Preprint. Submitted to Communications of the ACM.
Reductionism, emergence, levels of abstractions, and
generalized evolution
Russ Abbott
Computer Science, California State University, Los Angeles
Thirty five years ago Philip Anderson issued a challenge [1]. He didn’t disavow
reductionism.
[The] workings of all the animate and inanimate matter of which we have any detailed knowledge
are … controlled by the same set of fundamental laws [of physics]. … [W]e must all start with
reductionism, which I fully accept.
But he challenged the claim that
the ability to reduce everything to simple fundamental laws … implies the ability to start from
those laws and reconstruct the universe. … At each level of complexity entirely new properties
appear. … Psychology is not applied biology, nor is biology applied chemistry. … [T]he whole
becomes … very different from the sum of its parts.
Nearly 30 years earlier, Erwin Schrödinger made a similar point [2].
[L]iving matter, while not eluding the 'laws of physics' … is likely to involve 'other laws …,'
hitherto unknown, which … will form just as integral a part of [its] science.
Compare these statements with those of Steven Weinberg [3], a committed
reductionist.
[A]ll of nature is the way it is … because of simple universal laws, to which all other scientific
laws may in some sense be reduced. …
Every field of science operates by formulating … generalizations that are sometimes dignified by
being called principles or laws. … But 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 … do not need ultimately to be
understood through the study of the human brain, which in turn must ultimately be understood on
the basis of physics and chemistry.
This too is an echo of a grand tradition. David Gross quotes Albert Einstein [4].
The supreme test of the physicist is to arrive at those universal laws of nature from which the
cosmos can be built up by pure deduction.
I love this sentence. In one sentence Einstein asserts the strong reductionist view of nature:
There exist universal, mathematical laws … from which all the workings of the cosmos can (in
principle) be deduced, starting from the elementary laws and building up.
What follows is a compressed and extended version of [5], which shows how
computer science supports Anderson and Schrödinger against Weinberg, Gross,
and Einstein.
Preprint. Submitted to Communications of the ACM.
The Game of Life Turing machine
Most CACM readers know that the Game of Life is a cellular automaton in which
cells are either alive (on) or dead (off). At each time step:
 any cell with exactly three live neighbors will stay alive or become alive;
 any live cell with exactly two live neighbors will stay alive;
 all other cells die.
Think of these Game of Life rules as comparable to the fundamental laws of
physics. They determine everything that happens on a Game of Life grid.
Nevertheless there are “higher level” laws that are not derivable from them.
Certain Game of Life configurations create patterns. The most famous is the
glider, a configuration of on and off cells that moves diagonally across the grid.
Gliders and other patterns are epiphenomenal; they have no causal power. Only
the Game of Life rules make cells go on and off. Nonetheless, Rendel [6] shows
how to implement an arbitrary Turing machine by arranging such epiphenomenal
patterns.
Rendel’s Game-of-Life Turing machine is a level of abstraction implemented
using the Game of Life rules. Game-of-Life Turing machines are also
epiphenomenal. But once it’s determined that a Turing Machine can be
implemented as a Game-of-Life level of abstraction, the laws of computability
theory apply. And computability theory is not derivable from the Game of Life
rules. Thus while not eluding the Game of Life rules, new properties appear at
the Turing machine level of abstraction—just as Anderson and Schrödinger said.
Furthermore, conclusions about Turing machines can be extended to
conclusions about the Game of Life. Because the halting problem is unsolvable,
it is unsolvable whether an arbitrary Game of Life configuration will ever reach a
stable state. Call this “downward entailment”—not quite downward causation, but
close.
Evolution as a property of a level of abstraction
Evolution by natural selection depends on (a) the possibility of heritable variation
and (b) that survival and reproduction are affected by the relationship between an
entity to its environment. Evolution is not a reductionist theory. It neither depends
on nor is derived from lower level laws. Although evolution is implemented in part
by DNA, Darwin didn’t know about DNA. He didn’t have to know about DNA;
evolution occurs in any level of abstraction that satisfies the principles listed
above.
The reductionist blind spot
Levels of abstraction are epiphenomenal.1 They have no causal power; the
underlying physics turns the causal crank. Even so, the constraints2 embodied by
1
Nonetheless, their reduced entropy and special mass properties render them objectively real.
2
Anderson called this broken symmetry.
Preprint. Submitted to Communications of the ACM.
levels of abstraction give rise to new laws. (It would be surprising if they didn’t.)
Evolution and unsolvability are two such laws. Neither is derivable from nor
dependent on the mechanisms used to implement the level of abstraction to
which it applies. Each characterizes properties of a level of abstraction itself.
Epiphenomenal though they may be, reducing away a level of abstraction
produces a reductionist blind spot. No equations over the domain of Game-ofLife grid cells can describe the computation performed by a Game-of-Life Turing
machine unless the equations themselves model a Turing machine. The laws
that characterize the regularities at a level of abstraction become meaningless
when the abstractions are defined away.
Evolution and unsolvability illustrate how the level-of-abstraction3—a concept
familiar to most computer scientists but to few outside our field4—allows nature
(and programmers) to build new regularities within a reductionist framework.
Two definitions sum it up.
 Emergence: the implementation—either statically (at equilibrium) or
dynamically (far from equilibrium)—of a level of abstraction.5
 Generalized evolution: the principle that extant levels of abstraction
(naturally occurring or man-made) are those whose implementations have
materialized6 and whose environments support their persistence.
References
[1] Anderson, Philip W., “More Is Different,” Science, 4 Aug. 1972, (177, 4047), 393-396. 1972
[2] Schrödinger, Erwin, What is Life?, Cambridge University Press, 1944.
[3] Weinberg, Steven, “Reductionism Redux,” The New York Review of Books, October 5, 1995.
Reprinted in Weinberg, S., Facing Up, Harvard University Press, 2001.
[4] Gross, David, “Einstein and the search for unification,” Current Science, 89/12, 25 December
2005, pp. 2035 – 2040.
[5] Abbott, Russ, “Emergence explained,” Complexity, Sep/Oct, 2006, (12, 1) 13-26. Preprint:
http://cs.calstatela.edu/wiki/images/9/95/Emergence_Explained-_Abstractions.pdf.
[6] Rendell, Paul, “Turing Universality in the Game of Life,” in Adamatzky, Andrew (ed.),
Collision-Based Computing, Springer, 2002.,
[7] Laughlin, Robert B., A Different Universe, Basic Books, 2005.
[8] Wing, Jeannette, “Computational Thinking,” CACM, March 2006, 49/3.
3
This illustrates computational thinking in philosophy. See Wing [8].
4
Laughlin [7] used the term protectorate when he argued that Newtonian physics and the solid
state of matter are both levels of abstraction.
5
Formation or dissolution of a level of abstraction often manifests as a phase transition.
6
As in software, new levels of abstraction are often built on existing ones.