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

The reductionist blind spot:
higher-level entities and the laws they obey
Russ Abbott
Department of Computer Science
California State University, Los Angeles
[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.
— 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. — —
Anderson
The reductionist challenge
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? — Fodor, 1998
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
The point of this talk is to show why the higher level isn’t
redundant and why there is something besides physics.
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?”
Backup slide
Emergence … is simultaneously palpable and confusing.

Backup slide
It’s not all that mysterious
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.

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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
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.
Nothing really moves. Just
cells going on and off.
http://www.ibiblio.org/lifepatterns/
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 …

… 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 and nothing else.
Computability theory is independent of the GoL rules.

Just as
Schrödinger
said.
… 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.
Downward causation
causation?entailment
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.

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
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 rules
How can you use
two tablespoons
of water to break
a window?
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?
So if we constrain the
GoL to act like a TM, it
shouldn’t be surprising
that it is governed by
TM laws.
Russ Abbott
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.
A phase transition often signals the
imposition or removal of a constraint.
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.
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
Namely, autonomous.
Biology is physical.
Evolution is about
Let’s stipulate that it’s possible to
reduce biology to physics …



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.


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.
Recognize biological
entities as real and
apply the abstraction
of evolution to them.
In doing so,
Darwin and
Wallace
implicitly
predicted
that
biological
entities
must have a
way of
transmitting
information
about
properties.
DNA proved
them right.
Biology’s options
Deny the reality of
biological entities.
Reduce biology to
physics.
Throw away
evolution and
biological
entities — and
hence biology
— creating
another
reductionist
blind spot.
This is simply
bad science.
Two backup slides
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 implementation
without losing information.
If the level of abstraction is about nature, reducing it away is
bad science.
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 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
Extant entities and levels of abstraction
are those whose implementations have
materialized and whose environments
enable their persistence.
Is that it?
Does this resolve the problem of
reductionism vs. the special sciences?
Does it explain emergence?
Is it too easy?
Real: objectively observable
All have reduced entropy:
persistent patterns.
Three kinds of material entities

Static: atoms, molecules, solar systems, most engineered artifacts.


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
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.

Distinctive

mass
properties.
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.

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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.
Levels of abstraction

Used by scientists to characterize how some aspect of
nature, i.e., some groups of entities, operates.


Used by mathematicians as axioms for a mathematical
subfield—e.g., Peano’s axioms for the natural numbers.


How can I describe the level of abstraction that nature is
implementing—e.g., evolution in biology?
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
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
void push(stack: s, <element>: e)
abstraction—typically including a
<element> pop(stack: s)
number of abstract data types.
<element> top(stack: s)
Stack

top(push(stack: s, <element>: e)) = e
pop(push(stack: s, <element>: e) = s
1.
2.
3.
4.
5.

The things you can manipulate.
What you can (and can’t) do with
them.
Zero is a number.
Peano’s axioms.
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.
What’s different?

This is an bottom-up, platform-based, creativity, and implementation
based view rather than a top-down analysis view.

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Software developers (and engineers and practitioners in any other
creative discipline) ask:


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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.
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.