Properties of a Vision Field

Even though the fields of physics involve infinite parallel processing, they are not infinitely complicated, because they are subject to several restrictions, which are apparently inherent in the very structure of our Universe.

Very similar restrictions can reasonably be postulated on fields that are relevant to visual perception, according to the possible structure of the human brain.  The inference of these restrictions, and the derivation of an equation from them that follows, is not mathematically rigorous.  To some extent, they are motivated by familiarity with the fields of physics, and by a strong desire that the theory should contain no adjustable parameters.  Perhaps other fields could be postulated, that do not follow these restrictions, and that also are relevant to visual perception.  (That’s a source of opportunity.)

Postulated Properties of a Visual Field

1. The same processing occurs at every point.

   This supposes that an object has the same nature, and therefore should be perceived in the same way, wherever it is.

2. Any direction is equivalent to any other.

   Similarly, an object has the same nature, whatever its orientation is.

3. There is no action-at-a-distance; events at each point depend only on the point’s immediate neighborhood.

   In the brain, if there were long-range interactions in a planar structure, nerve fibers would have to pass from each point in the plane to every other point in the plane.  In the approximation of an infinite number of processors, this would be impossible.

4. The field is linear.

   This follows from the postulate that an object has the same nature, no matter how brightly it is illuminated.

These restrictions are reasonable for a low-level process, such as the perception of linearity, but not for the higher levels of perception, such as the recognition of objects.  For example, the characters “<”, “V”, “>”, and “Λ” are not the same, even though they differ only by rotation.  Similarly, a bird in the hand is worth two in the bush, and thus violates translation symmetry.