**Michael Aizenman**, Princeton University, Princeton, NJ

ArXiv (56): A geometric perspective on the scaling limits of critical… (PDF), Dec. 2021

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First email: 15 June 2022 at 10:31 AM

Reference: A geometric perspective on the scaling limits… of critical Ising and ϕ4d models (PDF)

Dear Prof. Dr. Michael Aizenman,

In 2011 we unwittingly made up our own scale from the Planck base units to the current time. We first started with simple geometries and did a 3D Zeno walk from our classroom’s tetrahedron to the Planck scale. There are about 45 base-2 notations down to the particle scale and another 67 to our goal.

We also went out by multiplying by 2, this time starting with Planck’s Time and Length to the classroom in those 112 notations, and then we continued another 90 notations to the age and size of the universe. It is a sweet little chart — https://81018.com/chart/ — but does it mean anything? We think it does.

Working with Brown University’s (and NIST) Phil Davis, we assumed the “first iteration of something” was a shell sphere with all its dynamics with attractors, repellers, and the Fourier transform and we assumed that it was also the beginning of scale invariance.

The problem is, this all came out of a high school. What do we know? Very little.

So, we’ve always looked for experts to advise us through their writings and I wanted to thank you and Hugo Duminil-Copin for your work.

Warmly,

Bruce

********************

Bruce E. Camber

https://81018.com/

214-801-8521

https://81018.com/bec/

***************************

PS. In your neighborhood, before they died, we also enjoyed communications with Freeman Dyson and a one-on-one visit with John Conway. He asked me, “Why are you so hung up on the tetrahedron and octahedron?” I answered, “…because they’re both keep teaching me something new!” Also, Princeton alum and professor, Frank Wilczek, was the first to assure us that we could multiply the Planck units by 2. -BEC

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