Bruce Camber sent the following email to Alan Dershowitz about Natural Law.

Background: January 2014, after 50 years of teaching at Harvard Law School, Dershowtiz has stepped down to give his many unfinished projects his undivided attention.

Reference: Rights from Wrongs: A Secular Theory of the Origins of Rights, Alan Dershowitz, Basic Books, 2005, page 31

First email: Feb. 4, 2014

Dear Prof. Dr. Alan Dershowitz:

Congratulations on a most-provocative, productive career; and, just think, you are just getting started!

I awoke this morning thinking about you and natural law. Now, that’s a first and it did seem a bit peculiar. I thought, “Maybe it’s an inspired moment.” So, at about 4:30 AM, I went to my computer and started reading about your disdain for natural law: “Human beings have no singular nature… We are creatures of accidental forces who have no preordained destiny or purpose” (Rights from Wrongs: A Secular Theory of the Origins of Rights, Basic Books, 2005, page 31). It is entirely obvious that you have very little patience for those who advocate natural law.

Given that you have spent so much time arguing the case against natural law, it may appear silly to learn that a group of high school geometry students may have found a basis for natural law. Though unusual, it is not frivolous. I would not waste your time or mine. It is instead based on simple logic and simple mathematics; and thus, it is simple enough to be compelling.

Base-2 exponential notation is a odd combination of words that simply mean, multiply by 2, then continue by multiplying each result by 2.

The Planck Length — http://en.wikipedia.org/wiki/Planck_length — uncovered in 1899, is theoretically the smallest possible measurement of a length.

There are an increasing number of measurements for the Observable Universe – http://en.wikipedia.org/wiki/Observable_universe — which, of course, is the largest measurement of an actual length. There are limits.

If we assume the Planck Length as calculated by Max Planck in 1899 and 1900 is close to being correct, then by multiplying it by 2, over and over again, there are only 202 notations (doublings, notations, steps, or layers) from the smallest to the largest. Although the range varies  for the calculation of the age of the universe, a total of 202 is a very good estimate. It’s a model, an outline of a potential model.

It is not easy to conceive of so few notations from the smallest to the largest so I’ll provide a link to the actual calculations so you can see that progression. https://81018.com/chart/  An explanation: https://81018.com/stem/

Basic geometries begin with the second doubling. It is not a gimmick, but a way of ordering the known universe that is efficient, relational, holistic, instructive, and simple. And, because it starts with an inherent geometry that expands rapidly (cellular automaton), it has an implicit structure (form/function) that evolves within every notation. Here, time appears to be derivative of number and space derivative of geometry.

Bottom line, this construct first pushes out an inherent continuity/order, symmetry/relations, and harmony/dynamics that is wonderfully complex, ordered and dynamic. It also allows the freedom of its inverse. The pentastar1 (five tetrahedrons, seven vertices) and the icosahedron (20 tetrahedrons, 12 external vertices, one internal) actually create a basis for imperfection, or degrees of freedom, or within science, quantum mechanics. Taken together, it seems we have the foundations or the beginnings of a natural law.

It lets group theory, set theory, and systems theory evolve in natural ways from the Planck Length to the Observable Universe. By the 60th notation there are over a quintillion vertices for constructions. Fermions and protons do not show up until the 65th.

The links to that chart and a quick tour is the start of many, many pages of analysis. I hope you are interested.

And, yes, and it all began in a high school geometry class in 2011 and is slowly evolving. Thanks.

Warmly,

Bruce

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