Chapter 1: The Foundations for a New Kind of Science

Section 4: The Personal Story of the Science in This Book

Statistical physics cover

The pictures show disks representing idealized molecules bouncing around in a box, and the book claims that as time goes on there is almost inevitably increasing randomization. The pictures were made in about 1964 by Berni Alder and Frederick Reif from oscilloscope output from the LARC computer at what was then Lawrence Radiation Laboratory. A total of 40 disks were started with positions and velocities determined by a middle-square random number generator (see page 975), and their motion was followed for about 10 collision times—after which roundoff errors in the 64-bit numbers used had grown too big. From the point of view of this book the randomization seen in these pictures is in large part just a reflection of the fact that a random sequence of digits were used in the initial conditions. But what the discoveries in this book show is that such randomness can also be generated without any such random input—finally clarifying some very basic issues in statistical physics. (See page 441.)

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From Stephen Wolfram: A New Kind of Science [citation]