1. The reductionist blind spot Russ Abbott Department of Computer Science California State University, Los Angeles Why square pegs don’t fit into round holes

2. Why won’t a square peg fit into a round hole? If a square peg can be “reduced” to the elementary particles that make it up, why can’t those particles fit through a hole of any shape? Because they are in a shape that’s not compatible with the dimensions of some given round hole. It’s common sense, isn’t it?

3. Is it quantum mechanics or solid geometry? Describe a particular square peg and round hole by characterizing the positions of the elementary particles that make them up.  Will be very different depending on materials: metal, glass, wood, ….  Argue that the elementary forces among particles when in a "peg" and "hole" configuration force them to satisfy various invariants: the geometric relationships among the peg particles are fixed (it doesn’t change shape); the hole has rotational symmetry. Conclude that the forces, invariants, and symmetries prevent the particles that represent the peg from moving to a position that would be described as being “in” the hole created by the round hole particles. A similar argument must be made for each peg-hole combination. Quantum mechanics

4. Is it quantum mechanics or solid geometry? Solid geometry Describe the abstract geometrical characteristics of square pegs and incompatible round holes, namely that the diagonal of the face of the square peg is greater than the diameter of the round hole. Based on the solid geometry property that solids are not inter-penetrable, conclude that any square-peg/round-hole pair with incompatible dimensions will not fit one within the other. Claim that whenever nature constructs entities that satisfy the properties assumed by solid geometry, their non-inter- penetrability is established on by this solid geometry argument.

5. 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. Why is there anything except physics? — Fodor The ability to reduce everything to simple fundamental laws [does not imply] the ability to start from those laws and reconstruct the universe. — Anderson [From 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. — Weinberg

6. Two more examples A Turing machine implemented on a Game of Life platform Evolution

7. Amazing as they are, gliders are also trivial.  Once we know how to produce a glider, it’s simple to make them. Can build a library of Game of Life patterns and their interaction APIs. By suitably arranging these patterns, one can simulate a Turing Machine. Paul Rendell. http://rendell.server.org.uk/gol/tmdetails.htm Game of Life as a Programming Platform A second level of emergence. Emergence is not particularly mysterious. http://www.ibiblio.org/lifepatterns/

8. Downward causation The unsolvability of the TM halting problem entails the unsolvability of the GoL halting problem.  How strange! We can conclude something about the GoL because we know something about Turing Machines.  Yet the theory of computation is not derivable from GoL rules. One can use glider “velocity” laws to draw conclusions (make predictions) about which cells will be turned on and when that will happen. (Also downward entailment.) Downward causation entailment GoL gliders and Turing Machines are causally reducible but ontologically real.  You can reduce them away without changing how a GoL run will proceed.  Yet they obey higher level laws, not derivable from the GoL rules. GoL gliders and Turing Machines are causally reducible but ontologically real.  You can reduce them away without changing how a GoL run will proceed.  Yet they obey higher level laws, not derivable from the GoL rules.

9. The reductionist blind spot Darwin and Wallace’s theory of evolution by natural selection is expressed in terms of  entities  their properties  how suitable the properties of the entities are for the environment  populations  reproduction  etc. These concepts are a level of abstraction.  The theory of evolution is about entities at that level of abstraction. Let’s assume 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 Even so, it is not possible to express the theory of evolution in terms of elementary particles. Reducing everything to the level of physics, i.e., naïve reductionism, results in a blind spot regarding higher level entities and the laws that govern them. Darwin and Wallace’s theory of evolution by natural selection is expressed in terms of  entities  their properties  how suitable the properties of the entities are for the environment  populations  reproduction  etc. These concepts are a level of abstraction.  The theory of evolution is about entities at that level of abstraction. Let’s assume 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 Even so, it is not possible to express the theory of evolution in terms of elementary particles. Reducing everything to the level of physics, i.e., naïve reductionism, results in a blind spot regarding higher level entities and the laws that govern them.

10. Level of abstraction: the reductionist blind spot A collection of concepts and relationships that can be described independently of its implementation. Every computer application creates one. A collection of concepts and relationships that can be described independently of its implementation. Every computer application creates one. A level of abstraction is causally reducible to its implementation.  You can look at the implementation to see how it works. A level of abstraction is causally reducible to its implementation.  You can look at the implementation to see how it works. Its independent specification—its properties and way of being in the world—makes it ontologically real.  How it interacts with the world is based on its specification and is independent of its implementation.  It can’t be reduced away without losing something Its independent specification—its properties and way of being in the world—makes it ontologically real.  How it interacts with the world is based on its specification and is independent of its implementation.  It can’t be reduced away without losing something A concept computer science has contributed to the world.

11. Backups

12. How are levels of abstraction built? By adding persistent constraints to what exists.  Constraints break symmetry by limiting the possible transformations. Symmetry is equality under a transformation.  Easy in software.  Software constrains a computer to operate in a certain way.  Software (or a pattern set on a Game of Life grid) “breaks the symmetry” of possible sequences of future states. A constrained system operates differently (has additional laws—the constraints) from one that isn’t constrained. I’m showing this slide to invite anyone who is interested to work on this with me. Isn’t this just common sense? Ice cubes act differently from water and water molecules.

13. How are levels of abstraction built? How does nature build levels of abstraction? Two ways.  Energy wells produce static entities. Atoms, molecules, solar systems, …  Activity patterns use imported energy to produce dynamic entities. The constraint is imposed by the processes that the dynamic entity employs to maintain its structure. Biological entities, social entities, hurricanes. A constrained system operates differently (has additional laws—the constraints) from one that isn’t constrained. I’m showing this slide to invite anyone who is interested to work on this with me. Isn’t this just common sense? Ice cubes act differently from water and water molecules.

14. How macroscopic behavior arises from microscopic behavior. Emergent entities (properties or substances) ‘arise’ out of more fundamental entities and yet are ‘novel’ or ‘irreducible’ with respect to them. Stanford Encyclopedia of Philosophy http://plato.stanford.edu/entries/properties-emergent/ Emergence: the holy grail of complex systems The ‘scare’ quotes identify problematic areas. Plato Emergence: Contemporary Readings in Philosophy and Science Mark A. Bedau and Paul Humphreys (Eds.), MIT Press, April 2008.

15. Are there autonomous higher level laws of nature? The fundamental dilemma of science How can that be if everything can be reduced to the fundamental laws of physics? The functionalist claim The reductionist position It can all be explained in terms of levels of abstraction. My answer Emergence

16. Gliders are causally powerless.  A glider does not change how the rules operate or which cells will be switched on and off. A glider doesn’t “go to an cell and turn it on.”  A Game of Life run will proceed in exactly the same way whether one notices the gliders or not. A very reductionist stance. But …  One can write down equations that characterize glider motion and predict whether—and if so when—a glider will “turn on” a particular cell.  What is the status of those equations? Are they higher level laws? Gliders Like shadows, they don’t “do” anything. The rules are the only “forces!”