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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

  • 3. Science and Time

    Science (or, for the sake of precision and the restriction of our discussion, natural sciences), is intimately connected with the question of "How." Be it when it presupposes laws of causality which exist throughout reality, or when it creates constructs on the basis of probability research (as is done in the quantum theory and elsewhere), science always strives to go from the "What" to the "How." True, in various sciences there is a first stage which is mainly descriptive, of collecting basic information of all sorts, and a later stage of attempting to classify that information. At some point, however - sometimes even in the first stage of observation and examination - an additional question arises, one that turns a mere collection of information or taxonomy into actual science: the question of mutual relationships, of time - and causality - relationships between phenomena.

    The connection between time and science is not just one aspect of science, but is in a sense the very purpose of all sciences. Natural sciences, both in research methods and in results, relate (much more than mathematics does) to the changes which occur in things. Experimental research, as well as scientific speculation, are to a great extent an elaboration of the question, "What will happen to a given object, phenomenon or system if such and such changes occur within it?" In many different areas of science, research deals mainly with question like: "What happens when there is a change in temperature, pressure, velocity, weather," etc.

    Because science deals with changing systems, it necessarily pays a great deal of attention to the basic, constantly changing variable: time. Be it in physical, chemical or biological systems, the constant question is always: "What occurs within this system with the passage of time?" The interlacing of time in every changing system is essential, up to the point of constructing and understanding existing scientific systems as functions (both functions that lend themselves to immediate quantification and mathematical formulation and those that do not reach that stage), one of whose elements is the time that passes in the course of any change in the system.

    However, although the moment of time is a fixed, common element in every scientific formula, it should be stressed that, in fact, scientific time is basically one-directional. The real time in science is always -t or, in other words, the time that has passed. At a first glance, this seems like a refutable statement, for the major success of science (and, to a great extent, the way to examine the validity of scientific theories) is in projecting things into the future. The successful experiment, or the theory which was validated, are those that predict future changes in a given system. A scientific theory which fails to predict the future (within its own limits of precision) is considered refutable or insufficiently validated, and - according to certain approaches in the philosophy of science - scientifically meaningless.

    Nevertheless, it is true that science actually deals with the past alone: i.e., every scientific experiment or observation occurs either in the present (which, for the sake of precision, is the amount of time required to absorb a fact), or in the past - namely, information about what has already happened. A scientific theory is established by applying data, which we know from the past, onto the future. In other words, predictions of the future are, invariably, extrapolations of the past onto the future. On the basis of the presupposition that laws or sets of changes that occurred in the past will continue to operate in the future, we turn the definition of already-observed changes into a prediction of what will happen in the future. This transformation of - into +, the extrapolation of a function that took place in the past on its continuation in the future, is the basis for all science.

    It should be remembered, however, that this conversion of - into +, which is entirely valid in mathematical equations, is in science a mere conjecture. The one-directional flow of time is different, in its essence, from other quantities in which it is truly possible to reverse direction. In this sense, a scientific statement cannot be verified as completely as a mathematical statement, for the truthfulness of any scientific statement can be actually examined only in the past. The past can indeed grant experimental verification of the validity of theories in a great number - even all - of the instances that have occurred; it cannot, however, verify their validity in the future.

    This restrictive statement about science is not intended to belittle it, but only to define its boundaries precisely. For, as we have said, science is, in essence, the search for the reason for things, the ongoing attempt to explain why they occur, or - in terms of time - to find the relationship between what is now and what occurred before. To be sure, the aspiration is to determine a specific causality, namely, a set of assumptions and principles according to which we understand the reasons for phenomena and can therefore predict them. However, science knows for certain only that which has already happened; and the future, as far as it is concerned, is but the extrapolation of the past.

    4. The Question of Purpose as a Non-Scientific Question

    In our day and age, it is accepted to claim that the question of purpose, "What For," is a non-scientific question. Yet this view was not always the prevalent one. The Aristotelian world-view (including its scientific components) is based largely on assumptions of purpose, and this world-view prevailed long after the Middle Ages. It was the influence of Galileo and Spinoza that caused it to be replaced by a causality world-view. Moreover, in the biological sciences of today, there occasionally arise theories which are teleological to varying degrees. Nevertheless, it can be stated that in essence, science does not consider the question of purpose to be scientifically significant.

    Given that the above-mentioned definition of science as based on the question of "How" and as inherently rooted in the past, this view is not only probable, but a necessary outcome of the overall scientific approach. Scientific causality is the discovery of a connection between the past and the present, and it views the future, or whatever does not yet exist, as a direct continuation of the past. The most basic scientific assumption is a modern rephrasing of the ancient verse, "The thing that has been is that which shall be" (Ecclesiastes 1:9), and every scientific philosophy is indeed based on this very presumption.

    However, even if we say that the question of purpose is not a scientific question, that does not negate its inherent validity. The provision that science deals with causality, and not with purpose, is merely a definition of the boundaries and methodology of science, and nothing more. To state that the question of purpose is scientifically meaningless is only to re-state the definition of science and is, in fact, a tautology. It is like making a statement (which, in itself, is true and valid) that the distance between planet Earth and Mars bears no significance for the craft of shoe-making. True as it may be, this statement has to do only with the theory and practice of shoe-making; it does not detract from the validity of questions such as the distance of Mars from Earth, the ways of operating rockets in space, or the problems of bee fertilization. All the problems of astronomy or entomology are still valid, even though they are totally insignificant from the perspective of shoe-making. In making shoes, the shoe-maker does not deal with these or many other issues, and yet this does not prevent him from being interested in them, thinking about them, and even resolving them.

    In the very same way, there are many questions that are meaningless from the perspective of natural science; yet they are, in and of themselves, meaningful.

    Science, as such, does not recourse to questions like "Is such-and-such a girl beautiful?" just as it does not deal with the question of "Is a certain figure congruent to another?" Questions of aesthetics or of number theory are scientifically irrelevant, because the sphere of science, by definition, does not include them. Science is also not concerned with many other fundamental issues in a great variety of fields, cannot deal with them, and certainly cannot resolve them. Neither the natural sciences nor, for that matter, the social sciences can answer the question "What is beautiful?" just as they cannot answer the question "What is just?" Social sciences can surely deal historically with the reasons why regarding certain things or people as beautiful influence society, and they can even try to find a causal explanation for it; similarly, they can discuss the development of the concept of justice in a given society. Yet observation of the past, and even setting principles for future development, relate only to certain, causal information.

    This is the limit of what these sciences can attain, and of their validity. They have no way of determining the criteria of beauty, or the general definition of justice. The psychologist can discuss the reasons for various phenomena which occur within man's psyche - namely, the cause-and-effect relationship between different occurrences - and determine their probable course. The scientist can document acts of cannibalism, make assumptions about the reasons for behaviors and investigate their social or medical implications; but he cannot, as a scientist, establish any opinion about the value of these acts and behaviors. All these numerous questions -aesthetic and ethical, philosophical and, to a great extent also mathematical -are beyond the boundaries of science. By definition, the scientist cannot deal with them within the framework of science, although they may still be fundamental issues of his existence as a human being. The question of purpose, then, belongs by definition to a specific sphere. It is not related to science, and science cannot relate to it, neither to validate it nor to invalidate it.

    Next...


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



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