The Philosophy of Science of James Jeans
Although written from the viewpoint of logic of language (which asks how an objective distinction is to be made between sense and nonsense in the language of philosophical problems), this paper it should not be taken to represent Wittgenstein's own views about physics.
The Mysterious or the Accidental Universe?
[The existence of a planet on which life can exist is] the result of what may properly be described as an accident. The use of such a word need not imply any surprise that our earth exists, for accidents will happen, and if the universe goes on for long enough, every conceivable accident is likely to happen in time. (James Jeans, The Mysterious Universe (1930) p. 4) [Note 1]
This is not even a possible hypothesis. Even if it were mathematically demonstrable -- that theorem (exactly like the theorems of deductive geometry) could not escape the question of verification, i.e. of whether or not it is applicable to reality. But the subsidiary rule 'in time' makes this a tautology; it cannot be falsified. (This is anyway a Greek notion; it is a thesis of metaphysics, not of physics.) Two pages later 'likely' becomes 'certain':
... a group of atoms might happen to arrange themselves in the way in which they are arranged in the living cell. Indeed, given sufficient time, they would be certain to do so ... (Jeans p. 6)
With that this picture has become "something we can't query, something that is the reality behind phenomena" (Drury). Whatever its use, it is not this: hypothetical explanation. "Might happen" is not an explanation (An explanation that can explain any and every thing is no explanation). What would need to be explained here is: Why was just this possibility realized? Jeans might say that we live in a universe where the extremely improbable sometimes happens, and that physicists do not try to explain the realization of any particular possibility, but accept it as a given.
If Jeans is not surprised by the existence of a life-sustaining planet like our earth, and of the ascent of the human species, then why does he call his book "The Mysterious Universe"? If the occurrence of something unlikely in the extreme isn't mysterious, then what is? If the earth were to suddenly open and swallow Jeans' cat, would Jeans say that he was not surprised? Why didn't Jeans call his book "The Accidental Universe"? At what point do you say: An accident that big is no accident? (cf. LC p. 61-2) -- But not as if that reply would be an hypothesis rather than a rule of grammar.
It makes no sense to call the whole universe 'mysterious', although some of its parts may be. The word 'mysterious' requires an antithesis: mysterious as opposed to what? If everything is a mystery, then nothing is. (The proposition that existence is a mystery is the world-picture of religion or metaphysics, not physics.)
Is Jeans implying that, "given time", we should on some occasions expect the water in our teapot to freeze when placed over a fire? "Accidents will happen in even the best of universes."
Outline of this page ...
- The Mysterious or the Accidental Universe?
- Feeling compelled by a Rule because we can imagine no Other Possibility
- Indeterminism and Levels of Investigation
- Relativity as an Hypothesis and as a Way of Looking at Things
- The Place of Mathematics in Physics ("mathematical pictures")
- Two Philosophers' Criticisms of James Jeans' Mysterious Universe
Feeling compelled by a Rule because we can imagine no Other Possibility
Each extension of the law of causation, and each success of the mechanical interpretation of nature, made the belief in free-will more difficult. For if all nature obeyed the law of causation, why should life be exempt? Out of such considerations arose the mechanistic philosophies of the seventeenth and eighteenth centuries ...
... until early in the nineteenth century life could still be regarded as something standing entirely apart form inanimate nature. Then came the discovery that living cells were formed of precisely the same chemical atoms as non-living matter, and so were presumably governed by the same natural laws. (Jeans p. 20)
While philosophers [of the nineteenth century] were still debating whether a machine could be constructed to reproduce the thoughts of Newton, ... of Bach ... or of Michelangelo, the average man of science was rapidly becoming convinced that no machine could be constructed to reproduce the light of a candle or the fall of an apple. (p. 21)
I wrote earlier that philosophers hardly needed physicists to suggest to them implications for 'Every event has a cause'. But it's true: I don't know that to be an historical fact.
But what was a tautology for philosophers -- i.e. a rule of grammar treated as a universal law, -- became for scientists an hypothesis to be tested, and, as it happened in this century, to be discarded. However, philosophers are still in the grips of that rule of grammar -- and still trying to draw conclusions about reality from it. Belief in the causal nexus is not only superstition (cf. TLP 5.1361); -- it is also feeling oneself trapped, captivated (PI § 115), by a picture-grammar. If, however, we treat 'Every event has a cause' as an induced generality, then we must state what would count as an anomaly. And if nothing is allowed to count against it, then we say nothing about reality with this generality; we only say how we look at things. If the lenses of my glasses are blue, then I cannot attribute blueness to what I see through my glasses.
'Every event has a cause' is not the same as 'Every effect has a cause'. The latter, but not the former, is necessarily a rule of grammar (i.e. entirely a matter of definition). The former should not be treated as if it were the latter; conceptual confusion should not be allowed to turn 'Every event has a cause' into a dogma.
Being held captive by a Picture
Being compelled, not by the facts, -- but by a rule. Feeling that there is no alternative, that the alternative is contradictory (a contradiction in sense, not merely in form).
E.g. someone who has never heard of anything but Euclidean space (i.e. "flat space") is told that: The universe -- i.e. space -- is finite. What are they to make of this? For they can imagine only a Euclidean plane. They think: you set out walking in a straight line and eventually you come to the end of the universe. This is absurd -- or what: is there a wall beyond which you cannot go? But it makes no sense to speak of a wall that has only one side; -- so what is on the other side? At school we were actually given the reply: 'There's not even a place for you to be.'
A similar picture was the ancient inscription on the pillar of Hercules at Gibraltar (Calpe), namely non plus ultra ("no more beyond"), marking the limit of the world, impassible to both wise men and fools, Pindar said. And on the other side? "There is no other side." (Cf. the tortoise on whose back the earth rests, the tortoise whose legs reach "all the way down".)
Now, what can anyone make of that? Well, what can anyone make of nonsense? One thinks: the universe must be an infinite space; like the Euclidean plane: you can walk forever without ever coming to the end.
This is an excellent example of the conviction that "Things just must be this way; there is no alternative". But why "must" things be this way? It is because one cannot imagine an alternative; and what can be imagined belongs to grammar. One is compelled to think this way: but what compels one is a rule. One is in the grips of a rule. So what is to be done?
Nothing is more important for teaching us to understand the concepts we have than constructing fictitious ones. (CV p. 74)
Wherein lies the importance of depicting anomalies precisely? If you cannot do it, this shows that you are not thoroughly familiar with the concepts. (ibid. p. 72)
This is not necessarily an easy thing to do. If Einstein had not made a distinction between "practical [verified by experience] geometry" and "axiomatic [deduced] geometry", the way forward -- i.e. the invention of his relativity theory -- would have been barred to him. [Note 2] If Euclid had been the only possible geometry; if no alternative had been available. Because one can dispute facts or pictures of the facts -- but one cannot dispute a rule, only follow it.
Thinking that space must be infinite is like thinking that the earth must be flat -- i.e. it is not having a picture to replace the present one with: 'must' means: this is grammar. 'When you come to the end of the universe, there is no further place for you to go.' That is nonsense. Rather, you don't come to an end; you only come back to where you began: you circle the universe like you circle the earth. You never come to the end: 'end' is undefined in the picture of "curved space".
A picture held us captive. And we could not get outside it, because it lay in [the grammar of] our language and language seemed to repeat it to us inexorably. (PI § 115)
We cannot even so much as try to imagine nonsense (i.e. undefined language), and so to break free of our captivity requires a new picture (i.e. a sense to be given to that previously undefined language).
Space is finite but Unbounded - An alternative Picture
So that, now we have two pictures, two grammars: space is infinite and unbounded (Euclid) and space is finite but unbounded (Einstein -- i.e. non-Euclid). Pictured as two-dimensional, the universe of space is like a flat sheet of paper (Euclid) or like the surface of a globe (Einstein). And "we now have two grammars" means that we now have an alternative way of looking at the thing.
"Two objects cannot occupy the same space at the same time"
Another example: the following statement seems undeniable because: "I cannot imagine the opposite" (and that means: I cannot imagine an alternative to it).
"Two objects cannot occupy the same space at the same time."
Suppose we asked, What about water in a sponge -- Don't the water and the sponge occupy the same space at the same time? Would the reply be: No, no, you see at the microscopic level of investigation the water molecule and the sponge molecule don't really --. But of course those who originally stated the principle knew nothing of microscopes. They believed themselves to be making a very general statement-of-fact about the nature of things, and they knew quite well about water and sponges when they did so. If we dissolved a teaspoon of sugar in a glass of water and a child asked what had happened to the sugar, the most natural thing to say would be that the water had absorbed the sugar just as a sponge absorbs water. Indeed, with sugar-water in a sponge, it would seem natural to say that we now have three objects occupying the same space at the same time.
But would we ever find it natural to say that two rocks occupied the same space at the same time? I don't know; I can't imagine an example to which it would be natural to apply that language. But is the limit here a limit of language -- i.e. is the limit that this language has been given no application (which is the case with any undefined combinations of words)? -- or is the limit here the limits of my imagination (my limited powers of imagination)? It is tempting to say that it would actually be both. It would be a limit of language because we cannot imagine nonsense (For 'imagine' we could write 'draw on paper'; logic does not concern itself with some occult mental powers but with whether a combination of words has been given an application or not).
But it would also be a limit of my imagination -- because any picture drawn with language is nonsense (e.g. 'finite but unbounded') until someone in fact draws it on paper or uses a three-dimensional model, a globe e.g. Any new combination of words or old combination in a new context is nonsense -- until someone invents an application for it.
The limit of science (and of philosophy) -- is concept-formation. [Note 3]
But any new application has to be commonly acceptable, of course, because what someone finds "natural" is not a matter of logical necessity. New rules can be suggested (as in the case of the combination of words 'square circle') but those rules may not necessarily be accepted; we might prefer and choose to keep the original rules and reject the suggested new rules.
So that, regardless of sponges and water, human beings have preferred the rule "Two objects cannot occupy the same space at the same time". But the water-and-sponge and sugar-and-water examples show that what has been made to masquerade as a profound truth of Logic is in fact nothing more than a rule of grammar, a more or less arbitrary convention for using language. Human beings have preferred the picture of the two rocks to the picture of water in a sponge; and they have invented picture-myths, e.g. the Greeks' atoms, to account for the water-and-sponge, making a rule of grammar appear to be a "a theory in logic" about the "really real" ("a necessary statement-of-fact" as it were).
But "Two objects cannot occupy the same space at the same time" is not an hypothesis: it is a statement about "logical space" not about real space. And this logic, like all logic, is founded on conventions (PI § 355), i.e. more or less arbitrary rules. And if we said: Look, the water and the sponge occupy the same etc., then we would only be suggesting an alternative rule for the use of language (grammar), not a counter-example (anomaly) to a verifiable or falsifiable statement of fact (Or at least the tradition has not been to use this statement to state an hypothesis). It is entirely up to us whether we follow the common rule or invent a new one: we are dealing here with linguistic conventions, not with "necessary facts" about reality.
"Every event has a cause"
Another example: "Every event has a cause." -- What is an alternative to that? Its negation? -- but then events look like phantasms. For example:
It is known that the atoms of radium, and of other radio-active substances, disintegrate into atoms of lead and helium with the mere passage of time ... The law which governs the rate of diminution is very remarkable. The amount of radium decreases in precisely the same way as a population would if there were no births, and a uniform death-rate which was the same for every individual, regardless of his age. Or again, it decreases in the same way as the numbers of a battalion of soldiers who are exposed to absolutely random undirected fire. In brief ... the individual radium atom ... does not die because it has lived its life, but rather because in some way fate knocks at the door.
... in all probability one, and only one, of [every] 2000 atoms [of radium] is destined to break up within the next year.
We do not know in what way this particular atom is selected ... [But every] physicist believes ... that every year fate knocks at the door of one radium atom in every 2000, and compels it to break up; this is the hypothesis of "spontaneous disintegration" advanced by Rutherford and Soddy in 1903. (Jeans p. 22-4)
Dirac finds it necessary to extend ... indeterminacy and uncertainty of knowledge [applied by Heisenberg's "uncertainty principle" only to the electron] over the whole of atomic physics. (ibid. p. 131)
"We do not know in what way this particular atom is selected ..." -- I.e. we find no reason to believe that the particular radium atom is selected -- except our belief in the "uniformity of nature" -- i.e. in causality. And if physicists treat "uniformity" as an hypothesis, then at the level of atomic particulars, they find that the evidence does not support this hypothesis. Yet if we discard this hypothesis, then we are left facing a phantasm:
[Nature] gives no hint as to what the absence of determinism or causation may mean.... what determines the course of events? If anything at all, we are thrown back on determinism and causation; if nothing at all, how can anything ever occur? (Jeans p. 31-2)
Now, what is the way out of Jeans' (and our) dilemma? It is of course a conceptual dilemma: we are in the grips of a rule. But "depicting an anomaly" -- i.e. an alternative, even a purely fictitious one -- here is not easy. We say: 'Either it happens for a reason or it happens for no reason; but then, either the reason is unknowable or the alternative is unthinkable.' We feel trapped. We don't know our way around the rules of this "language-game" (CV p. 72).
You need new conceptual glasses. (RPP ii § 525)
Einstein wanted "strict causality" -- i.e. that things should happen for reasons (in contrast to happening by chance). But if we look, and we look, and we look, and we find no reason -- then mustn't we say that there is no reason? (Eddington) Doubt -- in this case doubting that There is no reason -- requires grounds; and those grounds come to an end; and then we must say: There is no reason. Or must we? If we prefer to say instead No reason has been found, does this amount to the same thing?
Improbable versus Impossible
... there are people who say that it is merely extremely probable that water over a fire will boil and not freeze, and that therefore strictly speaking what we consider impossible is only improbable. What difference does this make in their lives? Isn't it just that they talk rather more about some things than the rest of us? (OC § 338)
Cf. My refusal to call a well-established generality a 'fact': "Can a generalization be a statement of fact?", for example. (Of course, it might be remarked that most philosophical distinctions appear to be a matter of "talking rather more about some things than the rest of us".)
Indeterminism and Levels of Investigation
... led many physicists to suppose that there is no determinism in events in which atoms and electrons are involved singly, and that the apparent determinism in large-scale events is only of a statistical nature. When we are dealing with atoms and electrons in crowds, the mathematical law of averages imposes the determinism which physical laws have failed to provide.
We may be tempted to instance [these large-scale events] as evidence of the uniformity of nature, and to infer the action of an underlying law of causation: in actual fact it is an instance only of the operation of the purely mathematical laws of chance.
... the number of half-pence in a million tons is nothing in comparison with the number of atoms in even the smallest piece of matter with which earlier physicists could experiment. It is easy to see how the illusion of determinacy -- if it is an illusion -- crept into science. (Jeans p. 30-31)
... [quantum theory's] abandonment of the uniformity of nature and its replacement of determinism by probabilities ... (ibid. p. 37)
Mathematical laws, then, would be Wittgenstein's "laws of physics" (as opposed to "laws of nature"). But does an absence of determinism at the atomic level entail that there also be indeterminism on other levels of investigation?
Causality at different levels of investigation
Bernard on statistics: It's a huge leap from saying there is no strict causality at the atomic level -- to saying there is no strict causality at any level. Jeans (like Eddington) says 'Ultimately everything is atoms; therefore there is no strict causality'. That is a tautology, not an inference justified by evidence.
At the atomic level investigators may be limited by their instruments of investigation -- but that need not be the case at every level. And isn't that all that the "principle of indeterminacy" amounts to: We are limited by our instruments; we cannot determine so-and-so; and, therefore, so-and-so does not exist? Here you can speak of a law of physics; -- but to call this a Law of Nature is absurd (except perhaps as a law of human nature). If I remove my eyeglasses, many things become indeterminate (blurry) for me -- but to infer from my glasses-less condition that nature is therefore indeterminate would be silly.
The real reality, mere appearance or neither of those?
If we want to understand the fundamental nature of things, it is to these small-scale phenomena [i.e. electrons, protons, and radiation] that we must turn our attention. Here the ultimate nature of things lies hidden ... (Jeans p. 48)
But recall Drury's remark that if we want to know e.g. what the human brain is, then we shall need to study the investigations of the anatomist, and of the physiologist, and of the biochemist, and of the pure physicist:
No one of the pictures that these various investigators build up to direct them in their work has any claim to priority over the other. All are necessary for a full knowledge of the subject.... At no level of investigation can we say, "Ah! now we have reached the real thing in itself; before, all we were concerned with was mere appearance." (M. O'C. Drury, The Danger of Words (1973), p. 80)
Levels of investigation: reality as like faces of a cube (Plato and moral virtue) maybe is the picture Drury's words suggest.
Atoms are theoretical constructs
At the "atomic level" cancer does not exist. There are cancerous cells, but there are no cancerous atoms. But, of course, cancer does exist. What doesn't exist is the atom.
Atoms are "theoretical constructs" -- i.e. they belong, not to the facts (not to what is observed), but to the physicist's "models, pictures, maps" that are used to summarize the facts. Another way of saying this is that: the word 'atom' is not the name of anything. That is not its role in our language. Drury:
Chemists tell us that a molecule of Water consists of two atoms of hydrogen and one of oxygen. This means that we can perform the familiar experiment of decomposing a given volume of water, by means of electrolysis, into two parts of hydrogen and one of oxygen. And in further experiment recombine these gases in suitable proportions to form water once again.
But now if we don't mention these experiments the statement about a molecule of water is liable to make us feel that science has discovered new entities, molecules and atoms, and that our senses are too crude, and somehow deceive us, so that we do not see the real nature of things.
The atomic theory consists of two things. First the discovery of some remarkable experiments, something we can now do. Then secondly an ingenious notation by means of which these experiments can be concisely recorded and further experiments suggested. It did not conduct us behind the curtain of sensation. [Note 4]
Water is a fact; the atom is a myth. Water is the reality; the atom is a work of the inventive imagination.
While still at school children are taught that water consists of the gases hydrogen and oxygen, or sugar of carbon, hydrogen and oxygen. Anyone who doesn't understand is stupid. The most important questions are concealed. (CV p. 71)
Electrolysis is shown to children at school. But it is not presented as belonging to a very complicated definition. E.g. the "water" in this "experiment" is not the water that we find in the river or at the spigot. The water that we are in fact familiar with is not the H₂O of chemistry. If we then reply "Pure water is ..." or "Water is essentially ...", then this is clearly a definition. In this case "essence belongs to grammar" (PI § 371).
"... clearly a definition." But a definition of what? What is complicated about chemistry's definition of 'water' is the academic background that is needed to understand it. This is not simply a case of holding someone's hand under the rushing water of a garden pump, which is a simple ostensive definition (but only if it is given to someone who already speaks a language).
Reductionism is the Project of Science
"If we boil this man at 200 degrees C. all that is left when the water vapor is gone is some ashes, etc. This is all he really is." Saying this may have a certain charm, but would be misleading to say the least. (LC p. 24)
If reductionism is a program of science, does it follow that this method should -- or even can -- be employed everywhere? Doctors do not perform surgery to remove "cancerous atoms" but to remove cancerous cells. And, indeed, much of the macroscopic -- and microscopic -- world is unintelligible at the atomic level of investigation. And if this is the case, are inferences drawn from the atomic level to other levels of investigation necessarily valid?
The Origin of the Human Species
It has been suggested that [cosmic] radiation, falling on germ-plasm, may produce the spasmodic biological variations which the modern theory of evolution demands; it may have been cosmic radiation that turned monkeys into men. (Jeans p. 25)
It may also not have been. How can anyone claim that the "modern theory of evolution" has become a fact!
Surely it is better to say that we do not know the origin of the human species than to treat a "maybe" as if it were a fact. Ape-like creatures evolving into men is a picture we have. But is there any evidence other than analogies -- which is no evidence at all -- that this happened?
This shows how you can be persuaded of a certain thing. In the end you forget entirely every question of verification, you are just sure it must have been like that. (LC p. 26-7)
But why are we persuaded of it? This is another instance of our inability to imagine an alternative picture.
Human beings are highly suggestible, highly superstitious, highly given to myth-making, highly given to making statements that have the form of an hypothesis but are unfalsifiable.
When a picture is treated as if it were a fact, this is superstition.
Hypotheses and Tautologies
These three conservation laws [i.e. of matter, mass, and energy] ought of course to have been treated merely as working hypotheses, to be tested in every conceivable way and discarded as soon as they showed signs of failing. Yet so securely did they seem to be established that they were treated as indisputable universal laws. Nineteenth-century physicists were accustomed to write of them as though they governed the whole of creation, and on this basis philosophers dogmatized as to the fundamental nature of the universe. (Jeans p. 54-5)
If there are nothing but "working hypotheses", then what is 'universal law' to mean? And then why speak of 'working hypotheses' -- if working is what every hypothesis should be used to do? We should not call any sign an 'hypothesis' merely because it has the form of an hypothesis; because if a sign is used as a tautology, then it is not an hypothesis. And so-called universal laws are used as tautologies.
The Status of Ether - Real or a Frame of Reference?
For we must always remember that the existence of the ether is only an hypothesis, introduced into science by physicists who, taking it for granted the everything must admit of a mechanical explanation, argued that there must be a mechanical medium to transmit waves of light, and all other electrical and magnetic phenomena. (Jeans p. 99)
Did Einstein posit ether because he wanted to maintain strict causality? Is all causality mechanical ("clocks and measuring-rods")?
Our difficulties have all arisen from our initial assumption that everything in nature, and waves of light in particular, admitted of mechanical explanation: we tried in brief to treat the universe as a huge machine. As this has led us into a wrong path, we must look for some other guiding principle.
A safer guide than the will-of-the-wisp of mechanical explanations is provided by William of Occam's principle: "Entia non sunt multiplicanda praeter necessitatem." (We must not assume the existence of any entity until we are compelled to do so.) Its philosophical content is identical with that of Newton's first "Rule of Philosophical Reasoning" ... It is purely destructive; it takes something away, in the present instance the assumption of a mechanical universe with an underlying ether transmitting mechanical action through "empty space" ...
... the primary function of the ether was to provide a fixed frame of reference ... (Jeans p. 104-5)
Einstein wrote that without "the ether" there could be no measuring-rods or clocks -- i.e. they would not be possible in empty space. (But I don't know what he meant by 'empty space'; I don't think he was using that expression in its everyday sense.) But is that to say any more than that empty space would not be quantifiable, and so [strict-causality] physics would be not be possible -- and Einstein doesn't want that? (What does the requirement of quantifiability tell us about reality -- other than about the reality of man, that this requirement is a method of human knowledge?) What is the relationship between "a fixed frame" and "an absolute frame" of reference? If 'absolute frame' is an undefined combination of words (and that's what it is), then there does not seem to be a difference: to designate a fixed reference point is to set the "absolute" point for out particular investigation (Cf. the choice of origin in Cartesian geometry.) Was Einstein asking for an, as it were, absolute [i.e. absolutely fixed] frame of reference -- i.e. is not even a relative fixed frame possible without "the ether"?
... as the hypothesis of relativity is the exact negation of the existence of the old ether, it is clear that any ether that relativity can allow to remain in being must be the exact opposite of the old ether. This being so, it seems a mistaken effort to call them by the same name.
... Eddington truly says that about half the leading physicists assert that the ether exists and the other half deny its existence, but continues: "both parties mean exactly the same thing, and are divided only by words."
Clearly if it is a matter of indifference whether we speak of the ether or of space, of the existence or non-existence of the ether, then even its most ardent devotees cannot claim much objective reality for it.
I think the best way of regarding the ether is as a frame of reference ...; its existence is just as real, and just as unreal, as that of the equator, or the north pole, or of the meridian of Greenwich. It is a creation of thought, not of solid substance. (Jeans p. 112-3)
"... the hypothesis of relativity" -- That is not physics but metaphysics, as would be "the hypothesis of absolutism" (e.g. the eye of God) -- i.e. it is not an hypothesis (if by 'hypothesis' we mean 'verifiable/falsifiable proposition'). It is grammar (in Wittgenstein's sense of 'grammar'): a frame of reference is a frame we place around the picture ("the picture being the independent facts") -- i.e. it is the facts plus imagination (i.e. the frame is not really there; it can be exchanged for another). But if anyone claims that "the ether" really exists although granting that it is completely imperceptible, that would be an example of metaphysics, of the type which tries to deduce the unknown [the reality underlying only apparent reality] from what is known -- i.e. to obtain new knowledge a priori solely by means of logical deduction, independently of empirical verification. [Rationalism's attempt to extend knowledge, or, "rational mysticism".]
And so before I had thought to write: We could say that the difference between Newton and Einstein is this: that Newton pictured the world through the eye of God ("absolute time and space") whereas Einstein pictured the world through the eyes of man ("relative time and space"). But now I don't know if that was really Einstein's intention ("God does not play at dice"), i.e. if that's what he meant by 'relativity'.
Pictures that have no Application
... if an ordinary bar-magnet is electrified and left standing at rest, the [picture is of] energy flowing endlessly round and round the magnet, rather like innumerable rings of children joining hands and dancing to all eternity round a maypole. The mathematician brings the whole problem back to reality by treating this flow of energy as a mere mathematical abstraction. Indeed he is almost compelled to go further and treat energy itself as a mere mathematical abstraction -- the constant of integration in a differential equation. (Jeans p. 117)
With a stream of water, we can say that a certain particle of water is now here, now there; with energy it is not so. The concept of energy flowing about through space is useful as a picture, but leads to absurdities and contradictions if we treat it as a reality. (ibid. p. 116)
In school we are shown a broken line drawing of "energy flowing" in loops around a magnet. We are never told how to compare the picture with what it supposedly pictures -- and we are never given an intelligible definition of 'energy' either. If this picture is "useful", then what is its use?
Reading Jeans' book, I am reminded again and again of Fichte's "Idealism is a speculative position" -- i.e. do not try to picture it. A misleading picture is worse than no picture. And if trying to make pictures in physics -- i.e. trying to make pictures of the invisible -- makes for confusion rather than clarity, then we must stop demanding pictures.
(By 'pictures' we usually mean drawings or models in which there is a one-to-one correspondence between the elements of the picture and the elements of what is pictured. The broken line drawing is not even that.)
No one tries to make a mechanical picture of God. But the absence of such a picture does not prevent our learning to use the word 'God'. We could also say that the vocabulary of physics does not have the grammar of name-of-object: 'electron', 'energy' -- these words are not names of objects. And the question then is: if they are not used to name, then what are these words used to do? For example, the word 'energy' is defined the same way the word 'length' is defined -- by how it is measured, and there is nothing that corresponds to the word 'it' in that definition (Cf. 'It is raining'): "The method of measurement is the meaning" in this case.
Relativity as an Hypothesis and as a Way of Looking at Things
... it seems appropriate to discard the word "ether" in favor of the term "continuum," this meaning the four-dimensional "space" we have already imagined, in which the three dimensions of ordinary space are supplemented by time acting as a fourth dimension.
Laws of nature express happenings in time and space, and so can be stated with reference to this four-dimensional continuum.
... the three dimensions of space and one of time enter as absolutely equal partners [i.e. all four are necessarily present] into the formulation of every natural law. If they did not, the law would be a variance with the principle of relativity.
... either Newton's law [of gravitation, which did not conform to the continuum requirement] or the hypothesis of relativity was wrong.... When the test was made, the decision was favorable to Einstein in every case. (Jeans p. 117-9)
It seems from this that time is called a 'dimension' only "figuratively" -- i.e. to stress its "equal partnership" with space. (But I don't know this.)
Jeans speaks of the "hypothesis of relativity". This is strange. If 'absolute time' and 'absolute space' (which Newton used) are now undefined, then how can relativity be an hypothesis -- i.e. how can an hypothesis be made with what can only be a way of looking at things? How can one so much as look for "absolute time" if the expression 'absolute time' is undefined? We speak of "relative rest", say that nothing is "absolutely at rest" (Jeans p. 96). But what is the antithesis of 'relative'; -- if 'absolute' is not applicable to anything, then what is 'relative' to mean (because then inapplicability belongs to grammar)? An hypothesis that can only be true is no hypothesis; what we have here, instead, is a definition of 'relative'.
Newton, so I believe, imagined a flat earth as a Euclidean plane (i.e. the x-axis and the z-axis); the third dimension (i.e. the y-axis) was "space" (as in 'outer space'). Would that be the definition of 'absolute space'? Then would this be like the geocentric and heliocentric models -- the only question then being: which gives the simpler description (as required by Newton's Rule I)? It may be this way; but I don't know that.
The effect of a mass of gravitating matter was not, as Newton had imagined, to exude a "force," but to distort the four-dimensional continuum in its neighborhood. The moving planet ... was no longer drawn off from its rectilinear [i.e. straight-line] motion by the pull of a force, but by a curvature of the continuum.
The universe is like a soap-bubble
To sum up, a soap-bubble with irregularities and corrugations [the effects of masses of "gravitating matter"] on its surface is perhaps the best representation ... of the new universe revealed to us by the theory of relativity. The universe is not the interior of the soap-bubble but its surface, and we must always remember that, while the surface of the soap-bubble has only two dimensions, the universe-bubble has four -- three dimensions of space and one of time. And the substance out of which this bubble is blown, the soap-film, is empty space welded to empty time.
Two main kinds [of irregularities and corrugations] may be discerned, which we interpret as matter and radiation [The latter uniformly travels at the speed of light], the ingredients of which the universe appears to us to be built. (Jeans p. 120-123)
How much of the "theory of relativity" is a testable hypothesis -- and how much a way of looking at things? For philosophers relativity is entirely a way of looking at things -- which shows that they are like Wittgenstein's savages (PI § 194) when trying to understand the language of the physicists.
Jeans puts the word 'force' in quotes here, meaning: so-called. But if we can only speak of "so-called force", do we say anything? (The picture, I believe, is of hands reaching out and grasping something. But I don't know.) The confusing thing is that Jeans still uses the expression 'mass of gravitating matter' -- and doesn't this suggest that a "force" is "distorting the continuum"?
Four Dimensions may not be Enough
It is conceivable that happenings entirely outside [our four-dimensional space-time] continuum determine what we describe as the "course of events" inside the continuum, and that the apparent indeterminacy of nature may arise merely from our trying to force happenings which occur in many dimensions into a smaller number of dimensions.
Appearance of a rain shower in two dimensions
Imagine, for instance, a race [in the sense of a people or tribe] of blind worms, whose perceptions were limited to the two-dimensional surface of the earth. Now and then spots of the earth would sporadically become wet. We, whose faculties range through three dimensions of space, call the phenomenon a rain-shower, and know that events in the third dimension of space determine, absolutely and uniquely, which spots shall become wet and which shall remain dry. But if the worms, unconscious even of the existence of the third dimension of space, tried to thrust all nature into their two-dimensional framework, they would be unable to discover any determinism in the distribution of wet and dry spots; the worm-scientists would only be able to discuss the wetness and dryness of minute areas in terms of probabilities, which they would be tempted to treat as ultimate truth. (Jeans p. 133)
Although the time is not yet ripe for a decision, this seems to me, personally, the most promising interpretation of the situation. (ibid.)
This is a most excellent picture of what I was trying to say (in "Questions without answers") with Father Copleston's question 'Is reality confined to what is in principle perceptible to the senses?' But what does Jeans mean by 'the time is not yet ripe'? What evidence could affect Jeans' "decision"? Can this even possibly be a question of a "working hypothesis" rather than a "question without an answer" -- i.e. an untestable picture? If it were possible to give a mechanical explanation of everything, could we not still ask: But if we could perceive other dimensions, might we not find that what we regard as strict causality is "really only" probability? Or would that question be nonsensical? If you have found what you were looking for, what sense can be given to 'further looking'? But is not what we are ultimately looking for in science a better understanding of the facts in front of us, and there is no necessary ending to that. Which shows that physics is essentially about theory-formation, not fact discovery (although of course facts are necessary to the construction of scientific theories, i.e. of "models, pictures, maps" that are consistent with a selection of data they organize).
The Place of Mathematics in Physics ("mathematical pictures")
The essential fact is simply that all the pictures which science now draws of nature, and which alone seem capable of according with observational fact, are mathematical pictures.
Most scientists would agree that they are nothing more than pictures -- fictions if you like, if by fiction you mean that science is not yet in contact with ultimate reality. Many would hold that, from the broad philosophical standpoint, the outstanding achievement of twentieth century physics is not the theory of relativity with its welding together of space and time, or the theory of quanta with its present apparent negation of the laws of causation, or the dissection of the atom with the resultant discovery that things are not what they seem; it is the general recognition that we are not yet in contact with ultimate reality. (Jeans p. 135)
Plato, Republic 515c
Jeans uses as a motto for his book Plato's myth of the cave: "To them, I said, the truth would be literally nothing but the shadows of the images" (p. v).
To speak in terms of Plato's well-known simile, we are still imprisoned in our cave, with our backs to the light, and can only watch the shadows on the wall. At present the only task immediately before science is to study these shadows, to classify them and explain them in the simplest possible way. [And the simplest way is the mathematical way.]
It is true, in a sense somewhat different from that intended by Galileo, that "Nature's great book is written in mathematical language". So true is it that no one except a mathematician need ever hope fully to understand those branches of science which try to unravel the fundamental nature of the universe -- the theory of relativity, the theory of quanta and the wave-mechanics. (Jeans p. 135-6)
When we try to discover the nature of the reality behind the shadows, we are confronted with the fact that all discussion of the ultimate nature of things must necessarily be barren unless we have some extraneous standards against which to compare them. For this reason, to borrow Locke's phrase, "the real essence of substances" is forever unknowable. (ibid. p. 139)
This amounts to saying that 'ultimate' is undefined, and that without such a definition there can be no testable hypothesis. But since there will never be a definition of 'ultimate' which is acceptable to everyone, there is not much point to Jeans' remark that "we are not yet in contact with ultimate reality" -- because, for this purely grammatical reason, we never shall be.
Mathematics is the language of physics and, apparently, of the mind of God
... the universe appears to have been designed by a pure mathematician. (Jeans p. 140)
... it may be suggested [that] the mathematician [is so engrossed in mathematics that he] only sees nature through the mathematical blinkers he has fashioned for himself.... it may be objected that we are merely molding nature to our preconceived ideas.... even if the mathematical interpretation is only [another] man-made mold, it a least fits nature incomparably better than the [others] previously tried [e.g. the mechanical or engineering mold]. (ibid. p. 140-143) ... It may be objected ...: other fictions might describe the motions of the shadows equally well. The answer is that, so far as our present knowledge goes, other fictions would not describe them so fully, so simply, or so adequately. (ibid. p. 155)
We go beyond the mathematical formula at our own risk; we may find a model or a picture which helps us understand it, but we have no right to expect this, and our failure to find such a model or picture need not indicate that either our reasoning or our knowledge is at fault. The making of models or pictures to explain mathematical formulae and the phenomena they describe, is not a step towards, but a step away from, reality ...
In brief, a mathematical formula can never tell us what a thing is, but only how it behaves; it can only specify an object through its properties. And these are unlikely to coincide in toto with the properties of any single macroscopic object of our everyday life.
We need no longer discuss whether light consists of particles or waves; we know all there is to be known about it if we have found a mathematical formula which accurately describes its behavior, and we can think of it as either particles or waves according to our mood and the convenience of the moment. (ibid. p. 151-2)
Indeed, what reason did we have to expect the invisible to be picturable as -- "to coincide in toto with" -- anything visible? We expected it only because picturing is our normal technique of understanding -- i.e. it was a requirement, not the result of an investigation (PI § 107). (Eddington's endless talk about "pointer-readings" does not make this point as simply and clearly as Jeans does.)
And Jeans does somewhat acknowledge Xenophanes' ridicule of man making his gods in his own image. But beyond that is Eddington's elephant discussion (although Eddington's assertion that what he calls "the poetry" is not reality -- is indeed "barbarous metaphysics"). If God is a mathematician, then why has he made π = C/2r and the other irrational numbers?
Atomic energy is a secret that God placed within the universe. Scientists have unlocked this secret. (Takashi Nagai, quoted in Glynn, A Song for Nagasaki (1988), xxiv)
And we can see the laws of physics, which man thinks of as laws of nature, this way.
The Views of Scientists Change
It is too often overlooked that we can only discuss these questions in terms of probabilities. The man of science is accustomed to the reproach that he changes his views all the time, with the accompanying implication that what he says need not be taken too seriously. (Jeans p. 156-7)
Thirty years ago, we thought, or assumed, that we were heading towards an ultimate reality of a mechanical kind. It seemed to consist of a fortuitous jumble of atoms, which was destined to perform meaningless dances for a time under the action of blind purposeless forces, and then fall back to form a dead world. Into this wholly mechanical world, through a play of the same blind forces, life had stumbled by accident. (ibid. p. 157-8)
... our main contention can hardly be that the science of to-day has a pronouncement to make, perhaps it ought rather to be that science should leave off making pronouncements ... (ibid. p. 160)
"... through a play of the same blind forces, life had stumbled by accident." People have been saddened by this picture, as in former times they were saddened by the picture that they might not be among God's predestined elect. Cf. Wittgenstein's simile of staring at a black door for so long that you begin to blame the door -- rather than your fixed focus -- for your unhappiness. This is another instance of why Drury cautioned against basing our philosophy or our religion on the theories of science. (DW p. 110)
Criticisms of James Jeans' Mysterious Universe
There is a widespread conviction that the new teachings of astronomy and physical science are destined to produce an immense change on our outlook on the universe as a whole, and on our views as to the significance of human life. The question at issue is ultimately one for philosophic discussion, but before philosophers have the right to speak, science ought first to be asked to tell all she can as to ascertained facts and provisional hypotheses. Then, and then only, may discussion legitimately pass into the realms of philosophy. (Jeans p. vii)
I am not a philosopher either by training or inclination ... (ibid.)
Jeans' book was disliked by some people. E.g. Etienne Gilson:
Etienne Gilson's Criticism
... the unknown is not necessarily a mystery; and science naturally proceeds upon the assumption that it is not [a mystery], because it is at least knowable, even though we do not yet know it. (God and Philosophy (1941) p. 123) [Note 5]
But Jeans' position, if I understand him, is that this assumption has not stood up to the test: "Thirty years ago, we thought, or assumed," that physics was going to be able to describe a deterministic universe, one where everything could be understood mechanically. Now it seems that, not only can much not be understood mechanically, but that this expectation was based on inadequate facts: "the number of half-pence in a million tons is nothing in comparison with the number of atoms in even the smallest piece of matter with which earlier physicists could experiment" (Jeans p. 30-31).
The true reason why this universe appears to some scientists as mysterious is that, mistaking existential, that is, metaphysical, questions for scientific ones, they ask science to answer them. (Gilson p. 123)
Gilson is talking about Jeans account of the existence of the earth and the evolution of the human species. But Jeans only reports what we find when we look, not how we assumed that things must be. It might well have turned out that the existence of life-sustaining planets was a commonplace development in our universe, as was the appearance of life (e.g. any child might have been able to produce it in the kitchen sink). But it did not turn out that way. It is on the basis of these findings that Jeans calls the existence of the earth and human life "accidental": it is not easy to account for (in the sense of accept) the existence of what is extremely improbable; but this existence might not have turned out to be improbable. Whereas Gilson maintains that, regardless of anything scientists might discover, the problem of existence was already present before they even began looking. But was Jeans asking that question, the question "Why is there something rather than nothing?"? No, Jeans asked: why does something, the existence of which is so improbable, exist?
Is it scientific to explain the existence of man by a series of accidents, each of which is more improbable than the other? The truth of the case simply is that on the problem of the existence of man modern astronomy [and modern physics have] strictly nothing to say. (Gilson p. 124)
No, it is not an explanation; it is only a description. But it is not to say nothing either: it is significant that astronomy and physics have just this to say on the subject, for it might have turned out otherwise.
Nobody denies that living organisms appear as though they had been designed, or intended, to fulfill the various functions related to life ... We would be bound to hold [this appearance] for an illusion if science could account for the rise of life by its usual explanations of the mechanical type ... Yet scientists much preferred to introduce into physics the nonmechanical notions of discontinuity and indeterminacy rather than resort to anything like design. (Gilson p. 129-30)
First, the principal point of Jeans' book is that the "usual explanations of the mechanical type" are not possible at the atomic level, and so that a mechanical model is no longer the ideal of explanation in physics. Instead physicists find "the nonmechanical notions of discontinuity and indeterminacy" forced upon them. And, Jeans could say, to insist on the old model is to misconceive -- i.e. form a false idea or picture -- of "the new teachings of astronomy and physical science"; or again, one will only insist on the old model if modern science does not fit one's preconceived notions of what science ought to be.
And second, "designed by God" is not a scientific explanation (It appears to be Bonhoeffer's "God as a working-hypothesis" -- i.e. physics doesn't explain the phenomenon, and therefore man uses God as the explanation). That picture simply puts a full stop to inquiry: it is not an hypothesis, and therefore it is of no interest to physics. Rather than explain, "the new teachings" of physics seem to describe only, if that is what mathematics does, and if I understand Jeans aright (a metaphor, a comparison, is not an explanation of the kind Gilson wants either, e.g. "the surface of a soap-bubble", "a rain shower in two-dimensions", "the universe appears designed by a pure mathematician").
Jeans calls himself "a stranger in the realms of philosophical thought" (p. viii). But what he means by the word 'philosophy' -- is not an unimportant question. (His remarks about human colored eye-glasses and mathematics are certainly philosophical.)
The Human Mind and the Mind of God
... the universe appears to have been designed by a pure mathematician. (Jeans p. 140)
... we need find no mystery in the nature of the rolling contact of our consciousness with the empty space-bubble we call space-time (ibid. p. 127) [Jeans supplies this page number], for it reduces merely to contact between [the human] mind and a creation of [the universe's] mind -- like reading a book, or listening to music. (ibid. p. 153)
We discover that the universe shows evidence of a designing or controlling power that has something in common with our own individual minds -- not, so far as we have discovered, emotion, morality, or aesthetic appreciation, but the tendency to think in the way which, for want of a better word, we describe as mathematical. (ibid. p. 159)
If, as the Apostle Paul says, the Creator is known by the things He has made, then why shouldn't Jeans write this? Because it is not science? Why shouldn't a scientist be allowed to "philosophize" about what no one else -- except a religious believer -- will?
Jeans' ideas recall the Pythagoreans: ultimate reality is mathematical (form and matter are both number). And why wouldn't this have as much right to be the metaphysical first principle as Thomas Aquinas' "act of being", which according to Gilson is the only possible one (although Gilson seems to assume that this combination of words can be understood without a definition). If mathematics is common to everything, then Jeans and the Pythagoreans cannot be accused of attributing to the whole what belongs only to its parts (although, as Jeans says, there remain "emotion, morality, or aesthetic appreciation" to account for) ... if I have understood Gilson aright.
Ludwig Wittgenstein's Criticism
Wittgenstein also disliked Jeans' book. Drury says that he mentioned Jeans' book The Mysterious Universe [Note 6] in conversation, and Wittgenstein replied:
These books which attempt to popularize science are an abomination. They pander to people's curiosity ... without [people's] having to do any of the really hard work involved in understanding what science is about. (Recollections p. 117)
We are all of us made to study science for several years at school. If we still do not know "what science is about", Jeans can hardly be blamed for that. And by presenting us with pictures that are different from the pictures that were forced on us at school, he gives us the opportunity to question what science is about.
Drury wrote that in The Mysterious Universe Jeans "makes startling assertions about the nature of the universe (The Universe is like a rapidly expanding soap bubble) but never tells us what the Astronomer actually does and observes. It is the skills and techniques which scientists make use of that constitute the very soul of each particular science." Whenever, on the other hand, in Natural History of a Candle Faraday "uses hypothetical language he immediately goes on to describe in minute detail the actual experiments on which the hypothesis is based". [Note 7]
The comparison between Faraday's and Jeans' lectures, while accurate, is not fair. Jeans was trying to describe a way of looking at nature that had superseded the 19th Century view -- a vision of the whole world, not of the workings of one little corner of that world (a candle's). Now, could he have made that description, in a brief series of lectures, on Faraday's model?
Jeans has written a book called The Mysterious Universe and I loathe it and call it misleading. Take the title. This alone I would call misleading. But in what way is it misleading? Where does it lead you to? Isn't it mysterious, or is it? Was Jeans deluded when he said it was mysterious?
I might say that the title includes a kind of idol worship, the idol being Science and the Scientist. (cf. LC p. 27)
But does Jeans make this claim -- even implicitly? [Note 8]
... our main contention can hardly be that the science of to-day has a pronouncement to make, perhaps it ought rather to be that science should leave off making pronouncements ... (Jeans p. 160)
Jeans, I think, wrote a rather modest book. And it does not seem to me to violate Drury's rule of "keeping wonder secure" (DW p. 114). Jeans does not try to harden any scientific hypothesis or theory into a "pseudo-fact" (ibid. p. 113). Quite the contrary.
Note 1: James Jeans, The Mysterious Universe ["an expansion of the Rede Lecture delivered before the University of Cambridge in November 1930" (p. vii)] (New York; Cambridge: 1930), p. 4. [BACK]
Note 2: Albert Einstein, "Geometry and Experience" in Sidelights on Relativity; tr. Jeffery and Perrett (orig. New York: 1922; repr. New York: 1983), p. 33. [BACK]
Is scientific progress useful to philosophy? Certainly. The realities that are discovered lighten the philosopher's task, [i.e. the task of] imagining possibilities. (Wittgenstein, Last Writings on the Philosophy of Psychology, tr. Luckhardt and Aue (1982) i, § 807)
Note 4: "Fact and Hypothesis", Drury's reply to a review of his book The Danger of Words, in the journal The Human World, Volumes 15-16 (1974), p. 136-137. [BACK]
Note 5: Etienne Gilson, God and Philosophy (New Haven: 1941), p. 123. [BACK]
Note 6: "Wittgenstein's [own] copy [of this book] has a few penciled comments in the margins; the last is on page 53." (Editor's note by Rush Rhees, Recollections p. 220) [BACK]
Note 8: In other lectures Wittgenstein referred to an essay on science and religious belief (LC p. 57-9): but reading that essay does not show Father O'Hara taking the position Wittgenstein says he does. It might be said, however, that Wittgenstein only looked for ideas when he read; that is, he was not a scholarly academic. On the other hand, Wittgenstein may never have read Father O'Hara's essay; he may simply have been responding to a characterization of that essay offered by one of his students.
Albert Schweitzer said that "if Goethe had known that someone was going to write down everything he said, he would never have opened his mouth". [BACK]
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