7 bit/symbol), and the Italian one the lowest (3.984 bit/symbol), corresponding to a small difference of 0.16 bit/symbol. A higher entropy corresponds to a fuller use of the alphabet "spectrum, which creates more uncertainty among the different symbols. Referring back to Fig. 4.3, we observe that compared with the other languages, English is richer in H, F, and Y, while German is richer in E, N, G, B, and Z, which can intuitively explain that their source entropies are the highest. Compared with the earlier survey of 1942, which gave H(1942) = 4.140 bit/ symbol, this new survey gives H(1956)= 4.147 bit/symbol. This difference is not really meaningful, especially because we do not have a basis for comparison between the type and magnitude of the two samples that were used. We can merely infer that the introduction of new words or neologisms, especially technical neologisms, contribute H. Fouché-Gaines, Cryptanalysis, a study of ciphers and their solutions (New York: Dover Publications, 1956). 4.3 Language entropy English German French Italian Spanish Portuguese English German French Italian Spanish Portuguese Figure 4.3 Probability distributions of character symbols for English, German, French, Italian, Spanish and Portuguese, as inventoried in 1956 or earlier and as ordered according to English. The corresponding source entropy and 10 most frequent letters are shown in Table 4.2. over the years to increase entropy. Note that the abandonment of old-fashioned words does not necessarily counterbalance this effect. Indeed, the old words are most likely to have a "classical" alphabet structure, while the new ones are more likely to be unusual, bringing a flurry of new symbol-character patterns, which mix roots from different languages and technical jargon. What does an entropy ranging from H = 3.991 to 4.147 bit/symbol actually mean for any language? We must compare this result with an absolute reference. Assume, for the time being, that the reference is provided by the maximum source entropy, which one can get from a