The mathematico-physicalist hypothesis states that our physical universe is actually a piece of math. It was famously popularized by Max Tegmark.
It’s one of those big-brain ideas that sound profound when you first hear about it, then you think about it some more and you realize it’s vacuous.
Recently, in a conversation with Clem von Stengel they suggested a version of the mathematico-physicalist hypothesis that I find provoking.
Synthetic mathematics
‘Synthetic’ mathematics is a bit of weird name. Synthetic here is opposed to ‘analytic’ mathematics, which isn’t very meaningful either. It has nothing to do with the mathematical field of analysis. I think it’s supposed to a reference to Kant’s synthetic/ apriori/ a posteriori. The name is probably due to Lawvere.
“In “synthetic” approaches to the formulation of theories in mathematics the emphasis is on axioms that directly capture the core aspects of the intended structures, in contrast to more traditional “analytic” approaches where axioms are used to encode some basic substrate out of which everything else is then built analytically.”
If you read synthetic read ‘Euclidean’. As in—Euclidean geometry is a bit of an oddball field of mathematics, despite being the oldest—it defines points and lines operationally instead of out of smaller pieces (sets).
In synthetic mathematics you do the same but for all the other fields of mathematics. We have synthetic homotopy theory (aka homotopy type theory), synthetic algebraic geometry, synthetic differential geometry, synthetic topology etc.
A type in homotopy type theory is solely defined by its introduction rules and elimination rules (+ univalence axiom). It means a concept it defined solely by how it is used—i.e. operationally.
Agent-first ontology & Embedded Agency
Received opinion is that Science! says there is nothing but Atoms in the Void. Thinking in terms of agents, first-person view concepts like I and You, actions & observations, possibilities & interventions is at best an misleading approximation at worst a degerenerate devolution to cavemen thought. The surest sign of a kook is their insistence that quantum mechanics proves the universe is conscious.
But perhaps the way forward is to channel our inner kook. What we directly observe is qualia, phenomena, actions not atoms in the void. The fundamental concept is not atoms in the void, but agents embedded in environments
(see also Cartesian Frames, Infra-Bayesian Physicalism & bridge rules, UDASSA)
Physicalism
What would it look like for our physical universe to be a piece of math?
Well internally to synthetic mathematical type theory there would be something real—the universe is a certain type. A type such that it ‘behaves’ like a 4-dimensional manifold (or something more exotic like 1+1+3+6 rolled up Calabi-Yau monstrosities).
The type is defined by introduction and elimination rules—in other words operationally: the universe is what one can * do *with it .
Actually instead of thinking of the universe as a fixed static object we should be thinking of an embedded agent in a environment-universe.
Clem’s Synthetic- Physicalist Hypothesis
The mathematico-physicalist hypothesis states that our physical universe is actually a piece of math. It was famously popularized by Max Tegmark.
It’s one of those big-brain ideas that sound profound when you first hear about it, then you think about it some more and you realize it’s vacuous.
Recently, in a conversation with Clem von Stengel they suggested a version of the mathematico-physicalist hypothesis that I find provoking.
Synthetic mathematics
‘Synthetic’ mathematics is a bit of weird name. Synthetic here is opposed to ‘analytic’ mathematics, which isn’t very meaningful either. It has nothing to do with the mathematical field of analysis. I think it’s supposed to a reference to Kant’s synthetic/ apriori/ a posteriori. The name is probably due to Lawvere.
nLab:
“In “synthetic” approaches to the formulation of theories in mathematics the emphasis is on axioms that directly capture the core aspects of the intended structures, in contrast to more traditional “analytic” approaches where axioms are used to encode some basic substrate out of which everything else is then built analytically.”
If you read synthetic read ‘Euclidean’. As in—Euclidean geometry is a bit of an oddball field of mathematics, despite being the oldest—it defines points and lines operationally instead of out of smaller pieces (sets).
In synthetic mathematics you do the same but for all the other fields of mathematics. We have synthetic homotopy theory (aka homotopy type theory), synthetic algebraic geometry, synthetic differential geometry, synthetic topology etc.
A type in homotopy type theory is solely defined by its introduction rules and elimination rules (+ univalence axiom). It means a concept it defined solely by how it is used—i.e. operationally.
Agent-first ontology & Embedded Agency
Received opinion is that Science! says there is nothing but Atoms in the Void. Thinking in terms of agents, first-person view concepts like I and You, actions & observations, possibilities & interventions is at best an misleading approximation at worst a degerenerate devolution to cavemen thought. The surest sign of a kook is their insistence that quantum mechanics proves the universe is conscious.
But perhaps the way forward is to channel our inner kook. What we directly observe is qualia, phenomena, actions not atoms in the void. The fundamental concept is not atoms in the void, but agents embedded in environments
(see also Cartesian Frames, Infra-Bayesian Physicalism & bridge rules, UDASSA)
Physicalism
What would it look like for our physical universe to be a piece of math?
Well internally to synthetic mathematical type theory there would be something real—the universe is a certain type. A type such that it ‘behaves’ like a 4-dimensional manifold (or something more exotic like 1+1+3+6 rolled up Calabi-Yau monstrosities).
The type is defined by introduction and elimination rules—in other words operationally: the universe is what one can * do *with it .
Actually instead of thinking of the universe as a fixed static object we should be thinking of an embedded agent in a environment-universe.
That is we should be thinking of an * interface *
[cue: holographic principle]