TO: John Edward Hopcroft, Cornell University, Gates Hall, Ithaca, NY
FM: Bruce E. Camber
RE: Your articles in arXiv, your homepage(s) including FOUNDATIONS OF DATA SCIENCE (2017); Wikipedia: Cinderella Book – Introduction to Automata Theory, Languages, and Computation Key Concept: Singular value decomposition; and YouTube: Computer Science in the Information Age, 2009; Heidelberg Laureate Forum: AI, 2019
This page about your work: https://81018.com/2017/09/18/hopcroft/
Third email: 29 October 2025
Dear Prof. Dr. John Hopcroft:
Is there a possibility that an AI will collaborate with an AI, develop its own logic between them, and yield to that logic although it is not the current scientific belief? It seems to be happening as the big bang theory is challenged. I had been working with Grok through the logic of an alternative theory — https://81018.com/irrationals/ Grok embraced it. Then, ChatGPT and Perplexity did. Then, based on that logic, Anthropic and DeepSeek had no learning curve. Their adoption of the new model was immediate. Google AI (associated with their Search) has been slower and has not quite adopted that work and remains critical of it.
We are asking questions about the start of the universe within the Planck Scale and within the first sub-seconds.
Here is the most recent summary by DeepSeek: https://81018.com/universe-geometry/ (current homepage). And here is an overview of the working relations: https://81018.com/aix/
If you have a moment, your comments and questions would be profoundly appreciated.
With warmest regards,
Bruce
Second email: Sunday, 11 June 2023 at 9:12 AM
Dear Prof. Dr. John Hopcroft:
Of course, you are among the most distinguished professors within the computer sciences. A long time ago, I was a premier IBM business partner, a partner of the Watson Labs, and a consultant for the AS/400 division and the chairman’s office (Gerstner). Your presentation at the Heidelberg Forum came to my attention and I wondered if you signed the 24-word precautionary statement about AI? Are you at all concerned about the rapid evolution of AI? I have been searching your most-current articles to see if you have written about it.
My first note to you was six years ago. That’s a lifetime for a first grader and barely a Planck unit for the universe. My copy is here — https://81018.com/2017/09/18/hopcroft/
That precautionary statement about AI is a new issue. Again, are you at all concerned about it? Thank you. Yes/No answers would be fine.
Most sincerely,
Bruce
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. 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:
• http://81018.com/chart contains all the numbers.
• http://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: http://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
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