The reductionist blind spot:Russ AbbottDepartment of Computer ScienceCalifornia State University, Los Angelesthree examples
Why wont a square peg fit into a round hole?If a square peg can be reduced to the elementary particles that make it up, why cant those particles fit through a hole of any shape?Because its shape isnt compatible with the dimensions of the hole.Common sense. Right?
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 doesnt 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 mechanicsFormalizing the common sense
Is it quantum mechanics or 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.Formalizing the common senseSolid geometry
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. Schrdinger.
Is it quantum mechanics or solid geometry?Is solid geometry reducible to physics? Is it just a convenient generalizationsomething that captures multiple physics cases in a convenient package?Or is it an independent domain of knowledge?My answer is that its an independent domain of knowledge. But this example seems somewhat borderline.Formalizing the common senseReducible or not?
By suitably arranging these patterns, one can simulate a Turing Machine. Paul Rendell. http://rendell.server.org.uk/gol/tmdetails.htmThe Turing machine and the Game of LifeA second level of emergence.Emergence is not particularly mysterious.http://www.ibiblio.org/lifepatterns/
The Turing machine and the Game of Life
Downward causationThe 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.)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.
The reductionist blind spotDarwin and Wallaces theory of evolution by natural selection is expressed in terms of entitiestheir propertieshow suitable the properties of the entities are for the environmentpopulationsreproductionetc.These concepts are a level of abstraction. The theory of evolution is about entities at that level of abstraction.Lets assume that its (theoretically) possible to trace how any state of the worldincluding the biological organisms in itcame about by tracking elementary particlesEven 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., nave reductionism, results in a blind spot regarding higher level entities and the laws that govern them.
Level of abstraction: the reductionist blind spotA 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.Its independent specificationits properties and way of being in the worldmakes it ontologically real.How it interacts with the world is based on its specification and is independent of its implementation.It cant be reduced away without losing somethingA concept computer science has contributed to the world.
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 lawsthe constraints) from one that isnt constrained. Im showing this slide to invite anyone who is interested to work on this with me.Isnt this just common sense? Ice cubes act differently from water and water molecules.
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 lawsthe constraints) from one that isnt constrained. Im showing this slide to invite anyone who is interested to work on this with me.Isnt this just common sense? Ice cubes act differently from water and water molecules.
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 systemsThe scare quotes identify problematic areas.PlatoEmergence: Contemporary Readings in Philosophy and Science Mark A. Bedau and Paul Humphreys (Eds.), MIT Press, April 2008.
Are there autonomous higher level laws of nature? The fundamental dilemma of scienceHow can that be if everything can be reduced to the fundamental laws of physics?The functionalist claimThe reductionist positionIt can all be explained in terms of levels of abstraction.My answerEmergence
Gliders are causally powerless.A glider does not change how the rules operate or which cells will be switched on and off. A glider doesnt 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 whetherand if so whena glider will turn on a particular cell.What is the status of those equations? Are they higher level laws?GlidersLike shadows, they dont do anything.The rules are the only forces!
Amazing as they are, gliders are also trivial.Once we know how to produce a glider, its 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.htmThe Turing machine and the Game of LifeA second level of emergence.Emergence is not particularly mysterious.http://www.ibiblio.org/lifepatterns/