Second email: Tuesday, November 19, 2019 @ 3 PM
Dear Prof. Dr. Manjul Bhargava:
You grew up tasting and knowing numbers profoundly. Primes became real friends. For most of us, those ruffians naturally became part of our street gang, but they spoke a rather refined language as if they were always multitasking and had multiple communications channels ongoing.
There were always natural groupings within our gang. We each had our role, but we were all on-again, off-again friends. We’ve also done some cherry-picking, a little from Euler’s group, and more recently from a Feigenbaum group, the Fourier family, as well as the Gauss and Poincare families. They all seem to be integrating, BUT, we’re not sure.
We know you know these families, groups, and sets like the back of your hand. Our simple, little base-2 group is leading our way. We’re trying to get a lock on 202 sets that start with the Planck base units, but that 202nd set is incomplete, quite young and rambunctious. We are hoping that you can help us understand what we are doing right and what we are doing wrong with attempt to integrate such diversity.
We asked for insights three years ago, but you have been oh-so-busy. And, we know you are still out straight. But, isn’t our problem, as simple as it seems from the outside, rather complex? And, couldn’t your knowledge and skill help keep us on the straight and narrow?
First email: Thursday, July 21, 2016, 2:12 PM
Dear Prof. Dr. Manjul Bhargava:
Would you, could you, please, help some high school people figure out what is wrong with our simple base-2 progression from Planck Time to the Age of the Universe? We started our project in a most peculiar way back in December 2011.
We went inside the tetrahedron.
We were dividing the edges by 2, and found the half-sized tetras in the four corners and an octahedron in the middle. We went inside that octahedron, dividing by 2, found the half-sized octas in each of the six corners and eight tetras, one in each face, all sharing a common center point. We kept going within all 19 objects.
BTW, you should know that I once visited with John Conway there in Fine Hall. He asked me, “Why are you so hung up on the tetrahedron and octahedron?” I will tell you that story sometime if you’d like to hear it.
Well, in just 45 steps going-within we were zipping by the fermions and protons and just kept going! In the next 67 steps, you wouldn’t believe what we saw along the way! We were then standing at the door of a so-called singularity that Max Planck gave us and all those secret codes, but it took 100 years and Frank Wilczek to begin to interpret them (2001, Physics Today, Scaling Mt. Planck I-III).
It didn’t take too long before we got the bright idea, “Let’s multiply by 2.” What an epiphany! It was 112 steps within to the Planck Length and Planck Time. In less than 90 steps multiplying by 2, we were out to the Age of the Universe and the Observable Universe.
We were lost within all this new information, so we decided to turn to the experts. We found Kees Boeke’s base-10 work from 1957 but he only had 40 quick jumps and missed so much of life! We found Stephen Hawking but he was in tight with a big bang.
Where are our experts? 202 base-2 steps from one end to the other, from the beginning of time to this day. It is totally idiosyncratic, we know. Would you help us work with it? Guide us on our way?