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 it is 65,536 processors, each capable of associating both with its neighbors and with an individual data point [Boghosian, 1990].

Giant and expensive parallel computers are an exception to the overall trend toward small personal computers. An emerging alternative to the parallel-processor supercomputers is distributed computing. Ten to twenty high-performance workstations (e.g., Suns) are used simultaneously, via message-passing software and a local area net, to run different parts of the same problem. Effectively, the workstations become a virtual parallel computer, and they do so at night or in the background so that their metamorphosis disturbs nobody.

The acceleration of processing capability is generating opportunities for scientific projects that were previously impossible. Modeling can encompass complex systems (e.g., econometric models) and three dimensions (e.g., global climate models). Inversion can involve huge datasets (e.g., Human Genome Project) and three-dimensional, non-invasive tomographic imaging (e.g., CT scans, tomography of Earth’s interior). Image analysis of immense datasets is feasible (e.g., astronomy).

For most scientists, personal computers are sufficient and in fact superior to supercomputers. Scientists value control, and having one’s own computer, with a simple enough operating system to eliminate system managers, provides that control. Indeed, the major obstacle to further expansion of distributed computing may be the reluctance of individuals to relinquish a fraction of their supervision of their own computers.

Neither large nor small computers have removed the need for a vintage type of scientific calculation: back-of-the-envelope calculations. Computers have 8-digit or more accuracy, but the backof-the-envelope calculation recognizes that the reliability of many calculations depends instead on huge uncertainty in one or two of the needed variables. Even the most advanced computer is naïve about pivotal concerns such as estimation and the difference between random and systematic errors. The scientist must provide the missing sophistication, either explicitly in a back-of-the-envelope calculation or implicitly in the data input to a computer algorithm. Chapter 2 addresses some of these concerns. Late at night, sharing a Coke, feeling guilty about its 130 calories, my wife and I recalled the cryogenic diet, which we had seen long ago in a Journal of Irreproducible Results. Total dietary impact is not 130 calories, but 130 calories minus the calories required to heat the liquid from ice-cold (0°C) to body temperature (~35°C). A calorie, I knew from recently preparing an Oceanography lecture, is the heat required to raise 1 cc of water 1°C. A back-of-an-envelope calculation showed the benefit of a 12-ounce ice-water diet:

12 oz x ~35g/oz x 1 cc x 35°C x 1 calorie/cc°C ≈ 13,000 calories!

We realized that a ‘Popsicle diet’ (2 6-oz Popsicles) would be even better: 13,000 calories for warming from 0°C to 35°C, plus 32,000 calories (400 cc x 80 calories/cc) heat of transformation from ice to water! Clearly, there was a problem, and not one that a calculator or computer could solve. Days later, my wife found the answer: oceanographers use ‘small’ calories (1 g heated 1°C), but dietary calories are ‘large’ calories (1 kg heated 1°C). Neither anticipated the loss of sleep that a factor of 1000 could cause in a couple of hapless scientists. When using calculators and personal computers, extra attention is needed concerning significant digits. Significant digits, or significant figures, are an implicit statement about the precision of a measurement. In general, a measurement of completely unknown precision is virtually worthless.