1. The Apriorist
Maxwell's 1859 deduction of the probability distribution over the velocity of gas molecules –
one of the most important passages in physics (Truesdell) – presents a riddle: a physical discovery of the first importance was made in a single inferential leap without any apparent recourse to empirical evidence.
2. The Historical Way
A close reading of Maxwell's derivation shows that it is more complex, and more enthymematic, than most writers have thought. The true probabilistic premises of Maxwell's inference are identified; their logical and psychological origin remains a mystery.
3. The Logical Way
Could Maxwell's premises be founded in a
principle of indifference? On closer examination, the principle of indifference is a conflation of two distinct principles with very different subject matter. One principle prescribes reasonable epistemic probability distributions in the face of ignorance; the other identifies objectively correct physical probability distributions in the light of information about the symmetries and other causally relevant properties of the physical world. Maxwell's inference appears to be based on a principle of the second sort, which I call an equidynamic principle.
4. The Cognitive Way
Equidynamic reasoning – inferring physical probabilities from non-probabilistic physical properties of a system – is present in very young children. Even children under a year old can think intelligently and correctly about probabilities in urn drawings and in hard sphere systems, that is, systems much like Maxwell's model of a gas.
An examination of everyday reasoning about physical probability reveals the principles of equidynamics, that is, the principles by which we humans, beginning at a very young age, infer physical probabilities from symmetries and other physical facts.
How we reason about wheels of fortune and tossed coins.
How we reason about tumbling dice and drawings of balls from urns.
How we reason about balls bouncing around a box – and about gas molecules.
Further sophistications of equidynamic reasoning in everyday life; then, the theory of equidynamics developed in the preceding chapters applied to explain Maxwell's successful derivation of the velocity distribution.
9. 1859 Again; 10. Applied Bioequidynamics
Equidynamic reasoning was central to Darwin's argument in the Origin; it continues to be central, though for slightly different reasons, to the model-building process in evolutionary biology today.
11. Inaccuracy, Error, and Other Fluctuations
The importance of equidynamics in the development of statistical thinking about error in astronomical measurement. The importance of equidynamics in the modeling of complex systems, with special emphasis on climate models. And more.
Before and After
12. The Exogenous Zone
Default assumptions about the probabilistic distribution of stuff in the absence of information about the generating process. The
perturbation argument from Bigger than Chaos revisited.
13. The Elements of Equidynamics
The principles of human equidynamic reasoning summarized.
14. Prehistory and Metahistory
Where did equidynamic reasoning come from? Why have historians and philosophers of science – and scientists themselves – failed to notice its importance? Toward a new kind of history of science in which cognitive psychology plays a major role.