In the Beginning was Information

H syll = 8.6 bits/syllable. (16)The average number of letters per syllable is 3.03, so thatH 3 = 8.6/3.03 = 2.84 bits/letter. (17)W. Fucks [F9] investigated the number of syllables per word, and foundinteresting frequency distributions which determine characteristic valuesfor different languages.The average number of syllables per word is illustrated in Figure 36 forsome languages. These frequency distributions were obtained from fictiontexts. We may find small differences in various books, but the overallresult does not change. In English 71.5 % of all words are monosyllabic,19.4 % are bisyllabic, 6.8 % consist of three syllables, 1.6 % have four,etc. The respective values for German are 55.6 %, 30.8 %, 9.38 %,3.35 %, 0.71 %, 0.14 %, 0.2 %, and 0.01 %.For English, German, and Greek the frequency distribution peaks at onesyllable, but the modus for Arabic, Latin, and Turkish is two syllables(Figure 36). In Figure 37 the entropy H S ≡ H syllable is plotted against theaverage number of syllables per word for various languages. Of theinvestigated languages, English has the smallest number of syllables perword, namely 1.4064, followed by German (1.634), Esperanto (1.895),Arabic (2.1036), Greek (2.1053), etc. The average ordinate values forsyllable entropy H syllable of the different languages have been found bymeans of equation (9), but it should be noted that the probabilities ofoccurrence of monosyllabic, bisyllabic, etc. words were used for p i. Thevalue of H syllable = 1.51 found for German, should not be compared withthe value derived from equation (16), because a different method of computationis used.3. Words: Statistical investigations of German showed that half of allwritten text comprises only 322 words [K4]. Using these words, it followsfrom equation (9) that the word entropy, H word = 4.5 bits/word. When onlythe 16 most frequently used words, which already make up 20 % of a text,are considered, H word is found to be 1.237 bits per word. When all wordsare considered, we obtain the estimated 1.6 bits per letter, as indicated inequation (14). The average length of German words is 5.53 letters, so thatthe average information content is 5.53 x 1.6 = 8.85 bits per word.It should now be clear that certain characteristics of a language may bedescribed in terms of values derived from Shannon’s theory of information.These values are purely of a statistical nature, and do not tell us anythingabout the grammar of the language or the contents of a text. Just as198