The geometry of hallucinations

A recent blog from Jennifer Ouellette (from the Scientific American Blog Network)  brought my attention once again to how mathematics is related to the structure-building functions of the brain. As I followed up on some of the references in her post, I found myself on a little journey through hallucinatory experiences that I really enjoyed.

Her post is generally about Turing models applied to patterns found in the characteristic features of animals.  But she got into territory that I find particularly provocative when she began to discuss the evidence for whether a Turing model can be applied to neurons in the brain.

If we really want to get into some interesting speculation, we can think about whether a Turing model can be applied to neurons in the brain, which could be “described mathematically as activators or inhibitors, encouraging or dampening the firing of other, nearby neurons in the brain.” And that could potentially explain why we see certain recurring patterns when we hallucinate.

I did a blog about how Turing insights appear to bridge otherwise disparate trends in science.  But the link to Turing in this context is drawn through hallucination patterns, categorized in the early 20th century by University of Chicago neurologist Heinrich Kluever, into what he called the form constants: checkerboards, honeycombs, tunnels, spirals, and cobwebs.

Over seventy years later, another Chicago researcher, Jack Cowan – who holds dual appointments in mathematics and neurology – set out to reproduce those hallucinatory patterns mathematically, believing they could provide clues to the brain’s circuitry.

The paper is very technical and involves quite a lot of mathematics as well as neuroscience.  But the authors succeed in modeling a structure of the primary visual cortex whose activity would produce “certain basic types of geometric visual hallucinations.”  Bressloff and Cowam conclude:

…thus our new work provides a stronger link between the nature of hallucinatory patterns and the actual structure of cortex.  Indeed, we hypothesize that the symmetries and length-scales of these hallucinatory images are a direct consequence of the geometry of cortical interactions as well as the retino-cortical map.

Apparently they found that the patterns predicted by their calculations closely matched what people will see when under the influence of hallucinogenic drugs, and they suspect that these patterns could be emerging from a kind of Turing mechanism.

While the random fluctuations in brain activity might technically just be “noise,” the brain will take that noise and turn it into a pattern. Since there is no external input when the eyes are closed, that pattern should reflect the architecture of the brain, specifically the functional organization of the visual cortex.

Ouellette also spoke with neuroscientist Robin Carhart-Harris, who has done quite a lot of work on the brain mechanisms that lead to hallucinatory experiences, and how they might be used to help in the treatment of depression and addiction.  I very much enjoyed watching an interview with him, shot as part of a forthcoming documentary on consciousness. There he made some really nice observations of the integrative function of  ‘brain hubs’  that unify activity from different regions of the brain into coherent patterns or narratives.  The geometric patterns of hallucinations are perceptual errors but, he tells us, the error “is a function of how the perceptual system works.”  Carhart-Harris argues that the way we currently understand the action of the visual system,  “says, very strongly, that reality is a construction. Reality only becomes something as we piece it together.”

With respect to how hallucinatory patterns reflect brain activity, Carhart-Harris tells Ouellette:

You are not seeing the cells themselves, but the way they’re organized – as if the brain is revealing itself to itself.

This is, in fact, what I have thought about mathematics.

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