**Wendy L. Freedman**, Kavli Institute for Cosmological Physics

Astronomy & Astrophysics University of Chicago, Chicago, Illinois

Articles: Cosmology at a crossroads, Nature, May 2017 (**PDF**)**ArXiv** (152): The Hubble Constant with Barry F. Madore, August 2010

_______Mathematical Underpinnings of the Multi-Wavelength Structure of TRGB, August 2020

Books: Measuring and Modeling the Universe: V2, Carnegie Observatories (2004)

Gruber Foundation

Homepage (KICP)

Hubblesite

inSPIRE^{HEP}

NASA Hubble (July 16, 2019)

Twitter**Wikipedia**

YouTube: Misel Family Lecture Series (2017)

First email: 17 October 2020 (started on October 8)

Dear Prof. Dr. Wendy Freedman:

You and your people have been teaching me so many things these past few weeks, I had to write and say, “Thank you.” I have even quoted one of your key summaries, “The Hubble constant is the cosmological parameter that sets the absolute scale, size and age of the universe; it is one of the most direct ways we have of quantifying how the universe evolves.”

**Out of high school**. High school teachers can be entirely naive and I am no exception. Yet, I love geometry and mathematics enough to explore what I don’t know even if it opens idiosyncratic questions: [1] Can geometries build from the Planck base units? Is it the first moment of time?

[2] Might the first manifestation defining space-time and matter-energy be the sphere?

[3] Could cubic-close packing of equal spheres be a primordial functional activity?

In 2011, our geometry classes were having some fun with embedded geometries. We went inside the tetrahedron, doing a Zeno-like walk, going deeper and deeper inside a tetrahedron and then the octahedron within it. In just 45 steps, dividing each of the edges by 2 and connecting the new vertices, we were quickly down within our CERN-scale of particle physics. In another 67 steps we were within the Planck-scale. To go back out, we used the Planck Length, multiplying by 2, and in the 112 steps we were back in the classroom. We decided to keep going and in just 90 additional steps were were approximately out to the size of the universe. In just 202 base-2 exponential notations we had mathematically encapsulated the universe. We thought it was amazing. Euler came alive. The universe became accessible. Everything, everywhere for all time was within a continuum.

**A little overview**: https://81018.com/home/

Just three layers of tetrahedrons-octahedrons: https://81018.com/tot/

Our perfect little STEM tool: https://81018.com/stem/

Our horizontally-scrolled chart: https://81018.com/chart/

Of course, we quickly discovered Kees Boeke base-10 work and all the related books, films, and websites. We still liked our chart better; the Planck numbers are so very basic, base-2 is so Euler, so biological — could it be related to period-doubling bifurcation, emergence, cubic close packing of equal spheres, homogeneity and isotropy, natural inflation?

We got so far ahead of ourselves.

**Back in 2014 we mapped in Planck time, then the other Planck base units**. The earliest notations jumped out at us with questions, so we created a horizontally-scrolled chart to follow the numbers more easily: https://81018.com/chart/

**Then, last week, I discovered your most prodigious work**. You have an observational framework. We have a strictly mathematical framework.

[1] Can they work together?

[2] Can your work tolerate time if it is derivative and finite?

[3] Can your work tolerate infinity defined as continuity, symmetry, and harmony?

[[4] Can the Hubble Constant tolerate 201 fully-symmetric notations and an asymmetric Notation-202 (which includes the edge of the current expansion)?

**Notation-202 is defined by 10.9816 billion years (346,545,888,147,200,000 seconds)**. The 201st notation is 5.4908+ billion years. All prior notations added together also amounts to 5.4908+ billion years. Taking 10.9816 billion years from 13.81 billion years is 2.8284 billion years. Perhaps a notation becomes symmetrical when “filled” with planckspheres. It immediately begins to create the next notation and the dynamics of that notation. There are what seems to be an unlimited number of variables to consider.

I hope our questions are not useless and that this inquiry is not a waste of your time. If it is, I apologize for all my naïvetés.

Thank you.

Most sincerely,

Bruce