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Archive for September 5th, 2008

I am reminded of an experiment done by a teacher, Jane Elliot, with her 32 3rd grade school students in 1968. Mrs. Elliot came to class one day and announced students were to be divided based on eye color. First, the brown-eyed group was given preference and regarded as “superior” based on their eye color, with the other group repeatedly being considered inferior in intelligence and learning ability as well as having fewer privileges and less recess. On the second day of the experiment, Mrs. Elliot said she was mistaken and it was the blue-eyed group that was superior in every way. Thus, the values, bias’ and attitudes of the groups were completely reversed with blue-eyed students being regarded as superior and the brown-eyed being seen as inferior in every way.

Elliott gave tests to both groups on each day of the experiment. The students scored very low on the day they were racially “inferior” and very high on the day they were considered racially “superior.”

Other results:

  • When expectations are set to do well and show improvement, people do. When those expectations are lacking, performance and the experiences are thwarted in a variety of ways.
  • When we believe “the others” are inferior, we treat them that way independent of the ridiculousness of the basis provided.
  • When we believe we are superior we treat others with discounted value showing that how we believe the world can have powerful effects on how things turn out.
  • It is justifiable to treat someone poorly if you are told they are ‘evil’. When the reverse conditions are used, the superior group who was previously the ‘evil’ group, has an additional set of emotions that contribute to their poor treatment of others.

It is dangerous carnival that the bigotry, meanness, triviality and lack of value toward others can be institutionalized publicly every four years in America by two governing bodies when the country is rudderless of government leadership and when programs de jour are punctuated with felony indictments, earmarks, corporate handouts and loss of constitutional rights perpetuated by both groups.

Certainly have come a long way in those 40 years!

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Here’s another nice piece from JEAB on determinism.

In About Behaviorism (1974), B. F. Skinner addresses how the discussion of self control may appear contrary to a behavioristic formulation suggesting some lack of determination. Or does the behaviorist’s use of ordinary language, or for that matter any of his own behavior, violate his behavioristic account? Had Skinner not decided to write that book? Skinner states the issue in another form:

If human behavior is as fully determined as the behaviorist says it is, why does he bother to write a book? Does he believe that anything matters? To answer that question we should have to go into the history of the behaviorist. Nothing he says about human behavior seriously changes the effect of that history. His research has not altered his concern for his fellow men or his belief in the relevance of a science or technology of behavior. Similar questions might as well be asked of the author of a book on respiration: “If that is respiration, why do you go on breathing?”

I remain unsatisfied with the conclusion that “Nothing he says about human behavior seriously changes the effect of that history.”   Certainly the act of writing a book (doing the research) has little impact, but a long exposure to researching behavior and determinism DOES change the effect on that history because it becomes the history.

When that happens, then what?

Does anything matter?  Let’s take that question on its own, outside of the context of any particular researcher or philosopher.  If determinism is true, then does any investigation matter?  

The trouble here is that what is determined and what we mean by “matter” is by no means clear.  

What is determined is hard to pinpoint because behavior is part of an open, dynamical system.  There are so many things pushing and pulling on a person at any given time, all of those things are determined.  They come together in ways that make it damn near impossible to tell what is being determined, in fact it’s so complex we often just chalk it up to choice and free will.  I like to think about the weather when trying understanding unpredictable determinism.  We can all agree the weather is completely determined by the air, water, land, jet streams, sunlight, etc. etc. and yet we like to say “it has a mind of its own” because what it actually does is hard to predict.  By determined we mean that there is no free will or random chance, everything is connected.

What “matters” in a behaviorist philosophy is always relative to the historical values of the person questioning what matters.  There is no universal matter.  The behaviorist investigates and writes down their investigations because their history (environment, genes) determined it so.  This is what Skinner implies with the line “Similar questions might as well be asked of the author of a book on respiration: “If that is respiration, why do you go on breathing?””   You can’t really stop breathing even if you understand it all.  You can’t stop believing what you believe and acting according to those beliefs simply because you grok behaviorism.  

All in all, nothing matters.  Nothing matters in some universal way.  It might matter to you and that is determined by your history.

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Here’s a nice argument promoting the use of mathematically modeling in the experimental analysis of behavior.

Described in this way, the predictions of these two theories are difficult to distinguish. Although they make their predictions for different reasons, both theories seem to predict the same general result: punishment will cause a decrease in the punished behavior. Once they are translated into mathematical form, however, the different predictions of the two theories can be seen more easily. Deluty (1976) andde Villiers (19771980) developed two different quantitative models of punishment, which can be viewed as mathematical versions of the avoidance theory of punishment and the negative law of effect, respectively. Both models begin with Herrnstein’s (1961) matching law, but then proceed in different directions.

In its simplest form, the matching law can be written as follows:

A mathematical equation, expression, or formula that is to be displayed as a block (callout) within the narrative flow. The name of referred object is jeab-85-02-02-e01.jpg
1

where B1 and B2 are the rates of response on reinforcement schedules 1 and 2, and R1 and R2 are the rates of reinforcement on these two schedules. This equation has often been applied to choice situations in which the two alternatives are variable-interval (VI) schedules of food reinforcement. Imagine that a pigeon responds on two keys, with Key 1 delivering 75 reinforcers per hour and Key 2 delivering 25 reinforcers per hour, so Equation 1 predicts that the pigeon will make 75% of its responses on Key 1. Now suppose that in addition to producing food, responses on both keys begin to deliver punishers (electric shocks) at a rate of 20 shocks per hour for each key. How can Equation 1 be expanded to deal with this situation? 

According to de Villiers (1977), if punishment is the opposite of reinforcement, as the negative law of effect states, then the punishers delivered by each alternative should be subtracted from the reinforcers delivered by that alternative:

A mathematical equation, expression, or formula that is to be displayed as a block (callout) within the narrative flow. The name of referred object is jeab-85-02-02-e02.jpg
2

where P1 and P2 are the rates of punishment on the two keys. 

In contrast, Deluty (1976) took the view that punishing one response increases the reinforcement for other responses, as proposed by the avoidance theory of punishment. Therefore, in his equation, the punishers for one alternative are added to the reinforcers for the other alternative:

A mathematical equation, expression, or formula that is to be displayed as a block (callout) within the narrative flow. The name of referred object is jeab-85-02-02-e03.jpg
3

To keep this example simple, one shock is given the same weight as one food delivery, but both models could easily give food and shock different weights by multiplying P1 and P2 by some constant other than 1. Using such a constant would not change the general conclusions presented here. In this example, with R1  =  75, R2  =  25, and P1  =  P2  =  20, Equation 2 predicts that the percentage of responses on Key 1 should increase from 75% to 92% when the shocks are added to both keys. Conversely, Equation 3 predicts that the percentage of responses on Key 1 should decrease to 68% when the shocks are added. In an experiment with pigeons, de Villiers (1980) found that preference for the key that delivered more reinforcers increased when shocks were added to both keys with equal frequency. This result therefore favors the predictions of Equation 2 over those of Equation 3

It should be clear that the issue here is more fundamental than simply whether a plus sign or a minus sign should be used in an equation. These two models are based on two very different conceptions of how punishment exerts its effects on behavior. The experimental evidence suggests that punishment exerts its effect by weakening the target behavior, as the negative law of effect stipulates, not by strengthening alternative behaviors, as the avoidance theory proposes. This example illustrates how two psychological theories that seem to make similar predictions when stated verbally actually may make very different predictions when they are presented in mathematical form.

Mathematical Models and the Experimental Analysis of Behavior
James E Mazur

Southern Connecticut State University
Correspondence should be addressed to James E. Mazur, Psychology Department, Southern Connecticut State University, New Haven, Connecticut 06515, e-mail: mazurj1@southernct.edu
Received July 21, 2005; Accepted October 3, 2005.
In the conclusion we get this nice warning.
In a commentary about some competing mathematical models of timing, Killeen (1999) wrote: “If you think models are about the truth, or that there is a best timing model, then you are in trouble. There is no best model, any more than there is a best car model or a best swimsuit model, even though each of us may have our favorites. It all depends on what you want to do with the model” (p. 275). Those who do not enjoy studying mathematical models might take this statement (from a preeminent mathematical modeler) as an excuse to avoid them. Why bother putting in the time and effort to understand current mathematical models of behavior when there is no best model, and when they all have their weaknesses and limitations? Killeen addresses this issue by asserting that “all understanding involves models—reference to systems that exist in a different domain than the thing studied. Loose models make vague reference to ambiguous and ad hoc causes. Tighter models are more careful about definitions and avoid gratuitous entities. Models of phenomena are not causes of phenomena; they are descriptions of hypothetical structures or functions that aid explanation, prediction, and control” (p. 276).
That’s true of mathematical modeling in behavior and pretty much anything else.  The model is not the thing.  However, models help structure thinking, investigation and make it easier to communicate.  
I also want to point out just how useful the Matching Law is in analysis of behavior.  You can use it as a basis for so many investigations and you see it play out in almost every situation you are observing behavior from web metrics to neural studies.

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Here’s a new study to be released soon about biological evidence of how the brain retrieves a memory. Your network of neurons and the unique paths taken by signals are the memories, there isn’t some central repository of memory.

I’m looking for the actual results, methods and some supporting work.

It’s not a groundbreaking idea, but it’s great to see some evidence.

It feeds a bigger notion at work in many disciplines that The Network Is The Thing.    There’s a growing body of evidence that space itself is a network. (wolfram)  Check out Network Theory and Graph Theory for more.

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