Chapter 4

Chapter IV

Perceived Reality

(Connectionist Theory)

Although Mathematics education, for that matter education as a whole is intended to "make students smarter", few educators know anything about how the human brain works. This is not surprising, especially when scientists and psychologists do not agree. Allman (1989) says:

Instead, most researchers have concentrated on studying either the biology of the brain or the behavior of the mind, without attempting the enormous task of figuring out how one produces the other.

Recently, however, there has been a new effort to join the various pieces of brain and mind research into one science. Spawned by the enormous strides made in neurobiology and computer science over the past several years and fueled by a deep frustration with the conventional approaches to understanding how we think, a rapidly growing group of researchers has taken a new tack in trying to understand the machinery of the mind. In this new scientific endeavor---some of the more passionate researchers are calling it a revolution that rivals the emergence of relativity and quantum mechanics in physics at the beginning of this century--scientists are creating a new model of the mind, one that attempts to understand how the mind works by examining how the brain works.(p.3)

This new scientific field, which is still in the process of defining itself, is usually referred to as Connectionist theory. The key piece for putting the other pieces together, seems to be the work done by computer scientists who are trying to build computers which are not digital, but rather neural networks that are modeled on how the human brain actually works. Such computers are not programmed, they are taught. Instead of having a central processing unit that very rapidly goes through a logical series of steps as in a binary digital computer, a neural net computer acts more like the real human brain, reacting to the data all at once. Allman (1989) says:

Unlike digital computers, neural nets don't have a "central processor" that operates on a few bits of data at a time. Instead, like our brains, the neurons act on data all at once, bringing the entire system to bear on a problem. Also like our brains, memories in a neural net are spread throughout the network, not housed in a separate memory bank.

Neural nets also process information differently from digital computers. Each neuron takes in signals from the other neuronlike components, adds them up, and decides on the basis of the answer whether to send out a signal of its own. In a way, the neural units in the machines are analogous to people in a jury talking among themselves, trying to influence each other to decide one way or another; when an input comes into a neural network, there is a mad jumble of changing votes and opinions at first, but eventually all the neurons settle on a decision and the machine produces an answer.(p.12)

Much has been learned about the way individual brain cells or neurons work. Camilo Golgi in Italy and Ramon y Cajal in Spain found ways of staining brain tissue so the individual brain cells stood out. They identified the nucleus or center of the neuron, and two different types of branches. The thicker branch, called the axon, has since been found to carry the electrical pulse away from the nucleus when the cell fires, or produces an electrical pulse. The other type of branch, called the dendrite, may be far more numerous, and has been shown to be the receiver of pulses from neighboring neurons. Alkon (1992) explains how it was done:

The Golgi technique, for reasons not entirely understood even today, picked out single neurons among a host of others in the immediate vicinity. It was as if by chance the stain, often appearing like black ink, found an opening through which it poured in to fill up every remote corner of the neuron's structure. This allowed Golgi, as well as his contemporaries, to reveal the complete structure of individual neurons. Even the often complex, delicate branches conducting signals to and from the main trunks of the neuronal tree could be defined.

Using Golgi's technique, Cajal revolutionized our concept of what the brain and, by implication, the mind is. The brain is a seemingly infinite collection of precisely ordered networks of cells communicating with each other in the language of electrical signals. The activity, or processing, of these networks allows us to sense, remember, feel, plan, decide, and act. The biological and physical basis for mind had at last been seen.

A particularly interesting implication arose from Cajal's stains and sketches that would be fiercely contested by Golgi and many other contemporaries. Cajal found that the branches of one neuron ended in very discrete terminals on the branches of other stained neurons. Using the idiosyncratic property of the Golgi technique to stain one neuron at a time in isolation from its neighbors, Cajal reasoned that the terminal endings of one neuron were sending signals to the next neuron at their discrete points of contact. These points of contact, which would come to be known as synapses, assumed a role of paramount importance in Cajal's mind. This was where information collected and integrated by one neuron was transferred to the next. From his studies of brain tissue at different stages of development, he further inferred that the points of contact multiplied as the networks developed postnatally. Presumably this was how networks could change not only during development but also with aging and perhaps even with experience. (p.38, 39)

In other words, different than the circuits of a computer where the circuits are "hard wired" and an electric current passes through the wires at a uniform and predictable speed. The circuits of the brain are instead "wet wired" or chemically dependent in that there are tiny spaces between the brain cells, the synapses, where the electric current does not go from cell to cell. Instead chemicals triggered by an appropriate amount of electrical energy must go across the synapse, and an appropriate amount of the chemical must be available to cause the adjoining cell to "fire". These chemicals are called neurotransmitters. Alkon (1992) continues:

The development of the electron microscope would, by the 1950's, allow direct visualization of the synapse. During the first four decades of the twentieth century, however, sufficient evidence was accumulated to make an overwhelming case in Cajal's favor. For example, studies would demonstrate that cuts across the axonal branches of one neuron caused the synaptic knobs and their branches of origin to degenerate without causing degeneration of target neurons. Charles Sherrington and others inferred delays between the electrical signals of one neuron, and the resulting electrical signal of a target neuron. Another event, presumably the release of a message at the synapse, must, he reasoned, require the additional time. The presence of synapses could, in fact, explain a host of observations made in his pioneering studies of the spinal cord.(p.51)

In 1921, a classic experiment by Otto Loewi finally proved that the chemical messengers, the neutransmitters existed. Alkon (1992) explains:

Loewi obtained two frog hearts. In one, the nerve that controls slowing of the heartbeat was intact; in the other, it was severed. He stimulated the intact nerve to slow one heart in a separate chamber. He then transferred the fluid bathing this first heart to a chamber that contained the other heart. Remarkably, the second heart slowed in response to the fluid alone. Loewi had shown that a substance in essence was the messenger released by nerve stimulation. Loewi repeated the same experiment with a nerve that caused quickening of the heartbeat and obtained the predicted result. It was left to Henry Dale, and English physiologist, to isolate and eventually identify the substance as acetylcholine. Loewi and Dale had provided strong evidence that the synapse between a nerve and a peripheral muscular target used chemical transmission.(p.54)

The human brain is then essentially a chemical computer. The ability for messages to pass through the brain is a direct result of the chemicals present in the brain. Alkon (1994) continues:

The predominance of chemical synaptic transmission in the central nervous system had been established and would be confirmed repeatedly in the following years. A large variety of chemical messengers would be identified and even begin to be linked to disorders of movement and mood. For example a deficiency of the messenger dopamine was implicated in Parkinson's disease, which often results in uncontrollable shaking. Other messengers, such a norepinephrine and serotonin, were implicated in altered emotional states such as depression. Although research in the directions is still in its infancy, the positive clinical benefit of even our primitive knowledge suggests the exciting promise of what had already been revealed about synapses.(p.55)

The study of neurotransmitters, and chemical processes in the brain, is a hot topic today. Certainly there is much to be learned in this area. In a recent study of suicidal patients, levels of neurotransmitters proved critical. Restak (1991) says:

A breakdown product to the neurotransmitter serotonin, 5-hydroxyindole acetic acid (5-HIAA), is perceptibly lower in the spinal fluid of successful suicides. This discovery was made by Marie Asberg, a psychiatrist at the Karolinska Hospital and Institute in Stockholm, where patients on the psychiatric wards undergo routine spinal tap. When the spinal fluids were compared, patients who attempted suicide (successfully or not) were found to have lower levels of 5-HIAA. Among those patients who attempt suicide and survive, 2 percent will try again, this time successfully. But for people with low levels of 5-HIAA and a previous suicide attempt, the figure jumps to 20 percent.(p.25)

Numerous studies could be sited with correlations between the level of a certain neurotransmitter and some associated behavior. The behaviors we are most interested in, are those associated with the classroom, and the process of learning. Unfortunately, much of the specifics of learning in the brain remain unproven. Alkon (1992) gives us a molecular scenario that is proven for lower life forms, and assumed to be similar to the procedure in humans:

In the early stages, the training stimuli act locally on particular neuronal branches. The resulting chemical messengers then change the electrical signaling of the neuron, as well as the movement of protein particles within its branches. As the memory record begins to gel and becomes longer-lasting, the protein we identified activates the machinery for making proteins in the neuron's nucleus. Still later when the memory starts to become permanent, the local branch that originally received the training signals begins to undergo structural alterations in response to proteins transported from the cell body. Within the last few years, another scientist in our laboratory, James Olds, has revealed in the rabbit hippocampus the same type of dialogue between the neuron's synaptic compartments and the main bodies of neurons. (p.116)

Although progress has been made at the molecular level, significant progress relating molecular processes to processes that are "whole brain" processes as indicated by work with neural nets is difficult at best Allman (1989) explains:

Suppose you put two molecules of gas in a box," says John Hopfield, a theoretical physicist turned brain and mind researcher at the California Institute of Technology. "They move around the box, and every once in a while they collide. If we put 10 or even 1,000 more molecules in the box, all we get is more collisions. But if we put a billion billion molecules in the box, suddenly there's a new phenomenon-sound waves. Nothing in the behavior of two molecules in the box, or ten or 1.000 molecules, would suggest to you that a billion billion molecules would be able to produce sound waves. Sound waves are a collective phenomenon of a complex system." (p.11)

So what conclusions can be drawn about the brain's ability to learn in a practical sense? Allman (1989) says:

If the genes don't direct the wiring of all the synapses, what does? It appears that for many connections between neurons the architect is experience.(p.68)

Alkon (1992) continues:

As an intelligence-gathering device, the brain is performing a specific function when it senses and records how events are related in time. Memories are the records of those relationships within the brain. The brain is measuring and recording the likelihood or probability, of events occurring together. The more times the brain encounters two events occurring together, the greater is the probability it assigns to their occurring together, the greater is the probability it assigns to their occurring together in the future. Repetition beyond a critical minimum number of times causes the brain to assign a 100% probability. The brain has determined that the events occur together with virtual certainty. Of all members of earth's animal kingdom, humans have by far the most sophisticated capacity to assign probabilities among events, make predictions based on these probabilities, and from these predictions arrive at choices. This is the essence of adaptive behavior. (p.5)

 

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