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In prior Notebooks, we identified certain qualities of Live Data Streams, i.e., the Average, the Deviation, the average Z-score. Each of these measures is cumulative and Decay. Hence each of these measures has a subscript associated with it. We don't take averages or deviations of the whole set or a part of it. Instead with Data Streams we use contextual decaying measures. Thus each Data Point has its own Average, Deviation, and Z-score, which are contextual to the Data points that went before. We related the Average to what was expected, the Deviation to the potentials, and Z-score to the tendencies of the system. In this Notebook we are going to delve into the urges towards and away from Equilibrium within a Live Data Stream.
In the first section of this Notebook we are going to explore the Life and Death Urges and their implications for behavior. The Death Urge is related to seeking or maintaining the equilibrium of the Average. When one's Average remains constant, both the Deviations and the Z-scores approach zero. In other terms, the potentials and tendencies of the system approach zero.
A Dead Stream is something followed by nothing while the Null Stream is nothing followed by nothing. All the derivatives of the Null Stream are zero, while all the derivatives, including the average, of a Dead Stream approach zero but never actually reach zero. In the Stable Stream, all the derivatives but the average approach zero, because the average is constant.
A Live Stream is nothing followed by something. Theoretically a Live Stream always starts with the Null Stream before it becomes something. Practically the beginning of many Live Streams is unknown, in which case other techniques are used to generate the stream's measures. {See the Notebook, 5. Data Stream Derivatives for more details.} A Stable Stream is a type of Live Stream. But because all the derivatives approach zero in the fashion of a Dead Stream, we call the tendency of a stream to have a stable average the 'Death Urge'. Conversely, we call the tendency of a Stream to produce non-zero derivatives, the 'Life Urge'.
Let us express the same concepts algebraically. First let us remember the notation we have developed in other notebooks. Each of the measures is based upon decay because we are dealing with Data Streams not Sets. Hence each of the measures has a subscript because it is not the measure of the whole set. A Data Stream is never whole because it is always growing. The measures are contextual and associated with one and only one data point.
The Data and derivatives of a Null Stream are all zero because nothing happens.
The Dead Stream dies. Before a distinct point, XN, the data and derivatives are something. Then at XN, it and all subsequent data points become nothing. As more and more zero points are added onto the Stream, all the derivatives approach zero.
For the Stable Stream, all the data points after a distinct point, XN, equal the average. Similarly to the Dead Stream, the Limit as S->° of all the derivatives except the average approach zero after this point.
The Data of the Live Stream have no restrictions and can be anything, within the realm of their reflection of reality. Hence their averages and deviations will always be greater than zero. Their average Z-scores, however, are relatively unlimited, except by the bounds of computation and probability.
For humans, the Life and Death Urges act like a thermostat. The Death Urge manifests when there has been too much instability, while the Life Urge manifests when there has been too much stability. There is a resistance to death. So when an average stabilizes, as in a Stable Data Stream, alternately and simultaneously, 1) the system begins to shut down because of the regularity, the predictability, the shrinking of tendencies and potentials and 2) also growing is the Life Urge, which is lurking behind it all, creating spontaneity and growth.
The hardworking human, who is locked into a routine, a schedule, a predictable pattern, might explode into a nice vacation or maybe emotional sickness or a hardening and rigidity. The Life Urge is on the level of Impulse and is an explosion outwards, an erection, a spontaneous movement, something unpredictable. On the positive side, it could be a vacation, a movie, anything to break the monotony of the Death Urge. On the negative side, getting angry, quitting a job, sickness, violence, getting drunk, breaks the Death Urge.
The Life Urge would be likened to the growing pressure on a fault line, which could break at any time in an earthquake, unless the pressure is relieved by smaller impulses. The Life Urge manifests as anything that causes an abrupt enough change so that the Derivatives quit shrinking and begin to expand.
When the Deviation remains constant over time the Data must bounce around a central axis, first higher, then lower, in order to avoid an ever-increasing upward or downward spiral. This causes the Average to vibrate around a central axis.
When the potential for change remains constant, vibration is a state of existence. Common examples of this are the vibration of the eye, the subtle vibration of the body to maintain balance when standing still. Maintaining a balance for potential change grants flexibility of movement. The organism sinks to its optimum level of flexibility signified by its deviation and wants to stay there. The only way to do this is by vibrating. To maintain equilibrium, vibration becomes a way of life in many areas.
The minimal vibration is a way to avoid the extra energy associated with start up. (As a parallel in the physical world static friction is greater than dynamic friction.) If the eye and body are moving a little all the time then they are more prepared for a major movement should that become necessary, would they have been had they been standing stock still. Thus vibration becomes a way of increasing flexibility of movement.
This vibration regulates many areas of our lives. We attempt to regulate and minimize the Deviation of our Sleep. We don't sleep zero hours one day and 24 hours the next. Instead we sleep approximately the same plus or minus each night. It has been found that radical sleep fluctuations are even bad for health.
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