Friday, July 3, 2015

Colour Vision and Mathematics

Contributed by Mikhail Filippov and Semir Zeki

That the experience of mathematical beauty, derived from a highly cognitive source, correlates with activity in the same part of the (emotional) brain as the experience of beauty derived from sensory sources makes it interesting to enquire what other common factors mathematics shares with sensory experiences.

We choose colour vision as an example.

One of the primordial functions of the brain is to acquire knowledge and it has to do so in the face of continually changing conditions, often referred to as the Heraclitan doctrine of flux (after Plato). To extract that knowledge, the brain has to somehow stabilize the world, since it is difficult to acquire knowledge in constantly changing and often unpredictable conditions.
With colour vision, a surface or object of any colour can be viewed in different lighting conditions (for example sunlight or indoors in tungsten or fluorescent light), when the composition of the light (in terms of energy and wavelength composition) reflected from it and from its surrounds changes continually.

Yet, by a process  dictated by brain logic (usually referred to as an algorithm), the brain discounts these continual changes to assign a constant colour to the object or surface. This is what is meant by colour constancy.

Without it, the task of acquiring knowledge about objects and surfaces through colour becomes difficult, if not impossible; without it, colour would lose its importance as a biological signaling mechanism.

How it does so, in terms of the neural mechanisms involved, is not entirely clear but it does involve a specialized centre in the brain and the pathways leading to and from it. Through this process the brain stabilizes an ever-fluctuating world and is thus capable of acquiring knowledge about it through the colours of objects in it.

Our Universe, at the other end of the scale, presents an even more complex picture; but, similarly, the only way to acquire knowledge about it is to stabilize it by reducing all its complexity to some fundamental rules, reflected in equations or mathematical formulations.

These formulations are the products of a deductive logical system that belongs to the brain; their end-result is to stabilize the world through simple, all-embracing formulae, and hence acquire knowledge about it.

Thus the knowledge-acquiring system of the brain uses a logical system to acquire knowledge about, on the one hand, a sensory category such as colour, which is continually experienced throughout the day and, on the other, knowledge about the structure of the Universe which is not possible to experience directly. The end-result is to stabilize the world, sensorially in the case of colour vision and cognitively in the case of what determines the structure of the Universe

There is another feature that mathematical formulations about  truths governing the Universe share with sensory experiences such as colour vision – in both, there is one route and one route alone and, once established, there is no appeal against its conclusions.

All knowledge that a green leaf is reflecting more red light (as it commonly does at dawn and at dusk) will not enable one to see the leaf as red. The operation that the brain applies to generating constant colours in spite of variations in the wavelength-composition of the light reflected from surfaces and objects under different lighting conditions allows one to see the green leaf as green only (although its hue, or shade, will change under different illuminants).

And all cognitive knowledge acquired through daily experience, that time and space are separate entities, will not invalidate the conclusions postulated by the theory of relativity, which show that time and space are continuous, at least to those who know the language of mathematics. 

There are, of course, conditions, in which two fundamental truths are in apparent contradiction to each other, as in macro- and micro- physics.

Here, too, the brain’s system for acquiring knowledge through the sensory system shows strong similarities with its system for acquiring more abstract knowledge.

We will return to it in the next post.