## Posts Tagged ‘Emergence’

### Reductionism versus Emergence

Friday, November 4th, 2011

A person from the West was visiting Japan and noticed people playing a game he had not seen before. They had black stones and white stones that they alternately placed on a playing board. He wants to learn how to play the game but since he does not speak Japanese he decides to learn about the game by watching it being played. (This was before the Internet.) He discovers that the goal of the game seems to be to surround one’s opponent’s stones and thus capture them.  He notices that the initial moves seem to follow a well-defined path but he is not sure if this is from the rules of the game or from strategy. Now from watching the game being played he tries to learn two distinct things: the rules of the games and the strategy used in playing the games. The game here is Go. The rules are very simple but the strategy very complex; probably more complex than chess. No one in their right mind would claim to know the game of go if they simply knew the rules—but to play the game they do indeed need to know the rules.

Science is much the same: by observation we try to determine the basic rules and the strategy. In Science, the strategy is how the rules manifest themselves in a particular case.  For example, we have Newton’s law of motion and gravity. From these, we can deduce the motion of the planets. But just as the rules of Go do not uniquely determine the play, Newton’s law do not uniquely determine planetary motion. They describe all possible arrangements of all possible planets. To get to the actual planetary motion we need the initial conditions and a method of getting from the laws to the phenomena. The latter is frequently complicated, and in the case of planetary motion, Newton invented calculus to do the job.

Here we see the two basic aspects of science:

1. Reductionism: determining the rules of the game. In physics these rules are frequently called the Lagrangian.
2. Emergence: going from the rules to the actual game play. In science, many unexpected phenomena emerge from the basic rules; for example, superconductivity and life.

Einstein was very much a reductionist. He stated, “The grand aim of all science is to cover the greatest number of empirical facts by logical deduction from the smallest number of hypotheses or axioms.” Here is the reductionist’s mantra and elusive dream: to reduce everything to a few rules. But it is an elusive dream. We keep pushing to higher energies and get more comprehensive models: Newtonian mechanics, quantum mechanics, quantum field theory, grand-unified models, string theory, whatever is beyond string theory, whatever is beyond whatever is beyond string theory, etc. There is no reason to believe the series will ever end, even if we have it correct up to some level (and string theory may or may not be the correct model, and yes string theory is, at best, just one more model in a string of models).

But even if we knew the rules, we would still need the strategy. Starting with string theory (or even the standard model of particle physics), derive the maximum temperature for superconducting material. For extra points construct the material.  Nothing discovered with the LHC will help solve this problem.

Poincare, in contrast to Einstein, was not a reductionist: “We seek reality, but what is reality? The physiologists tell us that organisms are formed of cells; the chemists add that cells themselves are formed of atoms. Does this mean that these atoms or these cells constitute reality, or rather the sole reality? The way in which these cells are arranged and from which results the unity of the individual, is not it also a reality much more interesting than that of the isolated elements, and should a naturalist who had never studied the elephant except by means of the microscope think himself sufficiently acquainted with that animal?” Fortunately the blind men who studied the elephant could not use a microscope or they would have had a least one more model to dispute about.

Particle physicists tend to think the rules (reductionism) are more fundamental while condensed matter physicists and chemists think the strategy (emergence) is more fundamental. In both cases fundamental means: “I think what I am doing is way cooler than what you are doing.” And yes, scientists do think what they are doing is cool. If they thought what someone else was doing was cooler they would be doing that.  But both reductionism and emergence are necessary for the advancement of science. Anyway I must now go and do some cool, oops! I mean, fundamental science.