Читать книгу The Form Within - Karl H Pribram - Страница 63

The processes of the retinal transformation, and those that follow, are not accurately described by the Fourier equation. I discussed this issue with Dennis Gabor over a lovely dinner in Paris one evening, and he was skeptical of thinking of the brain process solely in Fourier terms: “It is something like the Fourier but not quite.” At the time, Gabor was excited about showing how the Fourier transform could be approached in stages. (I would use his insights later in describing the stages of visual processing from retina to cortex.) But Gabor could not give a precise answer to why it was not quite how the brain process worked.

Gabor actually did have the answer—but he must have forgotten it or felt that it did not apply to brain processing. I found, after several years’ search, that the answer “to not quite a Fourier” had been given by Gabor himself when I discovered that J. C. R. Licklider, then at the Massachusetts Institute of Technology, had referred in the 1951 Stevens’ Handbook of Experimental Psychology to a paper by Gabor regarding sensory processing.

Missing from our Paris dinner conversation was Gabor’s development of his “elementary function” which dated to an earlier interest. He had published his paper in the IEE, a British journal. I searched for the paper in vain for several years in the American IEEE until someone alerted me to the existence of the British journal. The paper was a concise few pages which took me several months to digest. But the effort was most worthwhile:

Before he had invented the Fourier holographic procedure, Gabor had worked on the problem of telephone communication across the transatlantic cable. He wanted to establish the maximum amount a message could be compressed without losing its intelligibility. Whereas telegraphy depends on a simple on-off signal such as the Morse code, in a telephone message that uses language, intelligibility of the signal depends on transmission of the spectra that compose speech. The communicated signals are initiated by vibrations produced by speaking into the small microphones in the phone.

Gabor’s mathematical formulation consisted of what we now call a “windowed” Fourier transform, that is, a “snapshot” (mathematically defined as a Hilbert space) of the spectrum created by the Fourier transform which otherwise would extend the spectral analysis to infinity. Neither the transatlantic cable nor the brain’s communication pattern extends to infinity. The Gabor function provides the means to place these communication patterns within coordinates where the spectrum is represented on one axis and space-time on the other. The Fourier transform lets us look at either space-time or spectrum; the Gabor function provides us with the ability to analyze a communication within a context of both space-time and spectrum.