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6.5 Summary & Conclusions

Deviations always positive

What have we seen in this study of Average Deviations? We have seen that Deviations are always positive.

The Stratification of Deviations

Further we have seen that the Deviations of growing and static Data Streams tend to stratify. The Deviations of dying Data Streams do not necessarily stratify, but will begin to re-stratify once there is growth or normalization above non-existence.

Patterns not Rules & Indeterminate Causes

We discovered that our One Rule System leads to Patterns but not to Rules. Furthermore our One Rule System exhibits a situation of Indeterminate Cause. A Singular effect could have at least two different causes. There is no way to distinguish between the causes.

Continuous, Discontinuous? No long-term difference.

We confined our Derivations to the Data Streams that have continuous beginnings. All of our experimental examples were of Data Streams that had discontinuous beginnings. Failing to derive any general rules for Deviation Stratification, there was no further need, to distinguish between these two types of Data Streams. In long term studies the differences are indistinguishable. It is only after the first few points that there is a distinguishable difference. {See Proof in another Notebook.}

Only the First Deviation matters

One other conclusion was that the higher Deviations, beyond the first, were only a reflection of the first Average Deviation. This is the result of the Stratification of Deviations. Also the higher exponents of change, i.e. >1, only extend the boundaries of the first Deviation but do not yield any unique information. These conclusions were illustrated but not proved. Because of these illustrations we have decided only the First Deviation really matters. A lot of verbiage, over 40 pages, to decide that only one simplicity is relevant. Ah well, but what we have seen in the process!


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