Are lines always a means to more complex forms? Aleksander Rodchenko would not agree

Orientation selective cells of the visual cortex, which respond to lines of specific orientation, were discovered in 1959. They were first encountered in the primary visual cortex of the brain (area V1) – considered by many for much too long to be the only entering place of visual information into the rest of the visual brain.  Such cells have usually been thought of as the initial staging post for the elaboration of more complex forms. Some, indeed most, believe that they are the sole source for the elaboration of more complex forms such as faces, houses and objects. I am becoming increasingly skeptical of this view.

First of all, evidence which is largely ignored or at least marginalized, although it has been available since 1980, shows that V1 is not the only entering place of visual signals into other areas of the visual brain; there are alternative routes which reach them without passing through V1. Secondly, orientation selective cells are found in at least four other visual areas of the visual brain, and these cells survive functionally even when deprived of an input from V1 (i.e. they remain orientation selective cells); they are, very likely, fed by these alternative inputs. Thirdly, visual signals related to form (oriented lines) reach V1 and the other visual areas within the same time frame. And, finally, clinical evidence shows that humans can become agnosic (blind) for line drawings without at the same time becoming agnosic for real objects.

Hence, one must seek for sources besides V1 for elaborating orientation selective cells and complex forms, which is not to say that V1 cells do not contribute significantly to this process. But perhaps one should also consider, at the same time, that oriented lines stand on their own as forms in every sense, without their being mere “building blocks” for elaborating more complex forms.

Neurobiologists are not alone in considering oriented lines a means towards a more complex end. Mondrian, among others, sought for the constant elements in all forms and settled on the straight lines, provided they are vertical and horizontal. He abhorred diagonal lines, breaking off his working relationship with a colleague because “of the high handed way in which you have treated the diagonal line”. Ever the reductionist (though not accused of it, as we commonly are), he believed that “there are also constant truths concerning forms” and it was the function of the artist “to reduce natural forms to the constant elements”.

Many others, including Kazimir Malevich, Ellsworth Kelly and Barnet Newman, among others, have emphasized lines in some of their paintings, for different reasons. But it was perhaps Aleksander Rodchenko, the Russian Constructivist artist, who was most explicit in giving the straight line its autonomy. Influenced by Malevich and Suprematism, he wrote:  “ I introduced and proclaimed the line as an element of construction and as an independent form in painting”. In another context, he also wrote "I reduced painting to its logical conclusion” (although he, too, was not (as far as I know) accused of reductionism). There are, incidentally, very good perceptual reasons for why he should not have been accused of reductionism, but I will leave that to a future post.

The point of all this is simple: that lines are not only a means towards something more complex; they can also stand on their own as a form or forms; that, as the Gestalt psychologists emphasized, “the whole is other than the sum of the parts” and that a complex form, even when constituted from lines, is one that is other than a combination of lines – an important lesson in the physiology of forms; and that there is much more to the construction of forms in and by the brain than a single source which lies in the orientation selective cells of V1.

It seems to me that the physiology of form construction by the brain is still, in spite of all the excellent work that has been done in the field, a field that is rich for exploration but also requires some of the facts mentioned above to be taken into consideration. In that exploration perhaps the products of artists should also play some role, even if only a minor one.

© Semir Zeki

What does the brain do to ensure that contradictory truths are valid? Answer: it ensures that they never meet.

Contributed by Mikhail Filippov and Semir Zeki

Mathematical and physical theories constitute one means of acquiring knowledge about our Universe. We build models of the way the Universe is constructed through experimental facts. But what happens when they contradict each other. How do we accommodate them both?

In the sensory world, contradictions can occur in vision. This is commonly referred to as ambiguity or instability. We will discuss them first before addressing the question of contradictory truths about the nature of the Universe.

For vision, a good example of an ambiguous, though finished, work is Vermeer’s Girl with a Pearl Earring. The painting is capable of many interpretations – of someone who is distant or inviting or resentful or approving. The important point is that (a) there is no clear solution because all solutions are valid (see Zeki 2008) and (b) only one solution can be valid and occupy the conscious stage at any one moment (see Zeki 2004), before ceding place to another, equally plausible, solution or interpretation, which then becomes sovereign until it, too, is replaced.

With bi-stable or multi-stable figures, the image transmutes perceptually from, say, a face to a house. Again, only one image – face or house – is possible at any given moment, even if one knows that the image is bi-stable.

The transition from one perceptual state to another is not generally under our control. The images flip over between two or more states with prolonged viewing and it is not evident that even the length of time when one state reigns can be controlled.

Thus the brain has devised a system where, when there is no certainty as to the solution, it will entertain two more solutions as equally plausible, even if these solutions are significantly different. But it ensures that the two solutions do not coincide.

The same general rule applies, we believe, to grander and more exalted cognitive states. One such example is to be found in the laws of gravitation and time-space, which are derived from what has come to be known as classical logic. These laws are different from quantum logic, though we would say that both are derived from brain logic, just as two contradictory images are derived from the brain's perceptual mechanisms.

Indeed, it can be said that classical logic cannot reach the conclusions reached by quantum logic. 

In their statement on Quantum Logic, Birkhoff and von Neumann put it like this,  “The object …is to discover what logical structure one may hope to find in physical theories which, like quantum mechanics, do not conform to classical logic.”

We note that, in the above quote, they write of the logical structure of physical theories. We believe that the logical structure of physical theories is derived from brain logic.  We would therefore re-formulate what they say, as follows:

“The object …is to discover what variations there are in the logical system of the brain that allows it to accommodate the facts that lead to quantum logic as well as to logic dictating classical Newtonian mechanics”.

In truth, quantum logic and classical logic, both of which are brain logic, are not in contradiction. They are just two different models of the physical reality and, like bi-stable images, only one can occupy the conscious stage at any given moment. Also, as in ambiguous stimuli, there is no correct solution, because both solutions are correct.

The overall conclusion that we draw is that the brain does not devise too many  different solutions to acquire (apparently contradictory) knowledge about the world. It uses the same general approach to sensory knowledge as to cognitive knowledge. It accepts even what may amount to contradictory facts, if these conform to its logic system and will reject them both if they do not.

If it accepts them both, it will however not accept them both simultaneously, just as it will not accept two contradictory interpretations of a visual image at the same time.

Hence, in addition to deriving knowledge about the world through its logical deductive system, the brain has another, intrinsic, logical system which allows it to separate out contradictory models as truthful, whether derived from the sensory or cognitive world, but ensure that they do not contradict each other because only one can occupy the conscious stage at any given moment.  This it does by ensuring that they do not co-occur.

This, in fact, is the solution, that the brain has adopted to deal with contradictory but equally valid facts: by making sure that they do not co-occur. In more popular language, it ensures that they never meet.

©Mikhail Filippov and Semir Zeki