On following the work of Denis Weaire…


Denis Weaire, Trinity College Dublin (TCB), The University of Dublin
College Green, Dublin 2, Ireland

ArXiv: 2D foams above the jamming transition: Deformation matters
Facebook: Physics Today, 2011, Perfect Foam (2017)
Homepage(s): Academy of Europe, dbPedia, Philomorph Foam (PDF), 2001
YouTube: (at 6:00 minutes) The Science of Bubbles – Foam Bubbles Finally Brought to Order

Most recent email: 31 January 2019

Dear Prof Dr. Weaire:

In 2016 we took our base-2 chart and expanded it with the four Planck units of length, time, mass and charge and watched a natural inflation mimic the epochs of the big bang theory. We observed a simple doubling mechanism within cubic-close packing. We needed help, so we turned to scholars like you. Nobody has really looked at the numbers in the chart: https://81018.com/chart/

Would you? Would you tell us what is wrong with the simple logic and simple math? It seems to be worthy of the scholarly community’s time just to understand something about mathematical logic.

Thanks so much.


Second email: 13 November 2014


Dear Prof Dr. Weaire:

In the spirit of Cyril Smith, Reynolds, Thomson, the Philomorphs, and your comment, “Foam structures occur, or are conjectured to do so, on every length scale from the Planck scale (10 to the power of minus 35 metres) to that of the large-scale structure of the universe,” allow me please to ask three naïve questions:

1. Can we say that “from the Planck Length to the Observable Universe” is the finite universe?

2. Can we meaningfully parse that finite universe using base-2 exponential notation?

3. If either/or both answers YES, then why haven’t we seen this range used more within mathematics and geometry?

Thank you.

Most sincerely,


First email: Sat, Feb 4, 2012 at 8:21 PM

Updated: 17 September 2017, very small corrections

Dear Prof. Dr. Denis Weaire:

Thank you for your simply beautiful legacy to date. I am going to guess that your best work is yet ahead.

I just downloaded the Philomorphs.pdf which was the first up in a Google search of the word. I was a bit later than you and under the leadership of Arthur Loeb in 1971-81. I am also enjoying tremendously following all the links and seeing the pictures of you and your colleagues and your work. Just marvelous. You, like John Conway, would be among those who would readily know what is perfectly and most simply enclosed by an octahedron.

I find there are not many people who know; and among the most who do not know, there are far too many who should know.

Have you seen the inside of a hexacontagon made of sixty tetrahedrons?

Each cluster of five tetrahedrons make the pentagonal face so it was my first exploration (April 2011) of alternatives to a simple dodecahedron.

I am an old student who has spent a lot of time doing other things. Yet, when a person is studying and enjoying the work of another so much, I believe you should be aware of it! I thank you for what you have done and what you are doing!



Bruce E. Camber, founder, Small Business School: http://SmallBusinessSchool.org

Big Board-little universe Project: http://81018.com

PS. What is wrong with charting the universe using the base-2 notation so we see the smallest to the largest within 202 steps? Is it meaningful? -BEC

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