The reductionist blind spot:

The reductionist blind spot: higher-level entities and the laws they obey Russ Abbott Department of Computer Science California State University, Los Angeles

Living matter, while not eluding the ‘laws of physics’ … is likely to involve ‘other laws,’ [which] will form just as integral a part of [its] science. [Starting with the basic laws of physics] it ought to be possible to arrive at … the theory of every natural process, including life, by means of pure deduction. [Starting with the basic laws of physics] it ought to be possible to arrive at … the theory of every natural process, including life, by means of pure deduction. — Einstein All of nature is the way it is … because of simple universal laws, to which all other scientific laws may in some sense be reduced. There are no principles of chemistry that simply stand on their own, without needing to be explained reductively from the properties of electrons and atomic nuclei, and … there are no principles of psychology that are free-standing. All of nature is the way it is … because of simple universal laws, to which all other scientific laws may in some sense be reduced. There are no principles of chemistry that simply stand on their own, without needing to be explained reductively from the properties of electrons and atomic nuclei, and … there are no principles of psychology that are free-standing. — Weinberg Living matter, while not eluding the ‘laws of physics’ … is likely to involve ‘other laws,’ [which] will form just as integral a part of [its] science. — Schrödinger. The ability to reduce everything to simple fundamental laws [does not imply] the ability to start from those laws and reconstruct the universe. — The ability to reduce everything to simple fundamental laws [does not imply] the ability to start from those laws and reconstruct the universe. — Anderson Why is there anything except physics? — Fodor Why is there anything except physics? — Fodor

It comes down to this • Do higher-level entities exist? Yes. • Game of Life Turing Machines and biological entities. • Do higher-level entities obey independent higher level laws. Yes. • Turing machines are subject to the theory of computability, which is independent of the rules of the Game of Life. • Biological entities are subject to evolution through natural selection, which is defined independently of the underlying physics. • Is this surprising? No. • Higher level entities are built by imposing constraints on lower level elements. A constrained system will obey laws that don’t hold when the system is not constrained. • Ice and water act differently. • Is this trivial? Yes, but it has significant implications. • Higher level entities and laws are causally reductive but ontologically real. • Reducing away higher level entities and the laws that they obey creates a reductive blind spot.

Turing machines and the Game of Life A 2-dimensional cellular automaton. The Game of Life rules determine everything that happens on the grid. • A dead cell with exactly three live neighbors becomes alive. • A live cell with either two or three live neighbors stays alive. • In all other cases, a cell dies or remains dead. The “glider” pattern By suitably arranging GoL patterns, one can simulate a Turing machine. Can conclude that the Game of Life halting problem is undecidable. A proxy for physics Nothing really moves. Just cells going on and off. http://www.ibiblio.org/lifepatterns/

A GoL Turing machine • Is an entity. • Like a glider, it is recognizable; it has reduced entropy; it persists and has coherence—even though it is nothing but patterns created by cells going on and off. • Obeys laws from the theory of computation, which precedes and is independent of the GoL. Reductionism holds. Everything that happens on a GoL grid is a result of the application of the GoL rules and nothing else. Computability theory is independent of the GoL rules. • Is a GoL phenomenon that obey laws that are independent of the GoL rules while at the same time being completely determined by the GoL rules.

Not surprising A constrained system will very likely behave differently from one that isn’t constrained. People in a three legged race run differently than if they weren’t tied together. Their tied legs are synchronized—if they’re lucky. Ice behaves differently than water. The H2O molecules hold together in a block. Is this obvious? A trivial observation? So if we constrain a GoL configuration to act like a TM, it shouldn’t be surprising that it is constrained by TM laws.

Is it strange that the unsolvability of the TM halting problem entails the unsolvability of the GoL halting problem. We import a new and independent theory into the GoL and use it to draw conclusions about the GoL. Downward causation? Downward causation entailment This is called “reduction” in Computer Science. We reduce the question of GoL unsolvability to the question of TM unsolvability by constructing a TM within a GoL universe.

Causally reducible; ontologically real GoL Turing machines are causallyreducible but ontologicallyreal. • You can reduce them away without changing how a GoL run will proceed. • Yet they exist as higher level entities and obey laws not derivable from the GoL rules. • They come into being as a result of constraints imposed on an underlying system Naïve reductionism—reducing everything to the level of GoL physics—results in a blind spot regarding higher level entities and the laws that govern them.

Evolution is about biological entities Let’s stipulate that it’s possible to reduce biology to physics. • Nature builds biological entities from elementary particles. • It’s (theoretically) possible to trace how any state of the world—including the biological organisms in it—came about by tracking elementary particles plus quantum randomness. • This parallels the fact that it’s possible to trace the operation of a GoL Turing machine by examining the GoL cell transitions. Nevertheless, evolution is about the evolution of biological entities. • One explains evolution by talking about: populations of biological entities, the survival and reproduction of biological entities, the mutation and combination of properties that make biological entities more or less suited to their environment. • Biological entities must be understood to exist in order for this to make sense. Biology may be causally reducible to physics, but to do so is to throw away the biological entities—and hence the biology.

Level of abstraction A collection of entities and relationships that can be described independently of their implementation. • Every computer application creates one. E.g., PowerPoint. When implemented, a level of abstraction is causally reducible to its implementation. • You can look at the implementation to see how it works. Its independent specification makes it ontologically real. • How it operates is based on its specification, which is independent of its implementation. • The specification can’t be reduced away to the implantation without losing something.

Levels of abstraction • Used by scientists to characterize how some aspect of nature, i.e., some groups of entities operate. • How can I describe the level of abstraction that nature is implementing? • Used by mathematicians as axioms for a mathematical subfield—e.g., Peano’s axioms for number theory. • What are the logical consequences of this level of abstraction? • Used by computer scientists to create new applications. • This level of abstraction characterizes the entities and operations that we want the software to implement. • This level of abstraction is cool.

Three kinds of material entities • Static: atoms, molecules, solar systems, most engineered artifacts. • Persist within energy wells. Energy is required to destroy them. • Dynamic: biological and social entities, hurricanes. • Extract energy from the environment to persist. May be destroyed by cutting off energy supply. • Dynamic entities supervene over constantly changing collections of lower level elements. • The atoms and molecules making up our bodies change daily. • The members of most social units (a country, a corporation, a club, etc.) change frequently. • Symbolic: software entities, ideas. • Persist within a symbolic support framework: computers and our minds. May be destroyed by destroying the framework.

What was in that Kool Aid?

void push(stack: s, <element>: e) <element> pop(stack: s)<element> top(stack: s) top(push(stack: s, <element>: e)) = epop(push(stack: s, <element>: e) = s Stack • Zero is a number. • If A is a number, the successor of A is a number. • Zero is not the successor of a number. • Two numbers of which the successors are equal are themselves equal. • (Induction axiom) If a set S of numbers contains zero and also the successor of every number in S, then every number is in S. Peano’s axioms. Abstract data types &levels of abstraction A collection of “types” (categories), operations that may be applied to entities of those types, and often constraints that are required to hold. Typical examples: stack, naturals. Every computer program, e.g., PowerPoint, implements a level of abstraction—typically including a number of abstract data types. • The things you can manipulate • What you can do (and can’t) do with them

The reductionist blind spot: