Ralph H. Abraham
Visual Math Institute
Santa Cruz, California
Books: Dynamics: The Geometry Of Behavior
First email: 2 November 2019
Dear Prof. Dr. Ralph H. Abraham:
Thank you for asking the question about the emergence of the Planck scale:
“Using the concepts of the mathematical theory of self-organizing
systems in understanding the emergence of space-time at Planck scale.”
I am a simple person. My sense of emergence came from walking back inside
the tetrahedral-octahedral couplet while teaching high school kids about Plato’s
basic solids. Using base-2, 45 steps within got us down into the CERN-scale
and 67 steps further into the Planck scale. Thinking about emergence, it seemed
to be about the spheres, then sphere-stacking, and then other dynamics.
Crazy? Probably. But at least we are still thinking about things.
Thank you for your tenacity and work. Just perfect.
PS. The first reference to your work (that I now remember) is from this page:
The next reference was your homepage and CV:
You are quite remarkable. I wish I knew you back in the earlier days. -BEC