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 , contracting universe, big crunch, big bang,. . . No problem of what happens before the big bang or after the big crunch; an infinite cycle in both directions. The only concern was that not enough matter had been found to generate sufficient gravity to halt the expansion. But dark matter is elusive, and I was sure that it would be found. Now, however, this elegant model is apparently overthrown by evidence that the expansion is accelerating, not decelerating [Schwarzschild, 2001]. Symmetry and simplicity do not always triumph. Analogy is the description of observed behavior in one class of phenomena and the inference that this description is somehow relevant to a different class of phenomena. Analogy does not necessarily imply that the two classes obey the same laws or function in exactly the same way. Analogy often is an apparent order or similarity that serves only as a visualization aid. That purpose is sufficient justification, and the analogy may inspire fruitful follow-up research. In other cases, analogy can reflect a more fundamental physical link between behaviors of the two classes. Either type of analogy can bridge tremendous differences in size or time scale. For example, the atom and the solar system are at two size extremes and yet their orbital geometries are analogous from the standpoints of both visualization and Newtonian physics. Fractals, in contrast, also describe similar physical phenomena of very different sizes, but they go beyond analogy by genetically linking different scales into a single class.

Analogy is never a final explanation; rather it is a potential stepping-stone to greater insight and hypothesis generation. Unfortunately, however, analogy sometimes is misused and treated like firm evidence. The following two examples illustrate the power of exact analogy and the fallacy of remote analogy. Annie Dillard [1974] on the analogy between chlorophyll and hemoglobin, the bases of plant and animal energy handling: “All the green in the planted world consists of these whole, rounded chloroplasts wending their ways in water. If you analyze a molecule of chlorophyll itself, what you get is one hundred thirty-six atoms of hydrogen, carbon, oxygen, and nitrogen arranged in an exact and complex relationship around a central ring. At the ring’s center is a single atom of magnesium. Now: If you remove the atom of magnesium and in its exact place put an atom of iron, you get a molecule of hemoglobin.”

Astronomer Francesco Sizi’s early 17th century refutation of Galileo’s claim that he had discovered satellites of Jupiter [Holton and Roller, 1958]:

“There are seven windows in the head, two nostrils, two ears, two eyes and a mouth; so in the heavens there are two favorable stars, two unpropitious, two luminaries, and Mercury alone undecided and indifferent. From which and many similar phenomena of nature such as the seven metals, etc., which it were tedious to enumerate, we gather that the number of planets is necessarily seven.” Comparison often leads to a more detailed explanation: classification. Classification can extract simple patterns from a mind-numbing quantity of individual observations, and it is also a foundation for most other types of scientific explanation. Classification is the identification of grounds for grouping complexly divergent individuals into a single class, based on commonality of some significant characteristic. Every individual is different, but we need and value tools for coping with this diversity by identifying classes of attributes. Indeed, many neurobiologists have concluded that people never experience directly the uniqueness of individual objects; instead, we unconsciously fit a suite of schemata, or classifications, to our perceptions of each object (Chapter 6).