When we make decisions or when we think our brain
does not use any equations or math models. Our behaviour is fruit of
certain hard-wired instincts and experience that is acquired during our
lives and stored as patterns (or attractors). We sort of "feel the
answer" to problems no matter how complex they may seem but without
actually computing the answer. How can that be? How can a person (not to
mention an animal) who has no clue of mathematics still be capable of
performing fantastically complex functions? Why doesn't a brain, with
its immense memory and computational power, store some basic equations
and formulae and use them when we need to make a decision? Theoretically
this could be perfectly feasible. One could learn equations and
techniques and store them in memory for better and more sophisticated
decision-making. We all know that in reality things don't work like
that. So how do they work? What mechanisms does a brain use if it is not
math models? In reality the brain uses model-free methods. In Nature
there is nobody to architecture a model for you. There is no
mathematics in Nature. Mathematics and math models are an artificial
invention of man. Nature doesn't need to resort to equations or other
analytical artifacts. These have been invented by man but this doesn't
mean that they really do exist. As Heisenberg put it, what we see is not
Nature but Nature exposed to our way of questioning her. If we discover
that "F = M * a" that doesn't mean that Nature actually computes this
relationship each time a mass is accelerated. The relationship simply
holds (until somebody disproves it).
Humans (and probably also animals) work based on
inter-related fuzzy rules which can be organised into maps, such as the
one below. The so-called Fuzzy Cognitive Maps are made of nodes
(bubbles) and links (arrows joining the bubbles). These links are built
and consolidated by the brain as new information linking pairs of
bubbles is presented to us and becomes verifiable. Let's take highway
traffic (see map below). For example, a baby doesn't know that "Bad
weather increases traffic congestion". However, it is a conclusion you
arrive at once you've been there yourself a few times. The rule gets
crystallised and remains in our brain for a long time (unless sometimes
alcohol dissolves it!). As time passes, new rules may be added to the
picture until, after years of experience, the whole thing becomes a
consolidated body of knowledge. In time, it can suffer adjustments and
transformations (e.g. if new traffic rules are introduced) but the
bottom line is the same. There is no math model here. Just functions
(bubbles) connected to each other in a fuzzy manner, the weights being
the fruit of the individuals own experience.
As a person gains experience, the rules (links)
become stronger but, as new information is added, they can also become
more fuzzy. This is the main difference between a teenager and an adult.
For young people - who have very few data points on which to build the
links - the rules are crisp (through two data point a straight line
passes, while it is difficult for 1000 points to form a straight line -
they will more probably form something that looks like a cigar). This is
why many adults don't see the world as black or white and why they tend
to ponder their answers to questions. Again, the point is that there is
no math model here. Just example-based learning which produces sets of
inter-related Fuzzy Cognitive Maps that are stored in our memory.
Clearly, one may envisage attaching a measure of complexity to each such
map.
OntoSpace, our flagship product, functions in a
similar manner. It doesn't employ math models in order to establish
relationships between the parameters of a system or a process.
Essentially, it emulates the functioning of the human brain.
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