## John Edward Hopcroft

Cornell University

426 Gates Hall

Ithaca, NY 14853

**ArXiv**

Reference: FOUNDATIONS OF DATA SCIENCE (2017)

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

__________ Key Concept: Singular value decomposition

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

First email: September 21, 2017

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, assuming it to be the Planck scale, 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. These references to your work are being studied:

- “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 **Properties of the Unit Ball****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

November 2018 (update): “Generate n points at random in d-dimensions where each coordinate is a zero mean, unit variance Gaussian.” from* Foundations of Data Science,* 2.1 page 12