Gibb, Sophie C.

Gibb-SofiaProf. Dr. Sophie C. Gibb

Department Chair
Department of Philosophy
Durham University
Durham, UK


First email: Fri, Sep 21, 2018

Dear Prof. Dr. Sophie Gibb:

Our work began in December 2011 within our high school geometry classes in New Orleans, Louisiana, USA. That story is here: Asking questions about Zeno’s paradox, we were chasing embedded geometries, smaller and smaller units, until at the Planck scale: and

The students and I were fascinated by this exploration of the universe’s relative measurements at different scales. Those first discussions turned into an ongoing odyssey to explore the Planck unit-number relationships. This scaling unwittingly recalls the 1957 base-10 work of Kees Boeke (that was later popularized within a well-known book by Phyllis & Philip Morrison, Powers of Ten: About the Relative Size of Things in the Universe), but with a vital difference. We used the Planck base units to do a systematic doubling. It creates a truly fascinating scale that starts at the first moment of time and it goes to our current time.

With the typical enthusiasm of youth, we asked, “Isn’t this the most highly-integrated, mathematical, continuity equation for all time?”

We have been looking and looking for a means to justify or explain this doubling activity. We asked, “Could it possibly be related to the doubling phenomenon that occurs in a discrete dynamical system: period-doubling bifurcation?” Does it have anything to do with the doublings with sphere stacking and ccp, fcp and hcp (emergence)?

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 the literature for bifurcation, chaos theory, fractals, cosmology, or physics.

If it coheres, could it indicate that the universe itself is a continuous dynamical system?

That intriguing possibility suggested by this rather all-encompassing multiscale chart has been endlessly challenging for 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 are the measurements that resulted. One of our goals was to see if we could verify the age and size of the observable universe by a systematic exploration of these doublings. Another goal was simply to try to envision the universe.

Over the years, our exploratory work has burgeoned into this website:

Might you advise us? Where have we gone askew? If our logic hasn’t gone askew, are we on to something? If we are, we will need some serious coaching and would hope that you might be able to help us. Isn’t this direction of thought worthy to have more hands and minds focusing on it?

Thank you.

Most sincerely,


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