La Physique au Canada juillet/août 1996 / Physics in Canada July/August 1996 by Derek Paul, Professor Emeritus, Physics Dept., University of Toronto, Toronto ON, M5S 1A7
Being 65 last year, I was obliged to bid a formal farewell to my good colleagues in June 1995 and adopt the cognomen Emeritus. But I felt no less a physicist as I entered my 43rd year in physics. At the formal farewell generously provided by my department I expressed several good wishes to those still in harness, and the hope that they would see their way to putting science back into context, which my generation has largely failed to do.
The context of science should be the setting in which all the world’s activity takes place and not the confines of a narrow speciality — but I am getting ahead of myself.
Physics at the time of Newton was called natural philosophy, meaning that it was the part of thinking having to do with the natural world. As such it stood in the context of all thinking or all philosophy. Throughout my years as a physicist I have had difficulty comprehending the traditional discipline of philosophy, a weakness of mine that I was not keen to reveal. Since twentieth century physics carries with it a great element of its own home-grown philosophy, it had seemed good enough to leave the puzzles of the wider discipline alone until some future date. However, good fortune recently brought me new insights into this question, largely through the legacy of Jacob Bronowski1. In his Silliman lectures,2 published posthumously, he outlines a philosophy that provides sound groundwork for the modern scientist as well as for all humankind. He claims in those lectures to be attempting a job that Kant had set himself but had abandoned.
Because Bronowski’s theme is central to what I want to develop further, I shall summarise it here. He begins by discussing how knowledge is acquired and stresses that inference plays a central role even in the most important of the direct senses, that of vision3. The relevance of this reappears when we come to try to understand how we deduce and know things. He next discusses language and communication, and consciousness that can see the outside world in categories, including ourselves “as if we were objects in the outside world”. Because human language4 takes on a formal grammatical structure there is a close analogue to formal mathematical systems. Because we can see ourselves sometimes as an outside person, there is a dualism between mind and body, and a link between paradoxes in language and in mathematics.
Under the chapter title Knowledge as Algorithm and as Metaphor Bronowski next deals with formal mathematical systems, especially as applied to the sciences, and with the processes of scientific discovery, which I hardly need to expound for physicists. Here also he introduces his one major hypothesis, “that the world is totally connected: that is to say, that there are no events anywhere in the universe that are not tied to every other event in the universe.” – which is not to say that anyone is going to be able to make all the connections; on the contrary, to do anything in science we must make a cut, or a series of cuts, to limit the scope of the investigation, and we achieve this by discarding temporarily what seems to be irrelevant. Having done this, theoretical science becomes a mathematical system, designed to describe the known observations, and following the patterns of axioms and theorems of pure mathematics.
As long as the theory leads to no contradictions with its observational basis, it is selfconsistent, and thus provisionally sufficient.
We now come to questions of paradox in both language and mathematics, and to Gödel’s incompleteness theorem5. Logical paradox arises from the fact that any non-trivial formal language can include statements that refer to statements of that language6. This is the problem of self-reference in logical systems. With regard to Gödel’s theorem, Bronowski states: “… it is the axiomatisation of the system which produces the trouble. Nature is not a gigantic formalizable system. In order to formalize it we have to make some assumptions which cut out some parts. We then lose the total connectivity. And what we get is a superb metaphor, but it is not a system which can embrace the whole…”
Most thoughtful physicists in this day and age have probably concluded independently that there are limits to knowledge about the universe, and it is likely that they reached this conclusion by quite other routes than Bronowski’s. But it is interesting that the hypothesis of interconnectedness, linked to the incompleteness theorem, brings us to the same conclusion. That science cannot bring us to a complete knowledge of the natural universe is not a cause for depression or pessimism. The boundaries. of scientific knowledge can in principle always be pushed onwards or outwards to encompass a wider truth.
The process of learning about the universe is essentially creative. It depends on the essential difference between the human mind as it is and the human mind thought of as a digital computer – which it isn’t. Because we use our brains to learn about how our brains work, the problem of understanding creativity is itself one of self-reference, and is subject to paradox.
This, in brief, is a scientific foundation for late twentieth-century philosophy, not necessarily complete up to this point, though is seems to be self-consistent.
Furthermore, this philosophy will be subject to change, because new knowledge may tear down and replace its foundations. I now hark back to my own past discomfort with the traditional discipline of philosophy. What was it that was so difficult? Why did Kant abandon the task he had set himself? Kant would have had to work with the scientific and other knowledge of his day and would likely have come to very different conclusions from Bronowski’s. This is what makes it difficult for us to understand Kant. We cannot hope to understand the philosophers of old without immersing ourselves in their whole context of knowledge, and shutting out the newer knowledge that they did not have.
The Naturalistic Fallacy
All of the above served to reconcile me to the discipline of philosophy, as well as expanding the philosophy that (I have long maintained) physics implicitly carries with it. But it doesn’t end here. The interconnectedness of the universe – a premise for which I have no contrary evidence, though it may turn out to be a restricted principle rather than a completely general one – should have implications that go far beyond the laboratories of scientists.
It seems easy for scientists to escape social responsibility by taking refuge under the umbrella that claims science is neutral, that is, value-free. There is indeed a certain objectivity in such statements as “the speed of light is independent of the frame of reference” or, “the percentage of carbon dioxide in the atmosphere is rising at such and such a rate”. These statements are objective in the sense that they are the results of measurements and, provided appropriate uncertainty is attached to them, they fulfil all normal requirements for statements to be accepted as true. But truth and neutrality are different concepts. The truth of the statement above about the speed of light forced scientists many years ago to abandon the concepts of space-time that had held sway from Galileo to the beginning of this century. The statement about carbon dioxide is just one of several analogous statements of the kind that have driven the Royal Society of Canada to launch a major investigation of global climate change7. Presumably the motivation is that climate changes may affect the human race in disastrous ways, and that such a program might provide useful information leading to strategies for avoiding disaster. Evidently science is not always neutral. It is carried out by scientists, and these people have established concepts of disaster that should be avoided (not to mention more positive concepts, for the moment).
The naturalistic fallacy is the statement that the facts of science do not lead naturally to courses of action of social or moral import. Bronowski’s rejection of the fallacy is based upon the principle of interconnectedness and an attempt at a logical deduction from that premise which connects the scientist to the whole universe, and thus gives her or him a special responsibility. I also reject the naturalistic fallacy, but in addition I think its converse cannot be logically derived from the principle of interconnectedness, as Bronowski would have liked to have it.
To understand this it is useful provisionally to accept the naturalistic fallacy and its consequence that science is neutral. Under such an assumption there would, for example, be not a priori moral obligation to publish the findings of research, except to satisfy granting agencies, employers, or others directly involved8. Suppose, now, that a scientist makes an important discovery, say, on the dangers of global warming, and conceals the findings, what does this imply for the interconnectedness of the events in the universe? The kind of event we are here dealing with — the concealment of scientific truth — is a product of human consciousness, and Bronowski didn’t say specifically whether events of this type are included in the interconnectedness of the universe, though I fancy he meant to include them. Consciousness is a latecomer in the process of evolution; to study it we must use our conscious brains. Self-reference and paradox are built in to this process. Does that mean that we can go no further in this matter?
As an alternative to trying to resolve the question of the naturalistic fallacy logically, I will tell you about two of my own experiences arising from my 42 years in physics and what I have been able to make of them. The first was that I often had to teach thermodynamics to students of the life sciences, and I soon came to the conclusion that the only meaningful approach is the statistical one9. This approach makes obvious the relationship between entropy and disorder, and it facilitates an understanding of biological processes generally at a very fundamental level. It was through this teaching that I arrived at a definition of living systems which I have used widely since then, and which neither biologists nor medical people have objected to: a living system is one that of its own accord strives to maintain its entropy between appropriate limits. The entropy of the whole biosphere must also be held within limits if species are to survive, which leads on to the next points, and connects at once with scientific responsibility.
My second experience was the result of being asked in 1987 to write a review paper on Peace Research10. At that time I had little experience of peace research from a professional point of view, and I felt obliged to examine the values underlying research in general. I concluded that the values are often mixed but that, with peace research, the predominant underlying value is self-referent – life itself.
These two experiences open up an approach to viewing scientific responsibility that avoids having to attempt rejection through logical arguments the thesis of the neutrality of science, or the naturalistic fallacy. With the new approach, it ceases to be worthwhile to argue about them, as, likely, there is some freedom of choice in viewing these matters, which argumentation, because of inherent paradoxes, will not remove. Life and entropy, however, are scientific concepts that can be most valuable guides to human behaviour. It would appear that evolution has led to the development of more and more sophisticated life forms, especially homo sapiens. To preserve this degree of order, to preserve a level of global entropy within suitable limits, and also of local entropy, dictates preferences in social behaviour and in decision making. Therefore, even if scientific statements are neutral by themselves, they carry social imperatives when life itself is regarded as a value11. The broad awareness of this on the part of scientists is what will put science back into context.
In his last Silliman lecture Bronowski touches upon Law and Individual Responsibility, in which he recounts his interchange with Linus Pauling who asked why he should be bothered with the abstruse (philosophical) matters the other was raising. Bronowski’s reply to Pauling is worth noting: “ … you of all people are a man who has demonstrated that a scientist is not merely (one) who makes profound imaginative discoveries, but … who regards the world as a whole … the only man who has won … Nobel Prizes, … for chemistry and … for peace. And you ask me why the change in the world picture of science should affect scientists. You, Pauling, are the personal demonstration of the fact that a scientist is a complete person and that he can no more talk about chemistry without thinking of peace than he can talk of peace without thinking about chemistry.”
My thanks go first to Professor Bill Vanderburg of the Department of Industrial Engineering, University of Toronto, for introducing me to his expression putting science back into context.
Thanks go to Eric Fawcett and Terry Gardner who kindly read the draft typescript and made useful comments.
- Jacob Bronowski, The Origins of Knowledge and Imagination, Yale University Press 1978). This book was published four years after Bronowski’s death, and appears to be close to a verbatim version of the six lectures it encompasses.
- The Silliman lectures are given at Yale University.
- Signals received by the eye are, by its very nature, granular. However, images are not built up by the brain by scanning in the way an image is put onto a TV screen. Connections from the rods and cones of the eye to the brain are complex, and arranged so as to infer outlines from very small amounts of information. Thus the brain infers form very rapidly and confirms its picture, or corrects it, as more information comes in.
- Human language has been broken down into words, a process that requires the abstraction of many concepts, for example the distinction between cat and predator. Such a distinction does not appear in animal languages, in which the sounds consist of sentences; thus the sound for car, if we are talking about mouse language, would be a sentence (in fact an alarm or instruction) to beware of a cat-predator. Languages of words, with grammar, therefore postdate primitive languages of sentences or instructions, and represent the development of consciousness.
- Kurt Gödel’s incompleteness theorem, proof published in 1931, states that if you have a non-trivial self-consistent formal axiomatic system, with formal symbols and rules of manipulation, there are statements S within the system such that neither S nor not-S can be proved within the system.
- Perhaps the most often stated paradox in language is the one which can be found in the first Epistle to Titus, verse 12: “Even one of their own prophets has said, Cretans are always liars…” The effect of self-reference is very obvious in this example.
- The Canadian Global Change Program was set up in 1985. Its first Assembly took place in April 1990 (Delta 1, no. 2, Winter 1990).
- The fact that most scientists today accept their obligation to publish their findings does not invalidate my example; the obligation is often connected with granting, and is also a western cultural development of the last hundred years.
- The last time I was called upon to do this I could not find one elementary physics text treating thermodynamics in this way. Some of my lecture notes followed the Intermediate level text by R.K. Hobble (John Wiley, 1978), chapter 3.
- “Peace Research” in the Proceedings of the Thirty-Seventh Pugwash Conference on Science and World Affairs</cite, Gmunden, Austria, 1987.
- Most emphatically, this remark applies to all life, not merely human life.