Let me write for you two symbolic expressions. The first is one which occurs in the work of Newton; it says that “the gravitational attraction between two massive bodies is proportional to the product of their masses divided by the square of the distance between some point in each mass." If any single utterance by a scientist has reshaped history, it is this, the law of inverse squares. Ludwig Boltzmann’s gravestone was  inscribed with the symbol for entropy, S = klogW, and I suppose if Newton had had any control over what was to be put on his gravestone, he would have chosen . Now we all understand that as a symbolic expression which describes in some way the structure of our experience.

    Let me now write for you another symbolic expression which l take from “The Auguries of lnnocence” by William Blake. l take a couplet almost at random; this one says,
 
A Robin Red breast in a Cage
Puts all Heaven in a Rage.

Now the extraordinary thing about that verse is that it appears to have none of the formal structure of Newton’s formula. Yet it is a highly general statement and everybody in this room knows exactly what it means, and I mean exactly. My “exactly” may not be your “exactly,” but in some way we all know with an immediacy which we derive from language and experience what
 
A Robin Red breast in a Cage
Puts all Heaven in a Rage.

means. I would say that everybody understands this, whereas there must be a good many people in the audience who, in fact, are taking  on trust.

    Well now, l wish I could lecture on generalizations of the form of “a Robin Red breast in a Cage," but I can only do so much on one occasion. There are two things, however, I want to say about both of those statements. One is that they are both general statements; let no one tell you that this quotation is only a particular statement. It derives its general appeal to us all from its high specificity, and that is the miracle of this kind of remark; but it is a statement which says something about the human situation and not just about a robin or a cage. Secondly, neither statement has the form of a syllogism; neither says all "As are Bs" or any of those things that occur in the textbooks on logic in which sentences are always written as if they described classes. It is my view that that is very foreign to human language, that no scientific statement and no poetic statement is of the form, “all As are Bs." This is what these two have in common. This kind of symbolism is a highly active kind. Do not be deceived by the equals sign. It says something which describes what happens when you do something.

    In discussing statements of this sort, scientific statements, I am going to treat science as a language. I am going to say that this formula is a sentence in the language, that all such statements are sentences in the language, and that the way we construct this language mirrors the way human language evolved. However, I should make one preliminary about it and explain to you that science is a rather peculiar language because it only contains statements that are, in the context of a particular theory, true. We do not, for instance, say, “Well, is a sentence in this language. And is another sentence in this language." In the language that we are discussing, is not a sentence. There are statements in the language of science which have a simple and fairly descriptive form.

    For instance, when Kepler said in 1609 that the planets run on ellipses round the sun as focus and sweep out equal areas in equal time, that is a fairly descriptive sentence. The sentence which Newton wrote about the gravitational attraction is a more abstract sentence and in fact summarizes the description of what Kepler said. For the purpose of the discussion today that is not an important difference, and I will not labor it.

    We are always looking for a language in science which mimics or mirrors the structure of reality. And the problem is, How does it do that? My claim is that it does it in exactly the same way in which human language evolved from animal language, by analyzing the sentence into constituents which represent separable entities in the outside world-things or actions. So science constantly seeks in the descriptive sentences for separable entities which can either be perceived in the outside world or, more of ten, have to be inferred speculatively in the outside world.

    The structure of reality is not self-evident, and the structure of the scientific language is not self-evident. When Wittgenstein wrote the Tractatus during the First World War, he thought that you could make a language out of ordinary discourse, more or less, which could somehow give you the structure of reality. He said that the very fact that “l love you” and “I hate you” have the same kind of structure tells you something about the relations, that the relations are built into the grammar. Now, it is true that the relations are built into the grammar, but we have to get a very specialized grammar, the grammar of science, as Karl Pearson rightly called it, in order to demonstrate the structure.
 
    During the Second World War Craik tried to show that the nervous system actually mimics these structures within our brain, and that was an equally unsuccessful attempt.1  No, we have to tease out the structure from the observational sentences when we make them into abstract sentences. How do we do that? Well, we do it essentially by treating nature as, in Leibnitz’s phrase, a gigantic cryptogram, a gigantic series of coded messages. And we seek to decode it in such a way that entities emerge which are conserved under various changes and transformations.

    Mass is such an entity. Newton was not able to define mass; nobody in a sense can define mass. Indeed, you could say that the great step from Newton to Einstein was that Einstein was the first person who gave a reason for what had already puzzled Newton, namely, why gravitational mass and inertial mass are the same mass. Of course, you and I think we know what a mass is; we know it in the sense that we know what we think we are saying when we ask for a pound of butter. But that is a knowledge which itself comes late in the development of language. Incidentally, it also comes late in the development of children. Remember that children before the age of four are always very puzzled when you pour liquid out of a tall beaker into a broad beaker and say to them, “ls it the same amount of liquid? Which would you rather have?” Without exception, children say they would rather have the orange juice in the tall narrow beaker. And if you say to them, “Why?” they say, “Well, there is more." And then if you say, “But there is not more; I can pour it into here and I can pour it back,” they are not in the least persuaded. Why should they be? Why should they regard it as a law of nature that orange juice remains invariant in mass when you pour it from a narrow thin beaker into a small flat beaker? That is a real theorem.

    And I mention that theorem only to remind you that all our prejudices about the external world tend to be built into the language of science. Then, when somebody shows that the whole thing was nonsense, that we put our prejudices into it, we are always taken aback. I mean, in 1900 if you had said to somebody, “Could my watch run faster if l were standing at the equator than at the north pole?” everybody would have said, “But that is rubbish! Only children think that kind of thing." When in 1905 Einstein wrote a paper in which he said just that, everybody said, “But that is marvelous. What a chi|d’s vision he has." Which is true. Let me give you one more example. What about r, the distance between these two masses? Well, I suppose in theory you could say that you could take a foot rule, lay it down something of the order of 109 times, and say, “We have proved it, that is the distance between the earth and the moon.” But, of course, you cannot do astronomy with that kind of distance. And it is very interesting to see how these concept s again have to be teased out of the cryptogram of nature.
 
    Let me tell you one of the most beautiful and simplest experiments or this that was ever conceived. It was conceived by a man called Olbers; it is called Olbers’s paradox and is more than a hundred years old.2  Olbers said, “The sky is full of stars, and they are obviously pumping energy into space. Now we can assume that the universe is reasonably old, and that therefore it has settled down to some kind of state of equilibrium. If that is so, then every object in the universe has reached a stage at which the amount of  energy that is being radiated to it from the star must be exactly the same amount which it is radiating back." And so Olbers said, “lt is very clear that if we go out into the night sky, it should be as bright as daylight because there is all the energy in a state of equilibrium, and there should be no local disturbances. How can we avoid this?" And, indeed, there was no way of avoiding it at the time. The only possible way of avoiding it that could be suggested was that the universe was rather young and was only just settling down, which seemed slightly improbable.

    How do we avoid this? Why do we now say that it is really quite understandable? We can say this because Bondi made the following beautiful argument: “The stars are pumping energy into space, and it ought all to be coming back. It ought all now to be well mixed up, like the hot and the cold water in the bath. If it is not coming back, where is it going? It must be going into a volume of space which is greater than that from which it originated." And so Bondi says, “We can do a very simple experiment. We can say that there are three possible states for the universe: it might be contracting, it might be of stationary size, or might be expanding. If it is contracting, then night ought to be brighter than day because there ought to be more energy coming in simply from the background than the sun is actually supplying. If it is stationary, then night and day ought to be equally bright. And if the universe is expanding, then night ought to be dark.” I invite you to perform that experiment tonight. Go out and look, and when you observe that it is dark, you will have made the fundamental observation which shows that the universe is expanding.

    We had that information a hundred years ago at least, but until people did terribly expensive experiments with analysis of red shifts and so on, nobody was willing to believe this explanation. But let me invite your attention to the word “expanding.” What does it mean? It means that our measure of distance in this universe between us and any other galaxy must be growing larger. Do we have any way of actually measuring this? Of course we do not. We can only do it because the whole language in which we are writing “mass” and “radiation” and “distance” defines things like distance in such a way that all these things come out to make a consistent language. The thing about nature is that when you challenge her with questions as we have just done with Olbers’s paradox, you rely on the fact that she does not cheat, that she gives back consistent answers.

    If we treat our knowledge of the external world in this way, then we are constructing a language of science which has three features. There are, first of all, symbols which stand for concepts or inferred entities which have the character of the words in these sentences. Then then is a grammar which tells us how these things are to be put together, so that for instance is a grammatical sentence. If you did not put r2 down but r3, that would be ungrammatical and the sentence would not be allowed in the language. And finally there is a dictionary of translation which relates a sentence like this to specific problems like determining the period of the moon.

    After all, when Newton thought of that, the first thing he did was to calculate the period of the moon. And then he said modestly, when he told this story to his housekeeper, “l found it to answer pretty nearIy." He made the period of the moon twenty-eight days so he felt that r2 was right. These are the three characters of the language of science. The grammar is essentially the rules of operation specified by the axioms; the dictionary of translation is essentially the way we apply the sentences to our common experience; and the symbols or concepts are the solutions of the cryptogram.

    Let me give you a different kind of sentence.
2NaCl + H2SO4 = Na2SO4 + 2HCL

In the seventeenth century Mr. Glauber made Glauber’s salts. And after about another hundred years we learned to write his reaction in the form that if you mix salt with sulphuric acid you get Glauber’s salts and hydrochloric acid. Now if you actually were to read Glauber’s description, which is full of words like “muriatic acid” and other splendid phrases that I am afraid I have forgotten, you would not, of course, recognize it as the same reaction. Why not? Because you have all been brought up with a code in which NaCl is what you say for salt and H2SO4 is what you say for sulphuric acid. But, of course, the whole thing has been translated into a kind of Morse code. And what has been elucidated by the Morse code is that this sodium atom here is an element and that this hydrochloric acid is not an element—a fact which was much in dispute in the time, say, of Humphrey Davy. So that the code teases out the elementary symbols. We solve the cryptogram by doing this. And I do not have to tell you that if you were now to write this in terms of its valences and in terms of the free electrons and so on, you would be breaking down the code step by step into the codes that we now have for nuclear processes. This is why I say that we are making the language. We are making the symbols by the challenge of question and answer, which gives us real statements about the world that we then break down.

    I want to come back to this because it reminds you that the grammar has to do with explanation, the dictionary has to do with description, and the symbols have to do with those concepts with which the whole of our consciousness is now full but for which the only evidence for most of us is that somebody told us in a lecture or that it says so in the textbook. Words like hydrogen and helium, nuclear processes, inhibition in biology, inhibition in psychology have become new words in our vocabulary. But they owe their existence to being decoded out of statements of this kind.

    I have been giving you a highly personal account of how we practice science. And the obvious question is “Are we inventing the whole thing?” You may say to me, “Aren’t you just a thoroughgoing idealist? Do you really think that there are not any atoms?” I spoke of Boltzmann and the inscription on his gravestone a little while ago. Ludwig Boltzmann committed suicide in a fit of depression. Why? Because he could not persuade his colleagues that atoms were real. It may not seem to you something to take your life over, but it was to him. The irony, of course, was that had he only held his hand for another year or two, all his colleagues would have been persuaded.

    Now, are the atoms real or are they not? And if the atoms are real, are the electrons real or are they not? When we do this decoding, are we discovering something which is in nature, or are we not? Are we creating the concepts out of which we make science, or are they there hidden all the time? Now this is a tremendous intellectual bifurcation. And also a fairly emotional one. For example, the world is pretty well divided into people who are proud of being machines and people who are outraged at the thought of being machines. And the world is, therefore, pretty well divided into people who would like to think that our analysis of nature is a personal and highly imaginative creation and those who would like to think that we are simply discovering what is there.

I wrote the chapter on twentieth-century science for the UNESCO history.3 If you read it, you will find that it carries behind it a streamer as long as a comet’s tail of violent phrases of dissent by young Russian scientists saying: "This is all a terribly idealistic picture. This man does not believe that atoms are real,” and so on and so on. Now these questions are not idle ones. Picture yourself for the moment in 1867, a hundred years ago. Supposing you had then asked yourself, “Well, is it real? ls Newton’s gravitation a real thing?” Everybody would have said, “Well, of course.” Shortly after Newton published the Principia in 1687-88 Richard Bentley, the great classical scholar of Trinity College, asked his permission to give some sermons on Divine Providence.4 And the force of these sermons was that we now understood what Divine Providence was because it was really gravitation. I am simplifying Bentley's sermons somewhat, of course. But the point is that Bentley was enormously impressed with the fact that we now understood in some way how God worked, how nature worked. And from the time of Newton until well into the last century everybody was persuaded that this was so.

    Everybody was persuaded that we understood the great truths of science, had understood them since the time of Newton, and that what we were now doing was filling in the details. At the end of the last century there were physicists who were perfectly willing to say that there was no need to produce another Newton because there was nothing as fundamental as gravitation for another Newton to discover. And after all, they had the excellent evidence of Adams’s and Leverrier's discovery of a planet that no one had observed, one whose existence they had predicted entirely because the perturbations that they observed could only be explained by the presence of another planet, and there it was.

    Since then, the world has fallen about our ears. There is almost no scientific theory which was held to be fundamental in 1867 which is thought to be true in that form today. We have lived through a century of the most amazing firework display of new discoveries. Not discoveries of a superficial nature, but ones which have radically altered our whole picture of nature. In 1899 when Max Planck could not make the continuous equations work to match the experiments of his colleagues on black body radiation, he finally made up his mind that radiation came in discontinuous lump . And that afternoon, when he took his little boy for their usual walk, he said to him, “l have today made a discovery as profound as Newton’s." Those were very prophetic words. And the only sad thing about them is to say that the little boy whom he took for a walk was, in fact, murdered by the Nazis because he took part in the plot against HitIer’s life in 1944.

    From the moment that Max Planck made that statement, we have had a constant upset of the accepted notions. is no longer regarded as a picture of the ultimate reality in nature. In 1905 Einstein published the first paper on relativity, which made it clear overnight that there was something wrong with this concept. And then in 1915-16 he published the great paper on general relativity, which substituted an essentially geometrical view of space-time in its place. lf l may translate into geometrical terms, this really said, roughly speaking, that these two masses attract one another because they form depressions in space-time; and those depressions tend to make them run together just as if you put two lead balls into a bowl of jelly. Well, that is a fundamentally different conception of the world. It is a fundamentally different decoding of virtually the same sentences. No one would have thrown Newton out of the window if there had not been sentences which went wrong. lf the perihelion of Mercury had remained where it was supposed to be, nobody would have been very troubled.

    The new theory, of course, always subsumes more effects than the old. But the remarkable thing is that when it is discovered, it also wholly changes our conception of how the world works. Well then, was the decoding all a fiction? ls gravitational force a complete fiction? ls Einstein’s view of relativity now a fiction since it is by no means in as good order as it was in 1915-16? I regard this as a very important question. I regard it as a particularly important question in an audience like this which is not wholly composed of professional scientists.

    Now I believe that everybody in this room is real. I really believe that you are all there. Moreover, I believe that your blood is circulating just the way that Harvey said, and not the way that Galen said. In other words, I believe that all the kind of scientific descriptions that we can make about one another are perfectly real. And yet, I believe that any theory that we as human beings make at any point in time is full of provisional decodings which to some extent are as fictitious as the notion of force in Newton. How can this be?

    In my view, the answer is as follows. I believe that the world is totally connected: that is to say, that there are no events anywhere in the universe which are not tied to every other event in the universe. I regard this to some extent as a metaphysical statement, although you earth content than that. But I will repeat it: I believe that every event in the world is connected to every other event. But you cannot carry on science on the supposition that you are going to be able to connect every event with every other event. Even when you set a computer such a simple problem as playing a good game of chess on the hypothesis that the computer is really going to think out every consequence, it breaks down hopelessly. It is, therefore, an essential will see, as I develop it in the next lecture, it has a much more down-to-part of the methodology of science to divide the world for any experiment into what we regard as relevant and what we regard, for purposes of that experiment, as irrelevant.

    We make a cut. We put the experiment, if you like, into a box. Now the moment we do that, we do violence to the connections in the world. We may have the best cause in the world. I may say, “Well, come on, I am not really going to think that the light from Sirius is going to affect the reading of this micrometer!” And I say this although I can see Sirius clear with the naked eye, and I have the impertinence to say that though the light of Sirius affects my rods and cones it is not going to affect the experiment. Therefore we have always, if l may use another Talmudic phrase, to put a fence round the law, to put a fence round the law of nature that we are trying to tease out. And we have to say, “For purposes of this experiment everything outside here is regarded as irrelevant, and everything inside here is regarded as relevant."

    Now I get a set of answers which I try to decode in this context. And I am certainly not going to get the world right, because the basic and the irrelevant is in fact a lie. In the nature of things it is bound to give me only an approximation to what goes inside the fence. And whether I treat that as a statistical approximation, or whether I get out some other concept, I am doing so in less than the total context of the world. Therefore, when we practice science (and this is true of all our experience ) , we are always decoding a part of nature which is not complete. We simply cannot get out of our own finiteness. Now such decoding can certainly lead to good laws. If what we judge to be irrelevant is not very relevant, they will be good laws. But it does not follow that they give you the conceptual picture of what is in the world at all. And essentially the reason why we have made such enormous changes in our conceptual picture of the world in the last seventy years is because we have had to push out the boundaries of the relevant further and further. Every time we do so, we have to revise the picture totally. Now there is nothing to help us in the decoding. We have to do it in the same way that we invent any word in the human language—by an act of pure imagination.
 
1. K. J. W. Craik, The Nature of ExpIanation (Cambridge: Cambridge University Press,1943)
2. Wilhelm Olbers, “Uber die Durchsichtigkeit des Weltraums," Bodes Astronomisches Jahrbuch (1826), pp. 110-21.
3. J. Bronowski, “The New Scientific Thought and Its Impact,” in History of Mankind:  Cultural and Scientific Development, vol. 1, pt. 1, edited under the auspices of UNESCO by K. M. Panikkar and J. M. Romkin (London: Allen & Unwin, 1966), pp. 121-65.
4. Richard Bentley, Sermons Preached at Boyle’s. . . ( 1692) (London: Frances Macpherson, 1838).