Читать книгу The Form Within - Karl H Pribram - Страница 52

The strengths and weaknesses of the feature and the frequency (spectral) views of brain processes in perception provide a fresh look at the way science works. The experiments that led to the feature view showed the importance of the orientation of the stimulus. The experiments upon which the frequency view is based showed that the cortical cells were not detectors of stimulus “elements” but were responsive to interrelations among them. Furthermore, the frequency approach demonstrated that the power and richness of a spectral harmonic analysis could enable a full understanding of neural processing in perception. Unfortunately, those holding to the feature approach have tended to ignore and/or castigate the frequency approach and the results of its experiments. There is no need to exclude one or the other approach because the results of harmonic analysis can be translated into statistics that deal with features such as points; and into vectors that deal with features such as oriented lines.

There is a good argument for the ready acceptance of the feature detection approach. It is simple and fits with what we learned when taking plane geometry in high school. But the rules of plane geometry hold only for flat surfaces, and the geometry of the eye is not flat. Also, the rules of plane geometry hold only for medium distances, as a look at the meeting of parallel railroad tracks quickly informs us. A more basic issue has endeared brain scientists to the feature detection approach they have taken: the rules of plane geometry begin with points, and 20th century science insisted on treating events as points and with the statistical properties of combinations of points which can be represented by vectors and matrices. The frequency approach, on the other hand, is based on the concept of fields, which had been a treasured discovery of the 19th century.

David Marr, Professor of Computational Science at MIT, was a strong supporter of the feature view. But he could not take his simulations beyond two dimensions— or perhaps two and a half dimensions. Before his untimely death from leukemia, he began to wonder whether the feature detector approach had misled him and noted that the discovery of a cell that responded to a hand did not lead to any understanding of process. All the discovery did was shift the scale of hand recognition from the organism to the organ, the brain.

24. The Receptive Fields of Seven Ganglion Cell Types Arranged Serially

As I was writing the paragraphs of this chapter, it occurred to me that the resolution to the feature/frequency issue rests on the distinction between research that addresses the structure of circuits vs. research that addresses processes at the deeper neuro-nodal level of the fine-fibered web. The circuits that characterize the visual system consist of parallel channels, the several channels conveying different patterns of signals, different features of the retinal process. (My colleagues and I identified the properties of x and y visual channels that reach the cortex as identical to the properties of simple and complex cortical cells.) Thus, feature extraction, the creative process of identifying features, can be readily supported.

The frequency approach uses the signals recorded from axons to map the processes going on in the fine- fibered dendritic receptive fields of those axons. This process can generate features as they are recorded from axons. Taking the frequency approach does not require a non-quantitative representation of the dendritic receptive fields, the holoscape of the neuro-nodal process. Holoscapes can be quantitatively described just as can landscapes or weather patterns. The issue was already faced in quantum physics, where field equations were pitted against vector matrices during the early part of the 20th century. Werner Heisenberg formulated a comprehensive vector matrix theory and Erwin Schrödinger formulated a comprehensive set of wave functions to organize what had been discovered. There was a good deal of controversy as to which formulation was the proper one. Schrödinger felt that his formulation had greater representational validity (Anschaulichkeit). Heisenberg, as was Niels Bohr, was more interested in the multiple uses to which the formulation could be put, an interest that later became known as the Copenhagen implementation of quantum theory which has been criticized as being conceptually vacant. Schrödinger continued to defend the conceptual richness of his approach, which Einstein shared. Finally, to his great relief, Schrödinger was able to show that the matrix and wave equations were convertible, one into the other.

I shared Schrödinger’s feeling of relief when, three quarters of a century later, I was able to demonstrate how to convert a harmonic description to a vector description using microelectrode recordings taken from rats’ cortical cells while their whiskers were being stimulated. My colleagues and I showed (in the journal Forma, 2004) how vector representations could be derived from the waveforms of the receptive fields we had plotted; but showed that the vector representation, though more generally applicable, was considerably impoverished in showing the complexity of what we were recording, when compared with the surface distributions and contour maps from which the vectors were extracted.

25. The Holoscape

26. An example for the three-dimensional representation of the surface distribution and associated contour map of the electrical response to buccal nerve stimulation. The surface distributions were derived by a cubic interpolation (spline) procedure. The contour maps were abstracted from the surface distributions by plotting contours in terms of equal numbers of spikes per recording interval (100 msec). The buccal nerve stimulation whisked the rat’s whiskers against teflon discs whose textures (groove widths that determined the spatial frequency of the disc) varied from 200 to 1000 microns and whose grooves were oriented from 0 to 180 degrees. Separate plots are shown for each frequency of buccal nerve stimulation: 4Hz, 8Hz, and 12 Hz (top to bottom).

27. The cosine regressions of the total number of spikes for the orientation of the stimulus for the 4 Hz condition are shown.

28. Vectors

The use of both the harmonic and the vector descriptions of our data reflect the difference between visualizing the deep and surface structures of brain processing. Harmonic descriptions richly demonstrate the holoscape of receptive field properties, then patches—the nodes—that make up the neuro-nodal web of small-fibered processing. The vector descriptions of our data describe the sampling by large-fibered axons of the deep process.