Quantitative Psychological Theory and Musings

Wednesday, February 24, 2010

The Definition of Insanity? No.

I often hear the quote, "The definition of insanity is doing the same thing over and over again, and expecting a different result."  It is attributed to Einstein everywhere I look, but I wouldn't be surprised if Einstein weren't serious when the statement was uttered.  On the other hand, he did reject the uncertainty principle.

The definition, it is wrong in two ways.  First, insanity is neurological.  Second, even when people seem to be doing the same thing over and over, there are understandable reasons why they are.  They reflect the challenges all normal brains routinely face.

What are these challenges?  I submit that the tasks brains are engaged are often much more complex than seems commonly perceived.  All stimuli, or everything our senses can detect, become predictors for goal attainment, but usually not immediately.  A process of generalization is needed, even across seemingly unrelated contexts such as different rooms in a house, or even different states of mind.  For example, school children who test in the room they learn the material in perform better on average than those who are tested in a different  room. 

But, what if the predictive context is large and varied?  Apply the counting rules in probability, and the complexity of even a "simple" task is revealed.   For example, consider a mother who needs help from three kids raking the yard, and one to vaccum the house, simultaneously.  Apply the permutation rule, and there are 24 different ways to assign the children to these tasks.  That is, (4)(3)(2)(1) = 24.  Of course, some permutations are more helpful than others, and an educated guess might mean mom can narrow down the relevant possibilities.  Still, choosing the optimal permutation(s) can be very difficult, if not nearly impossible given practical limitations.

Of course, the number of permutations, which I sometimes call the permutation space, because I think it sounds cool, can be much, much greater(See other examples in the link above).  Numbers can even easily get into the trillions and much higher still.  Thsi is especially true when permuation spaces are dynamic, such as in the stock market, or in social relationships.  Perhaps this is a fundamental reason, along with the status quo bias and some other factors, investors often lose money seemingly employing the same strategies each time, or wives stay with abusive husbands, in many cases, trying many ways to stay with the abuser while trying to keep him calm.  The actual, "blind" dynamic permutation space can be terribly, and indeed, incalculably vast, but the situation is sometimes even worse when the perceived permutation space is smaller than the actual one.

So, here is another reason people have trouble escaping from behavioral ruts.  It is due to a phenomenon known as blocking in behavioral psychology,  functional fixedness(here too) in cognitive psychology, and another term in AI I don't presently recall.  This is the case in which a previously learned association prevents the learning of new ones.  These can occur due to explicit learning, such as failing to learn how to hit a curve ball, because you're so used to hitting other types of pitches, or due to implicit learning, even by forming associations from information already in one's head.  Such implicit processes are symmetric and transitive

Symmetry is a statement of equivalence, involving the recognition that two different elements are in fact at least functionally substitutable, in certain ways or in certain contexts.  For example, cars and trucks are different in certain ways, but each are equivalent in the sense that they both provide transportation.  Believing symmetries exist where they do not, or failing to recognize them when they do can obviously create problems in finding optimal paths to certain goals.

Transitivity can be summed up symbolically with:  If a = b, and b = c, then a also = c.  This may seem tivial, but it just takes symmetry a step further.  The recognition that a previously recognized two element equivalence is in fact a three element equivalance.  Of course, such perceptions can always be wrong.  Incidentally, brains can make such associations without need of conscious effort, and these tendencies are features of the nature of neural networks.  This is the stuff of imagination.

So, to summarize, vast permuations spaces can mean that a decision maker can be lost trying what they perceive to be new ways of obtaining the same goal.  As if this weren't problematic enough, they may also be limiting their choices within a range of permutations that not only may fial to  yield optimal results, but that may continually yield very bad ones.  They may fail to see similarities between similar situations either due to blocking, or simply as a matter of time and energy constraints.  They may likewise see situations as similar, when they are not.  Is it any wonder people get trapped in certain modes of behavior?

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