Is the Universe a Computer? | Steven Weinberg | The New York Review of Books

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by Stephen Wolfram

Wolfram Media, 1,197 pp., $44.95

1.

Everyone knows that electronic computers have enormously helped the work of science. Some scientists have had a grander vision of the importance of the computer. They expect that it will change our view of science itself, of what it is that scientific theories are supposed to accomplish, and of the kinds of theories that might achieve these goals.

I have never shared this vision. For me, the modern computer is only a faster, cheaper, and more reliable version of the teams of clerical workers (then called “computers”) that were programmed at Los Alamos during World War II to do numerical calculations. But neither I nor most of the other theoretical physicists of my generation learned as students to use electronic computers. That skill was mostly needed for number crunching by experimentalists who had to process huge quantities of numerical data, and by theorists who worked on problems like stellar structure or bomb design. Computers generally weren’t needed by theorists like me, whose work aimed at inventing theories and calculating what these theories predict only in the easiest cases.

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Steven Weinberg

Steven Weinberg (1933–2021) taught at the University of Texas, Austin. He was awarded the Nobel Prize in Physics and the National Medal of Science.

This Issue

October 24, 2002

1
A differential equation gives a relation between the value of some varying quantity and the rate at which that quantity is changing, and perhaps the rate at which that rate is changing, and so on. The numerical solution of a differential equation is a table of values of the varying quantity, that to a good approximation satisfy both the differential equation and some given conditions on the initial values of this quantity and of its rates of change. ↩
2
The automaton must tell you the color of a cell in one row for each of the 2 x 2 x 2 = 8 possible color patterns of the three neighboring cells in the row above, and the number of ways of making these eight independent decisions between two colors is 2⁸ = 256. In the same way, if there were 3 possible colors, then the number of coloring decisions that would have to be specified by an elementary cellular automaton would be 3 x 3 x 3 = 27, and the number of automata (calculated using Mathematica) would be 3²⁷ = 7625597484987. ↩
3
Wolfram says that the main elements of the proof were found in 1994 by one of his assistants, Matthew Cook, and he gives an unreadable updated version in this book, along with an admission that a few errors may still remain. I gather that the proof has not been published in a refereed journal. An article in Nature by Jim Giles titled “What Kind of Science Is This?” (May 16, 2002) reports that when Cook left his job with Wolfram in 1998, he gave a talk on his work at the Santa Fe Institute, but the talk did not appear in the conference proceedings; Wolfram took legal action against Cook, arguing that Cook was in breach of agreements that prevented him from publishing until after the publication of Wolfram’s book. ↩
4
Turing took pains to point out that this issue had not been settled by the famous 1931 theorem of Kurt Gödel, which states that there are statements in the general system of mathematics presented in the Principia Mathematica of Bertrand Russell and Alfred North Whitehead that can be neither proved nor disproved by following the rules of that system. ↩