Science, Mathematics, and Religion

Lecture delivered at the Russian Academy of Sciences, Department of Space Sciences, 1988

THE THREE FUNDAMENTAL QUESTIONS

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 doubts 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.

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 onto 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: 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 within an entity which is timeless. Thus, because Mathematics has no interest in the time dimension, there is also no meaning in Mathematics 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 existing in an ongoing present. Therefore, the concept of causality cannot exist within the world of Mathematics, nor the future and whatever is desired 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 the 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.

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 primarily descriptive, first stage 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 the t moment 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 t, 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 forecasting things into the future. The successful experiment, or the validated theory, are those that predict future changes within 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 to state that science actually deals with the past alone, in the -t of any equation: 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 perceive 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 t moment 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 t of the definition of already-observed changes into a prediction of what will happen in the future. This transformation of -t into +t, 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 as completely verifiable 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 continuation of the past, an extrapolation of -t into +t.

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 is based on the question of How and is inherently rooted in the past, this view is not only probable, but is 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, “That which 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; 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 the 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 a 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 or invalidate it.

THE QUESTION OF PURPOSE AND TIME

The question of purpose is also time-related, although the answers to this question cannot always be arrived at through a fixed mathematical function (linear or other) in which the moment of t features as an element. Nevertheless, the question of purpose is inherently related to the direction of time – namely, to something which does not exist now but which we would like to reach at some future time. Yet, unlike science, time in the question of purpose is, in essence, the future: The purpose is a goal in the future for which a certain thing or person is striving presently. The element of t within the realm of the question of purpose is therefore always +t, from the future to the present. According to this model, the past, too (in explaining past events), is reached by way of extrapolation – namely, by presenting the goal and then taking the necessary amount of steps back into the presently-existing reality.

Let us take, for instance, a goal that certain people may set for themselves: That a spaceship should reach Mars and document certain phenomena there. In this case, goal-definition is the starting point of the project. Setting this goal now creates other, secondary questions; i.e., what instruments are needed in order to record the phenomena in question, to set the space-ship in motion, to communicate the recorded date to the launching point, etc. Each of these needs, too, becomes, in turn, a question; and from here we return to the problems involved in achieving the secondary goals. These problems, too, may contain secondary goals, such as high-resolution films, ways of correcting deviations in the spaceship’s course, ensuring that the vessel has sufficient energy to bring it to its destination, etc.; and again, each one of these goals calls for thinking about the means required to attain it. Thus, the process of planning and thinking goes on and on, until it reaches the point of the present: The existing objects and resources.

The common denominator in this entire line of thinking is operation from the future back into the present – from something that exists, or that we want to exist, in the future, back to current reality. This way of thinking exists not only in the planned act, but also in any kind of goal-setting. Here, too, there is causality – namely, a cause-and-effect relationship; however, here the causality works in the opposite direction, for the result precedes the action, and is the impetus for the action. In the same way, this entire mode of thinking, which begins with the question What For, starts with the purpose, the goal to be reached, and returns from there to the existing reality. Similarly, when goal-oriented thinking surveys the past, it sees it through a projection of the existing reality onto the past.

In such a case, there is a meeting between two systems: The scientific causality system, which works from the past towards the future, converges with the goal-oriented system, which works from the future towards the present. Sometimes (especially where human reality and conscious goal-oriented thinking are concerned) these two systems become one – but not necessarily. In such cases, the process of scientific thinking and exploration deals with the mechanism of phenomena, whereas goal-oriented thinking deals with the purpose and the goals to which those mechanisms lead. When one asks, For what purpose does such-and-such a thing exist, he does not deal with the Howdid it come to be (or, in other words, with the causal mechanism for its existence), but rather with the purpose of that thing, its uses, its usefulness, or its influence on other things.

Is the question of purpose as real and objective as the questions of What and How? Or is it only a projection of our way of thinking upon reality?

Philosophically speaking, any question we ask is a human question, which depicts things in a way that will make them meaningful to our thinking processes. Scientific thinking, by nature, is one way of assuming causality in objective reality; and if one insists, one can say that things happen the way they do, and that personally, he is not interested in why it is so. But since this question is a human question, it is a question that human beings ask because they are human beings: Just as they strive to connect the past and the present in their effort to understand the How, so they strive to connect the future and present in an effort to solve the question of What For.

THE QUESTION OF PURPOSE AND RELIGION

Any religion, by its very essence, deals with the question of purpose. Moreover, the ethical and legal systems of any religion are, in a sense, a projection of the definition of its purpose. Since a certain goal is being set for man’s life, there is a need to take various measures, and to behave and think accordingly, in order to attain that goal. Surely, consensus about the purpose of man’s life – or, for that matter, any other goal set by man – does not necessarily lead to identical means of achieving it. There may be a number of different ways to reach a certain goal, and there may also be some -misleading ways; but the common point is that the primary goals and the secondary ones which stem from them – and which are, as we said, points in the future – operate on and influence life in the present.

The close connection between religion and purpose, then, is not only in that religion is a system based largely on purpose, and that it can therefore be seen as one of the most outstanding examples of this way of thinking. Rather, this connection has additional meaning: It can also be said that any question of purpose is, in essence, a religious question. Questions such as For what does the world exist,: or What is the purpose of society, cannot be neutral questions, because they imply a certain assumption – namely, that there is a certain objective point in reality which is the yardstick for everything else. Such an assumption about the existence of any such entity – namely, a basic point, metaphysical or material, above and beyond which there is no other primary entity – is in itself a religious assumption. In a broad definition not related to any specific religion, this assumption (that there is indeed some kind of a primary reality by which all else is measured and which, in itself, cannot be set by any other values) is the non-theological definition of the Primal Cause.

It should be stressed that this recognition of the Primal Cause in terms of time exists in various religions and, itself, is related to the system of scientific thinking – namely, to the question of causality. However, recognition of the Primal Cause in its future- and purpose-oriented sense is the basis for religious faith of all kinds. Although the question of purpose, the What For, is in essence a religious question, it does not necessitate a religious answer in the common sense of the word. Since it falls within the realm of religion, though, any answer to this question necessarily creates a religious system – namely, a set of principles stemming from an axiomatic premise regarding the reality towards which man strives.

Thus, if the question What is the purpose of society is answered by saying, that its purpose is to bring about a just division of economic resources, this answer creates a kind of religion which may be materialistic in its definition, but religious in its very essence. Whoever states that the purpose of man’s life is to eat caviar, drink vodka and enjoy other people’s suffering, also creates a religion – one which is both materialistic and hedonistic, and entirely atheistic. For here, too, there is the central religious element: Faith in a certain supreme, absolute value which is not questioned and which determines everything else. Such a religion may be quite unpleasant, and its god rather base, but it, too, is a religion, whose icon is, perhaps, the emptied bottle of liquor.

In any way that the question of purpose may be phrased – be it as a philosophical question: What is the purpose of existence?, or as an existential one: What is the purpose of my life?; and even when it is phrased more rudimentarily: What is the purpose that I strive to achieve in my life? – whenever such questions are asked, the questioner is launched into the third time-system, in which there is real meaning to +t, in which it is the future that determines the past. Or, in other words, into the realm of religion.

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