John Edward Hopcroft
426 Gates Hall
Ithaca, NY 14853
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.
PS. PS. Email has been a wonderful way for me to begin to collect references (to your work) currently 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
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.
Minimal Supersymmetric Standard Model:
• Joseph L. Walsh, Walsh matrix