Prediction of English
The new method of estimating entropy exploits the fact that anyone speaking a language possesses, implicitly, an enormous knowledge of the statistics of the language. Familiarity with the words, idioms, clichés and grammar enables him to fill in missing or incorrect letters in proof-reading, Or to complete an unfinished phrase in conversation. An experimental demonstration of the extent to which English is predictable can be given as follows:
Select a short passage unfamiliar to the person who is to do the predicting. He is then asked to guess the first letter in the passage. If the guess is correct he is so informed, and proceeds to guess the second letter. If not, he is told the correct first letter and proceeds to his next guess. This is continued through the text. As the experiment progresses, the subject writes down the correct text up to the current point for use in predicting future letters. The result of a typical experiment of this type is given below. Spaces were included as an additional letter, making a 27 letter alphabet. The first line is the original text; the second line contains a dash for each letter correctly guessed. In the case of incorrect guesses the correct letter is copied in the second line.
(1) THE ROOM WAS NOT VERY LIGHT A SMALL OBLONG
(2) ––––ROO––––––NOT–V–––––I–––––––SM––––OBL––– (8)
(1) READING LAMP ON THE DESK SHED GLOW ON
(1) POLISHED WOOD BUT LESS ON THE SHABBY RED CARPET
Of a total of 129 letters, 89 or 69% were guessed correctly. The errors, as would be expected, occur most frequently at the beginning of words and syllables where the line of thought has more possibility of branching out. It might be thought that the second line in (8), which we will call the reduced text, contains much less information than the first. Actually, both lines contain the same information in the sense that it is possible, at least in principle, to recover the first line from the second. To accomplish this we need an identical twin of the individual who produced the sequence. The twin (who must be mathematically, not just biologically identical) will respond in the same way when faced with the same problem. Suppose, now, we have only the reduced text of (8). We ask the twin to guess the passage. At each point we will know whether his guess is correct, since he is guessing the same as the first twin and the presence of a dash in the reduced text corresponds to a correct guess. The letters he guesses wrong are also available, so that at each stage he can be supplied with precisely the same information the first twin had available.
The need for an identical twin in this conceptual experiment can be eliminated as follows. In general, good prediction does not require knowledge of more than N preceding letters of text, with N fairly small. There are only a finite number of possible sequences of N letters. We could ask the subject to guess the next letter for each of these possible N-grams. The complete list of these predictions could then be used both for obtaining the reduced text from the original and for the inverse reconstruction process.
To put this another way, the reduced text can be considered to be an encoded form of the original, the result of passing the original text through a reversible transducer. In fact, a communication system could be constructed in which only the reduced text is transmitted from one point to the other. This could be set up as shown in Fig. 2, with two identical prediction devices.