## 6. Deviation Study

### Introduction

In this study we will be looking a little closer at the Average Deviation Series generated, inadvertently, by a Living Data Stream. {See Directionals Notebook.}  In the first part, Characteristics of Deviations, we will look at some of the features of Deviational Streams. We find that once they come into existence that they are always positive. We then look at the Deviations in a Real Data Stream, Exercise. We see wiggles, wobbles and wriggles. We also see the stratification of the higher Deviations from the low to the high. Our second and third parts examine the whens, whys and wherefors of these stratifications. The second part, Differences of Deviations, searches futilely for rules, derivations and proofs, that will explain the stratification. The third part, Looking for Patterns, examines why there are no rules but only patterns instead. The fourth part, Patterns vs. Rules: A meta-Context, places this whole study in a proper context. It points out that although the system is based upon only one Rule that there are no general Rules that will generate stratification. The Rules generate Patterns, which generate the stratification. Below are the contents of this Notebook.

1. Characteristics of Deviations

A. A Continuous & Discontinuous Data Stream
B. Notation for a Continuous Data Stream
C. A Casual Proof that all Deviations are always ≥ 0
D. Looking at Deviations in a Data Stream

2. Differences of Deviations or Which is larger?

A. The first simple, and not so simple, Deviations
B. The General Expression: A Derivation
C. P = 0 and N = 1
D. P = 1 and N = 1

3. Looking for Patterns

A. Experimental Patterns?
B. A Reexamination of the General Equation of Deviational Differences
C. Experimental Verification

4. Patterns vs. Rules: A meta-Context

A. A Context for our Exploration
B. Patterns not Theorems, another approach

Summary & Conclusions