Research Program
Foursome
 Another example: foursome
 Levels of knowledge.
 Example: the bottle
 Plato, Aristotle
 Idealism vs. materialism
 Peirce's signs
 progression in evolution
 natural transformations distinguish  icon, index
 thing  identity morphism = object (object is what has an identity morphism  whether it is an object)
 symbols  absolutely any relationship
 Yoneda Lemma, embedding
 functions like knowledge switch
Consider also the case where F is the identity I, and thus A is a set. Look at the natural isomorphism.
 global quantum  Maxwell's demon operates the knowledge switch  Bible story  how physicists talk about the global quantum  that you run out of tape  Rolf Landauer  but they don't specify the cut off
 automata theory Chomsky hierarchy.
In his comment at Math Stack Exchange, Nex describes the two functors {$ R $} and {$ L $} thusly:
 {$ R $} is {$ ((α,f):(F,A)→(F′,A′))↦(x↦α_{A′}(F(f)(x))) $} and the objects are mapped {$ (F,A)↦F(A) $}
 {$ L $} is {$ ((α,f):(F,A)→(F′,A′))↦(θ↦(α⋅θ⋅\textrm{Hom}(f,−))) $} and the objects are mapped {$ (F,A)↦\textrm{Nat}(\textrm{Hom}(A,−),F) $}

 Consider the distribution of the largest eigenvalue for a random matrix. The peak is at {$\sqrt{2N}$}. The distribution drops as {$e^{N^2}$} to the left and as {$e^{N}$} on the right.
 Finite automata  strong coupling  scale as N^2. Pushdown automata  subsystems  weak coupling  scale as N.
 How could the largest eigenvalue be larger than expected? There are not many ways and thus it drops down quickly. How could it be smaller than expected? There are many more ways, mixing positive and negative, and thus it drops down slowly.
 Quanta Magazine. Beyond the Bell Curve  A New Universal Law Satya Majumdar, Grégory Schehr. The critical point at √2N separates a stable phase of weakly coupled species, whose populations can fluctuate individually without affecting the rest, from an unstable phase of strongly coupled species, in which fluctuations cascade through the ecosystem and throw it off balance. In general, Majumdar and Schehr believe, systems in the TracyWidom universality class exhibit one phase in which all components act in concert and another phase in which the components act alone. The asymmetry of the statistical curve reflects the nature of the two phases. Because of mutual interactions between the components, the energy of the system in the strongcoupling phase on the left is proportional to N2. Meanwhile, in the weakcoupling phase on the right, the energy depends only on the number of individual components, N
 Universality principle " as the phase transition is approached, the scaledependent parameters play less and less of an important role, and the scaleinvariant parts of the physical description dominate. Thus, a simplified, and often exactly solvable, model can be used to approximate the behaviour of these systems near the critical point. "
 Two objects cannot be in the same place, and the same is true for fermions. But two arrows can be in the same place, and the same is true for bosons. I mean to say that two arrows can start at the same object and end at the same object but be entirely different arrows. So a shift from an "object point of view" to an "arrow point of view" may be like a shift from "fermion statistics" to "boson statistics".
 Univalence Axiom {$(A=B)\simeq(A\simeq B)$}
 Yates index theorem, the jump hierarchy.
 Unconscious, conscious, consciousness
 4 sheave functors
 Feynman diagrams with 4 fields
Nigel Goldenfeld: Seeing Emergent Physics Behind Evolution
 Condensed matter physics: collective effects. Horizontal gene transfer  network of life  exponential growth. But perhaps this hit a global quanta limit and that is why the cell arose as a subroutine.
Everything
Four properties of everything