Pickover, Clifford

Clifford Pickover
 IBM Thomas J. Watson Research Center
 Yorktown Heights, New York
 Author of over 50 books about mathematics and life


From Wikipedia: Pickover’s primary interest is in finding new ways to expand creativity by melding art, science, mathematics, and other seemingly disparate areas of human endeavor.[8] In The Math Book and his companion book The Physics Book, Pickover explains that both mathematics and physics “cultivate a perpetual state of wonder about the limits of thoughts, the workings of the universe, and our place in the vast space-time landscape that we call home.” [9]

24 April 2017  The Most Recent Communication

Dear Cliff:

You are a man for our times.

To encourage further exploration of your work, you now have a page on
our website:  https://81018.com/pickover

We are still pondering the meaning of the first 67 notations from the
Planck units as defined by base-2 notation to the Age of the Universe
(which is within notation 202).

I hope you are well and doing fine.

Most sincerely,


PS.  You might find our latest chart of base-2 numbers to be of some interest.
https://81018.com/chart/ We  put it up online last year since our last
note to you.  -B


February 2016  (Second email) 

Re: You are an amazing person, such a polymath, I’d like our students and readers to know your work

Dear Dr. Clifford:

This note is essentially to get your permission to use your work as an example of somebody who truly loves numbers, geometry, algebra, calculus, differential equations and the integration of ideas.  We have barely gotten to know you through just a few of your writings and from your wonderful website and plead, “Please let us know if you ever come to New Orleans to lecture. We would love to pack the room… with dozens of curious high school geometry students!

We lift up your work with the writings of Martin Rees, John Barrow, Roger Penrose, and James Stein (author, Cosmic Numbers). The link to that page is:

The article is still in draft mode and we want to bring it out in the open soon. Might we hear from you?

Thank you.

Most sincerely,
Bruce Camber, occasional Geometry teacher in a New Orleans high school

PS. A little thought exercise.  In 2011 our high school geometry class went inside a tetrahedron. We divided each edge in half and connected the new vertices; there are four half-sized tetrahedrons in each corner and an octahedron in the middle.  Taking that octahedron and the tetrahedrons, we went further within. We divided each edge of that octahedron in half and connected the new vertices; there is an octahedron in each of the six corners and a tetrahedron in each of the eight faces.* We kept going within. In about 40 steps we were in the area of the proton.  In another 67 steps we were in the area of the Planck Length.  That was fun, so we decided to multiply our original tetrahedron by 2 and within about 100 notations we were out in the area of the Observable Universe.  Rather amazing, we thought.  Here we tiled and tessellated the universe in somewhere over 201 steps.

Isn’t it incredible?

In 2012 we couldn’t find any references to base-2 notation from the Planck Length to the Observable Universe on the web. Today, all the references are ours.  Of course, we found the base-10 work of Kees Boeke but it’s just adding zeroes.  We are mimicking cellular reproduction, chemical bonding, and all forms of bifurcation.  Isn’t this significant?  It looks to us that Newton’s infinite sense of space and time is misplaced. Our view of space and time is that both are finite and various kinds of continuity and a diversity of symmetries are what is infinite.  Where are we going wrong?  Thanks!

April 2011:  First email (most links have been updated)

I think your work is phenomenal, quite remarkable.  You are such a polymath.

Three quick, simple questions:

  1. What is the simplest three-dimensional structure?
  2. What is most simply and perfectly enclosed by that structure?
  3. What is most simply and perfectly enclosed within each of those parts? (original)

John Conway, Princeton surreal numbers, asked me why I was so hung up on the octahedron.  I said, “…because you are the only one out of literally a 1000+ people who could answer the (third) question.”  I suspect even my old mentor, Arthur Loeb (author, Space Structures) might have hesitated.

Have you seen the parts-whole models (as opposed to the stick figures)?

My work back in the dark ages (1973-1980) was on the EPR paradox at BU with Bob Cohen and Abner Shimony, but at the same time I had a foot over in the School of Theology (and Harvard Divinity and others through the Boston Theological Institute.) I was working toward a dissertation on perfected states in space-time and the Nicene Formulas for a hypostatic union.

Might you have time to take a call?


Bruce Camber, CEO, Executive Producer
Small Business School, an educational television show
Private Business Channel, Inc.

PS.  You might find some of the links below useful as further backgrounder info.

  • The longest-running television series on PBS stations in the USA and the Voice of America around the world about best business practices.  http://smallbusinessschool.org/page18.html
  • Every business owner was recommended by many local business advocates, often the local Chamber of Commerce, and confirmed by their national trade association for their leadership, generosity of spirit, ethics, and courage.Nobody can pay or has ever paid to be on this show.  http://search.smallbusinessschool.org/page898.html
  • Many publishers, business associations, schools, and  journals provide their constituents with access to daily business tips:  http://smallbusinessschool.org/page2162.html