Jan Koenderink is a leading researcher in vision. He proposed the concept of

“scale-space representation” in relation to the understanding of how the front-end visual system works.

His paper “The brain a geometry engine” starts with:

According to Kant, spacetime is a form of the mind. If so, the brain must be a geometry engine. This idea is taken seriously, and consequently the implementation of space and time in terms of machines is considered. This enables one to conceive of spacetime as really embodied.

Later he writes:

There may be a point in holding that many of the better-known brain processes are most easily understood in terms of differential geometrical calculations running on massively parallel processor arrays whose nodes can be understood quite directly in terms of multilinear operators (vectors, tensors, etc).

In this view **brain processes in fact are space**.

This is a very interesting idea! As far as I understand, Koenderink is saying that somehow brain processes involved in vision and (external) space are similar!

In my opinion this is something to explore. However, my take is that this superb idea is clouded by his reliance on linear algebra and differential calculus of the exterior euclidean space (see “vectors, tensors, etc” as well as his derivation of the gaussian filter from invariance with respect to the same euclidean structure). If said brain processes are space and if those brain processes are a kind of computation (in a sense to be explained later) then space should appear as the result of a computation in the front-end visual system. No euclidean a priori!

Are those brain processes a kind of computation? The answer depends on what computation means. Anyway, nobody doubts that logical boolean computations are orthodox computations.

See then the following paper by Mark Changizi “Harnessing vision for computation” or check this Wired post

Scientists Build Visual Circuits to Harness your Brain’s GPU”

The abstract of the paper is:

Might it be possible to harness the visual system to carry out artificial computations, somewhat akin to how DNA has been harnessed to carry out computation? I provide the beginnings of a research programme attempting to do this. In particular, new techniques are described for building `visual circuits’ (or `visual software’) using wire, NOT, OR, and AND gates in a visual modality such that our visual system acts as `visual hardware’ computing the circuit, and generating a resultant perception which is the output

My conclusion: this is experimental proof that at least some brain processes related to vision can do something which simulates logical computation.

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