Looking in on the work of Paul J. Steinhardt…


Paul J. Steinhardt
Princeton University
Princeton, New Jersey

ArXiv (over 108 articles)
YouTube: The Myth of Inflation (2021),  A New Kind Of Matter (March 2019), Inflationary Cosmology on trial-2011 and dozens more

References to Steinhardt‘s work within this website:

Most recent email: 8 October 2021 @ 7:05 PM

RE: Still at it! Finally caught up with “Impossible”

Dear Prof. Dr. Paul Steinhardt:

Your book, The Second Kind of Impossible, Simon & Schuster, 2019, resurrects the importance of geometries within the small scale universe. I believe your discoveries, following Daniel Shectman‘s initial quasicrystal work, open a vitally important door. The next door to open is within the infinitesimal universe from the quark-gluon plasma and electroweak scale down to the Planck base units. I just found a group out of Durham University that hosted the 23rd conferences to focus on just that domain. Would geometries become increasing “simple” as we continue to approach Planck Time, i.e. automorphic forms and strings!?!

https://81018.com/hypostasis/ is our most recent speculation about it all. The numbers, of course, we started chasing in 2011: https://81018.com/chart/

I thought you would be interested to learn that I am keeping the fires burning within our most naive-but-logical-and-mathematical model.



Fourth Email: Thursday, 6 March 2021

Your writings are most encouraging. I am so very humbled and I am painfully aware of my naïvetés and limitations. So, I profoundly thank you for opening up the universe for me.

[1] You ask us to be aware of quantum origin.
Remember we backed into this entire domain by following Zeno down inside the tetrahedron and its octahedron. Within just the first 45 steps, we were down within the neutrinos. With another 67 steps, we were down with Max Planck discussing his infinitesimal units. We seemed to break free of the hard quantum fluctuations around Notation-64 and then free of all possible fluctuations around Notation-50. I wanted to call these less harsh fluctuations systemic or ontological (ontic) fluctuations and relate them to thought and consciousness. Again, my naïveté and limitations hold me back. The initial 50 notations I considered a place for pure geometries and numbers and combinatorial optimizations.

[2] Consider those stages when the universe is not inflating.
Those first 64 notations were initially quite upsetting. Struggling as I did, there was little more to suggest than Pati preons. I was just throwing anything I could find up against the wall to see if it would stick! The more obvious — Langlands, string theory — had to be studied. Then came theta functions, Quine* atoms (urelements), axiomatic set theories, etc (line 11 on my chart)… And more recently, causal dynamical triangulation, causal set theory, scalar field theory, loop quantum gravity, and the Spectral Standard Model.

[3] Inflation is about more than exponential expansion.
On that path, it was easy to imagine that every notation was always active, and that the base unit, this infinitesimal sphere (Lemaitre’s atom), is defined by the Planck units. Those first 50-to-64 notations are a precursor to direct measurements. It is a highly-refined, dynamic area where all kinds of mystery could hide. First, the dark stuff. That seemed obvious. The rate of expansion, if we assumed one sphere per Planck unit of time, was hard to imagine but possibly a proper, natural inflation. It certainly felt more logical than Alan Guth’s inflation. Applying base-2 was never some special mathematical magic, but always had “something” making space-and-time even if it was just geometry. But that first object eventually became that infinitesimal sphere that filled the universe and became the new aether whereby everything, everywhere, for all time became connected and its uniformity became the basis for homogeneity and isotropy.

It’s been an evolution. For pi day, I finally said, here is the most basic dimensionless constant of the many that define the first instance, that first infinitesimal sphere, a full 64 doublings from the first particle and wave. There is plenty of time to bring general relativity and gravitation into the equations. Yes, yes, still crazy after all these years!


PS. I once was a dinner guest of Quine’s in his home (as a graduate student)! -BEC

Third Email: Thursday, 9 April 2020

Dear Prof. Dr. Paul Steinhardt:

Thank you for all you do to guide our students and our world’s scholarship. I have enjoyed coming to know you through your writings and videos. You challenge me on every turn!

Notwithstanding, our little idiosyncratic model has not been debunked, just categorized as “idiosyncratic” and it is. There are five general assumptions from which this model emerged. These are as follows:

  • The four Planck base units define the first moment of time.
  • An infinitesimal sphere is the first expression of a physical thing.
  • There is a natural inflation whereby sphere stacking and cubic-close packing of equal spheres creates structure and emergence.
  • There is a finite-infinite relation and the infinite is defined, primarily as a result of discerning aspects of that sphere. It is: (a) continuity and it creates order and the face of time, (b) symmetry and it creates relations and the dimensions of space, and (c) harmony and it creates dynamics and a space-time moment. That is the sum total definition of the infinite (and infinity) and there is a constant working bridge between the finite and infinite.
  • These spheres continue stacking and become an aether and natural inflation. There are just 202 base-2 notations from the Planck Time to the current time. This endless stream of spheres is the current expansion and every notation is always active and present.

I’ll continue to work on this model and will attempt to become more compelling within each step of the way.

In today’s homepage there is a reference to you and the 1999 Structure Formation conference at Cambridge University’s Isaac Newton Institute so I was reminded once again of your most impressive history within this domain.  I thank you.

Most sincerely,


PS.  I recognize that our definitions of time and space are still quite primitive:
https://81018.com/redefinition/#Top  Although Turok, Arkani-Hamed, and Tegmark would never agree with a high school teacher, at least they forcefully raise the questions.

From within my impossibly-deep naivete, even though Planck Mass and Planck Charge are in some sense of the word, quantum, if they are well beyond measurements, might they be re-qualified as more systemic than quantum? I certainly don’t know. There are 64 notations, a virtual universe, between Planck Time-and-Length and actual physical measurements by devices. Wouldn’t it be polite to offer those 64 base-2 notations as a work area for Langlands programs and string theory?
Second email:  Tuesday, March 12, 2019, 1:23 PM
As earlier suggested, I have been trying harder to clarify my first principles. There are five very speculative assumptions (concepts) that form the basis of this idiosyncratic model.

1. Continuity: A simple mathematical grid to order things.  Apply base-2 notation to the Planck base units to encapsulate the universe within 202 base-2 notations. We start at Planck Time and go to the present time.

2.  Symmetry: A simple building block to create relations. Assume the first expression of physicality is the sphere; some have called it a plancksphere; and, back in 1955, John Wheeler called it quantum foam. Apply cubic-close packinghttps://81018.com/number/#Kepler –and form-and-structure become emergent. https://81018.com/circles-spheres/

3. Harmony:  A simple construct for quantum fluctuations and dynamics. Assume basic structures include a five-tetrahedral unit; we have called it a pentastar. It has a gap (0.12838822… radians or 7.356103172… degrees) that also manifests as the twenty-face icosahedron and the sixty-face pentakis dodecahedron. In each the same gaps could readily manifest as quantum indeterminacy by the 64th notation or doubling.

4. Time is derivative. Every notation is always emergent, never-ending, never-the-same. All time is Now. Obviously, within the 202nd notation, there is a perception of past-present-and-future, a sense of time. This notation is 10.9 billion years and only about 2.84 of it has emerged.

5. Re-open the door to define more deeply the concept of infinity. We’ve all got to lighten up a little. It is obvious nobody is making progress within the old-time debate, but some progress just might be made both within mathematics and physics: https://81018.com/infinity/

Summary. It is such a different model, it is hard to engage. It took me the better part of four years to realize in what ways this nascent model could become more than a STEM tool.

Our little history is here: https://81018.com/home/ My story is here; an introduction here.

My request (a plea). I know how idiosyncratic this model and these five constructs are. If the logic and/or mathematics fail, I would be deeply indebted to learn how. If this model is not a possibility, I would like to learn where and how the simple logic and simple math break down so I can give this work a fair burial as a theory and do a better analysis of its STEM possibilities.

Thank you. Thank you so very much.



First email: Wednesday, January 14, 2015, 3:55 PM

Dear Prof. Dr. Paul Steinhardt:

I came upon references to your work within the Kavli Foundation pages and then began reading about the breadth of your work on your own Princeton homepage. We’ve been looking for alternative approaches to understand our earliest universe.

We backed into this work by following simple geometries back to the Planck Length and then out to the Observable Universe. Our work is simple-simple (yes, possibly simplistic) and entirely idiosyncratic. Last month we added Planck Time to our base-2 progression and we are filled with questions.

Have you ever seen the simple compilations of the progressions from the Planck Length and Planck Time (using base-2 notation) to the Observable Universe and Age of the Universe respectively? Based on our initial observations, I think it raises questions about nature of space and time. We can guess. Although we have no conclusive answers, let me admit that we are a little prone to wild speculations and flights of the imagination.

Yet, as high school teachers and students — certainly not experts on the subject by any stretch of the imagination — we still had the audacity last September to begin asking questions. It may all just be an overactive imagination based on simplistic logic. Perhaps this challenge to our understanding of space and time is just too profound for us little folks with such little depth and background in cosmology and astrophysics.

I thought you at least would find such an unusual, rather idiosyncratic approach to these questions to be of some interest. If not, well, sorry to waste your time. However, if you feel that way, I have five classes of high school geometry students and this teacher who would be fascinated to know why.

Best wishes to you and your teams for 2015,

New Orleans
Bruce Camber, Mathematics, Geometry
PS. Given your work with quasicrystals and five-fold symmetries, you may also find this page about tilings and tessellations to be of some interest as well as the following:

  1. The references to your work (just above) for digging down further.
  2. Our “work” began in 2011 in a high school geometry class. That story is here: https://81018.com/home/
  3. This posting of the two progressions side-by-side was done in December 2014: https://81018.com/calculations/
  4. Earlier work from September 2014, mostly questions… one must start somewhere: Did A Quiet Expansion Precede A Big Bang? https://81018.com/2014/09/10/quietexpansion/