## 9. Potential Impact & Raveled Numbers

### Introduction

This Notebook deals with the theory behind the Potential Impact Graphs in the Notebook, Time, a Fractal Response. The reason, besides length, that a unique notebook is given for this derivation is that in the search for an equation for potential impact, Raveled numbers emerge as a new type of elemental number. One difference between a Raveled number and a real number is that, while a real number stands alone, a Raveled number contains traces of all that went before and then some. Before we give away all the surprises, read on. Below are the contents of this Notebook.

1. Theoretical Underpinnings of the Potential Impact Graphs

A. The Number of Elements in an Unraveling: Part 2
B. A Digression into Scaling Symmetry
C. The number of times each Data Point is used per Unraveling
D. Necessary Results for the Potential Impact Function: Impact & Non-Impact
E. Delayed Impact & the Now
F. The General Equation for the Potential Impact of Individual Data on a Raveling

2. Pascal's Triangle & a Binomial Expansion

A. A Binomial Diversion: Internal & External Operations in the Seed Equation
B. The Goal: Potential Impact of Data upon Derivatives
C. Soon: Operators & Operators

3. Raveled Numbers

A. Another Binomial Expansion: the # of elements in a Raveling
B. Mea Culpa, Fractional Scientists
C. Properties of Raveled Numbers
D. Raveled Numbers are Unitary

4. Finishing with a Pretty Picture of a Fractal Equation

A. The first round of simplifications with some new conventions
B. More simplifications and a prettier picture
C. An Old Friend: the square notation applied to Picture
D. Our Old Friend, the Folding Function
E. Back to the Pictures of the Higher Directionals

Conclusions