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.

The common picture of mechanics embodies many unfortunate misconceptions about the nature, scope, and structure of mechanics, with many people having the idea that mechanics consists of applying to physical systems the three axioms stated by Newton. Applying mechanics to psychology and economics requires a firmer theoretical basis than that provided by popular misconceptions. To proceed, we thus must confront and set aside mechanical misconceptions, lest the misconceptions prevent proper appreciation of the contribution mechanics makes to understanding the world. Accordingly, the present chapter examines the nature of mechanics at a high level, reconsidering the content and form of mechanical theories in light of the history of mechanical concepts and mathematical formalisms. This examination highlights the common misconceptions and how they divert one from the proper understanding needed for the following development.

Readers wishing to skip this somewhat philosophical discussion in favor of the development of the mechanical axioms themselves might proceed directly to Chapters 5 and 6, which review the structure and content of the axioms of modern rational mechanics. The modern axioms have enjoyed widespread use for decades among mathematicians studying mechanics and among mechanical engineers, although not in beginning physics textbooks. In contrast to the postulates of popular legend, the modern axioms provide a formal characterization of the notion of force, and reveal the true generality of mechanics in ways that usual textbook presentations do not.

Introduction

This chapter establishes an elementary lower bound on the computational complexity of differentiable functions between Euclidean spaces (actually, differentiable manifolds). The main motivation for this comes from mechanism design theory and as a result, the functions we examine are defined on products of differentiable manifolds and generally have values that are vectors in a Euclidean space. The complexity of computations required by a mechanism determines an element of the costs associated with that mechanism. The lower bound presented in this paper is useful in part because it does not require specification in detail of the computations to be performed by the mechanism, but depends only on the goal function that the mechanism is to realize or implement.

Our lower bound generalizes a bound due to Arbib and Spira (Arbib 1960, Spira 1969, Spira and Arbib 1967) for the complexity of functions between finite sets. The Arbib–Spira bound is based on the concept of separator sets for a function. A little later, in Section 4.1.2 of this introduction and in the next paragraph, we discuss briefly the concept and uses of separator sets. A complete description is given in Section 4.2. This concept is used to determine a lower bound to the number of Boolean variables – variables whose values are either 0 or 1 that the function actually depends on. In the finite case the number of variables can be counted easily. But a counting procedure is too crude to be used for functions between infinite sets.

While reasoning can produce temporary changes of location, learning produces persistent changes of mass or configuration. When someone temporarily responds to instruction or threat but then reverts to an old behavior when the teacher or threat departs, we say that person did not learn anything. Mechanically, we would identify such response with an elastic material that rebounds on relief from compression, but such elastic behavior does not produce the permanent changes we associate with thought. True learning, involving change of mass or deformation of spatial configuration, constitutes plastic changes in the character of the material, including dynamogenetic changes that affect material response. In this chapter, let us consider learning involving changes of habits represented in the mass and changes of configuration represented in position. We distinguish types of reasoning and learning both by the types of changes involved and by the types of forces producing the change.

Accretion

The simplest sort of changes to memory just add new elements to the long-term memory represented by the mass of the agent. Such accretion also represents the effects of the most common sort of inference and learning mechanisms.

Many psychological theories view learning as transfer of information from short-term memory to long-term memory. Different theories of learning posit different means for effecting this transfer. Some theories require transfer to long-term memory of some beliefs in short-term memory simply because they persist long enough in short-term memory.

This book uses concepts from mechanics to help the reader understand and formalize theories of mind, with special concentration on understanding and formalizing notions of rationality and bounded rationality that underlie many parts of psychology and economics. The book provides evidence that mechanical notions including force and inertia play roles as important in understanding psychology and economics as they play in physics. Using this evidence, it attempts to clarify the nature of the concepts of motivation, effort, and habit in psychology and the ideas of rigidity, adaptation, and bounded rationality in economics. The investigation takes a mathematical approach. The mechanical interpretations developed to characterize mechanical reasoning and rationality also speak to other questions about mind, notably questions of dualism and materialism.

More generally, the exposition sketches the development of psychology and economics as subfields of mechanics by showing how one might formalize representative psychological and economic systems in such a way that these formalized systems satisfy modern axiomatic treatments of mechanics. This formalization explicates psychological and economic concepts under study by identifying corresponding properties of certain mechanical systems. Not all concepts of psychology and economics correspond to mechanical notions, and among those that do, not all concepts currently popular in psychology and economics correspond to natural mechanical ones.

Many should find familiar the notions of materialism and reductionism, and should recognize that these doctrines enjoy large numbers of adherents. Fewer need have heard of finitism because of its presently smaller number of adherents, though many should recognize some of its aspects in current scientific and technological trends. This chapter tries to collect and address some of these issues as they relate to a broadened mechanics.

What is finitism?

I use the term finitism to refer to the thesis that the spatial and material world and its behavior are finite, not just finitely axiomatizable (as are the infinity of natural and real numbers) but actually finite in the sense of being composed of a finite number of bits of stuff that may undergo finite numbers of possible changes at each of a set of discrete temporal instants. The finitistic picture of the world in some locality thus resembles an enormous, possibly nondeterministic or probabilistic finite automaton, or more naturally, as a cellular automaton.

One can consider strengthenings of this local notion of finiteness to finiteness of space and time as well. Finiteness of space means that at each instant there are only finitely many places at which events may occur, so that the entire universe looks instantaneously like a cellular automaton. Finiteness of time means that the event world contains only finitely many temporal instants. Thus the strongest notion of finitism, involving both spatial and temporal finiteness, views the entire universe as a gigantic finite automaton.

The mechanical understanding of mind bridges both the gap between the mental and the physical and the gap between the rational and the dynamical. In addition to seeking a better understanding of the relation of mind to body, one specific motivation in pursuing this understanding stems from an interest in finding new means with which to characterize and analyze limits to rationality, a central interest common to psychology, economics, and artificial intelligence. Pursuing this motivation requires facing philosophical problems that have puzzled people for millennia.

Although science has answered some of these philosophical questions about nature and mind, it has left others unanswered. For example, one ancient question concerns determinism, or more generally, lawfulness. Many views hold the mind to exhibit essential freedoms not enjoyed by matter; other views hold the mind subject to various laws of psychology, economics, sociology, and anthropology, and argue about the precedence of these competing regulations. Though scientific progress has inspired some of the competing variants and the development of quantum theories has complicated the stark alternatives contemplated by earlier generations, scientific evidence has done less than one might expect to support or weaken the cases for the fundamental alternatives. The liberty or lawfulness of the mind remains controversial.

Unresolved questions do not represent failures of science. They represent the human condition.

This book presents an approach to the design of decentralized, informationally efficient economic mechanisms. We provide a systematic process by which a designer of mechanisms, who is presented with a class of possible situations by a client (perhaps a private agent, or a government) and with the client's aims and objectives, can produce informationally efficient decentralized mechanisms that achieve the client's aims in that class of situations.

HISTORY

Formal treatment of economic mechanisms and mechanism design began with Hurwicz's paper (1960). The background against which that paper was set included a debate on the comparative merits of alternative economic systems. The main participants in that debate included Lange (1938) and Lerner (1937, 1944) on one side, and von Mises (1920, 1935) and Hayek (1935, 1945) on the other. Hurwicz's paper provided for the first time a formal framework in which significant issues in that debate could be addressed. In a subsequent paper, Hurwicz (1972) treated the formal theory of mechanisms again. The problem is to select a mechanism from a set of alternative possible mechanisms. A mechanism is viewed as a value of a variable whose domain of variation is a set of possible mechanisms. Informational tasks entailed by the mechanism imply costs in real resources used to operate the mechanism (as distinct from the resources used in economic production and other real economic activities). Desiderata by which the performance of a mechanism is evaluated also come into play.