While the citation is:
Calvin, W. H. (1994). Compressing the cerebral code: Hebbian cell assemblies may be concentrated into a hexagonal macrocolumn. Society for Neuroscience Abstracts 20:315.
what follows is the handout for the poster as presented seven months later.

Copyright 1994 by W. H. Calvin.

Society for Neuroscience poster 138.3 handout, as presented in Miami, November 1994.


Hebbian Cell Assemblies May Be Concentrated into a Hexagonal Macrocolumn.

William H. Calvin

University of Washington
Department of Psychiatry and Behavioral Sciences, Box 351800
Seattle, Washington 98195-1800 USA


The simplest notion of a cerebral code is the Grandmother's Face Cell: one specialist neuron per percept, which fires when the percept is present or being recalled from memory. This unique specialist cell seems unlikely from the lesion evidence which suggests distributed memory storage with considerable redundancy.

Hebb's Cell-assembly postulates that recalling a memory involves reconstituting the activity pattern present at input, a pattern involving many neurons. Just as a bar code can uniquely represent a banana with an arbitrary pattern that looks nothing like a banana, so one expects the cerebral code for banana to be a pattern of activity in a number of cortical neurons. In long-term memory, this pattern is surely a spatial pattern of connection strengths (not unlike a washboarded road). Recalling the memory, however, involves recreating a spatiotemporal pattern (not unlike a bouncing car driving over the washboarded road, or a phonograph needle vibrating in the grooves), as any output (pronunciation, limb movement) involves creating a spatiotemporal pattern of activity in motorneuron pools.

But recall presumably does not involve recreating the exact spatiotemporal pattern of activity at the time of memorization, not that of the entire brain. What is the minimal Hebbian cell assembly? How many neurons? Extending over what distances in cerebral cortex? How is redundancy achieved?

In the present Darwin Machine model, insights from the periodic nature of the horizontal connectivity of the superficial pyramidal neurons are used to predict a triangular mosaic of synchronized neurons at 0.5 mm spacings. Like the unit pattern of mosaic wallpaper, the largest unique spatial pattern would be contained in a 0.5 mm hexagon -- despite initial separations of the activated feature detectors that span much longer distances. The initial representation appears to be collapsed by end-around overwriting into a compact one that has an inherent error-correction feature. This candidate seems worthy of the name Cerebral Code.


Pyramidal neurons of the superficial neocortex are excitatory to other pyramids and, since they tend to cluster axon terminals at a standard distance ("0.5mm"), some corticocortical cell pairs will mutually re-excite. Though refractoriness should prevent reverberation, even weak positive coupling can entrain oscillators when cells are active for other reasons.

Because each pyramid sends horizontal axons in many directions, simultaneous arrivals may recruit a 3rd and 4th pyramid at 0.5mm from the synchronized parental pair. A triangular mosaic of synchronized superfic- ial pyramids thus can temporarily form, extending for some mm (Calvin, Soc. Neurosci. Abstr.'92). At least at the V1-V2 border, the intrinsic horizontal connections change in character and in length, suggesting that mosaics might stay confined to the parent architectonic area, spreading to other areas only via the U-fibers of white matter.


Consider N neuron pairs respond- ing to different aspects of an apple: contour, color, motion, stereopsis. They form N triangular mosaics that interdigitate. There is thus a recycling temporal pattern (since synchrony is not needed between different feature detectors) imposed on a widespread cortical area. This should look like a wallpaper pattern that has spatial repeats. What is the elementary spatio- temporal pattern, equivalent to the unitary wallpaper pattern?


It consists of N neurons which, for geometric reasons, cover an area no larger than a 0.5mm hexagon (any larger and another member of a triangular mosaic would be encountered). This compact pattern becomes standardized across the mosaic (a variant must overcome six simultaneous EPSPs); such pattern "crystallization" is a form of error correction.


The synchrony could induce longer-term NMDA connectivity changes; later, partial patterns could "pop out" the complete spatio- temporal pattern for Apple by resonance with this connectivity pattern, even in cortex lacking the original feature detectors. A hexagonal matrix could thus house a Hebbian cell assembly and function as a cerebral code.


A 0.5 mm hexagon houses about 300 microcolumns, each of which has about 100 neurons. If a microcolumn acted as a unit (either on or off), there would be a code capacity of 2^300 without even considering the temporal aspect; this would not seem to be a limiting feature. The "matrix" could be sparse enough so that patterns could be overlaid to create hybrid patterns such as categories. How many memorized spatiotemporal patterns would the connectivity in a 0.5 mm hexagon support? There are about a half million hexagon pairs in human cerebral cortex. Even if a given pair supported no more memorized spatiotemporal patterns than the number of gaits supported by spinal cord circuitry, the memory capacity would be well in excess of the demands of vocabulary (10^5) and lifetime episodic memories.


More general background can be found in:

William H. Calvin and George A. Ojemann.Conversations with Neil's Brain: The Neural Nature of Thought and Language (Addison-Wesley, 1994).

William H. Calvin, "The emergence of intelligence," Scientific American 271(4):100-107 (October 1994).

Click here to send E-mail WCalvin@U.Washington.edu

Mailing address: University of Washington, Box 351800, Seattle WA 98195-1800 USA.

A list of my other books and articles can be found here. .....[Jump to Top]

Revised 27 Jan 95 WHC

[Current references to Darwin Machines and cerebral codes]