##### John Edward Hopcroft

Cornell University

426 Gates Hall

Ithaca, NY 14853

ArXiv

Key Concept: Singular value decomposition

Our Primary Reference: FOUNDATIONS OF DATA SCIENCE (2017)

Wikipedia: Cinderella Book – Introduction to Automata Theory, Languages, and Computation

YouTube: *Computer Science in the Information Age* (Use the CC; it helps!)

First email: September 21, 2017

###### 1.* *Foundations of Data Science (2017) is being sourced for conceptual frameworks now.

2. Updated the John Hopcroft page within Wikipedia to re-direct to the online document at Cornell. Navin Goyal (Microsoft) had once posted the document, but it is “No Longer Found.”

**Dear Prof. Dr. John Hopcroft**:

#### I am looking at data structure from a rather idiosyncratic place.

#### We are exploring applications beginning at the smallest possible scale (Planck’s) and going to largest (Age of the Universe, Observable Universe) all within just 202 base-2 exponential notations or doublings. I am most interested in your conceptual framework for singular value decomposition and its application using continuity and symmetry within the Planck scale to follow its progressive expansion into the large-scale universe and to the present time.

#### Silliness perhaps. Idiosyncratic for sure.

It all started in a high school geometry class in December 2011.

#### I would be pleased to hear your initial reactions to such a construct:

• https://81018.com/chart contains all the numbers.

• https://81018.com/planck_universe is an analysis of six groups of numbers out of the 202.

• I openly share my naiveté about your work within my introduction to *hypostatic structure*: https://81018.com/hypostatic (seventh paragraph)

#### Who am I? Although I have done a fair amount of work with IBM over the years,

my focus has been on first principles within information, knowledge, insight, and wisdom.

#### Thank you.

#### Most sincerely,

Bruce

**PS. PS. Email has been a wonderful way for me to begin to collect references (to your work) currently being studied.**

**Key concepts**:

“As an application of the Law of Large Numbers, let **z** be a d-dimensional random point whose coordinates are each selected from a zero mean, 1/2π variance Gaussian. We set the variance to 1/2π so the Gaussian probability density equals one at the origin and is bounded below throughout the unit ball by a constant.” Page 13ff

**2.4 Properties of the Unit Ball**

** 2.5 Generating Points Uniformly at Random from a Ball**

**Context-free** language: Hopcroft & Ullman 1979, p. 100, Theorem 4.7.

**DFA** Minimization

Minimal Supersymmetric Standard Model:

• https://en.wikipedia.org/wiki/Minimal_Supersymmetric_Standard_Model

• https://en.wikipedia.org/wiki/Supersymmetry_nonrenormalization_theorems

• https://en.wikipedia.org/wiki/Theory_of_computation

• Joseph L. Walsh, Walsh matrix