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COMPUTING SCIENCE

The World According to Wolfram

Brian Hayes

A Cellular Universe

It's all very well to dabble in disembodied bits and streams of digits, but what has all this to do with science in our world of atoms and energy? Wolfram's answer is that the same kinds of simple rules or programs are found at work everywhere in the universe.

One case where the mapping between the two realms is quite direct comes from biology, where certain mollusk shells are decorated with patterns similar to those produced by some cellular automata. And the resemblance is surely not a coincidence: The shell patterns are deposited by a row of pigment-secreting cells (that is, biological cells) that appear to act much like a one-dimensional cellular automaton, with neighboring cells communicating through the exchange of chemical signals. These resemblances have been noted before, but Wolfram argues for an unusually strong version of the idea, claiming that all possible cellular automaton rules in a certain class are observed on mollusk shells.

Figure 2. Pigment patterns on snail shells . . .Click to Enlarge Image

Elsewhere in biology, Wolfram applies similar methods of analysis to other pigment patterns, to the arrangement of stems and branches in plants, and to the shapes of leaves. In physics he treats the growth of snowflakes and other crystals, the fracturing of solids and the onset of turbulence in fluids. There is even a brief discussion of economics, suggesting that the kind of randomness observed in some cellular automata could account for price fluctuations in stock markets.

In another chapter of A New Kind of Science Wolfram presents his version of the thesis that the universe as a whole is something like a cellular automaton. The model looks below the level of everyday experience and even beyond the events studied in high-energy physics, where the world seems to be made up of electrons and quarks and other "elementary" particles, moving through a continuum of space. In Wolfram's view of the universe there is no continuum, and particles are a mere epiphenomenon; indeed, motion and geometry are also little more than illusions. In this cosmology, space and time are both assumed to be discrete, just as they are in a cellular automaton, and the only things that move are signals passing from cell to cell.

The most obvious way of implementing this idea would be to partition space into tiny cubical volumes, creating a cellular automaton on a three-dimensional grid. Wolfram looks with disfavor on this simplest solution because it imposes a particular geometry on space and also requires some kind of master clock to synchronize the updating of all the cells throughout the grid. His alternative is a model where the cells are nodes of a free-form network that has a well-defined topology but no specific geometry. In other words, the connections between nodes are all determined beforehand, but the spatial coordinates of the nodes are left unspecified. Concepts such as shape and position have no meaning at this level: The geometry of space emerges from the model rather than being built into it. Specifically, our world is perceived as being three-dimensional because each node of the network has three incoming links from other nodes and three outgoing links, creating the same connectivity as a three-dimensional lattice. Another feature of the model is that updating the cells requires no synchronizing master clock; updating events propagate along the links of the network itself. Making each link a one-way conduit defines a direction for time and causality; the whole structure is called a causal net.

This theory of everything is one of the book's wilder flights of fancy; there is no immediate prospect of testing it by experiment. But the same is true of all other attempts to explain the structure of the universe at this level of detail. In any case, Wolfram is not coy in his manner of proposing the model. When I asked him how seriously he intends it to be taken, he said he would be quite surprised if something very much like it doesn't turn out to be right.








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