Jacob Bourjaily, Assistant Professor of Physics, Niels Bohr Institute

Copenhagen University, Copenhagen, Denmark

**Article**s: Google scholar citations**ArXiv**: Amplitudes at Infinity, Prescriptive Unitarity**CV****Homepag**e

Twitter**Wikipedia****YouTube**

Second email: Wednesday, 18 September 2019 @ 8 PM

Dear Dr. Prof. Jacob Bourjaily:

So much has transpired in the five years since my first letter (below). We are still asking questions about our simple construct from 2011 when we started at the Planck Length and went out to the size of the universe in somewhere just over 202 doublings. Of course, we have all appreciated exponential notation as an academic study; this chart suggests it is part of our very being.

The first 64 doublings, coming up to just a few steps below where CERN’s scale of measurement picks up, are problematic. So, to explore these doublings, we treat the chart as a little mathematical puzzle. If take it as a given that these 64 doublings exist, what do they tell us about the nature of our universe? What can we do with them? The answer appears to be, “Quite a lot.”

https://81018.com/bottom-up/ is a page where I’ve begun to explore those 64.

More to come… This letter will be sent soon. -BEC

First email: May 28, 2014 @ 4:32 PM

Dear Dr. Prof. Jacob Bourjaily,

Besides engaging your research publications listed within your vitae, I thoroughly enjoyed your walk with harmony and Kepler. By the way, you already have a role in our work with our high school geometry classes (I’ll post it below and provide a link if you want to see more.)

We would love your best guess as to where to place your amplituhedrons within our 202+ base-2 exponential notations from the Planck Length to the edges of the Observable Universe.

It all started when we made models of a tetrahedron with a half-sized tetrahedron in the each corner and the octahedron in the middle. We then divided the edges of that octahedron in half, connected the new vertices, and found the six half sized octahedrons in each corner and eight tetrahedrons in each face: https://81018.com/tot/

We chased that progression first to the Planck Length and then out as far as we could. We then realized we just tiled the universe. Of course, it is all simple logic and an ideal construction. Yet, we found it useful, so for over two years now, our students have been using this range, we call it a Universe Table or the original, Big Board – little universe.

I’ll insert our current range and highlight our guess for the amplituhedrons.

Thank you.

Warmly,

Bruce

**Notes**:

Notation 66. ___ 1.19254509×10^{-15} m In the range of the diameter of a proton or a fermion

Notation 65. ___ 5.96272544×10^{-16}m In the range of neutrinos, quarks

Notation 64. ___ 2.98136272×10^{-16} Possibly in the range of largest possible strings**Notation 63. ___ 1.49068136×10 ^{-16}m Possible Amplituhedron**

Notation 62. ___ 7.45340678×10

^{-17}m

#12b. **May 2014: Discovering Quanta Magazine, amplituhedrons and more**

We have been discovering the writings of Natalie Wolchover within Quanta Magazine where she focuses on the work of Andrew Hodges (Oxford), Jacob Bourjaily (Harvard) and Jeremy England (MIT). We believe these young academics are opening important doors so our simple work that began in and around December 2011 has a larger, more current scientific context, not just simple mathematics. We are now pursuing all their primary references; our introductions are here:

• http://www.simonsfoundation.org/quanta/20130917-a-jewel-at-the-heart-of-quantum-physics/

• http://www.simonsfoundation.org/quanta/20140122-a-new-physics-theory-of-life/

• http://doublings.wordpress.com/2014/05/08/15/