Category Archives: colors

The green dot illusion and Opponent Process Theory

Mind Hacks has an interesting article mentioning green-dot illusion. The Green Dot illusion is possible because of the opponent process theory of color perception.

As an aside, for an excellent account on Opponent process theory and how many observable normal and abnormal behaviors may be realized as gated dipole opponent processes please read an article by Grossberg on the same.

As per this theory, as applicable to color-processing (the herring theory), the higher level processing and perception of colors happens as an outcome of 3 opponent processes. Two of these are chromatic processes : one involving red and green opponent process and the other involving blue and yellow. One supposedly “achromatic” opponent process utilizing black and white ‘colors’ is also involved. Thus, while the Hue of any perceived color may be determined by the value of the red green and blue – yellow opponent process; its Saturation (or the grayness or ‘impurity’) may be determined by adding the black-white opponent process value to determine the grayness of the stimuli while some other input (in the ‘luminance’ channel/ magnocellular channel of LGN) may be used for determining the Value or luminance or ‘brightness’ (refer HSV or HSL models of colors).

It is instructive to note that the red-green opponent process is realized by subtracting the output of Medium (green) cone from Long (red) cones and thus the R minus G signal should lead to either excitation of ‘red color perception’ and inhibition of ‘green color perception” or vice versa. Thus, depending on the signal strength and polarity, later processing by neurons would happen as opponent processes, with 1) if red is being perceived then inhibit green-perception and vice versa. Also the blue-yellow opponent process is realized by first summing the Long (red) and Medium( green) cone outputs to create a yellow ( R+G) signal and then subtracting this from the Short (or Blue) cones to give a final B minus Y signal. Again depending on the strength of this signal, either ‘blue color perception’ is encouraged and ‘yellow’ color perception is discouraged or vice versa. When later the B minus Y and R minus G signals are analyzed (and possibly aggregated), one can determine the Hue of the color depending on the relative strength of the 2 signals.

An account of how all hues can be realized using this opponent processing is explained beautifully at this site and I also include a graph from that site for illustration of how all hues (in the humanly visible spectrum) can be realized using these opponent process. That said, there still remains the issue of perception of non-spectrum colors like purple, olive green , brown etc., these have been partly addressed in my earlier post on this matter.

To sum up, the moving green dot illusion works because red and green are opponent processes. When pink (which may be conceived as low-saturation red) dots are present in the visual field, then for that portion of visual filed, Red Qualia is exaggerated and Green Qualia inhibited further down the visual pathways. Prolonged presence of Red stimuli ensures that there is no need to keep inhibiting ‘green qualia’ as habituation happens and as the Red signal is strong and continuous one so the need to inhibit Green does not arise. If one refers to the gated dipole opponent process theory of Grossberg, then it is apparent that due to the gating of the dipole, when the RED stimuli disappears from the on-channel then the ‘off channel’ (corresponding to Green qualia) would result in a sudden rebound and thus momentarily the Green qualia would be perceived. Here it is instructive to note that the signal is R minus G i.e Red is the presence of signal and green the absence (or below threshold or negative signal). Thus the green dot illusion would become more stronger if pure red is used and a similar illusion can be produced by moving yellow dot when blue dots are involved.

Color vision continued: What role do rods play in color vision, if any and how many dimensions/ variables we need.

There is a very descriptive and helpful book eye, brain and vision on Hravard’s site and I was going through the chapter on color vision. It is posited there that color blindness occurs if one of the 3 cone pigments are not present and consequently one is not able to distinguish white light from a monochromatic light of certain wavelength. It is also posited that for color vision only 3 types of receptors are required (and are present in the form of 3 types of cones in the retina). Now here is some experimental work that I would like done for this experiment. What happens to someone who lacks the green pigment and who is exposed to light in the wavelength of light between the non-overlapping visual fields of blue cone and red cone. As per the arguments in the book, that should lead to total loss of color (and actual colorblindness as opposed to color-defectiveness for that range of colors) and thus ability to use only rods and thus get a black and white view of world for those wavelengths. Is that really so, as per color blind people with the green cone not present?

The other thought that passed while reading the article is that it uses projection of 3 types of monochromatic light with same intensities as the metaphor of choice while describing how the brain processes color. Unfortunately as we know, the blue color cone does not overlap with red color cones and this metaphor may not be right. Even, with this metaphor it strikes one as to how black is perceived, because the picture that is shown of 7 colors (including white) produced depends on a dim room in which the 3 lights are projected and the rods that would be useful in producing this black color are integral to the experimental setup of demonstrating the tri-color sufficiency of explaining the color vision. I , personally believe that rods do have a role in color perception and color perception may more involve the CMYK model than the RGB. This also brings the ‘image formation’ metaphor over the ‘laser beam’ model. Also, at the same time, due to Kline-bottle associations I may even venture forth and propose that in reality 6 types of colors/ color detecting devices may be required to fully apprehend the colors and we may still be in the process of evolving/ detecting such pigments. Maybe the rods themselves of nocturnal animals like wild cats may throw some light. Total armchair speculation!

Interestingly, the author of the above book concedes that Brown color is a bit difficult to explain, though purple can be easily explained or be intuitive. As per this article on color naming universals which references the article Berlin and Kay (1969) published under the title ‘Basic Color Terms, their Universality and Evolution’. the brown appears in stage VI of a language evolution, where apparently as per my initial eight fold developmental model, a qualitatively different sort of leap needs to be taken. The original Harvard’s book excerpt from “Eye, brain and vision” takes recourse to Herring theory of opponent processes, specifically that of red and yellow mixing to give orange and that when seen through black contrast giving appearance to brown. Thus for brown to be explained,, the 2 extreme edges of blue-yellow dimensions and red-green dimensions have to mix spatially at a point and then this has to be seen in contrast to another extreme of black-white dimension. Seems a complicated explanation and involves taking recourse to brains excitatory and inhibitory processes to provide explanation. I might revisit this later if some more suitable explanations in terms of some other inherent property of cooler like using both the hue, saturation, value and R,G,B model may explain brown. While HSV explains purple (in the sense of it being complement of green and actually lying in the region that sort of make ultra-violet and infra-red meet), it is surprising why it is not one of the words that are found while going from stage V to stage VI of language evolutions.

Endgame: Is CMYK actually CMYKW model, with white of paper acting as background essential for the CMYK to work in reproducing images?

Cognitive Map continued :The importance of color and other irrelevant facts as to my journey towards color vision

There is an article on EurekaAlert regarding the necessity of colors for identifying say members of your favorite football teams when engaged in a match with an adversary team. The contiguity provided by colors of uniforms worn by players ensures we are able to keep track of which member belongs to which team. As per the article in the absence of colors , we cannot track more than 3 objects at the same time.

The application of this to the cognitive map is evident. In the absence of colors, we may view the world in Black, White and Gray and would be forced to make arbitrary decisions of clubbing everything in one category or the other. This will limit us to make sense of the world in TriColor (if color can be used in this B&W context) (say of satve, rajas and Tamas gunas) by joining some isolated regions together to bi-or-trifurcate the world in some 2 or 3 arbitrary qualities/regions. Thus the world as located on our cognitive map would be made up of 2 or 3 qualia and different colors used to represent different but interconnected and hence same regions. One is reminded of the shloka from Gita ” tri-state is all of creation, be non-tri-state O Arjun”

With even 3(RGB) or 4 (CYMK) or 6 colors (??) at our disposal (and in the language of cognitive maps the ‘colors’ may be equivalent to the ’emotions’ and thus reflect how we feel about that part (region) of the Map), we can have infinite combinations of colors to code the Map and thus either have a kaleidoscopic view of the world (in which there are more colors then can fit our working memory (limited by size constraints of 6 +-2 ); or we can stick to the 4 or 6 colors that are primary and see all the different regions of the cognitive map having the same color(out of the 4 or 6 primary colors) as one particular quality /qualia of the world. Thus all the red regions on our cognitive map may signify all the parts of our life (time-space event) that are felt by us as colored Red or arousing angry feelings (If Red is associated with Anger. Here is a link to V S Ramchnadran’s site that carries many research on synesthasia, though association of color with emotions is not discussed.)

Thus with the correct color coding (either MCYN or yet to be discovered 6 primary color schema….And that color mapped to ‘color’ as applicable in cognitive Maps) and the correct cognitive MAP nature ( a Rotating Sphere or a klien bottle ) with some other type of ‘spin’ one may be better adapted to understand reality and act accordingly knowing which parts of Cognitive map are more or less the same and which Cognitive Map is to be used for which season.

The article contains a quote from the original article viz

. “We found that humans are unable to store information from more than three sets at once,” Halberda said. “This places an important constraint on how humans think about and interact with sets in the world.”

As per this quote even when we have extended sets (say many regions on an Atlas covered in Cyan only- and thus forming one set), we can keep in memory no greater than 3 such sets. Thus we may be able to keep Cyan sets, Magneta sets and Yellow sets in the cognitive Map, but would miss on the Key (or Black set). This seems to be a limitation that has been observed experimentally and needs some thinking. Maybe later experiments (say done on Tibetan Lamas) could verify that more than 3- maybe upto 6 sets can be distinguished.

Before venturing forth and elaborating more on the Cognitive Map theme, I would like to backtrack a bit and again indicate from where I come: I believe that the personality traits from the Five-Factor Model can be mapped to successful or unsuccessful completion of the 5 development tasks that a child need to undergo before becoming an adult (or has an ego, or becomes a hero with a thousand faces!). After the first five developmental task are the 3 qualitatively different tasks that require him/her to reach out to others and thus develop traits that would not be captured by factor analysis that has as its reference an individual; but might possibly be revealed when one talks (or does a factor analysis) about say a pair. Are the pair intimate? are they a case of ‘sleeping with the enemy”? are they sacrificial etc? Broadly the first task and Factor would have to be intimacy and sharing and has to be attained not by an individual but by the pair. Intimacy with married partner may be one task that literally expands your horizons or lets you see issues from both sides of the coin, or with different spins applied to it!

The second (or sixth if the first 5 are also counted) task is related to group performance and solidarity. One could be instrumental and active in competitive groups, co-operating groups, creative/synergetic groups, or even destructive groups. How group dynamism is achieved, how synergy is created, how one submits one’s freedom to the greater good , how one starts understanding when to be competitive, when co-operative and when to go with the flow ( and when to stand up against the tide), all these would be tasks that need to be completed before achieving the feeling of efficacy.

The third (or last or eighth ) task would be to broaden your group identity and start extending it to others – say to whole of live creation. The end result of this would be peaceful death or passage to next life with no guilt feelings. Otherwise feeling of despair may occur instead of feelings of integrity with the world.

Much of the background for above is the ashtang yoga having 5 physical aspects – yam, niyam, asan, pranayam, pratyaharare and after these 3 mental aspects – Dhyan, Dharna and Samadhi.

Also, the analogy with the traditional 4 varna-ashrams that one should observe: Brahmacharya (in which ego identity is achieved while learning- and five personality factors deepened and come to terms with: this has to be completed by 25th B’day and till that time pure celibacy maintained), then Grahastha (next 25 years of your life devoted to marriage so that pure intimacy and union could be achieved), then Vanprastha ( next 25 years of life spent wandering in the forests with like minded people and planting seeds in the form of upnishads etc), Sanyas (the last 25 years of age being at peace with the world and oneself, relaxing and not felling bitter about old age/ physical conditions etc, reflecting on life). Thus the theory predicts to 3 more traits or factors , but these would be applicable to pairs, groups and universe respectively.

On another note, much of insights I have got regarding the 6th and 7th developmental tasks is from studying vision and Eye. After an eye is formed, then one needs a pair for binocular/depth vision. This is the 6th developmental task for eye (to pair up with another). after that one could have different movements of eye leading to different visual capacity: Smooth pursuit (involuntary), Saccadic (voluntary) and Nystagmus (sort of involuntary rhythmic movement).

Another parallel is formed in the physical motion subsystem with 6th step being the contraction and relaxation of muscle to produce desired motion and 7th step being differentiated muscle groups to serve different functions: Smooth muscles (involuntary for ex in stomach), striated/skeleton (voluntary used for locomotion) and cardiac (involuntary rhythmic with some randomness thrown in in the form of pacemaker cells).

Thus, to me the 6th stage of development/evolution normally corresponds to pairing with similar type (but different in some aspect) and then utilizing the pairing to achieve something qualitatively different. The 7th evolution/development stage is normally related either ‘colors or ‘movements’ or ‘group dynamics’ and again leads to new qualities and abilities. Finally the 8th stage is delegating control to someone higher up (say Eye delegating control to brain…Except for some control still retained over the Nystagmus or the muscles of entire body delegating control to brain (CNS) except for some pacemaker cells in the heart.

Pointers to other who would like to build:
1) start thinking about 5 ‘normal’ senses and then the other neglected senses like vestibular, kinesthetic etc.
2) revisit Howard Gardner’s 8 intelligences or EQ’s
3)revisit quarks their properties and dynamics etc

Why the number 8?

reason is Maths: Fibonacci series. Evolution works by building on what is. So assuming initially we have 1, the series of evolution, development becomes 1, 2, 3, 5, 8, 13, 21 and so on.

Assuming somehow that one unit of something gets created. Then any complex system can be theoretically reduced to that one unit. Next come dualist system who can differentiate between the qualities that came into existence when a pair was formed. After that 2+1 units merge to form a new unit with 3 qualities. After that 5 qualities are possible, then eight is possible and then 13 or 21 is possible. I’ll stop here because the Tarot that I used to decipher the Fibonacci (and DA vinci code) has only 21 cards in Major Arcana if one discount the 0 card representing the fool). More about that in later mail. (Some caution, I don’t much believe in Tarot etc, but believe in the archetypal strength of such concepts as they have stood test of time).

So we in 21st century may start with 0 or may move further to 45

Another teaser: Tolman in his other article hints behavior-cues, behavior-object and behavior act as the next 3 steps in his behavioristic cognitive map theory. This makes for the eight fold development stage complete. Interestingly he continues beyond that on problems of Motive and hints at the next 5 spiritual/mental qualities that may be involved ” Finally, the problem of the relation of behavior-act to behavior-object is the extremely important problem of motive. It is the problem of desire, emotion, instinct, habit, determining set.” .

also we should always remember that world and reality is more like Mandelbrot set and each components of one puzzle may end up making an equivalent puzzle to us.

Endgame: is it top down or bottom up: what about say hands (2 of which would come together on 6th stage, and which would individually contain 5 fingers/thumb specialists for different tasks- the result of earlier 5 developmental/evolutionary tasks; what about the seventh task? Also can we just like analyzing from bottom down, start with universe and come down to quantum equations and come to closer approximations in terms of determining sets etc that Tolman was hinting in his other article.

The Cognitive Map continued: Its nature and implications: Is my Map different from Yours?

Would like to elaborate a bit more on the theme of the Cognitive Map especially as applicable to Humans and focusing more on the last 3 learning mechanisms relevant to ensuring that your Map reflects Reality as well as possible and is in accordance with the Reality Principle instead of some other principle (like the Pleasure Principle if it exists!)

In the forthcoming discussion, when I’ll refer to Map, I would start with assuming it to refer to a literal spatial map as outlined on a sphere. ( say a globe representing earth in which all the countries are mapped). The Map is thus 2 dimensional in nature, though outlawed on a 3-D object (Sphere or Oval of the earth shape)

6) Which Map to use for Which Season ( Regression as a pathology?) :

The assumption is that successive Cognitive Maps are placed on a sphere and the globe keeps rotating ensuring that we have the arrest cognitive Map in front of us. If one doesn’t stick to the globe analogy, one can also see the Cognitive Maps as being placed on a tape and when rewinded, they may appear as a movie.

A number of earlier Cognitive Maps not relevant to today’s’ experiment are still with Mice as they had earlier learned or internalized those Maps: Once the Mice or men have formed a Cognitive Map reflecting say the actual spatial location and 2-D nature of the table surface and objects that was used in mice experiments and are able to understand the concepts of either R, theta angular geometry or X,Y Cartesian Geometry , then it may happen that over time they realize that different experiment situation require them to use different cognitive maps (say in one situation they would be required to use the cognitive map using angular geometry concepts and then in other X,Y geometry concepts, then they may come to a logical conclusion that at times it is necessary to use earlier Cognitive Maps that were relevant in some earlier situation and may Regress to an earlier Map when their current Map (more in touch with Reality) does not help in the latest experimental setup. This is the first of the Many problems that they have to overcome before ensuring that they can use a broadly consistent Cognitive Map and become immune from the problem of regression. Imagine a Mice, who has just formed a spatial cognitive Map that has given him insight as to the nature of 2-D space and the location of food object/light in it. Imagine suddenly that he finds that these concepts although valid across many previous situations are no longer valid in the present situation, but force him to change his cognitive map. Then the Rat in an attempt to use an appropriate cognitive Map may start using an earlier map (may regress)

Another Analogy is that of Spinning. You might store your Map in a right-spinning globe, while another rat may overlay the cognitive Map on a left-spinning globe. Thus though the maps are identical, but due to different spins the subjective perception may be different. This may be analogous to the fact that though most groups (tribes/clans) of humans have past in back and future in front, some tribes (eg.. Aymara) actually have past in front and future in back. A word of caution though, here too the past and future are so to say linearly spoken of. In Indian languages, the word for day-after as for day-before is same and may suggest a spherical or repetitive nature of Cognitive Maps/ Reality.

Thus, even when your Map is Correct, it is not a single Map but one that is overlaid on a sphere and thus needs to be revolved in a particular direction to update with most accurate cognitive Map. Even when you have done this, if you don’t want to regress, you may have to take help of another mice to ‘see the map from a different angle’/ Assuming that you pair with a mice of different spin orientation, you would then be able to is any Map for any situation. Interesting to note that recent experiments have revealed that people take help of their spouses in storing memories. This may also explain why loss of spouse may be the most triggering factor for regression.

7) How many Colors do you need to paint your Map (which color is your umbrella):

After the Cognitive Maps have been developed and the trick of spinning there globe in clockwise or anti-clockwise direction to get an appropriate Cognitive Map is learned, the difficult question of how to distinguish the cognitive Map appropriate for the situation arises. Before deciding appropriateness, one must first face the problem of how to distinguish the different Maps. (Here I take Map as referring to a contiguous region on a globe- like a country). The answer is simple; a -priori- we need four colors as per four-color theorem. This would be true if the cognitive Maps were indeed mapped on a sphere. In this case one can use CMYK system as used in color printers (a subtractive system). We want pure colors for Mapping- we do not want to mix colors as that may lead to confusion as to us remembering a lot of different colors due to different shaded maps.) Also by using these 4 colors we can still print on our mental map the different shades of all hues. Thus this can give us an opportunity for identifying regions/Maps in ‘pure’ colors as well as identifying regions/Maps in their ‘actual/mixed’ colors. Point to note that in CMYK, the K stands for Key which is usually represented by Black ink. Thus, in CMYK system some regions would be marked as black.

Some notes though:- There are other strong contenders for how we may color our maps.

1. One is the HSV model, whereby one would assign a different Hue to every region(and this is done in terms of an angle), and a saturation (how ‘pure’ and non-grey is the color) and a brightness (how bright or high energy the region/map is). This model would be learned most easily by this rats who learned the R.Theta angular geometry. HSL is also similar.

2. The second is RGB model. Here every region is given a Cartesian co-ordinate corresponding to R, G and B values which start form 0 at origin and move towards infinity as we move away from origin.

3. The third is YUV model. Hereby there is one luminance components (Y) and 2 chromonence componenets (u,v). The primary advantage of this model is that it is compatible with black and white (or grayish) view and coloring of Maps. Thus with this system, one can choose to see the Maps in color or in grey at whim!

Before closing on the color theory of maps, would like to throw one more gauntlet. It seems a Klien bottle (which is a surface that has no inside and outside ( and in this respect is similar to mobius strip) is the only surface that does not follow a rule in mathematic for calculating the number of colors needed to paint regions on that surface. The klien bottle requires 6 colors . My personal view is that our reality as well as the cognitive Maps we make follow more the Kline bottle surface and hence would need 6 colors to fully color them. These may be 6 colors or 6 factors related to color/luminance etc). I am pursuing thus path because of analogous 6 types of flavors in quarks (up,bottom, top, strange, charm, down). Also the previous discussion of spins is partly influenced by the isospin of quarks.

A dysfunctional (or incorrectly colored cognitive map) map would lead to problems like fixation. If the map is painted all Red and no other colors are used(and if red is associated with anger in that person’s internal language), then we have a case whereby the person who uses excessive red in his map is fixating his energy on anger (or a previous map that was excessively red)

Parting note on this: the colored cognitive map theory may explain the charm of Picasso or stained glass windows.

8) Who shares your map and who doesn’t :

Ultimately, when a mice or (wo)man acts, it has to determine not only what cognitive map is relevant for the situation, but also who else would share that cognitive map . This info is necessary irrespective of whether the motive is to compete or co-operate. Slowly over the different experiments the mice learn that not only they themselves know a bit about the maze, but that other mice (as well as the experimenter 🙂 ) knows about the Maze. In such insight situations, if the mice feels frustrated it may either seek help from conspecifics or direct his anger towards non-conspecifics (like the experimenter). Thus, after this last set of experiments he may start co-operating and sharing his Cognitive Map with others or retreat and exhibit “displacement of aggression”. This would work even in case of husband-wife agression displacement, if the spouse does not understand the map of the other.

An instructive way of looking at these Cognitive Maps an be form the other end of the spectrum (i.e instead of analogies with quarks/particles look at the analogies with light/waves) . tolman seems to have taken a similar approach in his another landmark article. Here he discusses behavior tendencies, behavior acts et and they seem more like quantum Fields and collapse of the quantum wave. More on that in a later post.

For now a parting link to a recent article that grants more intelligence to mice than was customary till now.