Why does atmospheric pressure decrease, the higher you go? Why does sodium chloride, but not silver chloride, dissolve in water? Why do complex things break down, fall apart, decay? An important element of the answer to each of these questions is provided by statistical mechanics, a kind of physical thinking that puts a probability distribution over the various possible states of the microscopic constituents of a system—over the positions and velocities of its molecules, for example—and reasons about the system’s dynamics by aggregating the microlevel probabilities to determine how the system as a whole will most likely behave....

Why did Maxwell find his derivation of the velocity distribution convincing or, at least, plausible enough to present for public consumption? Why did a significant portion of his public—the physicists of his day—regard it in turn as a promising basis for work on the behavior of gases?¹ And how did he get it right—what was it about his train of thought, if anything, that explains how he hit upon a distribution that not only commanded respect from his peers but accurately reflected reality? The same distribution made manifest in Otto Stern’s molecular deposits sixty years later?

Under...

The scientific power of Maxwell’s first paper on statistical physics sprang in large part, I have proposed, from an unofficial, alternative argument in which the mysterious premises of proposition IV, the equiprobability of velocity’s direction given its magnitude and the independence of its Cartesian components, function as intermediate steps rather than as foundations. The real foundations are specified in propositions I through III. They are of two kinds: dynamic facts about the physics of collisions, and further probabilistic posits.

The more salient of the new probabilistic posits is the assumption that a molecule is in some sense equally likely, en...

Take an eight-month-old infant; sit it down in front of an urn full of balls, mostly white but a few red. Draw five balls from the urn. The infant will expect your five-ball sample to consist mostly or entirely of white balls; they will be surprised if you draw mostly red balls. It seems, then, that based on their observation of the composition of the urn and the sampling procedure alone, and with no additional information about the frequencies with which balls of different colors are drawn, the infants will act as though the probability of a white ball is...

Equidynamic reasoning is guided, I will assume, by rules of inference—“principles of physical indifference”—that, though perhaps not directly accessible to introspection, make themselves manifest in the kinds of conclusions about physical probability that we are inclined to draw, from an early age, in the absence of statistical evidence.

The simplest of these rules assigns physical probability distributions to the outcomes of physical processes that have what I will call a stirring dynamics. Let me begin with this straightforward case and then treat several more complex cases in turn, building up an account of equidynamics step by step.

Take...

Most stochastic processes are not stirrers. Most gambling devices, even, are not stirrers. The dynamic property of microconstancy is, nevertheless, at the heart of the physical probabilities attached to these other devices (quantum stochasticity aside), and the same patterns of thought that take advantage of microconstancy to infer physical probability distributions over the outcomes of stirring processes may be applied, though with some considerable amendments, to what I will call shaking processes.

Toss a coin as before, but now let it land on the floor, bouncing. The coin’s dynamics may be divided into two parts: a stirring phase, and a...

Adults, like the children tested by Téglás et al. (2007), are at home probabilistically with bouncing balls, or so I suggested in chapter 4: we look at a collection of equally sized balls or other objects careening around a container and infer that each is equally likely, after a given time period, to exit the container, or that such an exit is equally likely to occur by way of any one of multiple equally sized apertures. What rules guide our equidynamic reasoning about bouncing?

There are two broad classes of equidynamic rules of inference that we might apply to the...

Humans’ equidynamic inferences about bouncing balls were explained in chapter 7 as guided by three rules: the microdynamic rule, the equilibrium rule, and the uniformity rule. Considered as a unified inferential strategy, call this trio the equilibrium rule package. The package is used in this chapter to explain other aspects of equidynamic inference, taking care of ends left loose in the earlier discussions of tumbling dice and urn drawings, asking some questions about the complexity of equidynamic inference, and finally making sense of Maxwell’s spectacular success.

The uniform distribution over the outcomes of the canonical die roll described in section...

Statistical physics was not 1859’s only theoretical innovation. On the Origin of Species set alight a star in biology to outshine even Maxwell’s achievement in the physical sciences. As well as its birthday, evolutionary theory shares with statistical physics a deep and essential foundation in equidynamic thinking.¹

This is not obvious, you are thinking. Maxwell’s 1859 paper begins with the postulation of a probability distribution. Darwin’s 1859 book contains no probability distributions, indeed, virtually no quantitative thinking at all. But not all probabilistic thinking is quantitative thinking; some is qualitative or comparative. In this sense, almost all of evolutionary biology...

One long argument—so Darwin aptly described the structure of On the Origin of Species. The premises of the argument are many, but one is perhaps more important than any of the rest. In order to convince his readers of the viability of the gradualist theory of evolution by natural selection, Darwin needed to persuade them that small differences in phenotype could and frequently did have long-term evolutionary consequences, with the more “adapted” phenotype most likely going to fixation at the expense of its slightly less adapted competitors.

He presses this point again and again in his discussion of natural...

Writing about the Battle of the Somme in his widely admired book The Face of Battle, John Keegan reasons as follows about the patterns of wounding from enemy fire:

The chest and the abdomen form about fifty per cent of the surface of the body presented, when upright, to enemy projectiles; skin surface covering the spine and great vessels—the heart and the major arteries—is less than half of that. We may therefore conclude that about a quarter of wounds received which were not immediately fatal were to the chest and abdomen. (Keegan 1976, 273)

Why should the frequency...

Adult specimens of Poli’s stellate barnacle (Chthamalus stellatus)—a common species of a genus mentioned several times in Darwin’s Origin—vary in length from about 0.2 to 1.4cm. Quickly: how will the probability of such a barnacle’s growing to between 0.8 and 0.81 cm in length compare to the probability of its growing to between 0.81 and 0.82 cm? The two probabilities will surely not differ by much, you will reply. Your default (though defeasible) assumption is that the size of the organism is distributed microequiprobabilistically. Natura non facit saltus.

You make this assumption despite your not having the knowledge...

The various inference rules that drive equidynamic reasoning in adult humans, postulated, exemplified, and applied in previous chapters, will here at last be assembled as an organic whole.

The rules of equidynamics may be divided into those that have no dynamical premises (that is, no premises about physical processes) and yield conclusions about physical probability distributions over initial conditions, and those that have dynamical premises and yield conclusions about physical probability distributions over outcomes. The root of the distinction lies in the nature of the premises, since the difference between an initial condition and an outcome is, extreme points aside,...

How do the elements of equidynamics get into our heads? The appearance of mature physical understanding in infants who have yet to take their first steps suggests, as I noted in chapter 4, a role for innate knowledge. Might our brains have been prepared to think equidynamically ahead of time? If so, the perpetrator would presumably be evolution by natural selection.

I am hardly in a position to offer an evolutionary explanation of the implementation of equidynamics in the human mind. But I can prepare the way by speculating intelligently about the advantages offered by equidynamic reasoning in the pre-agricultural...