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The reductionist blind spot:
three examples
Russ Abbott
Department of Computer Science
California State University, Los Angeles
Why won’t a square peg fit
into a round hole?
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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 its shape isn’t compatible
with the dimensions of the hole.
Common sense. Right?
Is it quantum mechanics or
solid geometry?
Quantum mechanics
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Describe a particular square peg and round hole by
characterizing the positions of the elementary particles that
make them up.
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Will be very different depending on materials: metal, glass, wood, … .
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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.
Is it quantum mechanics or
solid geometry?
Solid geometry
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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 interpenetrable, 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-interpenetrability is established on by this solid geometry argument.
[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
Why is there
anything except
physics?
— Fodor
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
Is it quantum mechanics or
solid geometry?
Reducible or not?
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Is solid geometry reducible to physics? Is it
just a convenient generalization—something
that captures multiple physics cases in a
convenient package?
Or is it an independent domain of
knowledge?
My answer is that it’s an independent domain
of knowledge. But this example seems
somewhat borderline.
The Turing machine and
the Game of Life
By suitably arranging these patterns,
one can simulate a Turing Machine.
Paul Rendell. http://rendell.server.org.uk/gol/tmdetails.htm
http://www.ibiblio.org/lifepatterns/
A second
level of emergence.
Emergence is not particularly mysterious.
The Turing machine and
the Game of Life
Downward causation entailment
Downward causation
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The unsolvability of the TM halting problem
entails the unsolvability of the GoL halting
problem.
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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.
GoL gliders and Turing Machines
One can use glider “velocity” laws to draw
are causally reducible but
conclusions (make predictions) about which cells
ontologically
real.will happen. (Also
will be turned on
and when that
 You can reduce them away
downward entailment.)
without changing how a GoL run
The reductionist blind spot
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Darwin and Wallace’s theory of evolution by natural
selection is expressed in terms of
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These concepts are a level of abstraction.
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entities
their properties
how suitable the properties of the entities are for the
environment
populations
reproduction
etc.
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
blind spot
A concept computer science has contributed to the world.
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
Itsworks.
independent specification—its properties
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and way of being in the world—makes it
ontologically real.
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How it interacts with the world is based on its
specification and is independent of its
Backups
I’m showing this slide to invite anyone who is interested to work on this with me.
How are levels of abstraction built?
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By adding persistent constraints to what exists.
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Constraints break symmetry by limiting the possible
transformations.
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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 GameIsn’t
ofthis
Life
justgrid)
common sense?
Ice cubes act differently
from
“breaks the symmetry” of possible sequences
of future
water and water molecules.
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.
How are levels of abstraction built?
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How does nature build levels of abstraction? Two
ways.
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Energy wells produce static entities.
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Activity patterns use imported energy to produce
dynamic entities.
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Atoms, molecules, solar systems, …
The constraint is imposed by the processes that the
dynamic entity employs to maintain its
Isn’tstructure.
this just common sense?
Ice cubes act differently from
Biological entities, social entities, hurricanes.
water and water molecules.
A constrained system operates differently (has
additional laws—the constraints) from one that
isn’t constrained.
Emergence: the holy grail of
complex systems
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/
Plato
The ‘scare’ quotes identify
problematic areas.
Emergence: Contemporary Readings in Philosophy and Science
Mark A. Bedau and Paul Humphreys (Eds.), MIT Press, April 2008.
The fundamental dilemma of science
Are there autonomous
higher level laws of
nature?
Emergence
The functionalist claim
The reductionist position
How can that be if everything can be
reduced to the fundamental laws of
physics?
My answer
It can all be explained in
terms of levels of
Gliders
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Gliders are causally powerless.
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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 …
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One can write down equations that characterize glider
motion and predict whether—and if so when—a glider will
“turn on” a particular cell.
shadows,
don’t “do”
What is theLike
status
of thosethey
equations?
Areanything.
they higher
The rules are the only “forces!”
level laws?
The Turing machine and
the Game of Life
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Amazing as they are, gliders are also
trivial.
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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
http://www.ibiblio.org/lifepatterns/
A second
level of emergence.
Emergence is not particularly mysterious.