The comparison of the spoken and the written languages offers a very illuminating proof of the much greater imperfection of the language of _words_. The number 18654 is expressed in the English language by eighteen thousand six hundred and fifty-four, that is, the second figure is named first, then the first, the third, the fourth, and the fifth. In addition, four different designations are used to indicate the place of the figures, -teen, -thousand, -hundred, and -ty. A more aimless confusion can scarcely be conceived. It would be much clearer to name the figures simply in their sequence, as one-eight-six-five-four. Besides, this would be unambiguous. If we should desire to indicate the _place value_ in advance, we could do so in some conventional way, for example, by stating the number of digits in advance. This, however, would be superfluous, and ordinarily should be omitted.[E] [E] The usual designation of the larger groups, ten, hundred, thousand, million, billion, etc., is also quite irrational. If it is our object to secure expressions for place values in as few words as possible, we find that the numbers of the form 10^{2n}, in which n is a whole number, must receive their own names, that is, 10, 100, 10,000, 100,000,000 etc. In this way the problem of designating as many numbers as possible by as few words as possible is solved. =32. Pasigraphy and Sound Writing.= There are two possibilities for co-ordination between concepts and written signs. Either the co-ordination is _direct_, so that it is only a matter of providing every concept with a corresponding sign, or it is indirect, the signs serving only the purpose of expressing the _language sound_. In the latter case the written language is based entirely upon the sound language, and the only problem, comparatively easy to solve, is to construct _an unambiguous co-ordination between sound and sign_. The Chinese script follows the direct process, but all the scripts of the European-American civilized peoples are based on the indirect process. This, it is true, is the case only in ordinary, non-scientific language, while for science the European nations also have to a large extent built up a direct concept writing. One example of this we have seen in the number signs. Musical notation furnishes another instance, though by far not so perfect. The use of the different keys destroys the unambiguous connection between the pitch and the note sign, and the signatures placed at the beginning of a whole staff have the defect of removing the sign from the place where it is applied. Despite this imperfection musical notation is quite international, and every one who understands European music also understands its signs.[F] [F] It is not difficult to perfect musical notation with a view to unambiguity, a thing which would greatly facilitate the study of music.