Home Science Page Data Stream Momentum Directionals Root Beings The Experiment
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 shutLR Knnu$$ :{t_ڕ U v^tLVx')
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