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4.1 Laying Foundations

A. Prior Notebooks: a Review

#1 Spiral Time

In Notebook #1, Spiral Time, we saw that time has a vertical and horizontal dimension. The horizontal dimension is real, complete and unchanging. This is the continuous time that we experience on a moment-to-moment basis. We are not concerned with this dimension of time. The vertical dimension of time is virtual, partial, and ever-changing. This type of time is at the basis of daily habits and routines. This is the dimension of time that we are studying. It was seen that this dimension of time has density and momentum, which influence our behavior in conjunction with Will.

#2 Data Stream Momentum

In Notebook #2, Data Stream Momentum, we developed the theoretical framework behind the density and momentum of the vertical dimension of time. It was seen that Data Streams have a life of their own, independent of the Source of the data. This life is based upon the measures of the Data Stream, which describe the Stream and make predictions concerning the probabilities of subsequent Data Bytes occurring. In DSM we looked at the Mean and the Standard Deviation to develop the concepts of Data Stream Flow and Current. Ultimately we found these traditional measures lacking because they were based upon N, the number of elements in the Stream. Because the number of elements in the Stream is always growing, the stability of the measures becomes static very quickly.

#3 The Decaying Average and Deviation

This problem was resolved in Notebook #3, Decaying Averages. We substituted D, the Decay factor, a constant, for N in the equations derived in DSM. This had many advantages. First our measures became sensitive to change. Second the measures now incorporated Decay, which is a feature of our experience of time and hence a feature of Data Streams based upon time. Third, because of the contextual nature of the Decaying measures, they are very easy to compute. Thus Decaying Averages were an effective way of characterizing Data Streams.

Neural Networks and Evolution

In addition, we found that the Decaying Average was a useful piece of information to store in order to facilitate survival. They were found to be descriptive and predictive. Its predictive aspect gave rise to anticipation, which facilitated survival by allowing the organism to store and analyze trends. Furthermore it was found that a simple neural network was more than adequate to form a decaying average by a simple process of overlay. The Decaying Deviation determines the Realm of Probability, another useful evolutionary device. As a bonus, the same neural network that calculated the Decaying Average was also able to calculate the Decaying Deviation, by the same process of continual overlays.

B. Virtual Numbers & the Power of Illusion

The Virtual Power of Data Stream Measures

The descriptive and predictive aspects of Data Stream measures are only part of their reality. The other aspect that we are focusing upon is the power of these measures, i.e. their ability to influence behavior. The power of these measures is virtual, i.e. there is nothing about the measures of a Data Stream, which are 'real' or substantial. There are no electrons, protons, magnetic fields, gravitation, or the like to push our subjects around. The power of these Data Stream measures is all an illusion created by our minds.

The Placebo Effect & the Effect of Illusion

Before we dismiss illusion as inconsequential we must remember the placebo effect. The illusion that the patient is taking medicine that will help him is sometimes as powerful, if not more so, than the actual physical properties of the medicine itself. Hence illusion can be a powerful force. In a confrontation the brute reality of a fatal disease overwhelms the virtual reality of a placebo. But the virtual reality of a placebo can influence people to mentally heal themselves. In a head on conflict the virtual loses to the real (most of the time), but the virtual can influence reality by nudging it this way and that. The virtual can be a driving force in its own right, especially when the individual abdicates his control over reality.

Dumbo's feather

We see this idea reflected in popular mythology. Dumbo's feather gives him the confidence to fly. Without it, he may have never flown. In the Buddhist way of thinking, one can't separate cause and effect. In this sense the feather was an integral ingredient in Dumbo's ability to fly, just as important as his big ears. Dumbo without his feather would be like an engine without a starter. Dumbo could fly eventually without his feather, just as an engine can move a car without its starter, as anyone who has jump-started a car will testify to. The virtual power of a Data Stream, the feather, and the starter are linked in their importance as catalysts to the actual behavior of their respective engines. Keep this idea in mind when we refer to the virtual reality of numbers.

C. Rocks & Plants don't need to make predictive computations

Not rocks or plants

We've mentioned a few different calculations, which facilitated survival, hence providing an evolutionary advantage. Which creatures use these techniques? For purposes of illustration, we're going to take a traditional view of creatures, not a specific, exception-ridden scientific view. A rock doesn't anticipate, doesn't grow, and doesn't compute. A plant doesn't have any mobility, which limits its choices. Because of the narrowness of its decisions, we are going to assume that there was no need to anticipate, hence no need to calculate. A plant responds to stimuli but does not anticipate it. It doesn't think to itself, "Last year I bloomed too soon because of unseasonably warm weather and lost all my fruit. This year I'm going to be prepared."

Plants: all Hardware, no Software

Plants seem to be all hardware and no software. All the computational decisions have been built into the system. The plant does respond to seasonal changes but does not anticipate them. Plants evolve defensive mechanisms against their enemies, but do not plan them. "I think this year that I'm going to camouflage myself as two big eyes to scare those birds away from me." This is not part of a plant's mental dialogue. Plants are either naturally camouflaged from their predator or they are not. They do not choose to hide from an animal to avoid being eaten. Successive generations of plants may evolve to more effectively facilitate survival. Individual plants do not cope separately with natural enemies. They form no ulcers. For practical purposes, plants are all hardware, no software, (always keeping in mind the idea of fractal boundaries).

D. Mobility Changes Everything

Animals are different

Because animals are mobile, they have many more choices than a plant. Witness a baby human prior to mobility. They only have a limited number of responses to their environment. If they are hungry, they cry. If they are tired, they cry. If a pin is sticking them, they cry. If an enemy, brother or sister, is bothering them, they cry. They do not search out food. They do not put themselves to bed. They do not remove the offending pin. They do not run away or defend themselves from their enemy. Such is a plant, but they can't cry. On the positive side, if the baby is happy, she laughs to encourage her parents to continue the activity. Contrarily she will cry if her parents stop the activity that is causing so much fun. If a plant is happy, then it grows, flowers and bears fruit. If a plant is unhappy, it does not complain; it withers and dies.

Motion and Choices

Once the baby begins moving around, however, we've moved to a different level of infinity. If the baby is lonely, she crawls around looking for someone. If the baby is bored, then she begins exploring her environment. Mobility increases the number of responses to the environment by a multitude. Because the number of responses to environmental stimuli are so vast, choice enters in, free will, if you want to call it that.

Motion and Danger

Along with motion comes an increased amount of danger. Anyone with a toddler will testify to this. While a plant can't search out food, it also will never fall off a cliff or down some steps. While the toddler can now explore her environment, she has multiplied her danger by an order of magnitude. The infant, while being totally dependent, is much safer than the toddler, who is more independent. The infant doesn't crawl out into the street, down stairs, put her fingers into light sockets, or any of the other myriad ways that toddlers endanger themselves. Because of the ability to move, the animal multiplies the number of dangerous possibilities.

Danger and Anticipation

However, along with the increased danger comes the ability to evade or avoid danger. The ability to move quickly allows one to escape from a predator to avoid being eaten. The ability to anticipate allows one to avoid danger, altogether. The creature doesn't need to run fast, if it can avoid the dangerous predators altogether. If an animal is strong enough, it may be able to find food no matter how intense the winter. If an animal is smart enough to anticipate the winter then it might store up enough food so that it doesn't have to rely on its strength to survive the winter. In long-term analysis the ability to anticipate seems, many times, to be a more important mechanism for survival than strength, speed or size, especially judging by the dominance of homo sapiens sapiens.

Prediction & Anticipation

The ability to anticipate is directly related to the ability to predict. In a simple way, the perception of patterns was the first form of prediction. This is the basis of positive and negative reinforcement. When I perform Behavior X, she performs Behavior Y. I enjoy Behavior Y. I predict that if I do Behavior X again that she will follow with Behavior Y. Therefore I perform behavior X again, hoping that my prediction is confirmed. Umm, Umm!

E. Positive Reinforcement vs. Computational Prediction

The Difference: an example, the athlete/hunter

There is a slight difference between positive/negative reinforcement prediction and computational prediction, which I will illustrate with the example of a baseball player hitting a baseball or a soccer player scoring a goal. The baseball player gets a lot of positive reinforcement for hitting a home run. The soccer player receives even more positive reinforcement for scoring a goal. So they would love to repeat this behavior. But the simple desire is not enough. Practice of a preordained movement is also not enough. Training your body to hit a baseball or to kick a soccer ball is much different than hitting a home run off a Major League Pitcher or scoring a goal in a World Cup match.

Triangulations and Complex Probabilities

The players must be able to compute endless complex probabilities, do triangulations on the run. Let us look at the soccer player. He must calculate probabilities and make instant predictions about which ways his teammates and his opponents might move. He must simultaneously consider alternate strategies should his immediate predictions prove wrong. Simultaneously he must calculate velocities, accelerations and impulses of the soccer ball, while it is bouncing and being kicked. Finally he must use triangulation, with all its horizontal and vertical projections, to ascertain the distance and direction from the goal. In this split second he must then determine how hard to kick his foot, how fast to swing his leg, the curvature of the intended arc to make it past the goalkeeper into the net.

Complementation between the Two Predictive Devices

His desire for the positive reinforcement stimulated his need to practice, in order that his body would be ready and able to perform properly when it was needed. However on the spot predictive computations were needed to put the player in the spot to use his well-trained body to score the goal. So these two mechanisms complement each other.

F. Predators and Preys must live within the Realm, & calculate Average Deviations

Another Neural Network

From all this computation, we come up with a neural network, which stores a running average that decays. The more competitive creatures also have a neural network, which stores an Average Deviation in order to calculate the Realm of Probability. Almost any animal that moves would require the ability to cultivate a sense of this Realm of Probability, in order to maximize the limited resources available to all creatures.

A Fishy example

Trout who are raised in a fishery are given a plentiful amount of food. They learn that the best strategy is to expend a lot of energy to be the first to get the food. They do not develop conservative hunting strategies because the food comes all at once, artificially. When they are introduced into the wild, they exhaust themselves going after a reduced amount of natural resources. The trout raised in the river develop a more conservative strategy of watching and waiting in order to not waste valuable energy needlessly. They have internally calculated a realm of Probability, which maximizes their fishy energy. They understand that the Range of Possibility is greater than the Realm of Probability but from experience focus on the Realm. The Average Deviation determines the Realm.

The Average Deviation and the Realm of Probability

The Average Deviation, arithmetically, is the point at which half the Differences are greater and half the differences are less. The Average Deviation as a descriptor says that 50% of the values in the existing Data Stream are less than one Average Deviation from the Decaying Average. Furthermore it says that 100% of the values in the existing Data Stream are between two Average Deviations from the Decaying Average. As a predictor the AD predicts that the next value of the Data Stream will be within 2 AD of the Decaying Average. These statements only hold true with an arithmetic distribution, i.e. the Data is evenly distributed over the Range. Of course if the distribution is non-arithmetic, then extreme values will fall outside the limits of 2 AD.

Predator & Prey or Even Fish calculate the Realm of Probability

Even our trout calculate this realm of probability when trying to determine what to hunt. Any predator must calculate how fast his prey is and how near he must get so that he may pounce effectively. He catalogues his successes, failures and near misses in neural networks of Decaying Averages and Average Deviations, meshing the boundary lines in an intricate pattern. He tries to stay within the boundary of the Realm but sometimes because of the vagaries of nature he must move to and test the boundaries. Of course the prey must just escape, so her task is a little simpler. The prey is always a step ahead of the predator in order to keep the cycle moving forward.

The Realm of Success

The concentric circles around the predator represent the distances and probabilities of success. Any prey that falls within the innermost circle becomes dinner 90 to 100% of the time. Any prey that falls between the innermost circle and the second circle becomes dinner 60 to 90% of the time. Any prey that falls between the second circle and the third circle becomes dinner 30 to 60% of the time. Any prey that falls between the third circle and the outermost circle becomes dinner 0 to 30% of the time. Any prey falling outside the outermost circle is not fair game. The prey's circles are similar but based upon the predator. The prey thinks, "If the predator reaches my innermost circle then I am dinner. If he is between the innermost and the second circle then I am dinner most of the time. If he is between the second and the third circle, I am dinner some of the time. If he is between the third and the outermost circle, I am hardly ever dinner. If he is outside the outermost circle, I am never dinner."

Predator develops software, the prey develops hardware

While the predator gets to experiment, the prey must rely on built in hardware. By the process of natural selection, the prey with the best estimates will survive and pass on her gene pool. If the prey's estimates are poor then she becomes dinner and does not get the liberty of trying again. The predator however performs an experiment every time he catches dinner. Chasing after a prey that is outside of his range or realm and going hungry, causes the predator to adjust his limits. If the boundaries of the predator are unsuccessful then he goes hungry, and his measures are readjusted. If the boundaries of the prey are unsuccessful then she is consumed and her gene pool is not passed on. Predators develop the software to catch the prey. This software is modified with age and experience. The prey only develops the hardware because they don't have the luxury of experimentation. "In the animal world wolves manage only one kill for every ten attempts, and even lions fail more often than they succeed." (Time-Life Books, Time Frame, The Human Dawn page 66)

The older the predator, the more important is the Realm of Probability

If the predator doesn't develop a good sense of the Realm of Probability then he wastes a lot of energy unsuccessfully. This might not matter when he is young with an abundance of energy, but as the predator becomes older and older it becomes more and more essential to develop an accurate sense of the Realm of Probability in order to conserve dwindling resources.

Most animals are predator and prey, hence most calculate Average Deviations

Of course most animals are predator and prey. Those of us who are predator and prey develop the hardware and software necessary for survival. But predator or prey, the ability to compute Realms of Probability is a key ingredient to survival. The key ingredient to the Realm of Probability is the Average Deviation. The Average Deviation is easily calculated and stored in a neural network. {See Decaying Averages Notebook.} Hence most moving animals must be able to calculate the Average Deviation for purposes of survival. Thus they probably store this information in some type of neural network.

The ability to compute confers an evolutionary advantage

At the Santa Fe Institute, Packard wrote a paper titled "Adaptation to the Edge of Chaos". This discussed some computer simulations that showed that the ability to compute seemed to confer an evolutionary advantage. He felt that the ability to compute was linked to the ability to adapt. The ability to adapt is a proven evolutionary strength, as witnessed by the dominance of homo sapiens sapiens. (Complexity, page 302, Waldrop 1993)


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