The concept of the entropy of natural languages, first introduced by S
hannon [A mathematical theory of communications, Bell Syst. Tech. J. 2
7, 379-423 (1948)] and its significance is discussed. A review of vari
ous known approaches to and results of previous studies of language en
tropy is presented. A new improved method for evaluation of both lower
and upper bounds of the entropy of printed texts is developed. This m
ethod is a refinement of Shannon's prediction (guessing) method [Shann
on, Prediction and entropy of printed English, Bell Syst. Tech: J. 30,
50-64 (1951)]. The evaluation of the lower bound is shown to be a cla
ssical linear programming problem. Statistical analysis of the estimat
ion of the bounds is given and procedures for the statistical treatmen
t of the experimental data (including verification of statistical vali
dity and significance) are elaborated. The method has been applied to
printed Hebrew texts in a large experiment (1000 independent samples)
in order to evaluate entropy and other information-theoretical charact
eristics of the Hebrew language. The results have demonstrated the eff
iciency of the new method: the gap between the upper and lower bounds
of entropy has been reduced by a factor of 2.25 compared to the origin
al Shannon approach. Comparison with other languages is given. Possibl
e applications of the method are briefly discussed.