The Nature of the Physical World quotes

I have settled down to the task of writing these lectures and have drawn up my chairs to my two tables.

Two tables! Yes; there are duplicates of every object about me—two tables, two chairs, two pens.

This is not a very profound beginning to a course which ought to reach transcendent levels of scientific philosophy. But we cannot touch bedrock immediately; we must scratch a bit at the surface of things first.

This is not a very profound beginning to a course which ought to reach transcendent levels of scientific philosophy.

But we cannot touch bedrock immediately; we must scratch a bit at the surface of things first.

And whenever I begin to scratch the first thing I strike is—my two tables.

It is part of a world which in more devious ways has forced itself on my attention.

My scientific table is mostly emptiness.

Sparsely scattered in that emptiness are numerous electric charges rushing about with great speed; but their combined bulk amounts to less than a billionth of the bulk of the table itself. Notwithstanding its strange construction it turns out to be an entirely efficient table.

In physics we have outgrown archer and apple-pie definitions of the fundamental symbols. To a request to explain what an electron really is supposed to be we can only answer, “It is part of the A B C of physics”.

The external world of physics has thus become a world of shadows.

In removing our illusions we have removed the substance, for indeed we have seen that substance is one of the greatest of our illusions.

Later perhaps we may inquire whether in our zeal to cut out all that is unreal we may not have used the knife too ruthlessly.

Perhaps, indeed, reality is a child which cannot survive without its nurse illusion.

But if so, that is of little concern to the scientist, who has good and sufficient reasons for pursuing his investigations in the world of shadows and is content to leave to the philosopher the determination of its exact status in regard to reality.

But if so, that is of little concern to the scientist, who has good and sufficient reasons for pursuing his investigations in the world of shadows and is content to leave to the philosopher the determination of its exact status in regard to reality.

In the world of physics we watch a shadowgraph performance of the drama of familiar life.

The shadow of my elbow rests on the shadow table as the shadow ink flows over the shadow paper. It is all symbolic, and as a symbol the physicist leaves it. Then comes the alchemist Mind who transmutes the symbols.

The shadow of my elbow rests on the shadow table as the shadow ink flows over the shadow paper. It is all symbolic, and as a symbol the physicist leaves it. Then comes the alchemist Mind who transmutes the symbols.

The sparsely spread nuclei of electric force become a tangible solid; their restless agitation becomes the warmth of summer; the octave of aethereal vibrations becomes a gorgeous rainbow.

Nor does the alchemy stop here. In the transmuted world new significances arise which are scarcely to be traced in the world of symbols; so that it becomes a world of beauty and purpose—and, alas, suffering and evil.

It is difficult to school ourselves to treat the physical world as purely symbolic. We are always relapsing and mixing with the symbols incongruous conceptions taken from the world of consciousness.

Untaught by long experience we stretch a hand to grasp the shadow, instead of accepting its shadowy nature.

Indeed, unless we confine ourselves altogether to mathematical symbolism it is hard to avoid dressing our symbols in deceitful clothing. When I think of an electron there rises to my mind a hard, red, tiny ball; the proton similarly is neutral grey.

and in the later lectures I shall try to focus that feeling and make inexpert efforts to find where it leads. But I should be untrue to science if I did not insist that its study is an end in itself.

The path of science must be pursued for its own sake, irrespective of the views it may afford of a wider landscape; in this spirit we must follow the path whether it leads to the hill of vision or the tunnel of obscurity.

Therefore till the last stage of the course is reached you must be content to follow with me the beaten track of science, nor scold me too severely for loitering among its wayside flowers. That is to be the understanding between us.

That gives an abrupt jar to those who think that things are more or less what they seem.

The revelation by modern physics of the void within the atom is more disturbing than the revelation by astronomy of the immense void of interstellar space.

The atom is as porous as the solar system. If we eliminated all the unfilled space in a man’s body and collected his protons and electrons into one mass, the man would be reduced to a speck just visible with a magnifying glass.

That gives an abrupt jar to those who think that things are more or less what they seem. The revelation by modern physics of the void within the atom is more disturbing than the revelation by astronomy of the immense void of interstellar space.

The atom is as porous as the solar system.

If we eliminated all the unfilled space in a man’s body and collected his protons and electrons into one mass, the man would be reduced to a speck just visible with a magnifying glass.

But the scientific rod is a swarm of electrical particles rushing about and widely separated from one another.

The marvel is that such a swarm should tend to preserve any definite extension.

The particles, however, keep a certain average spacing so that the whole volume remains practically steady;

It never occurred to him that in spite of all precautions the scale would change length when he did this; but unless the earth happens to be at rest a change must occur.

The constancy of a measuring scale is the rock on which the whole structure of physics has been reared; and that rock has crumbled away.

You may think that this assumption cannot have betrayed the physicist very badly; the changes of length cannot be serious or they would have been noticed. Wait and see.

A railway journey between two towns which was 100 miles at noon is shortened to 50 miles at 6 p.m. when the planet has turned through a right angle.

The inhabitants copy Alice in Wonderland; they pull out and shut up like a telescope.

I do not know of a planet moving at 161,000 miles a second, but I could point to a spiral nebula far away in space which is moving at 1000 miles a second.

There is no means of deciding which is right—to which of us the observed relative velocity of 1000 miles a second really belongs. Astronomically the galaxy of which the earth is a member does not seem to be more important, more central, than the nebula.

The presumption that it is we who are the more nearly at rest has no serious foundation; it is mere self-flattery.

“But”, you will say, “surely if these appreciable changes of length occurred on the earth, we should detect them by our measurements.” That brings me to the interesting point. We could not detect them by any measurement; they may occur and yet pass quite unnoticed.

The structure has also been supported by supplementary props because optical and electrical devices can often be used instead of material scales to ascertain lengths and distances.

But we find that all these are united in a conspiracy not to give one another away.

The rock has crumbled and simultaneously all the other supports have collapsed.

Each has hitherto taken it for granted that it is the other fellow who is making the mistake. We cannot settle the dispute by appeal to experiment because in every experiment the mistake introduces two errors which just compensate one another.

It is a curious sort of mistake which always carries with it its own compensation.

But remember that the compensation only applies to phenomena actually observed or capable of observation. The compensation does not apply to the intermediate part of our deduction—that system of inference from observation which forms the classical physical theory of the universe.

It is clear that their whole conception of space is distorted as compared with ours, and ours is distorted as compared with theirs.

We are regarding the same universe, but we have arranged it in different spaces.

The original quarrel as to whether they or we are moving with the speed of 1000 miles a second has made so deep a cleavage between us that we cannot even use the same space.

Space and time are words conveying more than one meaning. Space is an empty void; or it is such and such a number of inches, acres, pints. Time is an ever-rolling stream; or it is something signalled to us by wireless.

The physicist has no use for vague conceptions; he often has them, alas! but he cannot make real use of them.

So when he speaks of space it is always the inches or pints that he should have in mind. It is from this point of view that our space and the space of the nebular physicists are different spaces;

Is there any essential difference (other than its crudity) between this method and scientific measurements with a scale? It is partly obtained by vision—a crude version of scientific measurement with a theodolite.

Our common knowledge of where things are is not a miraculous revelation of unquestionable authority; it is inference from observations of the same kind as, but cruder than, those made in a scientific survey.

Within its own limits of accuracy the scheme of location of objects that I am instinctively “aware” of is the same as my scientific scheme of location, or frame of space.

Having any number of these systems of location, or frames of space, we can no longer pretend that each of them indicates “just where things are”.

Location is not something supernaturally revealed to the mind; it is a kind of conventional summary of those properties or relations of objects which condition certain visual and tactual sensations.

Does not this show that “right” location in space cannot be nearly so important and fundamental as it is made out to be in the Newtonian scheme of things? The different observers are able to play fast and loose with it without ill effects.

"You are seeking a frame of space which you call the right frame. In what does its rightness consist?"

You are standing with a label in your hand before a row of packages all precisely similar.

You are worried because there is nothing to help you to decide which of the packages it should be attached to. Look at the label and see what is written on it. Nothing.

The measurement of distance is not an absolute operation.

It is possible for two men to measure the same distance and reach different results, and yet neither of them be wrong.

I mark two dots on the blackboard and ask two students to measure very accurately the distance between them.

It is called “proper-distance”. Perhaps you feel a relief at getting hold of something absolute and would wish to follow it up. Excellent. But remember this will lead you away from the classical scheme of physics which has chosen the relative distances to build on.

The quest of the absolute leads into the four-dimensional world.

A more familiar example of a relative quantity is “direction” of an object. There is a direction of Cambridge relative to Edinburgh and another direction relative to London, and so on.

But

Nature has been too subtle for him; she has not left anything to betray the frame which she used.

Or perhaps the concealment is not any particular subtlety; she may have done her work without employing a frame of space. Let me tell you a parable.

Like the critic I do not think Nature has been particularly subtle in concealing which frame she prefers.

It is just that she is not enthusiastic about frames of space.

They are a method of partition which we have found useful for reckoning, but they play no part in the architecture of the universe. Surely it is absurd to suppose that the universe is planned in such a way as to conceal its plan.

Like the critic I do not think Nature has been particularly subtle in concealing which frame she prefers. It is just that she is not enthusiastic about frames of space.

They are a method of partition which we have found useful for reckoning, but they play no part in the architecture of the universe.

Surely it is absurd to suppose that the universe is planned in such a way as to conceal its plan. It is like the schemes of the White Knight—

It is just that she is not enthusiastic about frames of space. They are a method of partition which we have found useful for reckoning, but they play no part in the architecture of the universe.

Surely it is absurd to suppose that the universe is planned in such a way as to conceal its plan.

It is like the schemes of the White Knight—

The solution goes on famously; but just as we have got rid of the other unknowns, behold! V disappears as well, and we are left with the indisputable but irritating conclusion—

This is a favourite device that mathematical equations resort to, when we propound stupid questions.

If we tried to find the latitude and longitude of a point north-east from the north pole we should probably receive the same mathematical answer. “Velocity through aether” is as meaningless as “north-east from the north pole”.

The writing-down of lengths for balance-sheet purposes is the FitzGerald contraction.

The shortening of the moving rod is true, but it is not really true.

It is not a statement about reality (the absolute) but it is a true statement about appearances in our frame of reference.[1] An object has different lengths in the different space-frames, and any 6-foot man will have a length 3 feet in some frame or …

We have travelled far from the old standpoint which demanded mechanical models of everything in Nature, seeing that we do not now admit even a definite unique distance between two points.

The relativity of the current scheme of physics invites us to search deeper and find the absolute scheme underlying it, so that we may see the world in a truer perspective.

[1] The proper-length (p. 25) is unaltered; but the relative length is shortened.

Whatever may be time de jure, the Astronomer Royal’s time is time de facto. His time permeates every corner of physics.

It stands in no need of logical defence; it is in the much stronger position of a vested interest.

It has been woven into the structure of the classical physical scheme. “Time” in physics means Astronomer Royal’s time. You may be aware that it is revealed to us in Einstein’s theory that time and space are mixed up in a rather strange way.

This is called proper-time or interval. It is definitely separate from and unlike proper-space. Your protest in the name of commonsense against a mixing of time and space is a feeling which I desire to encourage.

Time and space ought to be separated.

The current representation of the enduring world as a three-dimensional space leaping from instant to instant through time is an unsuccessful attempt to separate them.

We have jumped to certain conclusions about time and have come to regard them almost as axiomatic, although they are not really justified by anything in our immediate perception of time. Here is one of them.

If two people meet twice they must have lived the same time between the two meetings, even if one of them has travelled to a distant part of the universe and back in the interim.

An absurdly impossible experiment, you will say. Quite so; it is outside all experience. Therefore, may I suggest that you are not appealing to your experience of time when you object to a theory which denies the above statement?

Now we must pass from this vague scheme of location to a precise scheme.

The first and most important thing is to put Myself into the picture.

It sounds egotistical; but, you see, it is my frame of space that will be used, so it all hangs round me. Here I am—a kind of four-dimensional worm (Fig. 2).

We can never agree. Certainly it looks from the picture as though my instants were more natural than yours; but that is because I drew the picture. You, of course, would redraw it with your Now lines at right angles to yourself.

But we need not quarrel if the Now lines are merely reference lines drawn across the world for convenience in locating events—like the lines of latitude and longitude on the earth.

There is then no question of a right way and a wrong way of drawing the lines; we draw them as best suits our convenience. World-wide instants are not natural cleavage planes of time;

There is then no question of a right way and a wrong way of drawing the lines; we draw them as best suits our convenience.

World-wide instants are not natural cleavage planes of time; there is nothing equivalent to them in the absolute structure of the world; they are imaginary partitions which we find it convenient to adopt.

We have been accustomed to regard the world—the enduring world—as stratified into a succession of instantaneous states. But an observer on another star would make the strata run in a different direction from ours.

We shall see more clearly the real mechanism of the physical world if we can rid our minds of this illusion of stratification. The world that then stands revealed, though strangely unfamiliar, is actually much simpler.

There is a difference between simplicity and familiarity.

A pig may be most familiar to us in the form of rashers, but the unstratified pig is a simpler object to the biologist who wishes to understand how the animal functions.

These hour-glasses (drawn through each point of the world considered in turn as a Here-Now) embody what we know of the absolute structure of the world so far as space and time are concerned. They show how the “grain” of the world runs.

Father Time has been pictured as an old man with a scythe and an hour-glass. We no longer permit him to mow instants through the world with his scythe; but we leave him his hour-glass.

Since the hour-glass is absolute its two cones provide respectively an Absolute Future and an Absolute Past for the event Here-Now. They are separated by a wedge-shaped neutral zone which (absolutely) is neither past nor future.

There is no absolute Now, but only the various relative Nows differing according to the reckoning of different observers and covering the whole neutral wedge which at the distance of Neptune is about eight hours thick.

She will have to think of you continuously for eight hours on end in order to circumvent the ambiguity of “Now”.

At the greatest possible separation on the earth the thickness of the neutral wedge is no more than a tenth of a second; so that terrestrial synchronism is not seriously interfered with.

But in practice the events we notice are of more than infinitesimal duration. If the duration is sufficient to cover the width of the neutral zone, then the event taken as a whole may fairly be considered to be Now absolutely.

From this point of view the “nowness” of an event is like a shadow cast by it into space, and the longer the event the farther will the umbra of the shadow extend.

As the speed of matter approaches the speed of light its mass increases to infinity, and therefore it is impossible to make matter travel faster than light.

but in addition we have direct experience of the time-relations that we ourselves are traversing—a knowledge of time not coming through external sense-organs, but taking a short cut into our consciousness.

When I close my eyes and retreat into my inner mind, I feel myself enduring, I do not feel myself extensive.

It is this feeling of time as affecting ourselves and not merely as existing in the relations of external events which is so peculiarly characteristic of it; space on the other hand is always appreciated as something external.

That is why time seems to us so much more mysterious than space. We know nothing about the intrinsic nature of space, and so it is quite easy to conceive it satisfactorily.

We have intimate acquaintance with the nature of time and so it baffles our comprehension.

It is the same paradox which makes us believe we understand the nature of an ordinary table whereas the nature of human personality is altogether mysterious. We never have that intimate contact with space and tables which would make us realise how mysterious they are;

The Four-Dimensional World. I do not know whether you have been keenly alive to the fact that for some time now we have been immersed in a four-dimensional world.

The fourth dimension required no introduction; as soon as we began to consider events it was there.

Events obviously have a fourfold order which we can dissect into right or left, behind or in front, above or below, sooner or later—or into many alternative sets of fourfold specification. The fourth dimension is not a difficult conception.

We are accustomed to think of a man apart from his duration. When I portrayed “Myself” in Fig. 2, you were for the moment surprised that I should include my boyhood and old age.

But to think of a man without his duration is just as abstract as to think of a man without his inside.

Abstractions are useful, and a man without his inside (that is to say, a surface) is a well-known geometrical conception. But we ought to realise what is an abstraction and what is not.

But it is a curious fact that if I speak of a velocity of 299,796 kilometres a second it is unnecessary to add the explanatory phrase. Relative to what? Relative to any and every star or particle of matter in the universe.

It is no use trying to overtake a flash of light; however fast you go it is always travelling away from you at 186,000 miles a second.

Now from one point of view this is a rather unworthy deception that Nature has practised upon us. Let us take our favourite observer who travels at 161,000 miles a second and send him in pursuit of the flash of light.

For example, imagine a search-light capable of sending an accurately parallel beam as far as Neptune. If the search-light is made to revolve once a minute, Neptune’s end of the beam will move round a circle with velocity far greater than the above limit.

This is an example of our habit of creating velocities by a mental association of states which are not themselves in direct causal connection.

The assertion made by the relativity theory is more restricted, viz.—

Whenever anything happens which cannot be undone, it is always reducible to the introduction of a random element analogous to that introduced by shuffling.

Shuffling is the only thing which Nature cannot undo.

When Humpty Dumpty had a great fall—

That is their common feature, and it is seen at once when (as usual) the laws are formulated mathematically.

There is no more distinction between past and future than between right and left.

In algebraic symbolism, left is , right is ; past is , future is . This holds for all laws of Nature governing the behaviour of non-composite individuals—the “primary laws”, as we shall call them.

But if the man had come back with past and future interchanged, then indeed the situation would have been lively. Mr. Wells in The Time-Machine and Lewis Carroll in Sylvie and Bruno give us a glimpse of the absurdities which occur when time runs backwards.

If space is “looking-glassed” the world continues to make sense; but looking-glassed time has an inherent absurdity which turns the world-drama into the most nonsensical farce.

Now the primary laws of physics taken one by one all declare that they are entirely indifferent as to which way you consider time to be progressing, just as they are indifferent as to whether you view the world from the right or the left.

It opens up a new province of knowledge, namely, the study of organisation; and it is in connection with organisation that a direction of time-flow and a distinction between doing and undoing appears for the first time.

Time’s Arrow. The great thing about time is that it goes on.

But this is an aspect of it which the physicist sometimes seems inclined to neglect. In the four-dimensional world considered in the last chapter the events past and future lie spread out before us as in a map.

The events are there in their proper spatial and temporal relation; but there is no indication that they undergo what has been described as “the formality of taking place”, and the question of their doing or undoing does not arise.

We see in the map the path from past to future or from future to past; but there is no signboard to indicate that it is a one-way street.

Something must be added to the geometrical conceptions comprised in Minkowski’s world before it becomes a complete picture of the world as we know it. We may appeal to consciousness to suffuse the whole—to turn existence into happening, being into becoming.

but there is no signboard to indicate that it is a one-way street. Something must be added to the geometrical conceptions comprised in Minkowski’s world before it becomes a complete picture of the world as we know it.

We may appeal to consciousness to suffuse the whole—to turn existence into happening, being into becoming.

But first let us note that the picture as it stands is entirely adequate to represent those primary laws of Nature which, as we have seen, are indifferent to a direction of time.

If an army of monkeys were strumming on typewriters they might write all the books in the British Museum. The chance of their doing so is decidedly more favourable than the chance of the molecules returning to one half of the vessel.

When numbers are large, chance is the best warrant for certainty.

Happily in the study of molecules and energy and radiation in bulk we have to deal with a vast population, and we reach a certainty which does not always reward the expectations of those who court the fickle goddess.

That would involve something much worse than a violation of an ordinary law of Nature, namely, an improbable coincidence.

The law that entropy always increases—the second law of thermodynamics—holds, I think, the supreme position among the laws of Nature.

If someone points out to you that your pet theory of the universe is in disagreement with Maxwell’s equations—then so much the worse for Maxwell’s equations. If it is found to be contradicted by observation—well, these experimentalists do bungle things sometimes.

I have called the laws controlling the behaviour of single individuals “primary laws”, implying that the second law of thermodynamics, although a recognised law of Nature, is in some sense a secondary law. This distinction can now be placed on a regular footing.

Some things never happen in the physical world because they are impossible; others because they are too improbable.

The laws which forbid the first are the primary laws; the laws which forbid the second are the secondary laws.

“A fortuitous concourse of atoms”—that bugbear of the theologian—has a very harmless place in orthodox physics. The physicist is acquainted with it as a much-prized rarity. Its properties are very distinctive, and unlike those of the physical world in general.

The scientific name for a fortuitous concourse of atoms is “thermodynamical equilibrium”.

Thermodynamical equilibrium is the other case which we promised to consider in which no increase in the random element can occur, namely, that in which the shuffling is already as thorough as possible.

It would not be true to say that such a region is timeless; the atoms vibrate as usual like little clocks; by them we can measure speeds and durations.

Time is still there and retains its ordinary properties, but it has lost its arrow; like space it extends, but it does not “go on”.

This raises the important question, Is the random element (measured by the criterion of probability already discussed) the only feature of the physical world which can furnish time with an arrow?

The conclusion is that whereas other statistical characters besides entropy might perhaps be used to discriminate time’s arrow, they can only succeed when it succeeds and they fail when it fails. Therefore they cannot be regarded as independent tests.

So far as physics is concerned time’s arrow is a property of entropy alone.

Are Space and Time Infinite? I suppose that everyone has at some time plagued his imagination with the question, Is there an end to space? If space comes to an end, what is beyond the end?

No one can conceive infinite space; we had to be content to admit in the physical world an inconceivable conception—disquieting but not necessarily illogical. Einstein’s theory now offers a way out of the dilemma. Is space infinite, or does it come to an end? Neither.

Space is finite but it has no end; “finite but unbounded” is the usual phrase.

Infinite space cannot be conceived by anybody; finite but unbounded space is difficult to conceive but not impossible. I shall not expect you to conceive it; but you can try. Think first of a circle;

it must, of course, be exceedingly great compared with ordinary standards. On rather insecure evidence it has been estimated to be not many times greater than the distance of the furthest known nebulae. But the boundlessness has nothing to do with the bigness.

Space is boundless by re-entrant form not by great extension.

That which is is a shell floating in the infinitude of that which is not. We say with Hamlet, “I could be bounded in a nutshell and count myself a king of infinite space”.

Time’s arrow will then be lost altogether and the whole conception of progress towards a future fades away.

But the difficulty of an infinite past is appalling.

It is inconceivable that we are the heirs of an infinite time of preparation; it is not less inconceivable that there was once a moment with no moment preceding it.

But the difficulty of an infinite past is appalling.

It is inconceivable that we are the heirs of an infinite time of preparation; it is not less inconceivable that there was once a moment with no moment preceding it.

This dilemma of the beginning of time would worry us more were it not shut out by another overwhelming difficulty lying between us and the infinite past. We have been studying the running-down of the universe;

I would feel more content that the universe should accomplish some great scheme of evolution and, having achieved whatever may be achieved, lapse back into chaotic changelessness, than that its purpose should be banalised by continual repetition.

I am an Evolutionist, not a Multiplicationist.

It seems rather stupid to keep doing the same thing over and over again.

From the side of scientific investigation we recognise only the progressive change in the random element from the end of the world with least randomness to the end with most; that in itself gives no ground for suspecting any kind of dynamical meaning.

The view here advocated is tantamount to an admission that consciousness, looking out through a private door, can learn by direct insight an underlying character of the world which physical measurements do not betray.

In any attempt to bridge the domains of experience belonging to the spiritual and physical sides of our nature, Time occupies the key position.

I have already referred to its dual entry into our consciousness—through the sense organs which relate it to the other entities of the physical world, and directly through a kind of private door into the mind.

The physicist, whose method of inquiry depends on sharpening up our sense organs by auxiliary apparatus of precision, naturally does not look kindly on private doors, through which all forms of superstitious fancy might enter unchecked.

But is he ready to forgo that knowledge of the going on of time which has reached us through the door, and content himself with the time inferred from sense-impressions which is emaciated of all dynamic quality?

It is so welded into our consciousness that a moving on of time is a condition of consciousness. We have direct insight into “becoming” which sweeps aside all symbolic knowledge as on an inferior plane.

If I grasp the notion of existence because I myself exist, I grasp the notion of becoming because I myself become.

It is the innermost Ego of all which is and becomes.

a thermometer) in order to discover which event is the later.[11] The division of labour is especially striking when we remember that our best clocks are those in which all processes such as friction, which introduce disorganisation of energy, are eliminated as far as possible.

The more perfect the instrument as a measurer of time, the more completely does it conceal time’s arrow.

This paradox seems to be explained by the fact pointed out in chapter III that time comes into our consciousness by two routes.

But this misses any world-features which are not located in minute compartments.

We often think that when we have completed our study of one we know all about two, because “two” is “one and one”. We forget that we have still to make a study of “and”.

Secondary physics is the study of “and”—that is to say, of organisation.

the language of arithmetic. It has a measure-number associated with it and so is made quite at home in physics.

Beauty and melody have not the arithmetical pass-word and so are barred out.

This teaches us that what exact science looks out for is not entities of some particular category, but entities with a metrical aspect.

When we analyse the picture into a large number of particles of paint, we lose the aesthetic significance of the picture. The particles of paint go into the scientific inventory, and it is claimed that everything that there really was in the picture is kept.

But this way of keeping a thing may be much the same as losing it.

The essence of a picture (as distinct from the paint) is arrangement. Is arrangement kept or lost? The current answer seems inconsistent. In so far as arrangement signifies a picture, it is lost; science has to do with paint, not pictures.

But is it rational? How can reason regard it otherwise than as a perverse misrepresentation of what is after all only a collection of atoms, aether-waves and the like, going about their business?

If the physicist as advocate for reason takes this line, just whisper to him the word Entropy.

Insufficiency of Primary Law. I daresay many of my physical colleagues will join issue with me over the status I have allowed to entropy as something foreign to the microscopic scheme, but essential to the physical world.

In sorting out the confused data of our experience it has generally been assumed that the object of the quest is to find out all that really exists.

There is another quest not less appropriate to the nature of our experience—to find out all that really becomes.

[11] To make the test strictly from another world he must not assume that the figures marked on the clock-dial necessarily go the right way round;

and similarly it is preferable to avoid a hammering on one’s body when it is being used as a channel of scientific knowledge. We get rid of this hammering when we cease to be supported.

Let us then take a leap over a precipice so that we may contemplate Nature undisturbed.

Or if that seems to you an odd way of convincing yourself that bodies do not fall,[13] let us enter the runaway lift again. Here nothing need be supported;

The Newtonian picture of gravitation is a tug applied to the body whose path is disturbed. I want to explain why this picture must be superseded. I must refer again to the famous incident in which Newton and the apple-tree were concerned.

The classical conception of gravitation is based on Newton’s account of what happened; but it is time to hear what the apple had to say.

The apple with the usual egotism of an observer deemed itself to be at rest; looking down it saw the various terrestrial objects including Newton rushing upwards with accelerated velocity to meet it.

But when they put in distant countries such as Greece the size must be exaggerated; or, as they would put it, there is a demon active in Greece who makes the journeys there seem different from what the flat map clearly shows them to be.

The demon is never where you are; it is always the other fellow who is haunted by him.

We now understand that the true explanation is that the earth is curved, and the apparent activities of the demon arise from forcing the curved surface into a flat map and so distorting the simplicity of things.

In referring the world to a flat frame of space-time we distort it so that the phenomena do not appear in their original simplicity. Admit a curvature of the world and the mysterious agency disappears.

Einstein has exorcised the demon.

Do not imagine that this preliminary change of conception carries us very far towards an explanation of gravitation. We are not seeking an explanation; we are seeking a picture.

Do not imagine that this preliminary change of conception carries us very far towards an explanation of gravitation.

We are not seeking an explanation; we are seeking a picture.

And this picture of world-curvature (hard though it may seem) is more graspable than an elusive tug which flits from one object to another according to the point of view chosen.

On no particular grounds the motion is divided into two parts, one of which is attributed to a passive tendency of the body called inertia and the other to an interfering field of force.

The suggestion that the body really wanted to go straight but some mysterious agent made it go crooked is picturesque but unscientific.

It makes two properties out of one; and then we wonder why they are always proportional to one another—why the gravitational force on different bodies is proportional to their inertia or mass.

You see the great change in our view. The Newtonian scheme says that the planet tends to move in a straight line, but the sun’s gravity pulls it away.

Einstein says that the planet tends to take the shortest route and does take it.

That is the general idea, but for the sake of accuracy I must make one rather trivial correction. The planet takes the longest route.

That is the general idea, but for the sake of accuracy I must make one rather trivial correction.

The planet takes the longest route.

You may remember that points along the track of any material body (necessarily moving with a speed less than the velocity of light) are in the absolute past or future of one another; they are not absolutely “elsewhere”.

But if they bend a little towards one another the connecting region can lie smoothly and satisfy the law of curvature. If they bend too much the illegal puckering reappears.

The law of gravitation is a fastidious tailor who will not tolerate wrinkles (except of a limited approved type) in the main area of the garment; so that the seams are required to take courses which will not cause wrinkles.

You and I have to submit to this and so our tracks curve towards each other. An onlooker will make the comment that here is an illustration of the law that two massive bodies attract each other.

5, namely yourself and myself. We are not empty space so there is no limit to the kind of curvature entering into our composition; in fact our unusual sort of curvature is what distinguishes us from empty space.

We are, so to speak, ridges in the four-dimensional world where it is gathered into a pucker.

The pure mathematician in his unflattering language would describe us as “singularities”. These two non-empty ridges are joined by empty space, which must be free from those kinds of curvature described by the ten principal coefficients.

But that is a harmless accident common enough in primary physics. The discrimination between cause and effect depends on time’s arrow and can only be settled by reference to entropy.

We need not pay much attention to suggestions of causation arising in discussions of primary laws which, as likely as not, are contemplating the world upside down.

Although we are here only at the beginning of Einstein’s general theory I must not proceed further into this very technical subject. The rest of this chapter will be devoted to elucidation of more elementary points.

The answer is that the fatigue arises from being shut up in a box and jolted about for nine hours; and it makes no difference whether in the meantime I move to Edinburgh or Edinburgh moves to me.

Motion does not tire anybody.

With the earth as our vehicle we are travelling at 20 miles a second round the sun; the sun carries us at 12 miles a second through the galactic system; the galactic system bears us at 250 miles a second amid the spiral nebulae;

the sun carries us at 12 miles a second through the galactic system; the galactic system bears us at 250 miles a second amid the spiral nebulae; the spiral nebulae....

If motion could tire, we ought to be dead tired.

Similarly change of motion or acceleration does not injure anyone, even when it is (according to the Newtonian view) an absolute acceleration. We do not even feel the change of motion as our earth takes the curve round the sun.

He was a clock measuring two sides of a time-triangle. He recorded less time than the stay-at-home observer who was a clock measuring the third side. Need I defend my calling him a clock?

We are all of us clocks whose faces tell the passing years.

This comparison was simply an example of the geometrical proposition about time-triangles (which in turn is a particular case of Einstein’s law of longest track). The result is quite explicable in the ordinary mechanical way.

Why not? All the knowledge is derived from measurements made with various instruments. The instruments used in the different fields of inquiry are not fundamentally unlike.

There is no reason to regard the partitions of the sciences made in the early stages of human thought as irremovable.

But mechanics in becoming geometry remains none the less mechanics. The partition between mechanics and geometry has broken down and the nature of each of them has diffused through the whole.

If the curvature were entirely arbitrary this would be the end of the explanation; but there is a law of curvature—Einstein’s law of gravitation—and on this law our further inquiry must be focussed.

Explanation is needed for regularity, not for diversity; and our curiosity is roused, not by the diverse values of the ten subsidiary coefficients of curvature which differentiate the world from a flat world, but by the vanishing everywhere of the ten principal coefficients.

All explanations of gravitation on Newtonian lines have endeavoured to show why something (which I have disrespectfully called a demon) is present in the world.

Relativity of Length.

There is no such thing as absolute length; we can only express the length of one thing in terms of the length of something else.[20]

And so when we speak of the length of the directed radius we mean its length compared with the standard metre scale. Moreover, to make this comparison, the two lengths must lie alongside. Comparison at a distance is as unthinkable as action at a distance;

Moreover, to make this comparison, the two lengths must lie alongside.

Comparison at a distance is as unthinkable as action at a distance; more so, because comparison is a less vague conception than action.

We must either convey the standard metre to the site of the length we are measuring, or we must use some device which, we are satisfied, will give the same result as if we actually moved the metre rod.

The whole thing is a vicious circle.

The law of gravitation is—a put-up job.

This explanation introduces no new hypothesis. In saying that a material system of standard specification always occupies a constant fraction of the directed radius of the region where it is, we are simply reiterating Einstein’s law of gravitation—stating it in the inverse form.

To see the force of the explanation we must, however, realise the relativity of extension. Extension which is not relative to something in the surroundings has no meaning.

Imagine yourself alone in the midst of nothingness, and then try to tell me how large you are.

The definiteness of extension of the standard rod can only be a definiteness of its ratio to some other extension.

And yet the non-occurrence of this impossible curvature is the law (of gravitation) by which we calculate the track of the earth!

The key to the paradox is that we ourselves, our conventions, the kind of thing that attracts our interest, are much more concerned than we realise in any account we give of how the objects of the physical world are behaving.

And so an object which, viewed through our frame of conventions, may seem to be behaving in a very special and remarkable way may, viewed according to another set of conventions, be doing nothing to excite particular comment.

And so wherever the sun, moon and earth may have got to, the light will not give them away. If the law of curvature predicts an eclipse the light will take such a track that there is an eclipse.

The law of gravitation is not a stern ruler controlling the heavenly bodies; it is a kind-hearted accomplice who covers up their delinquencies.

I do not recommend you to try to verify from Fig. 6 that the number of rods in (full line) and (dotted line) is the same.

these are test bodies of simpler structure. But they are still gross compared with atomic phenomena. The light-ray, for instance, is not applicable to measurements so refined that the diffraction of light must be taken into account.

Our knowledge of the external world cannot be divorced from the nature of the appliances with which we have obtained the knowledge.

The truth of the law of gravitation cannot be regarded as subsisting apart from the experimental procedure by which we have ascertained its truth.

We do not ask how mass gets a grip on space-time and causes the curvature which our theory postulates. That would be as superfluous as to ask how light gets a grip on the electromagnetic medium so as to cause it to oscillate.

The light is the oscillation; the mass is the curvature.

There is no causal effect to be attributed to mass; still less is there any to be attributed to matter.

The light is the oscillation; the mass is the curvature. There is no causal effect to be attributed to mass; still less is there any to be attributed to matter.

The conception of matter, which we associate with these regions of unusual contortion, is a monument erected by the mind to mark the scene of conflict.

When you visit the site of a battle, do you ever ask how the monument that commemorates it can have caused so much carnage?

The view, which some of us were taught at school, that the truth of Euclid’s axioms can be seen intuitively, is universally rejected nowadays.

We can no more settle the laws of space by intuition than we can settle the laws of heredity.

If intuition is ruled out, the appeal must be to experiment—genuine open-minded experiment unfettered by any preconception as to what the verdict ought to be. We must not afterwards go back on the experiments because they make out space to be very slightly non-Euclidean.

In certain directions in the sky our telescopes penetrate to the limits of the system, but in other directions the extent is too great for us to fathom.

The Milky Way, which on a dark night forms a gleaming belt round the sky, shows the direction in which there lie stars behind stars until vision fails.

This great flattened distribution is called the Galactic System. It forms a disc of thickness small compared to its a real extent.

It happens to be quite near the centre of the local star-cloud; but this apparently favoured position is discounted by the fact that the star-cloud itself is placed very eccentrically in relation to the galactic system, being in fact near the confines of it.

We cannot claim to be at the hub of the universe.

The contemplation of the galaxy impresses us with the insignificance of our own little world; but we have to go still lower in the valley of humiliation. The galactic system is one among a million or more spiral nebulae.

On ordinary grounds it would be difficult to explain why these other universes should hurry away from us so fast and so unanimously.

Why should they shun us like a plague?

But the phenomenon is intelligible if what has really been observed is the slowing down of vibrations consequent on the light from these objects having travelled an appreciable part of the way round the world.

On that theory the radius of space is of the order twenty times the average distance of the nebulae observed, or say 100 million light years. That leaves room for a few million spirals; but there is nothing beyond.

There is no beyond—in spherical space “beyond” brings us back towards the earth from the opposite direction.[28]

The Scale of Time. The corridor of time stretches back through the past. We can have no conception how it all began. But at some stage we imagine the void to have been filled with matter rarified beyond the most tenuous nebula.

Again the question raises itself, How far does this distribution extend?

Not the stars this time but universes stretch one behind the other beyond sight.

Does this distribution too come to an end? It may be that imagination must take another leap, envisaging super-systems which surpass the spiral nebulae as the spiral nebulae surpass the stars.

The Scale of Time.

The corridor of time stretches back through the past.

We can have no conception how it all began. But at some stage we imagine the void to have been filled with matter rarified beyond the most tenuous nebula. The atoms sparsely strewn move hither and thither in formless disorder.

But unless we can circumvent the second law of thermodynamics—which is as much as to say unless we can find cause for time to run backwards—the ultimate decay draws surely nearer and the world will at the last come to a state of uniform changelessness.

Does this prodigality of matter, of space, of time, find its culmination in Man?

Plurality of Worlds. I will here put together the present astronomical evidence as to the habitability of other worlds.

Anything that he has to contribute is of the nature of fragmentary hints picked up in the course of investigations with more practicable and commonplace purposes.

Nevertheless, the mind is irresistibly drawn to play with the thought that somewhere in the universe there may be other beings “a little lower than the angels” whom Man may regard as his equals—or perhaps his superiors.

It is idle to guess the forms that life might take in conditions differing from those of our planet.

But Venus has no moon, and since it seems to be similar to the earth in other respects, it may perhaps be inferred that it is a world which is all ocean—where fishes are supreme.

The suggestion at any rate serves to remind us that the destinies of organic life may be determined by what are at first sight irrelevant accidents.

The sun is an ordinary star and the earth is an ordinary planet, but the moon is not an ordinary satellite. No other known satellite is anything like so large in proportion to the planet which it attends.

The tidal deformation of the earth thus grew to large amplitude, ending in a cataclysm which separated the great lump of material that formed the moon. Other planets escaped this dangerous coincidence of period, and their satellites separated by more normal development.

If ever I meet a being who has lived in another world, I shall feel very humble in most respects, but I expect to be able to boast a little about the moon.

Mars is the only planet whose solid surface can be seen and studied; and it tempts us to consider the possibility of life in more detail. Its smaller size leads to considerably different conditions;

the work presents many complications and the results may not be final; but the researches of Sir J. H. Jeans lead to the conclusion that rotational break-up produces a double star and never a system of planets.

The solar system is not the typical product of development of a star; it is not even a common variety of development; it is a freak.

By elimination of alternatives it appears that a configuration resembling the solar system would only be formed if at a certain stage of condensation an unusual accident had occurred.

However doubtful this conclusion as to the rarity of solar systems may be, it is a useful corrective to the view too facilely adopted which looks upon every star as a likely minister to life. We know the prodigality of Nature.

How many acorns are scattered for one that grows to an oak?

And need she be more careful of her stars than of her acorns?

but—well, can you contemplate it? Assuming that the stage of highly developed life is a very small fraction of the inorganic history of the star, the rival earths are in general places where conscious life has already vanished or is yet to come.

I do not think that the whole purpose of the Creation has been staked on the one planet where we live; and in the long run we cannot deem ourselves the only race that has been or will be gifted with the mystery of consciousness.

But I feel inclined to claim that at the present time our race is supreme; and not one of the profusion of stars in their myriad clusters looks down on scenes comparable to those which are passing beneath the rays of the sun.

This is not a pose. It is not even scientific modesty, because the attitude is often one of naïve surprise that Nature should have hidden her fundamental secret successfully from such powerful intellects as ours.

It is simply that we have turned a corner in the path of progress and our ignorance stands revealed before us, appalling and insistent.

There is something radically wrong with the present fundamental conceptions of physics and we do not see how to set it right.

It is simply that we have turned a corner in the path of progress and our ignorance stands revealed before us, appalling and insistent.

There is something radically wrong with the present fundamental conceptions of physics and we do not see how to set it right.

The cause of all this trouble is a little thing called which crops up continually in a wide range of experiments. In one sense we know just what is, because there are a variety of ways of measuring it;

an electron, but we did not find ; then we turned our attention to a case in which the energy was obviously dissolving away through space, viz. light-waves, and immediately appeared.

The atom of action seems to have no coherence in space; it has a unity which overleaps space.

How can such a unity be made to appear in our picture of a world extended through space and time?

Not all the light-waves pass by without entering the eye; for somehow we are able to see Sirius. How is it managed?

Do the ripples striking the eye send a message round to the back part of the wave, saying, “We have found an eye. Let’s all crowd into it!”

Attempts to account for this phenomenon follow two main devices which we may describe as the “collection-box” theory and the “sweepstake” theory, respectively. Making no effort to translate them into scientific language, they amount to this:

A few minutes before the arrival some person takes it into his head to go out and admire the glories of the heavens and—in short—to stick his eye in the way.

The light-waves when they started could have had no notion what they were going to hit; for all they knew they were bound on a journey through endless space, as most of their colleagues were.

Their energy would seem to be dissipated beyond recovery over a sphere of 50 billion miles’ radius.

Undoubtedly it is the incident light which provides the energy of these explosions, but the phenomenon is governed by a remarkable rule. Firstly, the speed of the electrons is not increased by using more powerful light.

Concentration of the light produces more explosions but not more powerful explosions.

Secondly, the speed is increased by using bluer light, i.e. light of shorter period. For example, the feeble light reaching us from Sirius will cause more powerful ejections of electrons than full sunlight, because Sirius is bluer than the sun;

Nor can we appeal to any trigger action of the light releasing an electron already loaded up with energy for its journey; it is the nature of the light which settles the amount of the load.

The light calls the tune, therefore the light must pay the piper.

Only classical theory does not provide light with a pocket to pay from.

it is a uniform chance of energy. Following the rather old-fashioned definition of energy as “capacity for doing work” the waves carry over their whole front a uniform chance of doing work.

It is the propagation of a chance which the wave-theory studies.

Different views may be held as to how the prize-drawing is conducted on the sweepstake theory. Some hold that the lucky part of the wave-front is already marked before the atom is reached.

The energies of the orbits in hydrogen are calculated by classical laws; but one of the purposes of the calculation is to verify the association of energy and period in the unit , which is contrary to classical laws of radiation.

The whole procedure is glaringly contradictory but conspicuously successful.

In my observatory there is a telescope which condenses the light of a star on a film of sodium in a photoelectric cell. I rely on the classical theory to conduct the light through the lenses and focus it in the cell;

If we have ever scorned this attitude, Nemesis has overtaken us. For ten years we have had to divide modern science into two compartments; we have one set of beliefs in the classical compartment and another set of beliefs in the quantum compartment.

Unfortunately our compartments are not watertight.

We must, of course, look forward to an ultimate reconstruction of our conceptions of the physical world which will embrace both the classical laws and the quantum laws in harmonious association.

And so when the quantum number reaches infinity, and the atom bursts, a genuine classical electron flies out.

The electron, as it leaves the atom, crystallises out of Schrödinger’s mist like a genie emerging from his bottle.

[31] Prof. E. T. Whittaker.

actually the diffraction pattern then obtained is not the same.

The quantum must be large enough to cover a 100-inch mirror.

But if this same star-light without any artificial concentration falls on a film of potassium, electrons will fly out each with the whole energy of a quantum.

A whole quantum of light energy must have gone into the atom and blasted away the electron.

The quantum must be small enough to enter an atom.

I do not think there is much doubt as to the ultimate origin of this contradiction. We must not think about space and time in connection with an individual quantum; and the extension of a quantum in space has no real meaning.

I do not think there is much doubt as to the ultimate origin of this contradiction. We must not think about space and time in connection with an individual quantum; and the extension of a quantum in space has no real meaning.

To apply these conceptions to a single quantum is like reading the Riot Act to one man.

A single quantum has not travelled 50 billion miles from Sirius; it has not been 8 years on the way.

and the clearing away of false evidence for a partly corpuscular theory, which influenced Newton, is as much a part of scientific progress as the bringing forward of the (possibly) true evidence, which influences us to-day.

To imagine that Newton’s great scientific reputation is tossing up and down in these latter-day revolutions is to confuse science with omniscience.

To return to the wavicle.—If that which we have commonly regarded as a wave partakes also of the nature of a particle, may not that which we have commonly regarded as a particle partake also of the nature of a wave?

So, as a first step, instead of trying to clear up the mystery we try to extend it. Instead of explaining how anything can possess simultaneously the incongruous properties of wave and particle we seek to show experimentally that these properties are universally associated.

There are no pure waves and no pure particles.

The characteristic of a wave-theory is the spreading of a ray of light after passing through a narrow aperture—a well-known phenomenon called diffraction. The scale of the phenomenon is proportional to the wave-length of the light.

Nowadays we do not encourage the engineer to build the world for us out of his material, but we turn to the mathematician to build it out of his material.

Doubtless the mathematician is a loftier being than the engineer, but perhaps even he ought not to be entrusted with the Creation unreservedly.

We are dealing in physics with a symbolic world, and we can scarcely avoid employing the mathematician who is the professional wielder of symbols;

The outcome of it is a fundamental general principle which seems to rank in importance with the principle of relativity. I shall here call it the “principle of indeterminacy”.

The gist of it can be stated as follows: a particle may have position or it may have velocity but it cannot in any exact sense have both.

If we are content with a certain margin of inaccuracy and if we are content with statements that claim no certainty but only high probability, then it is possible to ascribe both position and velocity to a particle.

is there no conceivable way of fixing the position to ¹⁄₁₀₀₀₀ of a millimetre? Certainly; but in that case it will only be possible to fix the velocity with an error of 10 kilometres per second.

The conditions of our exploration of the secrets of Nature are such that the more we bring to light the secret of position the more the secret of velocity is hidden.

They are like the old man and woman in the weather-glass; as one comes out of one door, the other retires behind the other door.

it refrains from attributing to a particle a kind of determinacy which does not correspond to anything in Nature. But I would not regard the principle of indeterminacy as a result to be deduced from Schrödinger’s theory; it is the other way about.

The principle of indeterminacy, like the principle of relativity, represents the abandonment of a mistaken assumption which we never had sufficient reason for making.

Just as we were misled into untenable ideas of the aether through trusting to an analogy with the material ocean, so we have been misled into untenable ideas of the attributes of the microscopic elements of world-structure through trusting to analogy with gross particles.

A New Epistemology. The principle of indeterminacy is epistemological. It reminds us once again that the world of physics is a world contemplated from within surveyed by appliances which are part of it and subject to its laws.

What the world might be deemed like if probed in some supernatural manner by appliances not furnished by itself we do not profess to know.

There is a doctrine well known to philosophers that the moon ceases to exist when no one is looking at it.

We must not introduce anything like velocity through aether, which is meaningless since it is not assigned any causal connection with our experience. On the other hand we cannot limit the description to the immediate data of our own spasmodic observations.

The description should include nothing that is unobservable but a great deal that is actually unobserved.

Virtually we postulate an infinite army of watchers and measurers. From moment to moment they survey everything that can be surveyed and measure everything that can be measured by methods which we ourselves might conceivably employ.

We have at last realised the disconcerting fact that though it applies to the moon it does not apply to the electron.

It does not hurt the moon to look at it.

There is no inconsistency in supposing it to have been under the surveillance of relays of watchers whilst we were asleep. But it is otherwise with an electron. At certain times, viz.

We might arm our observers with flash-lamps to keep a more continuous watch on its doings; but the trouble is that under the flashlight it will not go on doing what it was doing in the dark.

There is a fundamental inconsistency in conceiving the microscopic structure of the physical world to be under continuous survey because the surveillance would itself wreck the whole machine.

I expect that at first this will sound to you like a merely dialectical difficulty. But there is much more in it than that.

A quantum action may be the means of revealing to us some fact about Nature, but simultaneously a fresh unknown is implanted in the womb of Time.

An addition to knowledge is won at the expense of an addition to ignorance.

It is hard to empty the well of Truth with a leaky bucket.

A quantum action may be the means of revealing to us some fact about Nature, but simultaneously a fresh unknown is implanted in the womb of Time. An addition to knowledge is won at the expense of an addition to ignorance.

It is hard to empty the well of Truth with a leaky bucket.

We have an intricate task before us.

We are going to build a World—a physical world which will give a shadow performance of the drama enacted in the world of experience.

We are not very expert builders as yet; and you must not expect the performance to go off without a hitch or to have the richness of detail which a critical audience might require.

Relation Structure. We take as building material relations and relata. The relations unite the relata; the relata are the meeting points of the relations.

The one is unthinkable apart from the other.

I do not think that a more general starting-point of structure could be conceived.

that he has not even begun to find the controlling laws.

The college may totter but the Bursar’s accounts still balance.

The law of conservation of momentum and energy results from the overlapping of the different aspects in which the “non-emptiness of space” presents itself to our practical experience.

and Hamiltonian differentiation is virtually the symbol for creation of an active world out of the formless background.

Not once in the dim past, but continuously by conscious mind is the miracle of the Creation wrought.

By following this particular plan of building we construct things which satisfy the law of conservation, that is to say things which are permanent. The law of conservation is a truism for the things which satisfy it;

You will understand that the building to which I refer is not a shifting about of material; it is like building constellations out of stars. The things which we might have built but did not, are there just as much as those we did build.

What we have called building is rather a selection from the patterns that weave themselves.

The element of permanence in the physical world, which is familiarly represented by the conception of substance, is essentially a contribution of the mind to the plan of building or selection. We can see this selective tendency at work in a comparatively simple problem, viz.

again the progress of a wave-group is not the progress of a wave. These forms have a certain degree of permanence amid the shifting particles of water.

Anything permanent tends to become dignified with an attribute of substantiality.

An ocean traveller has even more vividly the impression that the ocean is made of waves than that it is made of water.[39] Ultimately it is this innate hunger for permanence in our minds which directs the course of development of hydrodynamics, and likewise directs …

again the progress of a wave-group is not the progress of a wave. These forms have a certain degree of permanence amid the shifting particles of water. Anything permanent tends to become dignified with an attribute of substantiality.

An ocean traveller has even more vividly the impression that the ocean is made of waves than that it is made of water.[39]

Ultimately it is this innate hunger for permanence in our minds which directs the course of development of hydrodynamics, and likewise directs the world-building out of the sixteen measures of structure.

Statistical laws relate to the behaviour of crowds, and depend on the fact that although the behaviour of each individual may be extremely uncertain average results can be predicted with confidence.

Much of the apparent uniformity of Nature is a uniformity of averages.

Our gross senses only take cognisance of the average effect of vast numbers of individual particles and processes; and the regularity of the average might well be compatible with a great degree of lawlessness of the individual.

At present we can notice the contrast that the laws which we now recognise as man-made are characterised by continuity, whereas the laws to which the mind as yet lays no claim are characterised by atomicity.

The quantum theory with its avoidance of fractions and insistence on integral units seems foreign to any scheme which we should be likely subconsciously to have imposed as a frame for natural phenomena.

Perhaps our final conclusion as to the world of physics will resemble Kronecker’s view of pure mathematics.

It managed surprisingly well.

Ignorance of the nature of these entities was no bar to successful prediction of behaviour.

We gradually awoke to the fact that the scheme of treatment of quantities on the waiting-list was becoming more precise and more satisfying than our knowledge of familiar things. Familiar conceptions did not absorb the waiting-list, but the waiting-list began to absorb familiar conceptions.

Ignorance of the nature of these entities was no bar to successful prediction of behaviour. We gradually awoke to the fact that the scheme of treatment of quantities on the waiting-list was becoming more precise and more satisfying than our knowledge of familiar things.

Familiar conceptions did not absorb the waiting-list, but the waiting-list began to absorb familiar conceptions.

Aether, after being in turn an elastic solid, a jelly, a froth, a conglomeration of gyrostats, was denied a material and substantial nature and put back on the waiting-list.

No doubt there are more roundabout ways used in practice for determining the weights of elephants and the slopes of hills, but these are justified because it is known that they give the same results as direct pointer readings.

And so we see that the poetry fades out of the problem, and by the time the serious application of exact science begins we are left with only pointer readings.

If then only pointer readings or their equivalents are put into the machine of scientific calculation, how can we grind out anything but pointer readings? But that is just what we do grind out.

(It should be remembered that the hill also has been replaced by pointer readings, and the sliding down is no longer an active adventure but a functional relation of space and time measures.)

The word elephant calls up a certain association of mental impressions, but it is clear that mental impressions as such cannot be the subject handled in the physical problem.

We have, for example, an impression of bulkiness. To this there is presumably some direct counterpart in the external world, but that counterpart must be of a nature beyond our apprehension, and science can make nothing of it.

Or if he sees the folly of calling the most undoubted element of our experience an illusion, he will have to face the tremendous question,

How can this collection of ordinary atoms be a thinking machine?

But what knowledge have we of the nature of atoms which renders it at all incongruous that they should constitute a thinking object? The Victorian physicist felt that he knew just what he was talking about when he used such terms as matter and atoms.

But now we realise that science has nothing to say as to the intrinsic nature of the atom.

The physical atom is, like everything else in physics, a schedule of pointer readings.

The schedule is, we agree, attached to some unknown background. Why not then attach it to something of spiritual nature of which a prominent characteristic is thought.

Let me give an illustration which takes us to the root of the great problem of the relations of matter and spirit. Take the living human brain endowed with mind and thought.

Thought is one of the indisputable facts of the world.

I know that I think, with a certainty which I cannot attribute to any of my physical knowledge of the world. More hypothetically, but on fairly plausible evidence, I am convinced that you have minds which think.

Will this array of symbols give me the whole of Mr. X? There is not the least reason to think so. The voice that comes to us over the telephone wire is not the whole of what is at the end of the wire.

The scientific linkage is like the telephone wire; it can transmit just what it is constructed to transmit and no more.

It will be seen that the line of communication has two aspects. It is a chain of inference stretching from the symbols immediately associated with the sensations in my mind to the symbols descriptive of Mr. X;

Will this array of symbols give me the whole of Mr. X? There is not the least reason to think so.

The voice that comes to us over the telephone wire is not the whole of what is at the end of the wire.

The scientific linkage is like the telephone wire; it can transmit just what it is constructed to transmit and no more.

This knowledge has all been inferred and it was bound therefore to conform to the system of inference that was used.

The determinism of the physical laws simply reflects the determinism of the method of inference.

This soulless nature of the scientific world need not worry those who are persuaded that the main significances of our environment are of a more spiritual character.

Behind it is a subordinate background of space and time permeated by forces and unconcrete agencies to minister to the star performer.

Our conception of substance is only vivid so long as we do not face it.

It begins to fade when we analyse it. We may dismiss many of its supposed attributes which are evidently projections of our sense-impressions outwards into the external world.

Our conception of substance is only vivid so long as we do not face it.

It begins to fade when we analyse it.

We may dismiss many of its supposed attributes which are evidently projections of our sense-impressions outwards into the external world.

It offers nothing to satisfy our demand for the concrete. How should it, when we cannot formulate that demand? I tried to formulate it; but nothing resulted save a tightening of the fingers. Science does not overlook the provision for tactual and muscular sensation.

In leading us away from the concrete, science is reminding us that our contact with the real is more varied than was apparent to the ape-mind, to whom the bough which supported him typified the beginning and end of reality.

It is not solely the scientific world that will now occupy our attention. In accordance with the last chapter we are taking a larger view in which the cyclical schemes of physics are embraced with much besides.

If the criticism is made that certain aspects are touched on which come more within the province of the expert psychologist, I must admit its pertinence.

The recent tendencies of science do, I believe, take us to an eminence from which we can look down into the deep waters of philosophy; and if I rashly plunge into them, it is not because I have confidence in my powers of swimming, but to try to show that the water is really deep.

To put the conclusion crudely—the stuff of the world is mind-stuff. As is often the way with crude statements, I shall have to explain that by “mind” I do not here exactly mean mind and by “stuff” I do not at all mean stuff.

and if I rashly plunge into them, it is not because I have confidence in my powers of swimming, but to try to show that the water is really deep.

To put the conclusion crudely—the stuff of the world is mind-stuff.

As is often the way with crude statements, I shall have to explain that by “mind” I do not here exactly mean mind and by “stuff” I do not at all mean stuff.

By this very indirect and hypothetical inference all our supposed acquaintance with and our theories of a world outside us have been built up.

We are acquainted with an external world because its fibres run into our consciousness; it is only our own ends of the fibres that we actually know; from those ends we more or less successfully reconstruct the rest, as a palaeontologist reconstructs an extinct monster from its footprint.

The mind-stuff is the aggregation of relations and relata which form the building material for the physical world. Our account of the building process shows, however, that much that is implied in the relations is dropped as unserviceable for the required building.

The mind-stuff is not spread in space and time; these are part of the cyclic scheme ultimately derived out of it. But we must presume that in some other way or aspect it can be differentiated into parts.

Only here and there does it rise to the level of consciousness, but from such islands proceeds all knowledge.

Besides the direct knowledge contained in each self-knowing unit, there is inferential knowledge. The latter includes our knowledge of the physical world.

The term “mind-stuff” might well be amended; but neutral stuff seems to be the wrong kind of amendment. It implies that we have two avenues of approach to an understanding of its nature. We have only one approach, namely, through our direct knowledge of mind.

The supposed approach through the physical world leads only into the cycle of physics, where we run round and round like a kitten chasing its tail and never reach the world-stuff at all.

I assume that we have left the illusion of substance so far behind that the word “stuff” will not cause any misapprehension. I certainly do not intend to materialise or substantialise mind.

I assume that we have left the illusion of substance so far behind that the word “stuff” will not cause any misapprehension. I certainly do not intend to materialise or substantialise mind.

Mind is—but you know what mind is like, so why should I say more about its nature?

The word “stuff” has reference to the function it has to perform as a basis of world-building and does not imply any modified view of its nature.

It is difficult for the matter-of-fact physicist to accept the view that the substratum of everything is of mental character.

But no one can deny that mind is the first and most direct thing in our experience, and all else is remote inference—inference either intuitive or deliberate.

Probably it would never have occurred to us (as a serious hypothesis) that the world could be based on anything else, had we not been under the impression that there was a rival stuff with a more comfortable kind of “concrete” reality—something too inert and …

It is a grand word for a peroration. “The right honourable speaker went on to declare that the concord and amity for which he had unceasingly striven had now become a reality (loud cheers).”

The conception which it is so troublesome to apprehend is not “reality” but “reality (loud cheers)”.

Let us first examine the definition according to the purely scientific usage of the word, although it will not take us far enough. The only subject presented to me for study is the content of my consciousness.

The hypothesis only becomes useful when it is the means of bringing together the worlds of many consciousnesses occupying different view-points.

The external world of physics is thus a symposium of the worlds presented to different view-points.

There is general agreement as to the principles on which the symposium should be formed. Statements made about this external world, if they are unambiguous, must be either true or false. This has often been denied by philosophers.

The tossing up of the electron is a conventional way of depicting a particular change of state of the atom which cannot really be associated with movements in space as macroscopically conceived.

Something unknown is doing we don’t know what—that is what our theory amounts to.

It does not sound a particularly illuminating theory. I have read something like it elsewhere—

It would not be a bad reminder of the essential unknownness of the fundamental entities of physics to translate it into “Jabberwocky”; provided all numbers—all metrical attributes—are unchanged, it does not suffer in the least.

Out of the numbers proceeds that harmony of natural law which it is the aim of science to disclose.

We can grasp the tune but not the player. Trinculo might have been referring to modern physics in the words, “This is the tune of our catch, played by the picture of Nobody”.

provided all numbers—all metrical attributes—are unchanged, it does not suffer in the least. Out of the numbers proceeds that harmony of natural law which it is the aim of science to disclose.

We can grasp the tune but not the player.

Trinculo might have been referring to modern physics in the words, “This is the tune of our catch, played by the picture of Nobody”.

but by contemplating eight circulating electrons in one atom and seven circulating electrons in another we begin to realise the difference between oxygen and nitrogen. Eight slithy toves gyre and gimble in the oxygen wabe; seven in nitrogen.

By admitting a few numbers even “Jabberwocky” may become scientific.

We can now venture on a prediction; if one of its toves escapes, oxygen will be masquerading in a garb properly belonging to nitrogen. In the stars and nebulae we do find such wolves in sheep’s clothing which might otherwise have startled us.

yet I have not been able to form a satisfactory conception of any kind of law or causal sequence which shall be other than deterministic.

It seems contrary to our feeling of the dignity of the mind to suppose that it merely registers a dictated sequence of thoughts and emotions; but it seems equally contrary to its dignity to put it at the mercy of impulses with no causal antecedents.

I shall not deal with this dilemma. Here I have to set forth the position of physical science on this matter so far as it comes into her territory.

198); and the predictability of its configurations is not characteristic of natural phenomena in general but of those involving great numbers of atoms of action—such that we are concerned not with individual but with average behaviour.

Human life is proverbially uncertain; few things are more certain than the solvency of a life-insurance company.

The average law is so trustworthy that it may be considered predestined that half the children now born will survive the age of years. But that does not tell us whether the span of life of young A. McB.

But that does not tell us whether the span of life of young A. McB. is already written in the book of fate, or whether there is still time to alter it by teaching him not to run in front of motor-buses.

The eclipse in 1999 is as safe as the balance of a life-insurance company; the next quantum jump of an atom is as uncertain as your life and mine.

We are thus in a position to answer the main argument for a predetermination of the future, viz.

Because it admits only two lower states for the atom to go to. Further, it makes no attempt to find a definite answer, but contents itself with calculating the respective odds on the jumps to State 1 and State 2.

The quantum physicist does not fill the atom with gadgets for directing its future behaviour, as the classical physicist would have done; he fills it with gadgets determining the odds on its future behaviour.

He studies the art of the bookmaker not of the trainer.

The quantum physicist does not fill the atom with gadgets for directing its future behaviour, as the classical physicist would have done; he fills it with gadgets determining the odds on its future behaviour.

He studies the art of the bookmaker not of the trainer.

Thus in the structure of the world as formulated in the new quantum theory it is predetermined that of 500 atoms now in State 3, approximately 400 will go on to State 1 and 100 to State 2—in so far as anything subject to chance …

this tells me that nowhere in the world as yet is there any trace of a deciding factor as to whether I am going to lift my right hand or my left. It depends on an unfettered act of volition not yet made or foreshadowed.[48]

My intuition is that the future is able to bring forth deciding factors which are not secretly hidden in the past.

The position is that the laws governing the microscopic elements of the physical world—individual atoms, electrons, quanta—do not make definite predictions as to what the individual will do next.

This velocity, however, is of no use for prediction, because in making the second accurate determination of position we have rough-handled the particle so much that it no longer has the velocity we calculated. It is a purely retrospective velocity.

The velocity does not exist in the present tense but in the future perfect; it never exists, it never will exist, but a time may come when it will have existed.

There is no room for it in Fig. 4 which contains an Absolute Future and an Absolute Past but not an Absolute Future Perfect.

The classical view that a particle necessarily has a definite (but not necessarily knowable) velocity now, amounts to disguising a piece of the unknown future as an unknowable element of the present.

Classical physics foists a deterministic scheme on us by a trick; it smuggles the unknown future into the present, trusting that we shall not press an inquiry as to whether it has become any more knowable that way.

The same principle extends to every kind of phenomenon that we attempt to predict, so long as the need for accuracy is not buried under a mass of averages.

To every co-ordinate there corresponds a momentum, and by the principle of indeterminacy the more accurately the co-ordinate is known the less accurately the momentum is known.

Nature thus provides that knowledge of one-half of the world will ensure ignorance of the other half—ignorance which, we have seen, may be remedied later when the same part of the world is contemplated retrospectively.

We can scarcely rest content with a picture of the world which includes so much that cannot be known. We have been trying to get rid of unknowable things, i.e. all conceptions which have no causal connection with our experience.

In assessing whether the symbols which the physicist has scattered through the external world are adequate to predetermine the future, we must be on our guard against retrospective symbols.

It is easy to prophesy after the event.

Natural and Supernatural. A rather serious consequence of dropping causality in the external world is that it leaves us with no clear distinction between the Natural and the Supernatural.

because I have, or am persuaded that I have, “a will of my own”. Either the physicist must leave his causal scheme at the mercy of supernatural interference from me, or he must explain away my supernatural qualities.

In self-defence the materialist favoured the latter course; he decided that I was not supernatural—only complicated.

We on the other hand have concluded that there is no strict causal behaviour anywhere. We can scarcely deny the charge that in abolishing the criterion of causality we are opening the door to the savage’s demons.

I will take Lamb’s Hydrodynamics with me next time”. It is good that there should be such moments for us.

Life would be stunted and narrow if we could feel no significance in the world around us beyond that which can be weighed and measured with the tools of the physicist or described by the metrical symbols of the mathematician.

Of course it was an illusion. We can easily expose the rather clumsy trick that was played on us.

Get back to the solid substance of things, to the material of the water moving under the pressure of the wind and the force of gravitation in obedience to the laws of hydrodynamics.

But the solid substance of things is another illusion.

It too is a fancy projected by the mind into the external world. We have chased the solid substance from the continuous liquid to the atom, from the atom to the electron, and there we have lost it.

It is because the mind, the weaver of illusion, is also the only guarantor of reality that reality is always to be sought at the base of illusion.

Illusion is to reality as the smoke to the fire.

I will not urge that hoary untruth “There is no smoke without fire”. But it is reasonable to inquire whether in the mystical illusions of man there is not a reflection of an underlying reality.

I do not know whether it would be correct to say that reasoning is only applicable to symbolic knowledge, but the more customary forms of reasoning have been developed for symbolic knowledge only.

The intimate knowledge will not submit to codification and analysis; or, rather, when we attempt to analyse it the intimacy is lost and it is replaced by symbolism.

For an illustration let us consider Humour. I suppose that humour can be analysed to some extent and the essential ingredients of the different kinds of wit classified. Suppose that we are offered an alleged joke.

Logically, I suppose, our next procedure would be to laugh. But it may certainly be predicted that as the result of this scrutiny we shall have lost all inclination we may ever have had to laugh at it.

It simply does not do to expose the inner workings of a joke.

The classification concerns a symbolic knowledge of humour which preserves all the characteristics of a joke except its laughableness. The real appreciation must come spontaneously, not introspectively.

it is an everyday world to be compared with the material world of familiar experience. I claim it as no more real and no less real than that.

Primarily it is not a world to be analysed, but a world to be lived in.

Granted that this takes us outside the sphere of exact knowledge, and that it is difficult to imagine that anything corresponding to exact science will ever be applicable to this part of our environment, the mystic is unrepentant.

He would say, The familiar material world of everyday conception, though lacking somewhat in scientific truth, is good enough to live in; in fact the scientific world of pointer readings would be an impossible sort of place to inhabit.

It is a symbolic world and the only thing that could live comfortably in it would be a symbol.

But I am not a symbol; I am compounded of that mental activity which is from your point of view a nest of illusion, so that to accord with my own nature I have to transform even the world explored by my senses.

Granted that this takes us outside the sphere of exact knowledge, and that it is difficult to imagine that anything corresponding to exact science will ever be applicable to this part of our environment, the mystic is unrepentant.

Because we are unable to render exact account of our environment it does not follow that it would be better to pretend that we live in a vacuum.

If the defence may be considered to have held good against the first onslaught, perhaps the next stage of the attack will be an easy tolerance. “Very well. Have it your own way. It is a harmless sort of belief—not like a more dogmatic theology.

We must not interrupt the “practical men”, these busy moulders of history carrying us at ever-increasing pace towards our destiny as an ant-heap of humanity infesting the earth.

But is it true in history that material forces have been the most potent factors?

Call it of God, of the Devil, fanaticism, unreason; but do not underrate the power of the mystic. Mysticism may be fought as error or believed as inspired, but it is no matter for easy tolerance—

But is it true in history that material forces have been the most potent factors? Call it of God, of the Devil, fanaticism, unreason; but do not underrate the power of the mystic.

Mysticism may be fought as error or believed as inspired, but it is no matter for easy tolerance—

Reality and Mysticism. But a defence before the scientists may not be a defence to our own self-questionings. We are haunted by the word reality. I have already tried to deal with the questions which arise as to the meaning of reality;

Few deliberately hold the philosophy that the forces of progress are related only to the material side of our environment, but few can claim that they are not more or less under its sway.

We must not interrupt the “practical men”, these busy moulders of history carrying us at ever-increasing pace towards our destiny as an ant-heap of humanity infesting the earth.

But is it true in history that material forces have been the most potent factors? Call it of God, of the Devil, fanaticism, unreason; but do not underrate the power of the mystic.

Reality and Mysticism. But a defence before the scientists may not be a defence to our own self-questionings.

We are haunted by the word reality.

I have already tried to deal with the questions which arise as to the meaning of reality; but it presses on us so persistently that, at the risk of repetition, I must consider it once more from the standpoint of religion.

and it is an important condition that we who have to solve the problem are ourselves part of the problem. Looking at the very beginning, the initial fact is the feeling of purpose in ourselves which urges us to embark on the problem.

We are meant to fulfil something by our lives.

There are faculties with which we are endowed, or which we ought to attain, which must find a status and an outlet in the solution. It may seem arrogant that we should in this way insist on moulding truth to our own nature;

But although that is how the rainbow impresses itself on an impersonal spectroscope, we are not giving the whole truth and significance of experience—the starting-point of the problem—if we suppress the factors wherein we ourselves differ from a spectroscope.

We cannot say that the rainbow, as part of the world, was meant to convey the vivid effects of colour; but we can perhaps say that the human mind as part of the world was meant to perceive it that way.

Significance and Values. When we think of the sparkling waves as moved with laughter we are evidently attributing a significance to the scene which was not there.

If they can be held to have had any intention at all it was to satisfy certain differential equations—and that was because they are the creatures of the mathematician who has a partiality for differential equations.

The physical no less than the mystical significance of the scene is not there; it is here—in the mind.

What we make of the world must be largely dependent on the sense-organs that we happen to possess. How the world must have changed since man came to rely on his eyes rather than his nose!

What we make of the world must be largely dependent on the sense-organs that we happen to possess.

How the world must have changed since man came to rely on his eyes rather than his nose!

You are alone on the mountains wrapt in a great silence; but equip yourself with an extra artificial sense-organ and, lo! the aether is hideous with the blare of the Savoy bands. Or—

You are alone on the mountains wrapt in a great silence; but equip yourself with an extra artificial sense-organ and, lo! the aether is hideous with the blare of the Savoy bands. Or—

So far as broader characteristics are concerned we see in Nature what we look for or are equipped to look for.

Of course, I do not mean that we can arrange the details of the scene; but by the light and shade of our values we can bring out things that shall have the broad characteristics we esteem.

I have naturally tried to make the outlook reached in these lectures as coherent as possible, but I should not be greatly concerned if under the shafts of criticism it becomes very ragged.

Coherency goes with finality; and the anxious question is whether our arguments have begun right rather than whether they have had the good fortune to end right.

The leading points which have seemed to me to deserve philosophic consideration may be summarised as follows:

In regard to our experience of the physical world we have very much misunderstood the meaning of our sensations. It has been the task of science to discover that things are very different from what they seem.

But we do not pluck out our eyes because they persist in deluding us with fanciful colourings instead of giving us the plain truth about wave-length.

It is in the midst of such misrepresentations of environment (if you must call them so) that we have to live.

We cannot pretend to offer proofs. Proof is an idol before whom the pure mathematician tortures himself.

In physics we are generally content to sacrifice before the lesser shrine of Plausibility.

And even the pure mathematician—that stern logician—reluctantly allows himself some prejudgments; he is never quite convinced that the scheme of mathematics is flawless, and mathematical logic has undergone revolutions as profound as the revolutions of physical theory.

We cannot pretend to offer proofs.

Proof is an idol before whom the pure mathematician tortures himself.

In physics we are generally content to sacrifice before the lesser shrine of Plausibility. And even the pure mathematician—that stern logician—reluctantly allows himself some prejudgments;

And even the pure mathematician—that stern logician—reluctantly allows himself some prejudgments; he is never quite convinced that the scheme of mathematics is flawless, and mathematical logic has undergone revolutions as profound as the revolutions of physical theory.

We are all alike stumblingly pursuing an ideal beyond our reach.

In science we sometimes have convictions as to the right solution of a problem which we cherish but cannot justify; we are influenced by some innate sense of the fitness of things.

at least it is in harmony with it. But if so, all that our inquiry justifies us in asserting is a purely colourless pantheism.

Science cannot tell whether the world-spirit is good or evil, and its halting argument for the existence of a God might equally well be turned into an argument for the existence of a Devil.

I think that that is an example of the limitation of physical schemes that has troubled us before—namely, that in all such schemes opposites are represented by + and -. Past and future, cause and effect, are represented in this inadequate way.

or, to be more explicit, the direction of the arrow could be determined by statistical rules, but its significance as a governing fact “making sense of the world” could only be deduced on teleological assumptions.

If physics cannot determine which way up its own world ought to be regarded, there is not much hope of guidance from it as to ethical orientation.

We trust to some inward sense of fitness when we orient the physical world with the future on top, and likewise we must trust to some inner monitor when we orient the spiritual world with the good on top.

We are anxious for perfect truth, but it is hard to say in what form perfect truth is to be found.

I cannot quite believe that it has the form typified by an inventory.

Somehow as part of its perfection there should be incorporated in it that which we esteem as a “sense of proportion”.

I must do this whilst hanging from a round planet head outward into space, and with a wind of aether blowing at no one knows how many miles a second through every interstice of my body. The plank has no solidity of substance.

To step on it is like stepping on a swarm of flies.

Shall I not slip through? No, if I make the venture one of the flies hits me and gives a boost up again; I fall again and am knocked upwards by another fly; and so on.

Then again it is necessary to determine in which direction the entropy of the world is increasing in order to make sure that my passage over the threshold is an entrance, not an exit.

Verily, it is easier for a camel to pass through the eye of a needle than for a scientific man to pass through a door.

And whether the door be barn door or church door it might be wiser that he should consent to be an ordinary man and walk in rather than wait till all the difficulties involved in a really scientific ingress are resolved.

There was a time when the whole combination of self and environment which makes up experience seemed likely to pass under the dominion of a physics much more iron-bound than it is now.

That overweening phase, when it was almost necessary to ask the permission of physics to call one’s soul one’s own, is past.

The change gives rise to thoughts which ought to be developed. Even if we cannot attain to much clarity of constructive thought we can discern that certain assumptions, expectations or fears are no longer applicable.

It is worse nonsense to deny it. Or as that ardent relativist the Red Queen puts it, “You call that nonsense, but I’ve heard nonsense compared with which that would be as sensible as a dictionary”.

For if those who hold that there must be a physical basis for everything hold that these mystical views are nonsense, we may ask—What then is the physical basis of nonsense?

The “problem of nonsense” touches the scientist more nearly than any other moral problem. He may regard the distinction of good and evil as too remote to bother about;