The reductionist blind spot: Russ Abbott Department of Computer Science California State University, Los Angeles higher-level entities and the laws they obey * Laws may not be the right term. *

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. 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. [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 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. 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 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? The reductionist challenge If a higher level explanation can be related to physical processes, it becomes redundant since the explanatory work can be done by physics. — Maurice Schouten and Huib Looren de Jong, The Matter of the Mind, 2007 Why is there anything except physics? — Fodor, 1998 Well, I admit that I don’t know why. I don’t even know how to think about why. I expect to figure out why there is anything except physics the day before I figure out why there is anything at all.

Emergence Phenomena that arise from and depend on some more basic phenomena yet are simultaneously autonomous from that base. The very idea of emergence seems opaque, and perhaps even incoherent. When we finally understand what emergence truly is [we will know] whether there are any genuine examples of emergence. How should emergence be defined? … irreducibility, unpredictability, conceptual novelty, ontological novelty, supervenience? In what ways are emergent phenomena autonomous from their emergent bases? … irreducible to their bases, inexplicable from them, unpredictable from them, supervenient on them, multiply realizable in them? Does emergence necessarily involve novel causal powers, especially powers that produce “downward causation?” Emergence … is simultaneously palpable and confusing. Paul HumphreysMark Bedau Backup slide Emergence, 2008

It’s not all that mysterious Do higher-level entities exist?  Game of Life Turing Machines and biological entities. Do higher-level entities obey autonomous higher level laws?  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?  Higher level entities are built by imposing constraints on lower level elements. A constrained system implements additional laws/mechanisms. Is this trivial?  Higher level entities and laws/mechanisms are causally reducible but ontologically real, resolving the reductionist challenge.  Reducing away higher level entities and the laws/mechanisms they implement creates a reductionist blind spot and is bad science.  Corollary: the principle of ontological emergence. Backup slide Do higher-level entities exist? Yes. Higher level entities are “real.”  Game of Life Turing Machines and biological entities. Do higher-level entities obey autonomous 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 implements additional laws/mechanisms. Is this trivial? Yes, but it has significant implications.  Higher level entities and laws/mechanisms are causally reducible but ontologically real, resolving the reductionist challenge.  Reducing away higher level entities and the laws/mechanisms they implement creates a reductionist blind spot and is bad science.  Corollary: the principle of ontological emergence. Too audacious?

By suitably arranging Game of Life patterns, one can simulate a Turing machine.  The GoL can compute any computable function. Its halting problem is undecidable. By suitably arranging Game of Life patterns, one can simulate a Turing machine.  The GoL can compute any computable function. Its halting problem is undecidable. 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 A proxy for physics Nothing really moves. Just cells going on and off.

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. … is a GoL phenomenon that obeys laws that are independent of the GoL rules while at the same time being completely determined by the GoL rules. 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. Just as Schrödinger said.

People in a three legged race run differently than if they weren’t tied together. Their tied legs are synchronized—if they’re lucky. Phase transitions often signal the imposition or removal of a constraint. Not surprising A constrained system will very likely behave differently from one that isn’t constrained. So if we constrain the GoL to act like a TM, it shouldn’t be surprising that it is governed by TM laws. Is this a trivial observation? How can you use water to implement a solid?How can you use water to implement a solid? Constrain its molecules to form a rigid lattice structure. That is, freeze it.

Causally reducible; ontologically real GoL Turing machines are causally reducible but ontologically real.  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  This is the essence of software. Software constrains a computer to behave like something else—such as a slide projector. oI can’t use it to add 2+2 when I’m showing slides.  All executing software applications are causally reducible yet ontologically real. Reducing everything to the level of the GoL rules results in a blind spot regarding higher level entities and the laws/mechanisms that govern them.

Darwin and Wallace implicitly predicted that biological entities must have a way of transmitting information about properties. DNA proved them right. Evolution is to Physics as Computability is to the Game of Life Namely, it’s an autonomous theory. Evolution is an abstract process that operates on abstract entities.  Evolutionary computing, for example, is used to generate solutions (the entities) to difficult optimization and design problems. Evolution is about  populations of abstract entities  the mutation and combination of abstract properties that make those abstract entities more or less suited to their abstract environment  the influence that suitability has on the ability of those abstract entities to survive and reproduce—thereby generating more abstract entities. Biological evolution applies this abstract model to biological entities.  For evolution to make any sense in a biological context, one must presume the existence and reality of biological entities.

But biology is physical Let’s stipulate that it’s possible to reduce biology to physics …  that nature builds biological entities from elementary particles;  that it’s (theoretically) possible to trace how any state of the world—including the biological organisms in it— came about by tracking elementary particles—along with quantum randomness. This parallels the fact that it’s possible to trace the operation of a GoL Turing machine by tracking GoL cell transitions.

Biology may be causally reducible to physics, but to do so is to throw away the biological entities—and hence the biology. Another reductionist blind spot.

Level of abstraction A collection of entities and relationships that can be described independently of their implementation. A Turing machine; biological entities; every computer application, 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 description makes it ontologically real. How it behaves depends on its description at its level of abstraction, which is independent of its implementation. The description can’t be reduced away to the implantation without losing information. If the level of abstraction is about nature, reducing it away is bad science. Two backup slides

Does nature use levels of abstraction? Given the imposition of some random constraints, what entities result? Two possibilities.  There are none, or they don’t persist. Back to nature’s drawing board.  They persist and by their interaction create a new level of abstraction.  Nature then asks: what can I build on top of that? (Think James Burke’s Connections.) Software developers do the same thing. It’s all very bottom-up—and in nature’s case random. Each new level of abstraction creates a range of possible laws/mechanisms that didn’t exist before and that could not have been “deduced” from lower levels—except by exhaustive enumeration. Extant entities and levels of abstraction are those whose implementations have materialized and whose environments enable their persistence. The principle of ontological emergence A backup slide

What was in that Kool Aid?

Three kinds of material entities Static: atoms, molecules, solar systems, most engineered artifacts.  Persist within energy wells. Energy is required to destroy them.  Supervenience works well.  Less mass than the aggregate of their components. Dynamic: biological and social entities, hurricanes.  Extract energy from the environment to persist. May be destroyed by cutting off energy supply.  Since dynamic entities supervene over constantly changing collections of lower level elements, supervenience doesn’t work well. The atoms and molecules making up our bodies change daily. The members of most social units (a country, a corporation, a club, etc.) change.  More mass than the aggregate of their components. Symbolic: software entities.  Persist within a symbolic support framework: computers. May be destroyed by destroying the framework. No individual energy issue.  Since symbolic entities supervene over (potentially unbounded numbers) of bits supervenience, doesn’t work well. Debugging can be hard.  No mass issue. Real: objectively observableAll have reduced entropy: persistent patterns. Distinctive mass properties.

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? 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. Downward causation entailment

Levels of abstraction Used by scientists to characterize how some aspect of nature, i.e., some groups of entities, operates.  How can I describe the level of abstraction that nature is implementing—e.g., evolution in biology? Used by mathematicians as axioms for a mathematical subfield—e.g., Peano’s axioms for the natural numbers.  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.

Abstract data types & levels of abstraction void push(stack: s, : e) pop(stack: s) top(stack: s) top(push(stack: s, : e)) = e pop(push(stack: s, : e) = s Stack 1.Zero is a number. 2.If A is a number, the successor of A is a number. 3.Zero is not the successor of a number. 4.Two numbers of which the successors are equal are themselves equal. 5.(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. A collection of “types” (categories/kinds), operations that may be applied to entities of those types, and often constraints that are required to hold. Simple 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 (and can’t) do with them.

What’s different? This is an bottom-up implementation view rather than a top-down analysis view.  Yes, there is multiple realization, but what matters is what functionality gets created, not whether there are multiple ways to realize it.  The eye may or may not have evolved multiple times. What matters is that it added vision each time it did. Software developers (and engineers) ask:  How can I implement some (higher) level of abstraction using elements from a given level of abstraction? The specification of the higher level is not derived from the implementation. The challenge is to find some way to implement a given specification—or fantasy—given what currently exists. How can I turn my dream into reality?  Once that’s done, we ask: now, what I can build using this as a building block? In nature, there is no advance specification—other than the implicit specification implied by the environment. Once created, each new entity class offers new abstraction possibilities built upon how it acts and interacts with what already exists.