**Marcus du Sautoy**

Simonyi Professorship for the Public Understanding of Science

Fellow of New College, Oxford University

Oxford, England

ArXiv

Books: What We Cannot Know: Explorations at the Edge of Knowledge, Fourth Estate, 2016

_______ The Music of the Primes, Harper Collins, 2003 (YouTube: Clay Institute)

Homepage

Research

Twitter

Wikipedia

YouTube: Reality is A Riddle

First Tweet: Tuesday, April 24, 2018

If I were in England, I’d be there! Base-2, period-doubling bifurcation, and multiscale modeling just might awaken us all to an integrated scale of the universe. http://81018.com and my open letter to you: https://81018.com/2018/04/18/sautoy/ Congratulations. Best wishes!

Note: In response to today’s Simonyi Lecture lecture by Geoffrey West (Santa Fe Institute) and his recent book, *Scale*.

Most recent email: February 14, 2019 @ 6:21 PM

Dear Prof. Dr. Marcus du Sautoy:

It is coming up on a year now since we sent the note below.

We are still questioning ourselves. Yet, there is so much confusion

within big bang cosmology, we just keep moving forward.

Our horizontally-scrolled chart with just 202 columns is a fascinating

study of the actual numbers that result in those successive doublings.

Is there any hope for it?

Thank you.

Most sincerely,

Bruce

First email: April 18, 2018

Dear Prof. Dr. Marcus du Sautoy:

I have spent some time on your website and with your ArXiv papers; you are over-qualified to render a judgment on our multiscale modeling work using the Planck units which are doubled over and over again up to the age and size of the universe within just 202 notations or steps. The work is naive. It comes out of a high school in the USA.

Please allow me to tell you the story.

In 2011 my nephew asked me to substitute in his high school geometry classes in New Orleans. The students knew me as Uncle Bruce because in a few prior encounters, I had them build geometric forms based on Plato’s solids. Here is a sample of that work: https://81018.com/tot

On the last day of class before Christmas break, instead of serving milk and cookies and reading stories, the students and I began developing a scaling chart of the universe: https://81018.com/home/ The kids and I were equally fascinated by our exploration of the universe’s relative measurements at different scales.

In the high school, that single day turned into an ongoing odyssey of exploration in Planck unit number relationships. Such scaling recalls a well-known book, Powers of Ten: About the Relative Size of Things in the Universe, but with a vital difference. We used the Planck base units to discover a systematic doubling that goes on from scale to scale.

We have long been looking for a means to justify or explain this behavior. It just might be a variant of the doubling phenomenon that occurs in a discrete dynamical system: Period-doubling bifurcation (Wikipedia). It seems to us that this doubling occurs as measurement moves from scale to scale in the universe, but we do not find that observation mentioned anywhere in your literature or the chaos theory literature.

If just taken as a given, could it indicate that the universe itself is a continuous dynamical system?

The intriguing possibility suggested by our rather encompassing multiscale chart has been endlessly fascinating to us… that the entire universe could be encapsulated within the scaling bandwidth of 202 doublings! Who would have ever thought….?

The Planck units were the ruler. The doublings were the measurement that resulted. The goal was theoretically verifying the age and size of the observable universe by a systematic exploration of these doublings.

Over the years, our exploratory website has burgeoned: https://81018.com/chart

Might you advise us? Where has our logic gone askew? If it hasn’t gone askew, are we on to something? If so, we will need some serious coaching and would hope that you might be able to help us a little.

Most sincerely,

Bruce

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

Thinking about very large numbers…

**Mathematician Marcus du Sautoy: **Sand is rock with a diameter of between 0.625mm and 0.2mm. Assuming a grain of sand is roughly spherical, the average volume of a grain is 4/3 x pi x r^{3}=0.00947mm^{3}, where r is the radius. So how many grains of sand are there in a metre cube box? It has 10^{9}mm cubes inside (10^{N} is how mathematicians write a 1 followed by N zeros), and if they are arranged randomly, about 65% of the box will be sand and the rest air. So we can estimate that the number of grains of sand in a metre cube box is 10^{9} x 0.65/0.00947, or roughly 70bn grains. Now, let’s go for an average of 5% of the surface of the Earth being covered in sand with a depth of 100m. The surface area of the Earth is 4 x pi x r^{2} where r is the radius of the Earth, which is 6,378,000 metres. So the volume of sand comes out at: 2.5 x 10^{15}m^{3}. So my rough estimate is that the number of grains of sand on the Earth is a number with 27 digits.

Marcus du Sautoy, author, The Number Mysteries (Fourth Estate).