Eddington’s New Pathways

A.S. Eddington New Pathways in Science: The Messenger Lectures, 1934, Cambridge University Press, 1935


“Does the harmony which human intelligence thinks it discovers in Nature exist apart from such intelligence ? Assuredly no. …What we call “objective reality” is, strictly speaking, that which is common to several thinking beings and might be common to all; this common part, we shall see, can only be the harmony expressed by mathematical laws.”

POINCARE, The Value of Science


As a conscious being I am involved in a story. The perceiving part of my mind tells me a story of a world around me. The story tells of familiar objects. It tells of colours, sounds, scents belonging to these objects; of boundless space in which they have their existence, and of an ever-rolling stream of time bringing change and incident. It tells of other life than mine K.tcy [?] about its own purposes.

As a scientist I have become mistrustful of this story. … One of our first tasks must be to try to understand the relation between die familiar story and the scientific story of what is happening around us.

Scientific thinkers generally agree that the channel of communication between the external world and man’s consciousness is severely limited in this way; but, whilst giving intellectual assent, they do not always adjust their scientific outlook to correspond. They are strangely reluctant to doubt the assertions of the familiar story teller even when it is evident that he is talking through his hat.


Broadly speaking the task of physical science is to infer knowledge of external objects from a set of signals passing along our nerves. But that rather underrates the difficulty of the problem. The material from which we have to make our inferences is not the signals themselves, but a fanciful story which has been in some way based on them. It is as though we were asked to decode a cipher message and were given, not the cipher itself, but a mistranslation of it made by a clumsy amateur.

It is the inexorable law of our acquaintance with the external world that that which is presented for knowing becomes transformed in the process of knowing.

The solution of a cryptogram is found by studying the recurrency of the various signs and indications. I do not think we should ever have made progress with the problem of inference from our sensory experience, and theoretical physics would never have originated, if it were not that certain regularities and recurrencies are noticeable in sensory experience. We call these regularities of experience laws of Nature. When such a law has been established it becomes also a rule of inference, so that it helps us in further decipherment just as in solving an ordinary cryptogram.

I do not know how a logician would classify the process of solving a cryptogram. The decoded message is inferred from the cryptogram, but the method of inference can scarcely be described as logical deduction. In saying that the scientific description of the external world is inferred from our sensory experience, and that the entities of the physical world are inferences, I use the word inference in this broad sense.


But, it may be suggested, if all observation is reduced to coincidences and pointer-readings, can we ever infer from it anything but a system of relationship of coincidences and pointer-readings? In one sense the answer is No. But if the question is put in the form ‘ * Can we by manipulating pointer- readings ever arrive at a knowledge which does not smell of pointer-readings?” I suggest that it might equally well be asked “Can an artist by manipulating paint ever achieve a creation which does not smell of paint ? ” But I do not wish to set this question aside lightly, for it goes to the very heart of the difference between the new and the old scientific outlook. We shall see later that a scheme of relationship, or a structure, has a significance which can be abstracted from the intrinsic nature of that which is the subject of the relationship. The structure is the object of our search, and when we have reached knowledge of the structure we can disregard the scaffolding by which we reached it. It does not lessen the dignity of the structure that its elements are pointer- readings which after all is only the story teller’s name for them.


The rejection of determinism is in no sense an abdication of scientific method. It is rather the fruition of a scientific method which had grown up under the shelter of the old causal method and has now been found to have a wider range. It has greatly increased the power and precision of the mathematical theory of Observed phenomena. On the other hand I cannot agree with those who belittle the philosophical significance of the change.


[The] measurement of probability employed in mathematics and physics has an altogether different basis, as we shall see. …

[There] is no reason to think that these probabilities can be graded systematically in order of magnitude. It has been maintained by some writers that probability always has a numerical measure even when the word is used in this elementary way; and that the beliefs of a right-thinking person could ideally be arranged in a unique sequence in order of intensity. I rate this on a level with the view that to a person with a right sense of humour all jokes can be arranged in a unique sequence in order of funniness.

The probability is p that an event a has an outcome e has to be translated:

The event a is a member of a certain class of events A, and the proportion of events in the class A which have an outcome e is p.

[It] is often assumed that certain events will in the future occur with the same frequency as they have been observed to do in the past. The study of probability is often distracted by a discussion as to whether we have any proof of these assumptions. But the function of probability theory is to utilise such information, not to supply it. When once it is realised that there is nothing illogical in a numerical probability being itself only probable, we can utilise any reasonable belief as to the frequency of events and so determine “a reasonably probable probability”; just as we may use a reasonable belief as to the cause of the recession of die spiral nebulae and so determine a reasonably probable cosmical constant. …

If we maintained, as some have done, that scientific (numerical) probability is the basis of all rational belief other than strict logical deduction, thereby annexing the whole subject of inference to the mathematical theory of probability, it would be necessary to go into the matter further. But that is not the position here adopted.


According to the principle of relativity we can only observe and have knowledge of the relations of things. So when we refer to the properties of any object we must always have a comparison object in mind. …


“There has been a great deal of speculation in traditional philosophy which might have been avoided if the importance of structure, and the difficulty of getting behind it, had been realised. For example, it is often said that space and time are subjective, but they have objective counterparts; or that phenomena are subjective, but are caused by things in themselves, which must have differences inter se corresponding with the differences in the phenomena to which they give rise. Where such hypotheses are made, it is generally supposed that we can know very little about the objective counterparts. In actual fact, however, if the hypotheses , as stated were correct, the objective counterparts would form a world having the same structure as the phenomenal world In short, every proposition having a communicable significance must be true of both worlds or of neither: the only difference must lie in just that essence of individuality which always eludes words and baffles description, but which, for that very reason, is irrelevant to science.”

BERTRAND RUSSELL, Introduction to Mathematical Philosophy, p. 61. I

Let us suppose that a thousand years hence archaeologists are digging over the sites of the forgotten civilisation of Great Britain. They have come across the following literary fragment, which somehow escaped destruction when the abolition of libraries was decreed.

‘Twas brillig, and the slithy toves
Did gyre and gimble in the wabe,

All mimsy were the borogoves
And the mome raths outgrabe.

This is acclaimed as an important addition to the scanty remains of an interesting historical period. But even the experts are not sure what it means. It has been ascertained that the author was an Oxford mathematician; but that does not seem wholly to account for its obscurity. It is certainly descriptive of some kind of activity; but what the actors are, and what kind of actions they are performing, remain an inscrutable mystery. It would therefore seem a plausible suggestion that Mr Dodgson was expounding a theory of the physical universe.

Our account of the external world (when purged of the inventions of the story teller in consciousness) must necessarily be a “Jabberwocky” of unknowable actors executing unknowable actions. How in these conditions can we arrive at any knowledge at all? We must seek a knowledge which is neither of actors nor of actions, but of which the actors and actions are a vehicle. The knowledge we can acquire is knowledge of a structure or pattern contained in the actions. [ think that the artist may partly understand what I mean. (Perhaps that is the explanation of the Jabberwockies that we see hung on the walls of Art exhibitions.) In mathematics we describe such knowledge as knowledge of group structure.

It does not trouble the mathematician that he has to deal with unknown things. At the outset in algebra he handles unknown quantities x and y. His quantities are unknown, but he subjects them to known operations addition, multiplication, etc. Recalling Bertrand Russell’s famous definition, the mathematician never knows what he is talking about, nor whether what he is saying is true; but, we are tempted to add, at least he does know what he is doing. The last limitation would almost seem to disqualify him for treating a universe which is the theatre of unknowable actions and operations. We need a super-mathematics in which the operations are as unknown as the quantities they operate on, and a super-mathematician who does not know what he is doing when he performs these operations. Such a super- mathematics is the Theory of Groups.

It is sufficient to say that what physics ultimately finds in the atom, or indeed in any other entity studied by physical methods, is the structure of a set of operations. We can describe a structure without specifying the materials used; thus the operations that compose the structure can remain unknown. Individually each operation might be anything; it is the way they interlock that concerns us. The equation P 6 P a =P c [I need to fix this!] is an example of a very simple kind of interlocking.The mode of interlocking of the operations, not their nature, is responsible for those manifestations of the external universe which ultimately reach our senses. According to our present outlook this is the basal principle in the philosophy of science.

This mathematical way of describing everything with which we deal emphasises, perhaps inadvertently, an important physical truth. Usually when we wish to consider a problem about a hydrogen atom, we take a blank sheet of paper and mark in first the proton and then the electron. That is all there is in the problem unless or until we draw something else that we suppose to be present. The atom thus presents itself as a work of creation a creation which can be stopped at any stage. When we have created our hydrogen atom, we may or may not go on to create a universe for it to be part of. But the real hydrogen atoms that we experiment on are something selected from an always present universe, often selected or segregated experimentally, and in any case selected in our thoughts. And we are learning to recognise that a hydrogen atom would not be what it is, were it not the result of a selective operation performed on that maze of interrelatedness which we call the universe.


His difficulty rather suggests that a cyclic scheme of knowledge with which science has familiarised us is not yet appreciated in philosophy. I have formerly [ The Nature of the Physical World, p. 262.] illustrated the nature of a cyclic scheme by a revised version of “The House that Jack Built” which instead of coining to an end repeats itself indefinitely ” . . .that worried the cat, that killed the rat, that ate the malt, that lay in the house, that was built by the priest all shaven and shorn, that married . . .”. Wherever we start in the cycle we presuppose something that we reach again by following round the cycle. The scheme of physics constitutes such a cycle; and equally we may contemplate a wider cycle embracing that which is beyond physics. Starting at the point of the cycle which corresponds to our individual perceptions, we reach other entities which are constructs from our perceptions. From these we reach other entities, and so on for a number of steps. When we seem to have travelled a long way from our starting point, we find that our perceptions (or more strictly the recurrencies in our perceptions) reappear as constructs from the last-reached entities. The fact that we return by a circuit and not by retracing our steps secures that our adventure is an extension of knowledge and not an excursion in tautology. By the method of Chapter xii we can extract the group structure from the cycle and so express the same truth symbolically without a formal presupposition if we prefer.


Modern science, in so far as I am familiar with it through my own scientific work, mathematics and physics make the world appear more and more as an open one, as a world not closed but pointing beyond itself. . . . Science finds itself compelled, at once by the epistemological, the physical and the constructive-mathematical aspect of its own methods and results, to recognise this situation. It remains to be added that science can do no more than show us this open horizon; we must not by including the transcendental sphere attempt to establish anew a closed (though more comprehensive) world.


[I Intend to read this!]

I think it is insufficiently recognised that modern theoretical physics is very much concerned with the study of organisation; and from organisation to organism does not seem an impossible stride. But equally it would be foolish to deny the magnitude of the gulf between our understanding of the most complex form of inorganic matter and the simplest form of life. Let us suppose, however, that some day this gulf is bridged, and science is able to show how from the entities of physics creatures might be formed which are counterparts of ourselves even to the point of being endowed with life. The scientist will perhaps point out the nervous mechanism of the creature, its powers of motion, of growth, of reproduction, and end by saying “That’s you”. But it has yet to satisfy the inescapable test. Is it concerned with truth as I am ? Then I will acknowledge that it is indeed myself. The scientist might point to motions in the brain and say that these really mean sensations, emotions, thoughts; and perhaps supply a code to translate the motions into the corresponding thoughts. Even if we could accept this inadequate substitute for consciousness as we intimately know it, we must still protest: “You have shown us a creature which thinks and believes; you have not shown us a creature to whom it matters that what it thinks and believes should be true”. The inmost ego, possessing what I have called the inescapable attribute, can never be part of the physical world unless we alter the meaning of the word ‘physical” o as to be synonymous with ” spiritual” a change scarcely to the advantage of clear thinking. But having disowned our supposed double, we can say to the scientist: “If you will hand over this Robot who pretends to be me, and let it be filled with the attribute at present lacking and perhaps other spiritual attributes which I claim as equally self-evident, we may arrive at something that is indeed myself”.

Our present conception of the physical world is hollow enough to hold almost anything. I think the reader will agree. There may indeed be a hint of ribaldry in his hearty assent. What we are dragging to light as the basis of all phenomena is a scheme of symbols connected by mathematical equations. That is what physical reality boils down to when probed by the methods which a physicist can apply. A skeleton scheme of symbols proclaims its own hollowness.

It can be nay it cries out to be filled with something that shall transform it from skeleton into substance, from plan into execution, from symbols into an interpretation of the symbols. And if ever the physicist solves the problem of the living body, he should no longer be tempted to point to his result and say “That’s you”. He should say rather “That is the aggregation of symbols which stands for you in my description and explanation of those of your properties which I can observe and measure. If you claim a deeper insight into your own nature by which you can interpret these symbols a more intimate knowledge of the reality which I can only deal with by symbolism you can rest assured that I have no rival interpretation to propose”. The skeleton is the contribution of physics to the solution of the Problem of Experience; from the clothing of the skeleton it stands aloof.


The scientific conception of the world has come to differ more and more from the commonplace conception until we have been forced to ask ourselves what really is the aim of this scientific transmutation. The doctrine that things are not what they seem is all very well in moderation; but it has proceeded so far that we have to remind ourselves that the world of appearances is the one to which we have actually to adjust our outward lives.

So long as physics in tinkering with the familiar world was able to retain those aspects which appeal to the aesthetic side of our nature, it might with some show of reason make claim to cover the whole of experience; and those who claimed that there was another, religious aspect of our existence had to fight for their claim. But now that its picture omits so much that is obviously significant, there is no suggestion that it is the whole truth about experience, To make such a claim would bring protest not only from the religiously minded but from all who recognise that Man is not merely a scientific measuring machine.

Physics provides a highly perfected answer to one specialised problem which confronts us in experience. I do not wish to minimise the importance of the problem and the value of the solution. We have seen (p. n) how in order to focus the problem the various faculties of the observer have been discarded, and even his sensory equipment simplified, until the problem becomes such as our methods are adequate to solve. For the physicist the observer has become a symbol dwelling in a world of symbols. But before ever we handed over the problem to the physicist we had a glimpse of Man as a spirit in an environment akin to his own spirit.

Why should anyone suppose that all that matters to human nature can be assessed with a measuring rod or expressed in terms of the intersections of world-lines?

If our method consists in codifying, what can we possibly obtain but a code?

Interpreting the term material (or more strictly, physical); in the broadest sense as that with which we can become! acquainted through sensory experience of the external world, we recognise now that it corresponds to the waves not to the water of the ocean of reality. My answer does not deny the existence of the physical world, any more than the answer that the ocean is made of water denies the existence of ocean waves; only we do not get down to the intrinsic nature of things that way. Like the symbolic world of physics, a wave is a conception which is hollow enough to hold almost anything; we can have waves of water, of air, of aether, and (in quantum theory) waves of probability. So after physics has shown us the waves, we have still to determine the content of the waves by some other avenue of knowledge. If you will understand that the spiritual aspect of experience is to the physical aspect in the same kind of relation as the water to the wave form, I can leave you to draw up your own answer to the question propounded at the beginning of this section and so avoid any verbal misunderstanding. What is more important you will see how easily the two aspects of experience now dovetail together, not contesting each other’s place. It is almost as though the modern conception of the physical world had deliberately left room for the reality of spirit and consciousness.

It is a commonplace reflection that we understand very little about our own minds, but it is here if anywhere that all knowledge begins. As for the external objects, remorselessly dissected by science, they are studied and measured, but they are never known. Our pursuit of them has led from solid matter to molecules, from molecules to sparsely scattered electric charges, from electric charges to waves of probability. Whither next?

… I think there can be no doubt that the scientist has a much more mystic conception of the external world than he had in the last century when every scientific ” explanation” of phenomena proceeded on the assumption that nothing could be true unless an engineer could make a model of it. The cruder kind of materialism which sought to reduce everything in the universe, inorganic and organic, to a mechanism of fly-wheels or vortices or similar devices has disappeared altogether. Mechanical explanations of gravitation or electricity are laughed at nowadays. You could now safely hand over the human intellect to the tender mercies of the physicist without fear that he would discover in its workings a grinding of cog-wheels. But we must not make too much of these signs of grace in modern physical science. The tyranny of the engineer has been superseded by the tyranny of the mathematician. At least that is a view very widely taken. But alongside this there is a growing realisation that the mathematician is less oppressive a master than the engineer, for he does not claim any insight deeper than his own symbols.

In an earlier book [The Nature of the Physical World, pp. 104, 209] I have referred to the unconscious habit of the modern physicist of looking on the Creation as though it were the work of a mathematician. Perhaps the irony of these passages is not so evident now as it was at the time. I could not foresee that a few years later a colleague would seriously put forward the view that “from the intrinsic evidence of his creation, the Great Architect of the Universe now begins to appear as a pure mathematician” [Sir James Jeans, The Mysterious Universe, p. 134]. Jeans has previously considered but rejected another explanation. ” So it may be suggested, the mathematician only sees nature through the mathematical blinkers he has fashioned for himself.”

In rejecting what seems to me to be the right explanation, Jeans dwells on the failure of anthropomorphic theories and later the devices of the engineer to explain the universe, and he contrasts them with the success of the mathematical conception. There are two factors which, it seems to me, explain the comparative success of the mathematician. In the first place the mathematician is the professional wielder of symbols; he can deal with unknown quantities and even unknown operations. Clearly he is the man to help us to sift a little knowledge from a vast unknown. But the main reason why the mathematician has beaten his rivals is that we have allowed him to dictate the terms of die competition. The fate of every theory of the universe is decided by a numerical test. Does the sum come out right ? I am not sure that the mathematician understands this world of ours better than the poet and the mystic. Perhaps it is only that he is better at sums.


The stress here laid on the limitations of physical science will, I hope, not be misunderstood by the reader. There is no suggestion that science has become a declining force; rather we obtain a clearer appreciation of the contribution which it is able to make, both now and in the future, to human development and culture. Within its own limitations physical science has become greatly strengthened by the changes. It has become more sure of its aims and perhaps less sure of its achievements. Since the last most bewildering revolution of physical theory (wave mechanics) there has been an interval of some years during which it has been possible to settle down to steady progress. Recently the most striking developments have been on the experimental side. In quick succession the artificial transmutation of the elements, the discovery of the neutron and the discovery of the positive electron have startled the scientific world and opened up new realms for exploration. But I count this as normal prosperity rather than revolution.

In contemplating the gradually developing scheme of
scientific knowledge which never seems to reach finality in any direction, there are times when we are tempted to doubt the substantiality of our gains. Questions, which seem to have been settled, become unsettled.

… I sometimes think that the progress of knowledge is to be measured not by the questions that it has answered but by the questions that it provokes us to ask.


All this new growth of science has its roots in the past. If we see farther than our predecessors it is because we stand on their shoulders and it is not surprising if they receive a few kicks as we scramble up. A new generation is climbing on to the shoulders of the generation to which I belong; and so it will go on. Each phase of the scientific advance has contributed something that is preserved in the succeeding phase. That, indeed, is our ground for hope that the coming generation will find something worth preserving something that is not wholly illusory in the scientific thought of the Universe as it stands to-day.


This all seems very reasonable. I shall try to reduce my quotes above to make them an easier read without – hopefully – mangling their meaning too much. Please let me know if you think I have already gone too far, or if you have any good arguments against the views expressed above.

Dave Marsay

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