As was noted earlier, the traditional conception of what we call mechanical computation or computation by machine relies on a purely kinematical conception of mechanics. It entirely omits any notion of force and focuses attention only on abstract states and motion between them. In this it follows a trend in mechanical formalism that moved away from considering forces and spatial motions to considering mainly Hamiltonian motion through abstract spaces, with no mention of either the central notion of force or the key notion of mass (cf. Hermann 1990, Sussman & Wisdom 2001).

This disconnect between mechanical computation and mechanics comes closest to being bridged in the related field of information theory, in which some authors have viewed information content as a type of mass measure (Manthey & Moret 1983) and have produced formal relations between information content and thermostatic theories of entropy (Chaitin 1975). These ropes tossed across the gap lack tether to the notion of force and still leave the crossing perilous.

Let us now reconsider the notion of computation from the mechanical point of view, to treat “mechanizability”—viewed in terms of machines—as mechanizability—viewed in terms of mechanics. We seek to understand the notion of effectiveness as involving not just abstract kinematics but also those fundamental concepts that distinguish mechanics from geometry, especially the concepts of rate of motion limited by limits on force and bounds on the rate of work.

Discussions in previous chapters have touched on these ideas already.

The preceding treatment of reasoning indicates how we can interpret psychological rationality in terms of mechanical processes. Let us now look at the ways in which mechanical concepts enter into characterizing forms of economic rationality.

Limits on rationality

The difficulty and slowness with which real agents change their mental state constitutes one of the most evident limitations on rationality. As noted earlier, we can see reflections of the mechanical connection between momentum and force in “the more you need to change, the more you have to force yourself,” “the more you know, the harder it is to change your mind,” and other truisms of popular psychology. We can read the first of these truisms as stating a monotonicity relation between the size of changes and the size of the required forces and work done, and the second as stating a monotonicity relation between the mass and the force required for given changes. Notions of monotonicity and proportionality among the numerical magnitudes of momentum and force are familiar in traditional mechanics, but how do these apply in the discrete mechanical setting?

A mechanical interpretation of thinking also naturally relates slowness of change to inertia. From the same perspective, the unreality of ideal rationality appears because when we determine actions by finding the maxima of an expected utility function generated by instantaneous beliefs and desires, large changes can come from small impulses.

The preceding chapters presented the beginnings of a mathematical and mechanical theory of mind.

We began by examining the curious divorce between mechanical understandings of mind and nature that occurred when natural philosophy developed mathematical techniques useful in characterizing physical mechanics but inapplicable to mental mechanics. The mathematical study of mental materials developed separately, but with the key mathematical theories of logical and economic rationality lacking any connection to mechanics. The mechanical reconciliation of mind and nature began to take shape only when the development of artificial computers enabled construction of artificial minds precise and concrete enough to relate to a new rational mechanics broad enough to encompass mental as well as physical materials. The reconciliation promises not only to open traditional philosophical questions to new forms of technical analysis, but also to provide a new formal vocabulary for describing agents of limited rationality and for engineering computational and social systems based on such agents.

We then examined two sides of the reconciliation of physical and mental mechanics. On the physical side, we recast the axioms of modern rational mechanics so as to cover discrete mechanical systems and their hybrids with physical mechanical systems.

The preceding development of mental mechanics does not require determinism of mechanical systems. It instead requires only that motion satisfy mechanical relationships independent of determinism requirements.

The preceding chapters also illustrated several sources of possible indeterminacy. Reasoning, whether habitual or deliberate, can produce indeterminism when several reasons apply at the same instant, requiring serialization or conflict resolution. In addition, rational deliberation can result in several possible self-constructions from reasoning rules; conservative update in response to reasoned changes can follow multiple resolutions; and volition can encompass multiple choices of action on the basis of the same desires and intentions. These sources of mechanical indeterminism complement the forms of indeterminism acknowledged in traditional mechanics, including situations of indeterministic collapse and bifurcation considered in continuum mechanics and the pervasive indeterminacy of quantum physics. All of these forms of indeterminacy represent theoretical allowances of multiple possibilities that stand separate from uncertainties arising from the practicalities of measurement connected with repeatability and resolution of measuring apparati.

From the viewpoint of psychology, mechanical indeterminism generates what one can call a “kinematical” notion of uncertainty, in which one seeks to measure the amount of indeterminism, or degree of uncertainty about predictions introduced by indeterminism. In the simplest terms, qualities of motion shared by all possible histories represent certain predictions about motion, while qualities exhibited by some histories but not by others represent uncertain predictions about motion. The kinematic conception of uncertainty provides means for comparing these degrees of certainty and uncertainty in quantitative terms.

Understanding psychology and economics in mechanical terms requires looking at specific concepts of psychology and economics from the mechanical point of view. If we look to the literature, however, we find that the cognitive sciences study a wide range of possible or hypothesized psychological organizations as explanations of human thought. For example, the ideally rational agents of economics have one kind of mind, a kind very different from almost all known human minds. But even among humans, individual minds have very different characters, exhibiting different levels of intelligence at different tasks, different temperaments, different degrees of adaptability, and so on. The well-known Myers–Briggs test (Myers & Myers 1980), to give another example, sorts minds into sixteen well-populated classes. These classes correspond to recognizable and common types of personal character, types that give some insight and enable reasonable, though not perfect, predictions of individual behavior.

It does not take deep reflection to realize that if we are already on page 225 and just starting the mechanical examination of psychology and economics, we cannot hope to examine all the concepts of all hypothesized mental organizations in this book, no matter how long, without exhausting all patience. I therefore undertake to examine the structure and mechanical nature of some special kinds of minds that serve to illustrate the mechanical nature of thinking, in part to open the special classes to mechanical investigation, and in part to suggest ways of understanding other kinds of minds in mechanical terms.

Many theories of psychological organization posit both long-term and short-term memories. The long-term memories serve as persistent (but not necessarily perfect) repositories of knowledge, skills, and other elements of human capital; the short-term memories serve to store the fleeting facts of present experience, which then either are discarded or incorporated into long-term memory.

The notion of memory in these theories concerns the function of memory structures in thinking, but this function has mainly to do with issues of persistence, not with the content of memory. In common theories, memory content is assumed to contain elements of what we can call the outlook, point of view, or attitudes of the agent, as well as habits, skills, and other aspects of mind.

This chapter examines the notions of memory and outlook from the mechanical point of view, without adopting a position on the exact set of mental elements that define outlook. The fundamental identifications explored take mental outlook to constitute mental position, and memory to consist of both mental mass and persistent aspects of internal configuration reflected in the position. Thinking of memory as mass and configuration fits well with everyday usage. Mass persists across motion, and this also holds for long-term memory; some aspects of configuration, such as the support one belief has in others, also persist and can be used in explaining behavior. Thinking of mental attitudes as positions also finds a good home in everyday usage.