The article that brought Mark Colyvan’s work to our attention:
Indispensability Arguments in the Philosophy of Mathematics
First email: Saturday, 23 Feb 2019, at 10:25 am
Dear Prof. Dr. Mark Colyvan:
I am so old I remember many times sitting next to Hilary Putnam at the lectures of the Boston Colloquium of Philosophy of Science and on one occasion joining him at the home of W.V.O. Quine for dinner with a small group of graduate students and faculty. I have been circling back and, of course, discovered your Stanford article and I had to say, “Thank you.”
Then I went to your home page and CV and I am very impressed. You might be able to help me discern the proper approach to a problem of mathematics and logic.
It arose in 2011 out of work with my nephew’s geometry classes. We went inside the tetrahedron and octaherdon. By dividing the edges by 2, then connecting the new vertices, in 45 steps we were looking at particles (physics); and in another 67 steps within, we were looking at a Planck wall. Back in the classroom, we multiplied by 2, and in 90 steps we were out to the approximate age and size of the universe.
It was a treat: https://81018.com/home/
It was also quite baffling to overnight become so idiosyncratic. Of course, it was helpful to discover Kees Boeke’s base-10 scale of the universe. It was good to discover MIT/Nobel laureate Frank Wilczek’s 2001 work, Scaling Mt. Planck. But the simple process of doubling those units and then emerging with a chart of 202 notations. That chart — https://81018.com/chart/ — has raised more questions than given us assurances.
What do we do with this madness? Does it mean anything? Of course, we think meaning can easily be instantiated, but real meaning must be substantiated.
What do we do with it? Are the first 64 notations particularly interesting because nobody has ever imagined that they are there? Each is defined by actual numbers, doublings of the Planck base units.
Might you help us a bit with your deep knowledge of logic, mathematics, and mathematical logic? I hope so. Thank you.
Note: We do not share the correspondence we receive from scholars unless they encourage us to do so. I can only guess, however, that once the concept of a base-2 outline of the universe from Planck Time and Planck Length is entertained, most scholars would say, “It just a bunch of numbers. Cute, but not particularly meaningful.”
The most-highly recognized thought leaders of our time, people like Hawking, ‘t Hooft, Penrose, Rees, …Zichichi, I can well imagine, when it just seems too idiosyncratic and would take too much time to respond, would just pat our head, and gently smile, “Someday you may understand.” We sometimes get such responses, …not sure what to make of it, …not an area in which I have any expertise, …good luck and have fun.
These are the basic concepts that first need to be internalized:
• Ordering principles come within the Planck base units. Taken as given, all the dimensionless constants that give rise to these Planck units come along inside. There are many more than initially meet the eye.
• An infinitesimal sphere is projected to be the first manifestation of physicality. That sphere brings with it all the dimensionless constants and interior dynamics, i.e. functions like the Fourier transform. There are many other dynamics we are also trying to grasp.
• Base-2 is the next ordering principle created through simple sphere stacking.
• A finite-infinite relation is assumed and it is defined most simply and is limited to it.
• Here is a domain of at least 64 notations to accommodate Langlands programs, string theory, consciousness and all those discoveries below the thresholds of measurement.