You’ve touched on two topics near and dear to my heart:
1. The timeline for the universe
2. Pi: You conclude, “Now π is second nature to us…”
Both have so much to do with how we understand time and space. If we stick to the numbers and the logic of numbers and shapes (symmetries), we may actually discover a more simple timeline and a bewilderingly new sense of pi (π).
In our time we are specially privileged to have the Planck base units within our intellectual arsenal. Unfortunately for science, these numbers were virtually ignored for over 100 years. Frank Wilczek (MIT, Nobel laureate 2004) did a series of three articles, Scaling Mt. Planck, in 2001 for Physics Today, yet even he did not stop long enough to make them simple and even more accessible.
We are high school people. I think the university people kind of snicker at our naivete. We’ve asked for feedback, but we are hard pressed to get it. If we are on the right path, then there are some exciting possibilities for science. If we are on the wrong path, somebody should be able to tell us why.
May I send you an even longer overview of our simple-simple numbers (third-and-fourth graders can handle it – multiplication of very small and then very large numbers by 2)?
PS. However ancient and known, Pi is still rather new to us. It is exciting to see so many new constructions and formulations come out of it.
https://bblu.org/2016/01/08/number/#4 is where my discussions about pi begin.
https://bblu.org/2016/01/08/number/ is an article, “Constructing the Universe From Scratch.” -B
PPS. I just posted this comment on your pi article:
We haven’t even scratched the surface. Our Newtonian logic has kept our minds in a straight jacket. We need to see how pi opens up to the tetrahedron, then the octahedron, then imperfect wheels of tetrahedrons, and then the symmetries of the universe in a finite-infinite dance.
Here’s a beginning for our initial two-step: https://bblu.org/2016/01/08/number/
The source file is here: https://en.wikipedia.org/wiki/Close-packing_of_equal_spheres#Simple_hcp_lattice
All quite elementary. Just think of all the new learning we have to do!