From 2 . Possible Worlds1 also 4 . "Outlook of Science"2 by J. B. S. Haldane
"The unending quiet of those unending spaces," said Pascal, looking at the stars and between them, "puts me in fear," and this fear, which has little enough reason in it, has been sounding on in men's minds for hundreds of years.
It is common to say that one is unable to get any idea of the distance even of the nearest fixed stars, and to make no attempt to get an idea of the number of atoms2 in one's thumbnail. This tendency makes it quite unnecessarily hard for the man in the street to get clear in his mind about the chief discoveries of present-day science; a great part of which are quite straightforward, but for the fact that the numbers they are based on are of some size. Pascal's feeling, in fact, has nothing to do with science, or with religion. "I will be over the top of him in a short time," said Sir Thomas More, when he took his last look at the sun before his head was cut off; and in the view of the present-day expert in astronomy the sun is a somewhat small but more or less representative star.
There is no reason for the belief that outer space is unlimited. Very probably all space is of fixed size, and certainly the distances to all the stars we see are not outside the range of man's mind. To be unlimited is a property of mind and not of material things. We have the power of reasoning about what is unlimited but not of seeing it. As for the quiet of outer space, one would be unable to go on living in it, and so would be unable to say if it was quiet or not. But if one was shut up in a steel box in it, like the men in Jules Verne's book who went to the moon, there would probably come to one's ears quite frequently, at any rate when near a star, the sound of a very small bit of dust moving at a very great rate and coming up against the box.
The common man frequently makes the protest that he is unable to get any idea of the eighteen million million miles which is the unit used in astronomy in connection with the fixed stars, and is named a parsec because the parallax of a star at that distance seems to be a second; in other words, the circle the earth makes round the sun would take up an angle of two seconds at that distance, or seem the size of a halfpenny three thousand yards away. Naturally one is unable to see a parsec in one's mind. But one may have thoughts about it, quite clear ones.
Every person of education has got used to a process which is most complex, and makes necessary a quite surprising change of scale. That process is map-reading. Our smallest unit for everyday use is about a centimeter, or two-fifths of an inch. It is not necessary for most of our normal measuring to make less error than this. Now if we take a look at a map of the earth on a ball measuring 16 inches round, we are using something on a scale of one in a hundred million (10 -8), and the common man is able to see its purpose and make use of it. An Englishman hearing that his son is going to New Zealand has only to take a look at the map to see that letters will take longer to come from there than from his other son in Newfoundland. But though we are quite happy with this scale (a scale of 1,000 kilometers, or about six hundred miles, to a centimeter) so long as we keep to the earth, the normal person has still not got used to the fact that on the same scale the sun is a mile off and about the size of a church.
Our sons' Sons will have got used to the opposite trick, that is to say, they will be happy working with things on a scale of a hundred million to one. On this scale the common sorts of atom are seen as less than an inch across, and molecules of quite complex substances from living bodies are a foot or so long. The electrons in these atoms and the nuclei which, on the present view, they go round, would be so small as not to be seen, but the way they go might be marked out, as railway lines are on a map, though only by making them wider than they would in fact be. it is to be doubted if there would be any purpose m having a greater scale than this. When we come to events inside the atom it is no longer possible to give an account of them in space and time; or at any rate the properties of space and time in very small amounts are so unlike those of common-sense space and time that scale-copies are not of much value. On the other hand scale-copies of molecules, based on X-ray discoveries about crystals, are of great use as guides, and are taking us forward to a new stage of chemical discovery.
Let us now take a second step in the opposite direction, and make a scale-copy such that in it the ball will be made as much smaller as the earth was made to get it down to the size of the ball. That is to say, our copy will be on a scale of one in ten thousand million million (10 -16). This would, in fact, do very little for us, because not only the earth, but the circle it makes round the sun, would be so small that we would be unable to see it, and even the circle made by Neptune would go with comfort on a pin's head, which would at the same time give the size of the greatest star we have knowledge of. But unhappily, even on this scale the nearest fixed star would be four yards away, and only about a hundred would be less than thirty yards off. The Galaxy would be a good day's walk across. Light would go much more slowly than a snail, but quicker than the growth of most plants!
There would probably be some purpose in taking a third step in the same direction. If we again made our scale smaller by a hundred million times, the Galaxy would be so small that we would be almost unable to see it at all,
the nearer 'spiral nebulae' would be only a small part of an inch away from it, and probably all the 'spiral nebulae' which we are able to see with the best instruments would be less than half a mile away. It is not clear that we would be able to do the operation a fourth time. Because the general theory of Relativity seems necessarily to take us to the belief that space is limited, and that to go straight on in any direction would in the end take one back to the starting-point. An attempt to make a copy on this scale would possibly give an outcome as false as that got when, by Mercator's system, we make an attempt at copying all the earth on one plane. On the fourth-order scale the size of all space might be as small as one hundred thousandth part of a solid measuring a millimeter long and a millimeter wide, though this is a lower limit.
We have now seen that it is possible, and frequently of use, to make copies of things up to a hundred million times their true size and down to a scale of about a million million million millionth. Outside these limits space does not have the properties given to it by common sense, and it is no use attempting to get pictures of things. We have to go into the mathematics of the Quantum Theory at the small end and of Relativity at the other end. But long before that is necessary, the normal man's powers of thought have come to a stop, from a fear, it seems, of the word 'million.' This is because it is generally used for things like a million bits of gold or a million years, which it is hard for us to get an idea of, though in fact a quite normal room would take a hundred million bits of gold money, as long as the floor did not give way. But it would be a good thing for us to get into the way of using millions by keeping in mind that our bath every day has about ten million drops of water in it, and at we have frequently done ten million millimeters in a day, walking.
It is to be regretted that outside India one has no chance of seeing a million men and women, because such numbers only together for the great Hindu journeys for purposes of religion, and very interesting they are. Sometimes three million men and women may be seen at the Kumbh Mela, a public event which takes place every twelve years (it last took place, if my memory is right, at Allahabad in January 1930). Anyone who is unable to get an idea of a million would do very well to go and see it. And it is said, by the way, that by going to it you get out of two or three million future births.
In science we get used to these great numbers. The astronomer quite happily goes from measuring the distance of a star in kiloparsecs -- light takes 3,000 years to go a kiloparsec -- to measuring how long the waves of its light are, with an error much less than an 'Angstrom' unit, which is a hundred-millionth of a centimeter. And there is a certain shock of pleasure when the outcome of a mathematics operation in which one has made use of hundreds of millions, comes out at one or two -- when up till the last minute it seemed as if it might have been anything from a million to a millionth -- and so gives you a simple theory. I have in mind, for example, the great discovery of Eddington as to why stars have so little weight (not one of those whose weight has been measured is as much as a hundred times the weight of the sun). Starting from the facts of physics he got at the degree of heat inside the stars; and because waves of heat or light give a push to the material they come against he was able to see by mathematics what part of the weight of a star of given mass was supported by the waves of the heat or light produced in the star itself. The part which is supported in this way is so small as to be unimportant for stars of less weight than the sun, but comes up to half the weight in a star about five times the sun's weight, and a star with much more weight is in danger of bursting. In this way, through a waste of millions, we come to a clear account of why all stars have about the same weight.
In the same way Gorter and Grendel, and Fricke and Morse, have made it clear by quite different tests that the thin skin of oil round a red blood-cell is two molecules thick. Gorter got the oil separate from the blood-cell and put it on water so that a thin skin was formed; Fricke took the measure of the power of the blood-cells as condensers by putting blood in a very quickly changing electric field. They made use of such numbers as the five thousand million blood-cells in a milliliter and the six hundred thousand million million million atoms in a gram of hydrogen (H2), but the answer at the end was 'two' for Gorter and 'one or two' for Fricke. It is the agreement of such processes which makes it necessary for a person trained in science to put belief in the numbers on which they are based.