**Gerardus ‘t Hooft**

Institute for Theoretical Physics & EMMEΦ

Centre for Extreme Matter and Emergent Phenomena

Utrecht University Utrecht

ArXiv: Free Will in the Theory of Everything

Books: *Time in Powers of Ten: Natural Phenomena and Their Timescales, 2015*

_ _ _ _ _* In Search of the Ultimate Building Blocks*

CV

Homepage

Nobel Prize

Wikipedia

YouTube (and many others)

Update: 8 February 2018 First email: Sun, Jun 16, 2013

**References**: How to become a GOOD theoretical physicist

One of your pages that the students enjoy: Tilings

Dear Prof. Dr. Gerald ‘t Hooft:

Our geometry classes worked with clear, plastic tetrahedrons and octahedrons. We created the twenty-tetrahedral icosahedron, and the sixty-tetrahedral dodecahedron (Pentakis dodecahedron). We’ve built models and looked inside each (more pictures here). When asked if there were any questions, one of the students conjured up Zeno and sweetly asked, “How far within can we go?”

Using just the perfectly-fitting octahedron and tetrahedron, on paper we went inside each object about 112 times, dividing by 2 to discover that we were in the range of the Planck Length. We also discovered how each group of models was growing exponentially as we went further inside.

Next class we went the other way. We multiplied by 2 until we were in the range of the Observable Universe. That was just 90 steps. We thought it was very cool until we couldn’t find any references to it on the web. Of course, we found Kees Boeke’s work from the 1957. Back in days long gone by, I often had dinners with Phyllis & Phil Morrison; they helped to popularize Boeke’s work with their classic coffee table book, *The Powers of Ten*.

Yet, now many of us are asking, “Where do the powers of 2 and base-2 exponential notation fit into the larger picture? Do we live in an exponential universe? Does Euler’s equation capture the universe as well?” We initially thought it was a very good STEM tool, but now we think it just might be more.

Six years later, we are still asking the experts, “What are we doing wrong?” Thanks.

Warmly,

Bruce

PS. Since our first email (a first-draft of this email), we followed your work with Stefan Vandoren on *Time in Powers of Ten: Natural Phenomena and Their Timescales* and we have begun to engage your work within ArXiv. Long, long ago I studied the foundations of physics with Abner Shimony and Robert Cohen at BU (1973-1980), and then with David Bohm, Costa de Beauregard, and J. P. Vigier (1977 & 1980). But, I was idiosyncratic. Siding more with Leibniz than Newton, I began my graduate studies thinking that the essence of the infinite was continuity, symmetry and harmony, not absolute time. Though I enjoy Frank Wilczek’s work (2012 to now), I am even too idiosyncratic for him. Notwithstanding, if you’ll look at our current chart you will see that only two relatively brief epochs — the Grand Unification and Inflationary Epochs — are defined a little differently. -BEC