The needle in the haystack: How experience in cryptoanalysis and mathematics may help in detecting and forming gestalts

Abstract

Experimental psychology and anatomy have shown that the recognition of a gestalt is a cerebral process. The appearance of a gestalt is not limited to the visual channel – the auditory and tactile channels allow the gestalt effect as well. The gestalt phenomenon can and should be extended to more subtle mental processes, such as pattern recognition and recognition by Fourier transformation. Whereas cryptoanalysis involving a search for a probable word is a gestalt recognition problem, cryptoanalysis achieved by finding a periodic key is a task requiring the formation of a gestalt. Moreover, in mathematics a family of equivalent theories has a gestalt, and methods developed for recognising such gestalts may one day be transferred to studies in physics, biology, and psychology to decrypt the secrets of nature.

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References

Figure 2 shows (row-wise) the first 1200 fractional digits of the transcendental number e^−π (0·043213918…). It is highly unlikely that there is any other sort of pattern or gestalt hidden here.

The figure is an autostereogram, with the shape of the letter E formed by raised digits.

The digits 0, 1, 2, 3, 4, 5 are used to indicate the six extra control signs of the teletype alphabet. They will most likely not be used in the plaintext and keytext, except perhaps for 2, which stands for the word space. We use 0 to indicate the space symbol ‘⊔’.

The cryptogram is fictitious, but not unrealistic: the plaintext was encrypted for transmission on insecure Allied lines, and the cryptotext could have been picked up by German Y stations. (According to Winterbotham, however, the British used an individual key.) The plaintext itself is authentic.

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F. L.

: ‘Decrypted secrets’; 1996, Berlin and Heidelberg, Springer.

Bauer

F. L.

and Wirsing

: ‘Crypt-equivalent algebraic specifications’, Acta Inform., 1988, 25, 111–153.