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    Time and Purpose in Science and Mathematics

    Rabbi Adin Even-Israel (Steinsaltz)

    Table of Contents
  • Introduction
  • Mathematics and Time
  • Science and Time
  • Question of Purpose
  • Purpose and Time
  • Purpose and Religion

  • 1. Introduction

    The infinite number of questions asked in every sphere of human culture can be reduced to three general, fundamental questions. These questions contain many more detailed, more elaborately phrased questions, which can be expressed in complex philosophical forms, or spelled out through professional scientific analysis. These questions relate to both the simplest objects encountered in everyday life and to complex cultural or scientific systems, to concrete objects and realities that people cannot help but notice, and to creations of the mind, whose actual existence is uncertain. These three questions may be summarized in very simple words: "What?" "How?" "What For?"

    In more abstract language we can say that "What" is the question about the essence of things, their definition and identity, and their relationship to other entities. "How" is the question of the reason for things: why do things happen the way they do, what brings about their existence, and what causes various events. "What For" is the question of purpose: what is the purpose for which certain things are done, or exist.

    One can cast doubt on the philosophical validity of these questions, and there are surely areas in which these questions can be considered meaningless, as will be explained below. Nevertheless, these three questions are undoubtedly fundamental ones which human beings, qua human beings, ask, and try to resolve.

    These three questions can be analyzed according to many different criteria: historical, epistemological, critical, and others. In this essay we shall examine the relationship between these questions and one component: the time dimension. We shall try to show that time exists in different forms in various fundamental spheres of human consciousness and that, accordingly, the more general questions can be asked only in reference to specific spheres, for beyond them they have no meaning, and therefore cannot be answered therein.

    2. Mathematics and Time

    For the sake of simplicity we shall begin with mathematics which, despite the great variety of subjects it encompasses, is one of the simpler systems, being based primarily on human logic, and almost not at all on empirical proof. (The question of whether mathematics contains an empirical aspect at all is a matter unto itself, related to the theory and philosophy of mathematics.) Within the sphere of mathematics, the moment of time is always 0. In other words, time has neither meaning nor significance within mathematical operations. Of course, one can relate to time and calculate it; but time is calculated just like any other quantity possessing some dimension. Time, in this sense, is treated as a mathematical quantity with nothing unique about it, and time units are calculated like objects, like indefinite terms within the function.

    It can be said that the world of mathematics exists in an eternal present, a state in which neither the past nor the future have any meaning; there is no significance to the questions of what came before, or of what will happen next. Surely, a mathematical function can be an evolving one; but this development of a function occurs not within the dimension of time, but rather within a timeless entity. Thus, because mathematics has no interest in the time dimension, there is also in mathematics no meaning to the question of reason. The question of what causes something or a certain relationship to exist is not a quest for the cause that preceded it, but a search for relationship and order within a system which exists in an ongoing present. Therefore, the concept of causality cannot exist within the world of mathematics, nor does the future and whatever is liable or likely to happen then. The area which mathematics does address is the clarification and exhaustion of the "What," both in the basic sense of definition of things - be they things of this world or creations of the mathematician's mind - and in the sense of determining the relationships between various objects: how they connect with each other, how they are transformed from one form to another. These problems are all basically clarifications of the "What" of the world of numbers and forms: from the various questions concerning number theory that were already addressed by the ancient Greeks, through geometrical problems in any number of dimensions, to complex functions in various algebras. This world, although dealing with relationships between stable and changing things, is entirely outside the dimension of time.


    * Based on a lecture given at the Russian Academy of Sciences, Dept. of Space Sciences, 1988.

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