### Equifinality

Ludwig von Bertalanffy, who proposed general system theory, pointed out that equilibrium states could be reached using many different pathways. He called this equifinality (Bertalanffy, 1950b).

If you drop a marble into a round-bottomed bowl, the marble will follow a unique path while it rolls, then it will settle onto the lowest spot on the bottom. There it achieves a temporary static equilibrium (until the bowl is moved).

The marble can be dropped in from any angle. Its path will be different each time, depending on how and where it is dropped. As long as the bowl itself is not moved, the marble will always end up at the same spot. That is equifi­nality.

A physicist would say that the marble at the bottom of the bowl is at its lowest energy (highest entropy) configuration. The second law of thermodynamics specifies that closed systems move inevitably toward lowest energy states. The marble, influenced by gravity, behaves as though it is drawn to the same position each time.

Equifinality occurs also in systems with dynamic equilibria. No matter what the temperature is outside (within reason­able limits) a furnace will raise the temperature in a dwelling to the level set on the thermostat.

No matter how healthy human skin is accidentally cut (within reasonable limits) it will be restored to a normal appear­ance. If an open system approaches equilibrium, it can approach from any direction, but it will reach the same ending point, just like a marble in a bowl.

The principle of equifinality: Equilibrium can be approached from many different starting points. A variety of paths can lead to the same stable endpoint.

The opposite of equifinality is sensitivity to initial conditions. If a person throws a marble across a room, the place where it comes to rest will depend on the angle and velocity and direction it is thrown. Changes in any of those initial conditions will change where the marble comes to rest.

Sensitivity to initial conditions is the rule, where systems do not guide or constrain activity. Equifinality depends on special arrangements (the organization of a system) such as the round shape of a bowl or the mechanisms of a furnace.

Ludwig von Bertalanffy, the founder of general system theory, realized that equifinality could explain some strange observations in biology. These issues were important to the vitalism/mechanism debate that smoldered throughout the 19th and early 20th Century.

Vitalists claimed that a mysterious vital principle (called élan vital by Henri Bergson in a 1907 book) was required to explain living systems. How else could life violate the second law of thermodynamics by growing and changing?

Vitalists were opposed by mechanists, who endorsed Descartes' idea that organisms were like a machine. But mechanists could not explain how living systems were able to grow and change.

A German biologist named Hans Driesch demonstrated in the 1890s that frag­ments of a sea urchin embryo could develop into a whole animal. Stranger still, if two fragments were joined together, they developed into a single sea urchin.

Driesch found this so hard to explain that he became a vitalist. His observations seemed to contradict the deterministic laws of physics, which required that early conditions of a system determine later conditions. How could the same later conditions (a whole animal) be reached from different starting points?

Bertalanffy recognized Driesch's findings as an example of equifinality. The embryo starts from different configurations but ends up at the same endpoint: a whole animal. To explain this, one need not reject the laws of nature; one must recognize that living systems can be organized to move toward dynamic equilibrium states.

In this respect and many others, living systems do not act like isolated, closed systems described by classic laws of thermodynamics. This led to Bertalanffy's 1932 concept of open systems: systems that use energy to build and maintain themselves (Bertalanffy, 1950b).

In cognitive psychology there are many examples of equifinality. Consider memories. Retrievable memories are stable configurations in the brain.

We can get back to the same memory repeatedly, as far as we can tell. In fact, the stability of a memory is the explana­tion for how we can get back to it.

Once established, a stable form of interaction between neurons is a dynamic equilibrium. Therefore it can be reached using different associative paths. That is equifinality.

Similarly, we recognize objects from a variety of angles. This despite the fact that stimulation entering the eye is never the same two times in a row.

If a living creature or computer program detects the right distinctive features (compo­nents) of an object, it can activate an internal representation despite changes or missing data. That is what we call recognition, re-cognition or repeating a cognitive act.

Pattern recognition is possible in differ­ent situations because a categorization is a stable outcome. As such, it can be activated from a variety of starting points. Even if you are looking at a dog through a rain-spattered window that blocks much of the information, you can still recognize that it is a dog.

The formation of a stable endpoint in cognition can be called learning, percep­tion, labeling, or gestalt formation. When a complicated gestalt is experienced even once, the mind is forever altered, making that pattern easier to see in the future.

To make that point in class, I would show a famous photograph:

An example of gestalt formation

I first came across this example in Lindsay and Norman's Human Infor­mation Processing (1977) one of the first introductory psychology textbooks using the cognitive perspective. The image was attributed to photographer R. C. James.

Students seeing the image for the first time sometimes could not perceive any object in it. With the image projected to a big screen in the auditorium, I used a pointer to show various features... the dog's nose touching the ground, the shoulder, legs.

Suddenly the gestalt would snap into place (for various individual students). This small act of emergence would provoke students to laugh or exclaim aloud: the proverbial "Aha!" reaction (called Aha-Erlebnis in German).

I told the students in class, "From this day forward if you see that image, you will have no trouble seeing the dog." I sug­gested that would be true even if they did not see it again until they were in their 90s.

I do not think that is an exaggeration, and it is a remarkable fact. Once an equil­ibrium state of gestalt perception occurs even once, particularly for such a unique and distinctive figure, people can return to it easily.

Equifinality can also produce mistakes in perception. Consider the phenom­enon known as overgeneral­ization. People fixate on certain patterns, and then they see them everywhere.

A person I knew said she had ADD (attention deficit disorder). She also tended to spot ADD in almost every­body else around her, such as her son, her ex-husband, and many of the people she knew. The pattern or category of ADD had become a stable endpoint where pattern recognition processes could arrive from a variety of starting points.

The same problem occurs in computer pattern recognition. A graduate student in a seminar on neural networks developed a computer-simulated network to detect a fictitious object called a Schmoo. The Schmoo was defined as a small square stacked on top of a big square, on a two dimen­sional grid.

The goal was to design a program to recognize Schmoos from partial data (like seeing through a rainy window). It worked: when tested on Schmoos with missing data; the program recognized a Schmoo every time.

However, a problem emerged. The program saw every pattern as a Schmoo. Even a random input was categorized as a Schmoo after the program ran through a few cycles. The program overgeneralized.

The solution to this problem was to improve the program's ability to discriminate. This required using more distinctive and informative details to specify a Schmoo, so the program could tell the difference between Schmoos and non-Schmoos.

That sort of thing is required of pattern recognizing systems generally. To perform without constant errors, they must go through a training period. During this time they learn from successes and errors, until they settle on feature combinations permitting accurate pattern recognition judgments.

Toddlers are famous for overgeneral­izing. In developmental psychology this is called overregularization. It is due to equifinality in a young nervous system.

A two year old may call every four-legged animal a doggie. Alec, at nearly 2 years old, called every flying creature a bee.

With more experience, a child makes finer distinctions. Categorization judg­ments improve with increasingly detailed feature analysis, as a child's models of reality are refined.

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References:

Bertalannfy, L. (1950b) The theory of open systems in physics and biology. Science, 111, 23-29. doi:10.1126/science.111.2872.23

Lindsay, P. H. & Norman, D. A. (1977) Human Information Processing. New York: Academic Press.

Write to Dr. Dewey at psywww@gmail.com.

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