Article (one of many): On the correspondence between arithmetic theories and propositional proof systems – a survey, Mathematical Logic Quarterly, 55 (2). 116 – 137, ISSN 0942-5616. https://doi.org/10.1002/malq.200710069, 2009
Computational Complexity Foundation (CCF)
Homepage (also in German) (Jena): Simons Institute, ACM
Templeton Foundation: Intuitionism
Wikipedia: Bounded Arithmetic, Univalent Foundations of Mathematics
Most recent email: 11 August 2021
Dear Prof. Dr. Olaf Beyersdorff:
Congratulations on your move from Leeds to Jena. I hope it is working well for you.
I noticed some activity on our webpage about your work so I pulled it up to be sure it was current.
Information is so volatile. It always needs updating.
Although you did not have time to respond to my earlier questions (admittedly idiosyncratic), they remain open. I have come to realize that most people would readily discount the inherent concepts:
1. Would applying base-2 notation to the Planck base units render useful information?
2. Are those 202.34 notations or doublings or steps, a very unique map of the universe, at all useful?
Do you think those questions have any merit whatsoever?
First email: 22 August 2018
RE: Computational simplicity quick evolved into computational complexity. Where’s the logic? What are we doing?
Dear Prof. Dr. Olaf Beyersdorff:
Would applying base-2 notation to the Planck base units render useful information?
I hope so.
Unwittingly, back in 2011 in a New Orleans high school, we backed into the tetrahedron (and the octahedron within it) and have not yet re-emerged! We were studying the interior geometries of the tetrahedron by dividing each edge in half and connecting those new vertices. We discovered the four “half-sized” tetrahedrons in each corner and the octahedron in the middle. Applying the same process with our octahedron, we discovered the six “half-sized” octahedrons in each corner and the eight tetrahedrons, one in each face, and all sharing a common centerpoint. We also found the four hexagonal plates surrounding that centerpoint and could see how we could quickly tile the universe with them. We also found the plates of squares, triangles, and other configurations.
It was all quite fascinating, but our adventure was just starting.
We continued to divide the edges in half for both objects, going deeper and deeper inside. We had Zeno in mind. By the 45th step inside (of course, on paper only), we were in the range of the sizes measured within particle physics. We called it the CERN-scale. In another 67 steps within, we were down within the Planck scale. That was a total of 112 steps from our little 2.5″ tetrahedron down to the all those dimensionless constants that make up the Planck base units. We rather quickly learned that what we were doing was applying base-2 notation by using the Planck base units for scaling. We then learned about Kees Boeke’s base-10 work in 1957 (also in a high school).
And, rather quickly, we thought about multiplying by 2. That was the biggest surprise.
In just 90 steps or doublings going out, we were at the Hubble’s measurement of the approximate size of the universe. A NASA scientist helped us with that calculation. Many others did as well. But three years later, we finally added Planck Time to the scale and it blew us away. The two scaled so well together. But then, we thought, “Of course they do!”
In another year, we added Planck Charge and Planck Mass and that was totally challenging. We are still working on those numbers and have a long way to go. But, in the process, we have talked with some of the finest people on the planet. Yet, we know what we have done is quite idiosyncratic and naive because nobody is critical, yet everybody is reluctant to engage such simplicity.
Do we trust simple logic and math?
The implications are just too strange. With those 202.34 notations or doublings or steps, we have a very unique map of the universe. But, is it useful? Or, is it just a collection of useless numbers? What does a retired high school teacher do? What would you do with this odd-duck collection of simple math and simple logic? Just forget it?
PS. Here are links to some of our work:
1. Our tetrahedral-octahedral models: https://81018.com/tot/
2. Our horizontally-scrolled working chart: https://81018.com/chart/
3. The most recent work is always here: https://81018.com