Wednesday, May 19, 2010

Thought and percolation threshold

Persistence of thought
Thought may persist within a human brain a long time after the last significant amount of stimuli fired it up. For example, you read this phrase, close your eyes and think of your own experience about thinking... And now I think of you thinking about thinking. Human brain is very strong at this kind of role playing exercise. These strange skills take part in self-consciousness and deserve a whole dedicated chapter.

 Our present topic needs a simpler example of thought:
You are lying back on your bed in the darkness and you are planning your next week-end. During several minutes, you are building a project. Maybe you will postpone this project and you will resume it tomorrow.
Paths of thought
This continuous thought moves from an idea to the next one. Thought may be considered as a flow of small pieces of knowledge linked together. This recollection itself is memorized: we can recall our past thought. An intelligent being shall link together all different events in order to take into account a complex world. A path can be found from every idea to every other one. However, when we plan our next week-end, we avoid a  total recollection of our past  holidays. We avoid an entire recollection of our whole geographical knowledge. Not all information is activated. This is a matter of proximity. If a part of knowledge is close enough to the present thought, then this part is more or less activated. What happens if activated knowledge is not enough? The thought process is broken. What happens if too much knowledge is activated? A huge amount of irrelevant and useless path is to be searched. An optimized thought would be just below the system calculation power limit.
In order to obtain an efficient thought we need:
- Clever activation rules in order to trigger knowledge activation steps.
- Clever real time control rules in order to monitor the total amount of path being explored. This feedback loop is compulsory.
Without this feedback loop, we encounter a percolation phenomenon.
Thought can be compared to a blaze in many ways.

Percolation
A forest fire needs propagation conditions. Let us suppose there is no wind. Consider tree density as a main propagation condition. Below a given threshold of tree density, the fire decreases because of gaps remaining between groups of trees. "Islands" of trees are all surrounded by paths of bare ground. If you outreach a density threshold, a fire grows up more and more, because of paths of trees linking most groups of trees together. The configuration has suddenly moved from islands of trees to islands of bare ground.
This kind of phenomenon is called percolation.
Thought proceeds in the same way. Below a given threshold, thought needs external stimulations to be fired up. Above this threshold, thought runs through the entire mind as a fire does in a dry forest.

Online demo applets of percolation
This simple applet comes from this page. Try it out first.
Another applet on this page.
A nice applet on this page simulates forest fires. This is worth playing a while with its control panel. You can run it without reading comments.
You will see how tree density alters fire propagation. A slight modification on this tree density from 0.58 to 0.62 induces big consequences on fire propagation (tree density=probability cursor).

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