# La Disparition, by George Pérec, and conditional probabilities

As mentioned here (about dust on keyboards), E is undoubtedly the most important letter in French… So, what else do we use if we do not use the E ?

Here is the empirical frequency we obtained on two books, by Mauss and Durkheim (which seem to be representative of what we usually observe)

So if we look at the conditional distribution we have without letter E, we obtain

But does this conditional distribution can be interpreted ? For instance, if on your keyboard E is broken, will the distribution of letters used be like that ? We might think that the answer is no, because if we cannot use a letter, we adapt ourselves, and try to use words that do not contain E.

Actually it is possible to see how we would write if we try to avoid letter E : in 1969, Georges Pérec published a book “la disparition” where the challenge was to write a novel (with a story inside) without using letter E. If we look at the distribution of letters in that book, we have

We can see that we still need to use vowels: if we look at the difference between Pérec, and the conditional distribution obtained from Mauss and Durkheim, we have

i.e. if we cannot used E then we use much more A or I or even U.It is clearly a substitution effect: the French language needs a constant dose of vowels. In Mauss and Durkheim, 37% of the letters are vowels (17% for E and 20% for A, I,O, U and Y). In Pérec, A, I, O, U and Y represent now 30% of the letters…