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

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the reductionist blind spot

The reductionist blind spot:

higher-level entities and the lawsthey obey

Russ Abbott

Department of Computer Science

California State University, Los Angeles

slide2
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

the reductionist challenge
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

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.

Why is there anything except physics?

Why is there anything except physics? — Fodor, 1998

The point of this talk is to show why the higher level isn’t redundant and why there is something besides physics.

emergence
Emergence

Emergence, 2008

Mark Bedau

Paul Humphreys

  • 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.

Backup slide

it s not all that mysterious
It’s not all that mysterious

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.
  • 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.
turing machines and the game of life
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.

http://www.ibiblio.org/lifepatterns/

Nothing really moves. Just cells going on and off.

The “glider” pattern

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.

a gol turing machine
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 computability.

Reductionism holds. Everything that happens on a GoL grid is a result of the application of the GoL rules andnothing else.

Computability theory is independent of the GoL rules.

  • … 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.

Just as Schrödinger said.

downward causation
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.

not surprising a constrained system is likely to obey special rules

How can you use two tablespoons of water to break a window?

Russ Abbott

Not surprisingA constrained system is likely to obey special rules

1. Spoon the water into an ice cube tray.

2. Freeze the water, thereby constraining its molecules into a rigid lattice structure.

3. Remove the frozen water from the tray.

4. Hurl the “water stone” at the window.

not surprising a constrained system is likely to obey special rules1

How can you use two tablespoons of water to break a window?

Russ Abbott

Not surprisingA constrained system is likely to obey special rules

Frozen water implements a solid. It can be used like a solid, and it obeys the laws of solids.

(That’s because it is a solid—which is an abstraction.)

Is this a trivial observation?

Is it just common sense?

1. Spoon the water into an ice cube tray.

2. Freeze the water, thereby constraining its molecules into a rigid lattice structure.

3. Remove the frozen water from the tray.

So if we constrain the GoL to act like a TM, it shouldn’t be surprising that it is governed by TM laws.

4. Hurl the “water stone” at the window.

A phase transition often signals the imposition or removal of a constraint.

causally reducible ontologically real
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.

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.

  • This is the essence of software. Software constrains a computer to behave like something else—such as a slide projector.
  • All executing software applications are causally reducible yet ontologically real.
evolution is to physics as computability is to the game of life
Evolution is to Physics as Computability is to the Game of Life

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 particle wave functions—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.

Namely, autonomous.

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 of that suitability on the ability of those abstract entities to survive and reproduce—thereby generating more abstract entities.

Evolution is an abstract process that operates on abstract entities.

  • E.g., evolutionary computing generates solutions to difficult optimization and design problems.
slide14

Recognize biological entities as real and apply the abstraction of evolution to them.

Deny the reality of biological entities. Reduce biology to physics.

Biology’s options

In doing so, Darwin and Wallace implicitly predicted that biological entities must have a way of transmitting information about properties. DNA proved them right.

Throw away evolution and biological entities — and hence biology — creating another reductionist blind spot.

This is simply bad science.

level of abstraction
Level of abstraction

Two backup slides

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 implementation without losing information.
  • If the level of abstraction is about nature, reducing it away is bad science.
does nature use levels of abstraction
Does nature uselevels 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 entity or level of abstraction creates a range of possible laws/mechanisms that didn’t exist before.
  • These could not have been “deduced” from lower levels—except through exhaustive enumeration.
the principle of ontological emergence
The principle ofontological emergence

Extant entities and levels of abstraction are those whose implementations have materialized and whose environments enable their persistence.

is that it
Is that it?

Does this resolve the problem of reductionism vs. the special sciences?

Does it explain emergence?

Is it too easy?

three kinds of material entities

Real: objectively observable

All have reduced entropy: persistent patterns.

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.

Distinctive mass properties.

levels of abstraction
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, <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/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
What’s different?
  • This is an bottom-up, platform-based, creativity, and implementation based 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 (some sort of) vision each time it did.
  • Software developers (and engineers and practitioners in any other creative discipline) ask:
    • How can I create something new, e.g., a new level of abstraction a novel, a painting, a sculpture by molding/shaping what currently exists?
    • The higher level is no more “deduced” from the substrate than a painting, a novel, or a sculpture is deduced from the palette, set or words, or clay.
    • Once done, we ask: 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 adds new abstraction possibilities.