Wednesday, June 07, 2006

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.

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