We have already mentioned that one of the basic questions in the investigation of human cognition is whether our thoughts are typically highly structured and if so how this structure comes about.
The question as posed presupposes that we know what we mean
when we say that something is structured or unstructured. Actually,
we can't really talk about structure in a careful way until we
have adopted some sort of mathematical framework. For example,
we could talk about the set of names of persons in this
class and we could contrast this with the names of persons in
this class that are alphabetically ordered. A set is an
unordered collection of things. If there are 100 persons in this
class, then there are 100! (recall that ' ! ' is read as factorial
and n! is n x (n-1 ) x ... x 1) possible ways to order the list
of names. Assuming that no two persons have the same name, then
there is only one way in which to alphabetically order the list
of names. Consequently, we might decide that a distinguishing
feature of structure is that it is rare relative to the set of
possibilities. But, there is a problem here because I could pick
out any one of the 100! orderings and it would, in this sense,
be just as rare as the alphabetic case. So that doesn't quite
work.
(To give you some idea of the magnitude of these
numbers, 20! = 2,432,902,008,176,640,000. 100! is much larger.)
Another tack is to simply consider how some collection of stuff was generated. The two "pictures" (7 x 7 cells filled with the colors red, blue, green and yellow) below were generated randomly. That is, I used a random number generator to assign a color to each cell. This procedure can yield an enormous number of different 7 x 7 pictures. For example, if there were only two cells instead of 49, then each of these cells could have any of the 4 colors. Thus, there are 4 x 4 or 16 different two cell "pictures". For the 49 cell case you need to raise 4 to the 49 th power. Since there are 7 cells in a row and each of these could be colored in 4 ways, there are 16,384 different ways in which to color a row. And there are 7 rows! And, if you are still curious, there are 316,912,650,000,030,518,197,354,496 ways to color the total 7 x 7 square.
 |
 |
||
 |
 |
||
Notice, that these last two pictures could have been randomly generated. (I may be lying to you about following some rules.) But, because we can see regularities....because it looks like the generator of these pictures was following rules ... we think it unlikely that they were randomly generated.
And, this is analogous to the way cognitive psychologists
reason in studying the mind....if they can describe the products
of the mind as exhibiting regularities or following rules, then
they assume that the thinking is a structured process. BUT, minds
seem to be able to create infinitely many products and regularity
is not always so obvious in these products. So the cognitive
scientist who studies human reasoning will have to be very clever,
and maybe a little lucky as well, to be able to unravel the way
the mind works.