Reductionism, emergence, levels of abstractions, and generalized evolution

НазваниеReductionism, emergence, levels of abstractions, and generalized evolution
Дата конвертации25.10.2012
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Preprint. Submitted to Communications of the ACM.

Reductionism, emergence, levels of abstractions, and generalized evolution

Russ Abbott

Computer Science, California State University, Los Angeles

Can there be independent higher level laws of nature if everything can be reduced to the fundamental laws of physics? The computer science notion of a level of abstraction explains why there can be. In explicating this issue I illustrate [1] how computational thinking has solved one of philosophy’s most vexing problems.

More than half a century ago, Erwin Schrödinger [2] put it this way.

[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.

To understand how radical Schrödinger’s statement is consider this extract [3] from David Gross, another physics Nobel laureate, in which he quotes Albert Einstein.

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.

Gross and Einstein represent strict reductionism: physics explains everything. Schrödinger and those of us who use computer science to study complex systems say that there is more to nature than the fundamental laws of physics. We argue that chemistry is not just physics, biology is not just physics and chemistry, psychology is not just biology and chemistry, sociology is not just biology and psychology, etc.

The term “emergence” has been used to describe the phenomenon whereby higher level laws arise from but are not derivable from some lower level. The very term suggests something mysterious. How can new laws emerge?

We software developers know one way: the properties of a software system are generally quite different from those of the underlying computer. Furthermore, the explosion of computer science specialties—graphics, languages, databases, etc.—demonstrates that all sorts of higher level laws can come into existence. And these new laws come into existence even though everything that goes on in a computer can be explained in terms of the machine instructions executed by a cpu.

One might argue that man-made emergence is different from naturally occurring emergence. That emergence can happen in nature without a programmer may seem startling, but it’s the same phenomenon. Our surprise is really not the issue.

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 [4] 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 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. I 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. It is tautologous to say that entities that are better adapted to their environment will survive and reproduce more effectively than those that are less well adapted. That’s what it means to be better adapted. In reproducing more prolifically, those better adapted entities will pass on whatever features make them better suited. Hence evolution. Should some variation occur that enables its possessors to survive and reproduce even more effectively, that variation will be passed on.

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 has the properties of heritable variation and environmentally mediated survival and reproduction.

The reductionist blind spot

Levels of abstraction are epiphenomenal. (Nonetheless, their reduced entropy and special mass properties render them objectively real.) Because they are epiphenomenal, levels of abstraction have no causal power; the underlying physics turns the causal crank. Even so, the constraints embodied by a level 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. Each characterizes properties of a level of abstraction itself.

Epiphenomenal though it may be, reducing away a level of abstraction produces a reductionist blind spot. No equations over the domain of Game-of-Life 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-abstraction—a concept familiar to most computer scientists but to few outside our field—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.

  • Generalized evolution: the principle that extant levels of abstraction (naturally occurring or man-made) are those whose implementations have materialized and whose environments support their persistence.

Emergence is real. But one can sympathize with the reductionist impulse. What emerges are epiphenomena—a relatively strange concept on which to base a view of nature.

Probably most computer scientists would not normally associate the term epiphenomenon with the notion of a level of abstraction. But it’s because levels of abstraction are epiphenomenal that computational thinking can help scientists understand nature.


[1] Abbott, Russ, “Emergence explained,” Complexity, Sep/Oct, 2006, (12, 1) 13-26. Preprint:

[2] Schrödinger, Erwin, What is Life?, Cambridge University Press, 1944.

[3] Gross, David, “Einstein and the search for unification,” Current Science, 89/12, 25 December 2005, pp. 2035 – 2040.

[4] Rendell, Paul, “Turing Universality in the Game of Life,” in Adamatzky, Andrew (ed.), Collision-Based Computing, Springer, 2002.,

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