things, can sense these patterns as strong perception.
Prime numbers are obviously not reducible to physics. Physical forces can instantiate primes but not explain them. Economic patterns are also not reducible to physics. The fact that marginal benefit = marginal cost is the optimal stopping point for behavior doesn’t arise from physical forces either.
So economics works like a science, but it studies empirical phenomena that arise from non-physical patterns, such as a market organizing around an equilibrium price. Economics is the domain where strong perception of non-physical patterns is most directly subject to rigorous third-person science and is something we all have first-person experience dealing with (e.g., we’ve all gone shopping). This makes economics a potential bridge between math and science, a paradigmatic example for studying Platonic space ingression.
Here are a few interesting things that economics shows us about these non-physical patterns:
They are a consequence of relational homeostasis (or allostasis). Things like prices and marginal values arise as a consequence of our interactions with each other and the world. The result is a multicausal construction, made out of the relationships between people and the world, that brings a pattern into being.
They serve to govern systems of interacting elements. Things like prices and marginal values show up to solve coordination problems. Without prices or marginal values, markets or behavior, respectively, would never find balance. These patterns show up when the conditions are ripe for a virtual governor (or social choice dictator) to arise.
Causality between physical and non-physical influences goes both ways. Points 1 and 2 together imply that we construct the very patterns that in turn governs our behavior—it’s circular causality, where top-down causality is as real as bottom-up.
The patterns use us as affordances to scale up and network into units that in turn multicausally summon new patterns that govern the patterns that govern us. Individual prices that govern individual markets face their own coordination problems as they compete to absorb portions of the economy’s total budget, a budget that stretches across all markets. The shared constraint reservoir puts prices into competition, which is resolved via the construction of the price system, the economy’s cognitive glue. The price system is just another one of these non-physical patterns, one that shows up to govern other non-physical patterns!
Economics could help to explain how pattern ingression occurs from Platonic space as people use physical forces to align to non-physical patterns (e.g., physically putting something into your shopping cart based on its price). But simplicity argues in favor of only one kind of pattern, physical or non-physical. So another possibility is that even the physical laws are non-physical, arising to govern interactions among the coupled elements of a single shared system.
What picture of the world does this perspective offer? Strong perception, the process by which we align to these patterns, is all about invariants: regularities that exist at some scale and substrate. We can tier pattern types by the reliability of the invariants, or how consistent they hold as substrate, scale, and time change.
Mathematical invariants (primes, geometry, etc.)—this is (apparently) the limiting case, where the coordination is so deep it appears to hold atemporally and across all timescales and substrates. It’s hard to imagine anything anywhere in any way changing such that 6 becomes a prime number.
Physical invariants (gravity, light propagation)—maximally consistent and reliable in our light cone. Other universes may have different laws of physics, or changes over some timescale at some scale may alter the laws of physics in our universe, but we won’t live to see it.
Ecological invariants (optic flow, tau)—consistent within the relevant niche, or at a maximum, within a cognitive light cone.
Social/economic invariants (prices, traffic lights)—consistent within institutions and certain patterns of coordination. In practice these invariants could be as reliable as ecological invariants—green meaning go and red meaning stop might hold thousands of years into the future—but they don’t have to be, and could change in pretty sudden and unpredictable ways, such as via price controls.
Game-state invariants (marginal value of a basketball shot)—consistent within rules. And those rules aren’t even enforced consistently within a single game, let alone across games!
Ultimately, direct perception is about coupling to whatever level of invariant is relevant to your action. Strong anticipation works at every level because at every level the current state of the invariant specifies its near-future states in a way that’s proportional to how deep the underlying coordination runs. The organism, or any other behaving system, doesn't need to know which level it's coupled to; it just needs to align to the pattern. Doing so will pulls it into an anticipatory relationship with the variables it needs to regulate.
Mathematicians may thus indeed have an extra sense for mathematics. In a strong perception sense, this means that they couple to a highly consistent invariant structure that channels (or “enslaves”, in Haken’s terminology) their intellectual degrees of freedom into a trajectory through possibility space that reliably, though imperfectly, constraints them away from false conjectures and toward true and interesting ones. Economics students are trained to “think like an economist” to create this kind of sense in economics-space, indicating that this kind of extra sense can be learned, just like how a baseball fielder can learn to notice and do a better job of maintaining the visual relationship with the fly ball that allows them to catch it.
This builds to a potential resolution where where physical laws and mathematical structures are the same kind of thing, differing only in depth of coordination. All kinds of patterns and laws be thought of as invariants that emerge from coordination at different scales and at different levels of stability. This is why organisms can directly perceive all of them. Economics is a window into how this works because the patterns are deep and robust, non-physical but subject to a high degree of physical interaction and testing, and capable of exhibiting surprising changes when the conditions for their multicausal assembly break down.