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The phrase "A law of Nature" is probably rarer in modern scientific writing than was the case some generations ago. This is partly due to a very natural objection to the use of the word "law" in two different senses. Human societies have laws. In primitive societies there is no distinction between law and custom. Some things are done, others are not. This is regarded as part of the nature of things, and generally as an unalterable fact. If customs change, the change is too slow to be observed. Later on kings and prophets could promulgate new laws, but there was no way of revoking old ones. The Greek democracies made the great and revolutionary discovery that a community could consciously make new laws and repeal old ones. So for us a human law is something which is valid only over a certain number of people for a certain period of time.
Laws of Nature, however, are not commands but statements of facts. The use of the same word is unfortunate. It would be better to speak of uniformities of Nature. This would do away with the elementary fallacy that a law implies a law-giver. Incidentally, it might just as well imply a parliament or soviet of atoms. But the difference between the two uses of the word is fundamental. If a piece of matter does not obey a law of Nature it is not punished. On the contrary, we say that the law has been incorrectly stated, It is quite probable that every law of Nature so far stated has been stated incorrectly. Certainly many of them have. Nevertheless, these inaccurately stated laws are of immense practical and theoretical value.
They fall into two classes-qualitative laws such as "All animals with feathers have beaks", and quantitative laws such as "Mercury has 13,596 times the density of water"(at 0°C and 1 atmosphere's pressure). The first of these is a very good guide. But it was probably not true in the past. For many birds which were certainly feathered had teeth and may not have had beaks. And it is quite possibly not today. There are about a hundred thousand million birds on our planet, and it may well be that two or three of them are freaks which have not developed a beak. But have lived long enough to grow feathers. It was thought to be a law of Nature that female mammals (defined as warm-blooded vertebrates with hair) had mammary glands, until Prof. Crew of Edinburgh found that many congenitally hairless female mice lacked these organs, though they could bear young which other females could then foster.
And quantitative laws generally turn out to be inexact. Thus water is nothing definite. It is a mixture of at least six different substances. For in the molecule H20, one or both of the hydrogen atoms may be either light or heavy, and so may the oxygen atom. Similarly, mercury consists of several different types of atom. Thus the ratio of the densities of mercury and water is not fixed, though in the case of ordinary samples the variation is too small to be detected. But it can be detected if the water happens to have been taken from an accumulator which has been used for some time.
In his theory of Probability (Oxford, 1939) Jefferys has something new to say about induction. Two contradictory theories are in vogue as to the laws of Nature. The older view is that they are absolute, though of course they may have been inaccurately formulated. The extreme positivistic view, enunciated by Vaihinger, is that we can only say that phenomena occur as if certain laws held. There is no sense in making any definite statements, though it is convenient to do so.
Now Jeffreys points out that, if a number of observations have been found to conform to a law, it is highly probable that the next one will do so whether the law is true or not. In Jeffrey's words? "A well-verified hypothesis will probably continue to lead to correct inferences even if it is wrong. "
Positivists and idealists have made great play with the fact that many laws of Nature, as formulated by scientists, have turned out to be inexact, and all may do so. But that is absolutely no reason for saying that there are no regularities in Nature to which our statements of natural law correspond. One might as well say that because no maps of England give its shape exactly it has no shape.
What is remarkable about the laws of Nature is the accuracy of simple approximations. One might see a hundred thousand men before finding an exception to the rule that all men have two ears, and the same is true for many of the laws of physics. In some cases we can see why. The universes is organized in aggregates, with, in many cases, pretty wide gaps between them. Boyle's law that the density of a gas is proportional to its pressure, and Charles' law that the volume is proportional to the temperature, would be exact if gas molecules were points which had no volume and did not attract one another. These laws are very nearly true for gases at ordinary temperatures and pressures, because
the molecules occupy only a small part of the space containing the gas, and are close enough to attract one another only during a very small part of any interval of time. Similarly, most of the stars are far enough apart to be treated as points without much error when we are considering their movements.
And most men manage to protect themselves from injury so far as is needed to keep both ears. Whereas trees cannot protect themselves form the loss of branches. It is very rare to see a completely unmutilated, and therefore completely regular tree. Mendel's laws, according to which two types occur in a ratio of 1： 1 in some cases and 3 ： 1 in others, are theoretically true if the processes of division of cell nuclei are quite regular, and if neither type is unfit so as to die off before counts are made. The first condition never holds, and the second probably never does. But the exceptions to the first condition are very rare. In one particular case a critical division goes wrong about one in ten thousand times. The effect of this on a 1 : 1 ratio or 3 ! 1 ratio could be detected only by counting several hundred million plants or animals. Differences in relative fitness are more important. But even so the Mendelian ratios are sometimes fulfilled with extreme accuracy, and are generally a good rough guide.
Jeffreys points out that in such cases it is often much better to stick to the theoretical law rather than the observed data. For example, if you are breeding silver foxes and a new colour variety occurs which, if crossed to the normal, gives 13 normal and 10 of the new colour, you are much more likely to get a ratio of about 1:1 than 13:10 if you go on with such matting, even though if you breed many thousands the 1: 1 ratio will not hold exactly. The mathematical theory which Jeffreys has developed concerning such cases is particularly beautiful, but can hardly be summarized here.
1. Ordinarily, gas molecules are so close that they attract one another for only a very short time.
2. The statement that atoms in the molecule H2O may be light or heavy is a sample of quantitative laws.
3. Human law is similar to natural law in essence.
4. Charles' law and Boyle's law are based on observations made at ordinary temperatures and pressures.
5. Since cell-division is sometimes irregular and certain types die off early, we sometimes get neither 3 ： 1 ratio nor 1 : 1 ratio.
6. Differences in relative fitness are more frequent than irregular cell-division.
7. We must see many human beings before stating the rule that all men have 2 ears.
8. Compared with human laws, laws of nature are accurate because they are expressed in the form of_______.
9. In considering the movements of stars, scientists need not consider their_______.
10. _______laws can serve as good guides.
