The reductionist blind spotWhy square pegs won’t fit into round holes

Russ Abbott

Department of Computer Science

California State University, Los Angeles

Why won’t square pegs fit into round holes?

If a square peg can be “reduced” to the elementary particles that make it up, why can’t those particles fit into a hole of any shape?

Erwin Schrödinger

“[L]iving 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.” Erwin Schrödinger, What is Life?, 1944.

Steven Weinberg

Why is there anything except physics?

Jerry Fodor

The ability to reduce everything to simple

fundamental laws [does not imply] the ability to

start from those laws and reconstruct the

universe. … [We] must all start with reductionism,

which I fully accept. “More is Different” (Science,

1972)

Philip Anderson

The ultimate reductionist.

The ability to reduce everything to simple

fundamental laws [does not imply] the ability to

start from those laws and reconstruct the

universe. … [We] must all start with reductionism,

which I fully accept. “More is Different” (Science,

1972)

Albert Einstein

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

The Game of Life

Click Open

File > Models Library > Computer Science > Cellular Automata > Life

In the full course,

students would

run NetLogo.

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!”

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

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.

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.

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.

Practical corollary: feasibility ranges Physical levels of abstraction

are implemented only within feasibility ranges.

When the feasibility range is exceeded a phase transition generally occurs.

Require contractors to identify the feasibility range within which the implementation will succeed and describe the steps taken to ensure that those feasibility ranges are honored—and what happens if they are not. (Think O-rings.)

Require contractors to identify the feasibility range within which the implementation will succeed and describe the steps taken to ensure that those feasibility ranges are honored—and what happens if they are not. (Think O-rings.)

Backups

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.

How are levels of abstraction built? By adding persistent constraints to what exists.

Constraints “break symmetry” by ruling out possible future states. Should be able to relate this to symmetry breaking more generally.

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. 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.

A satellite in a geostationary orbit:one of the simplest possible “complex systems”

But nothing is tying it down. No cable is holding it in place.

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period of the orbit = period of the earth’s rotation

Typical of complex system mechanisms.Multiple independent or quasi-independent processes

— which are not directly connected causally (agents) —interact within an environment to produce a result.

Typical of complex system mechanisms.Multiple independent or quasi-independent processes

— which are not directly connected causally (agents) —interact within an environment to produce a result.

Fixed with respect to the earth as a reference frame.Fixed with respect to the earth as a reference frame.

An “emergent” property

What is the environment?

Mechanism, function, and purpose Mechanism: The physical processes

within an entity. The chemical reactions built into E.coli that result in its

flagella movements. The DSCA mechanism.

Function: The effect of a mechanism on the environment and on the relationship between an entity and its environment. E. coli moves about. In particular, it moves up nutrient

gradients. Snakes are killed and delivered; money is exchanged.

Purpose: The (presumably positive) consequence for the entity of the change in its environment or its relationship with its environment. (But Nature is not teleological.) E. coli is better able to feed, which is necessary for its

survival. Snake farming is encouraged?

Compare to Measures of Performance, Effectiveness, and UtilityCompare to Measures of Performance, Effectiveness, and Utility

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Socrates

Teleology: building “purpose”E.g., E. coli locomotion to food Evolve a new mechanism Experience the resulting

functionality If the functionality enhances

survival, keep the mechanism “Purpose” has been created

implicitly as part of a new level of abstraction

E.g., E. coli locomotion to food Evolve a new mechanism Experience the resulting

functionality If the functionality enhances

survival, keep the mechanism “Purpose” has been created

implicitly as part of a new level of abstraction

E.g., Reduce snake population Envision a purpose Imagine how a function can

achieve that purpose Design and develop a

mechanism to perform that function

Deploy the mechanism and hope the purpose is achieved

E.g., Reduce snake population Envision a purpose Imagine how a function can

achieve that purpose Design and develop a

mechanism to perform that function

Deploy the mechanism and hope the purpose is achieved

DesignedNature

Most of the design steps require significant conceptualization abilities.

In both cases, the world will be changed by the addition of the new functionality. The purpose is more likely to be achieved in nature.

In both cases, the world will be changed by the addition of the new functionality. The purpose is more likely to be achieved in nature.

Two levels of emergence

No individual chemical reaction inside the ants is responsible for making them follow the rules that describe their behavior.

That the internal chemical reactions together do is an example of emergence.

No individual rule and no individual ant is responsible for the ant colony gathering food.

That the ants together bring about that result is a second level of emergence.

Colony results

Ant behaviors

Ant chemistry

Each layer is a level of abstraction

Notice the similarity to layered communication protocols

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 ScienceMark A. Bedau and Paul Humphreys (Eds.), MIT Press, April 2008.

Cosma Shalizihttp://cscs.umich.edu/~crshalizi/reviews/holland-on-emergence/

Someplace … where quantum field theory meets general relativity and atoms and void merge into one another, we may take “the rules of the game” to be given.

But the rest of the observable, exploitable order in the universe

benzene molecules, PV = nRT, snowflakes, cyclonic storms, kittens, cats, young love, middle-aged remorse, financial euphoria accompanied with acute gullibility, prevaricating candidates for public office, tapeworms, jet-lag, and unfolding cherry blossoms

Where do all these regularities come from?

Call this emergence if you like.

It’s a fine-sounding word, and brings to mind southwestern creation myths in an oddly apt way.