What I have said concerning the very imperfect state of our present concept system is true also of these two groups. On the other hand, the written signs are not subject to such great change as the sound signs, because the sound signs must be produced anew each time, whereas the written signs inscribed on the right material may survive hundreds, even thousands of years. Hence it is that the written languages are, upon the whole, much better developed than the spoken languages. In fact, there are isolated instances in which it may be said that the ideal has well-nigh been reached. As we have already pointed out, such a case is furnished by the _written signs_ of numbers. By a systematic manipulation of the ten signs 0 1 2 3 4 5 6 7 8 9 it is not only possible to co-ordinate a written sign with any number whatsoever, but this co-ordination is strictly unambiguous, that is, each number can be written in only one way, and each numerical sign has only one numerical significance. This has been obtained in the following manner: First, a special sign is co-ordinated to each of the group of numbers from zero to nine. The same signs are co-ordinated with the next group, ten to nineteen, containing as many numbers as the first. To distinguish the second from the first group, the sign one is used as a prefix. The third group is marked by the prefixed sign two, and so on, until we reach group nine. The following group, in accordance with the principle adopted, has as its prefix the sign ten, which contains two digits. All the succeeding numbers are indicated accordingly. From this the following result is assured: First, no number in its sequence escapes designation; second, never is an aggregate sign used for two or more different numbers. Both these circumstances suffice to secure unambiguity of co-ordination. It is known that the system of rotation just described is by no means the only possible one. But of all systems hitherto tried it is the simplest and most logical, so that it has never had a serious rival, and the clumsy notation with which the Greeks and Romans had to plague themselves in their day was immediately crowded out, never to return again upon the introduction of the Indo-Arabic notation, which has made its way in the same form among all the civilized nations and constitutes a uniform part of all their written languages.