Carskadon, Mary A.

Prof. Dr. Mary A. Carskadon
Alpert Medical School, Brown University
Bradley Hospital Sleep Lab, 300 Duncan Drive, Providence, RI 02906


First email: 30 October 2020

Dear Prof. Dr. Mary A Carskadon,

You have much better things to do with your time than to respond to this note; however, as an exercise, I need to get some thoughts down about circadian rhythms and the metaphor of an old computer’s overnight recompile. Of course, I found several references to your lifetime of work. Congratulations.

Yes, the kids need the most sleep. They are trying new things, absorbing a lot of new data, and de facto asking what-if questions. So, although the body rests, the mind remains active. I would postulate that the more organized our sleep becomes, the more creative our next day may be.

Further, if we take as a given that Max Planck’s base units are real (validated in many ways including dividing Planck Length by Planck Time to yield the speed of light), the circadian rhythms are profoundly part of the rhythms of the universe. That idea may well be worth exploring further. By applying base-2 notation to the Planck base units, we encapsulate the universe within 202 notations. Yet, simple logic tells us that only the current notation, Notation 202, is directional and asymmetric. The other 201 notations are complete and symmetric. My simple guess: Sleep, using the metaphor of recompiling, establishes a certain symmetry each day with and within our universe.

I often wonder if there is anybody within the scholarly sleep community who is asking such silly questions and who are attempting to couple it with the current dialogue about the very nature of time.  Thank you.

Most warmly,


PS. You look like my kid sister and project such a warmth and gentle spirit, I thought you wouldn’t mind my looking in on your work to further push my questions about circadian rhythms!  Thanks. -BEC
PPS. I hope your trip to Adelaide happens this year. Disdain for the cold is a sign of maturity!

Carroll, Bonnie

Bonnie Carroll
Founder and Chief Executive Officer
Information International Associates, Inc. (IIA)
Oak Ridge, Tennessee

Secretary General, CODATA

Executive Director of CENDI, the federal scientific and technical information (STI) managers’ group of 12 Federal US STI programs

First email: Oct 25, 2020, 3:40 PM

Request for SI and ISO names for the six groups from the Yoctosecond to the Plancksecond

TO: CODATA Executive Committee
Dear Ms. Bonnie Carroll:

We are doing an analysis of the range of natural groups from the Yoctosecond down to what we call the Plancksecond at Planck Time.

We would like to make a formal request of the CODATA Executive Committee to consider meeting to name those six logical groups between the yoctosecond and Planck Time.  Thank you.

Most sincerely,

Bruce E. Camber

PS: My report online is here:
“The measurement of the Zeptoscond, just one sextillionth of a second — that’s a trillionth of a billionth of a second — is work led by a laser physicist, Martin Schultze. It is truly a measurement by devices, not just a mathematical calculation, and Schultze steps us back into Notation-74 to Notation-77 within our horizontally-scrolled chart.

“On to Planck Time. As fast as it is, that zeptoscond is still rather slow when compared to 10−44 seconds given within Planck Time. Next will be the Yoctosecond (10−24), just one septillionth of a second (10−24). Within our chart, the Yoctosecond ranges from Notations 65-to-67.

“No Names. The actual words for the next six categories (or groups) down to the Planck scale do not yet exist. Hardly trivial, until each group has a name, they have a limited identity and study of them is more difficult.

“The last International System of Units (SI) categories to be added were in 1991. It may well be time to call them back together again. They need to name those next six new groups: 10−27, 10−30, 10−33, 10−36, 10−39, and 10−42 seconds. Planck Time at 5.391 16(13)×10^-44 seconds is within the 10−42 seconds’ expansion. It could be named a Plancksecond or PlanckSecond. To date, that combination of words has only been used casually to refer to an extremely short period of time.”


This letter and reference later became the basis for this page:

Grossberg, Stephen

Stephen Grossberg
Wang Professor of Cognitive and Neural Systems
Boston University
Boston, Massachusetts

Articles: special Issue in Honor of the 80th Birthday of Stephen Grossberg, 2019
Digital Bibliography & Library ProjectDBLP
Google Scholar
YouTube:  Solving the Hard Problem of Consciousness, International Neural Network Society, 2017

Memories: In 1979 I made references to you and your work for a display project under the dome of Building 7 at MIT
2. Gian Carlo-Rota:
3. Nonlinearity:  “…where he first conceived of the paradigm of using nonlinear differential equations to describe neural networks “

 First email: 18 October 2020

Dear Prof. Dr. Stephen Grossberg:

My instincts were right; about 40 years ago, when we were young, you were perhaps the youngest scholar included in my little display project at MIT. Today, in reviewing your website, you have given me a lot of work to do! Sensational. You never slowed down — how entirely prodigious — and, you are still going strong.

Congratulations! I have come back around to you because I just wrote this paragraph within my top-level post:

I said, “Consciousness is also a fact. We assume it is within the earliest sixty notations. Back in and around 2016, our guesses for consciousness was that a primitive consciousness might emerge as early as Notation-48 and that domain could be considered a place for the introduction of a type of fluctuation. We are now researching to see if there may be a better nomenclature already established to distinguish the emergence of various kinds of fluctuations. At Notation-48 there are 2.2300745×1043 scaling vertices. It may well be the area in which we begin our search for the first manifestations of a gap integral to creating a system for the five most primitive perceptions”

The story begins at the top of that posting:

I’ll be working on that posting for a few weeks to tighten it up. But, the basic premise may well be all wet! I’ll be searching among all your work to see if it helps clarify issues. 

Yes, it has been many, many years and I am looking forward to being reintroduced to all your work that I can find online.  Thanks.



Benacerraf, Paul Joseph Salomon

Paul Benacerraf

PublicationsWhat Mathematical Truth Could Not Be in Benacerraf and His Critics, A. Morton
_____________ and S. P. Stich, eds., Blackwell’s, Oxford, 1996, pp 9-59
_____________ Philosophy of Mathematics, with Hilary Putnam, CUP l983

References within this website:  Password: Infinite:
• Consider PBS Crisis in the Foundation of Mathematics | Infinite Series, Oct 19, 2017

First email: Wed, Jul 22, 2020 @ 3:27 PM

Dear Prof. Dr. Paul Benacerraf,

I often start letters to people with your background, “Now, I am so old I remember many lectures with Quine and Putnam, even a spirited dinner with them at Quine’s Beacon Hill home.”  …but you have me beat by 16 years.

I apologize for my rather stupid questions for someone of your history and caliber:
1. Is your commonsense view of space and time ostensibly Newton’s absolute space and time? 
2. If not, how do you characterize your understanding of space and time?
3. Wasn’t David Hilbert’s commonsense view of space and time ostensibly Newton’s absolute space and time?
Thank you.


PS. Behind a security wall, I have placed a reference to your work with Hilary Putnam, Philosophy of mathematics, as well as Hilbert’s article, On the infinite.

Is time discrete?

RE: An experiment to test the discreteness of time (ArXiv, 16 Jul 2020)

TO: Andrea Di Biagio (La Sapienza), Marios Christodoulou (Oxford), Pierre Martin-Dussaud (Aix-Marseille Univ, Université de Toulon)

Third email: Monday, November 9, 4:11 PM

Dear Andrea, Marios, and Pierre (AMP),

Of course, you know if you can “prove” that time is discrete, you will be have knocked off Newton’s absolute 333 year hold on our commonsense worldview! Your doctorates will be legendary, you’ll be welcomed anywhere for your postdoc, and fame will follow!

So, without question, I’m fascinated to follow your budding careers.

I have updated our page on discrete time (this page) and will continue to do so as I learn more from you. If you followed some of those links that were in the past two emails, you know we recognize how entirely idiosyncratic our work is. John Baez told us in 2012, but Frank Wilczek found it curious that high school people were asking such unusual questions with such little background. Freeman Dyson had been an old acquaintance back when I first met him in 1977. He always encouraged anybody who was thinking, yet in 2012 he thought we had not accepted some of the cherished first principles of physics (probably because we didn’t know what they were).

I continue our efforts here with these two works in progress:

  1. which is titled, Work Toward a Mathematically-Integrated Model of the Universe
  2. titled, The Expansion of this Universe. Not too modest, it needs a lot of help. If any of you or all of you think there is any hope for that article, I would welcome your insight and advice.

I wish you three well, the best of all insights and the special gifts of this world (I am a classic older one, i.,e. wine-women-and-song).



Second email: Monday, November 2, 6:41 AM

Thank you for your response to my rather oblique note (just below). By studying your experimental designs, you’ll teach us about discreteness! Sir Isaac Newton may learn a few things from you all as well. And, I am sure your work will help us with our own ideas and models about time’s discreteness.

What we have is a simple geometry (embedded geometries), which took us down to the Planck scale. We then adopted Max’s numbers and turned around to emerge within 112 doublings back up into our classroom. Because we were so surprised with that circular journey, we just continued to multiply by 2 until we were at the approximate size of the universe. We had some help from a NASA mathematician and the Hubble’s measurements. We were even more surprised that it took only 90 more additional doublings, just 202 notations in all. Too cool to let go, we wrote it up: and thought we’d get a pat on the head from the STEM folks (and thought, “Maybe they’ll publish it as our letter to the editor in Scientific American.” But, no, everyone essentially asked, “Why?” or said, “So what.”

Hardly a theory, it is a bunch of very interesting progressions.

When we finally followed Planck Time out alongside Planck Length in 2015, it certainly seemed a bit more compelling. It just prodded us further, “What do we do with this cache of base-2 progressions? Is Euler pushing us (and the universe) into a fundamentally exponential order?”

Having lived with these progressions for a few years (and knowing how entirely idiosyncratic they are), I pulled our project out of the high school curriculum. We could image our best and brightest trying to explain it in their sophomore physics and astronomy classes! Now we only look for work like yours that might be doing something to help us interpret our little multiplication-and-division-by-2 STEM project.

Obviously, your work is important to us. In our simple model time not only appears to be discrete, but necessarily linked to space, an aspect of light, and within a most intimate family with mass and charge.

So that little reference to your ArXiv research sparked my interest.

You’ve got a groupie! I believe your work can help us understand our own work better!

Our numbers are 100% predictive; they exhibit a simple and sweet logic. …but, are they really logical? In the face of all that is big bang cosmology, I (and a few others) think these numbers are especially logical.

Closer to Pythagoras than to Hawking, may we be a “Greek chorus” and sing your praises hoping that you don’t mind having some folks look over your shoulder! Thanks.

Best wishes indeed,

RE: An experiment to test the discreteness of time –

TO: Marios Christodoulou, Andrea Di Biagio, Pierre Martin-Dussaud

Did you know that there are 202 base-2 notations from the Planck base units to the current day and size of the universe?

To follow the numbers:

Beginnings: We’re just a bunch of high school people exploring a tetrahedron and the octahedron and tetrahedrons within it, and so on down.

112 steps to the Planck Length:

Current explanation:

Tong, David

David Tong
Department of Mathematics and Theoretical Physics (DAMPT)
Cambridge University, Wilberforce Road
Cambridge, England

ArXiv (99)A Matrix Model for WZW (2016), DBI in the Sky (2004)
Google Scholar
Video:  YouTube Quantum Fields: The Real Building Blocks of the Universe, The Royal Institution, 15 Feb  2017

Most recent email: September 30, 2020

Dear Prof. Dr. David Tong:

Just over three years ago I sent a  little note after listening to your 2017 Royal Institution Faraday Lecture. Today, I pulled from my shelf a periodical, Fields Within Fields…Within Fields, that back in 1970 in NYC, Julius Stuhlman gave me. He was the founder of the World Institute Council and the Publisher of a Fields Within Fields… Within FieldsDr. Ervin Laszlo was part of his entourage of writers.

There were people who would cheer and support your work even before you were born!

Of course, we’ve had the benefit of Frank Wilczek’s work to exegete the 1899 insights and calculations of Max Planck, along with Max’s 1905 publication of The Theory Of Heat Radiation, and the 1914 English translation with Morton Masius.

My questions are few:
1. Can we take the Planck units as a starting point for the universe?
2. In the spirit of John Wheeler and his quantum foam, is there any possibility that it could instantiate as an infinitesimal sphere?
3. If so, might that sphere inculcate all the dynamics of cubic close packing of equal spheres

I will include an updated copy of my earlier note. As I continue my studies of your work, I will build on those references to your work and to my notes here:

Again, I thank you for your most formidable work, truly an inspiration.

Most sincerely,


First email: June 30, 2017, 9:13 PM

Dear Prof. Dr. David Tong:

What a lovely thing to do on Friday evening — I listened to your Faraday lecture* about magnetic fields. Excellent. It has taken awhile to appreciate the deep mysteries of our electromagnetic fields. Perhaps Planck’s 1899 insights that opened the way to his Planck base units of Time, Length, Mass and Charge might open some interesting, even deeper explanations.

It has taken awhile for Planck’s work to be appreciated. Even Planck ignored his base units. Frank Wilczek seemed to open the door and turned on the lights in 2001 with his Physics Today three-part article, Scaling Mt. Planck. It took the naivete of a high school geometry class to drill down inside the tetrahedron and octahedron the 45 steps to the CERN-scale and 67-additional steps to the Planck scale. Multiplying by 2 was easy. In just 90 steps we were in the range of the Observable Universe and the Age of the Universe! The infinitesimal scale went from Planck’s numbers to the 67th doubling. The human scale went from Notation-67 to Notation-134. And, the large-scale went from from Notation-135 to 202.

That’s all there is: 202 doublings, notations, steps, layers, groups, clusters sets… from the Planck Time to the current Age of the Universe, right now, this second.

Perhaps science visualizes the waves, fluids, bundles and fields a little too quark-like. Perhaps if we were to start at the Planck units and follow that simple multiplication by 2, each doubling being the power of 2, we are given 67 new layers to explore! Wouldn’t that be novel? …even fun? The CERN-scale is just so gross.

What might we do with all that math? If we start simple, and we also start with a few scaling vertices, perhaps we can build all the mathematics and geometries and spin that we need… Fields Within Fields Within Fields.

Here’s all our sweet, little math:
Horizontally scrolled:

Novel. Fanciful. But, is it useful?

To date, it is a simple STEM tool with many open questions. Obviously it is not a big bang but a quiet expansion and rather natural inflation that is  entirely predictive as it defines the cosmological epochs. Thanks.

Most sincerely,

* Quantum Fields: The Real Building Blocks of the Universe, The Royal Institution (London)

Page, Don Nelson

Don N. Page
Institute for Theoretical Physics, Department of Physics
University of Alberta
Edmonton, Alberta

ArXiv: Possible Superluminal Propagation inside Conscious Beings (Jan 28, 2020), Cosmic Mnemonics, Douglas Scott, Ali Narimani, Don N. Page (2013), Anthropic Estimates for Many Parameters of Physics and Astronomy, Don N. Page, Alberta  (2017)
AIP Interview by Alan Lightman
Google Scholar
Homepage (OEIS, Univ. Alberta)
Video: Closer to the Truth   YouTube

References within this website:

Most recent email: 29 September 2020

Dear Don,

Thank you. I am most pleased to get reconnected. And, now that I have stopped long enough to read more deeply into your history, your work, and background, I am honored to know you.

Now, I should tell you that we have family all throughout Alberta. When I was a young teenager, we visited my old great-uncle, John Muir. He was a wildcatter, literally and figuratively. He married a woman whose roots in that area went back hundreds of years. Uncle John was truly a character among characters. …so many stories… There is a strain of those Muirs that runs in the family and runs in my work so I’ll always be open to criticism, even rebuke. Paul Simon’s 1975 song, “Still Crazy After All These Years,” resonates.

I now have a page of references to you: 

Every reference posted is my current de facto homework assignment. Your work will inform my work. Yet, by now, you’ve realized that I have that bias to start to build with the most fundamental concepts. I already have read enough to know that you do, too. When I have grasped enough of your work to be dangerous, I’ll send along some comments. Thanks again for your scholarship and your lifetime of work.

Most sincerely,


PS. Long ago, I set aside Alan Lightman’s December 2012 Harper’s essay,, What Came Before The Big Bang? and, of course, now rediscover the reference to you and your faith. With Cosmic Mnemonics and Anthropic Estimates for Many Parameters of Physics and Astronomy, there is already so much to discuss. Thanks again for those recommendations.  -BEC

Email: Saturday, July 23, 2016 at 4:28 PM
Dear Prof. Dr. Don Page:

There are so many questions I would like to ask you, but I do not want to waste your time with my lack of depth.

Our work comes out of a high school in New Orleans; it is an idiosyncratic construction of the universe using base-2 exponential notation starting with Planck’s base units and goes out to the Age of the Universe in 202 notations.

The first 67 notations, taken as a whole, open paths from the Planck base units to current research. This model of the universe seems to be more liberating than the big bang in as much as it introduces time symmetry, notation by notation. And most importantly, it opens a very different view of the finite-infinite relation. The entire universe adopts a deeper sense of charm and flavor.

Would you take a look and could you tell us why we are so far off?

With great thanks,



First-known email: Monday, November 29, 2010 

Dear Don:

Bill (Williams) introduced us through email a couple of years ago. Are you a close friend?

Did I read correctly that Bill died in February 2010? Do you have any details? Thank you so much.



Collins, Francis

Francis Sellers Collins
National Institutes for Health
Washington, DC

Awards: Presidential Medal of Freedom, National Medal of Science, Pontifical Academy of Sciences, The Templeton Award
Books: The Language of God: A Scientist Presents Evidence for Belief.
CV (41 pages, last update 2013)

Note: Many articles make references to Collins. For my own edification, I specially note the work of Don Page (Alberta), Does God So Love the Multiverse? (2008) (PDF)

2021 recent email: January 30, 2020, 12:25 PM

Dear Dr. Francis Collins:
In the darkness of these days and our times,
we all need an attitude adjustment. For most,
believing in God’s grace and God’s light is too
big a jump. I just ask all my atheist friends
(seems it’s cool to be an atheist these days), my
Democrat friends and my Republican friends,<
“Just break out of your solipsistic nonsense, get
over your enduring narcissism, spare me of your
nihilism, and please stop fooling around with
all that dystopian madness.”

Worldviews are so yesterday.
We all need a highly-integrated view of the universe!” 

March 14 is coming up soon. It’s pi day and in
my slowly-emerging model of the universe,
pi is pivotal:
(Y’all can have a little laugh at my expense.)
It’s OK.

Notwithstanding, I send you my warmest
thoughts for the continued success of all your work.
Poor Dr. Fauci; he seems so lost without you.

Again, best wishes,

2020 email: August 20, 2020, 4:47 PM

RE: Congratulations indeed! The Language of God has 2020 vision.

Dear Dr. Francis Collins:

Congratulations on winning the Templeton Award! Outstanding. Legendary!

It has been over seven years since we’ve communicated, yet I now have several references to you within my evolving website:

I’ll be updating these pages and I will be developing a primary page of references. Best wishes with your work to grasp and control all the parasites and viruses and other pathogens of this world!

Best wishes,

2014 Email: 7 February 2014, 4:04 PM

Dear Dr. Francis Collins:

As a sequel to the Big Board-little universe, you might find this of
some interest:

Your most critical comments would be profoundly appreciated.


2013 Email: Thursday, April 25, 2013 6:31 PM

Dear Dr. Francis Collins:

Thank you for your work to bring new light to old belief systems. Your book, The Language of God, is on my bookshelf. That you are a profound Christian thinker is obvious. That you have been profoundly criticized by the best of the atheists is also quite obvious.

Most atheists do not have answers to some rather simple questions about life.

In December 2011 I was helping a high school teacher, part of our extended family, to engage his students in base-2 exponential notation applied to the smallest and largest known measurements within our physical world. We started with the Planck :Length and went out to the Observable Universe. Both measurements are well-known but base-2 notation had not been applied to that range. We discovered 202.34 notations (doublings, layers or steps) by simply multiplying the Planck Length by 2 and then multiplying each result by 2 until we reached the largest measurement.

It is a different kind of ordering system than base-10 because its granularity has a parallel construct to many processes in chemistry and biology.

Is it useful? Should it be encouraged? If you would like to take a look at some of the discussions around it, some of our work is posted here:




Overduin, James

James Overduin

Towson University, 8000 York Road, Towson, MD 21252

Articles: What If There Were No Gravity? – Scientific American
ArXiv: Waves and causality in higher dimensions with Paul S. Wesson .
——Scaling Relations for the Cosmological “Constant” in Five-Dimensional Relativity, 2014.
——Finite cosmology and a CMB cold spot, 2006
Book(s): Principles of Space-Time-Matter: Cosmology, Particles and Waves in Five Dimensions with Paul Wesson
Google Scholar
Homepages (Towson)
YouTube: Why do we need a single theory of physics?

First email: 18 September 2020

Dear Prof. Dr. James Overduin:

Your significant work with Paul Wesson has come to my attention. I must say, “Congratulations.” You did so much work together I had to create a reference page just to keep things straight:

Now I am hoping that you can help interpret your colleague’s quote within a Wikipedia article about the Planck units. Though I am not a scholar, I do ask questions about the presuppositions that we all bring to bear on any conceptual frame of reference. I have four:
1) What is the assumed understanding of the nature of time? …of space?
2) What, if anything, is assumed about the finite-infinite relation?
3) How is light defined?
4) How are quantum fluctuations defined?

Of course, these questions are never easy to answer and finding even a semblance of an answer is often difficult.

With all your work, I am confident there is clarity within all four areas and that information will help me to understand Paul Wesson’s comments about the proper handling of the Planck units.

This particular track of my work began back in 2011 in our high school geometry classes where we were examining how tetrahedrons and octahedrons can readily tile and tessellate going within smaller-and-smaller and going out larger-and-larger. We got carried away using base-2 notation. We also got carried away with Euler and Zeno and Planck… and, yes, also with pi, spheres, sphere stacking and cubic close packing of equal spheres.

We mapped the universe! Now it is time to reel it in and get real.

I need another week or so with all your writings so I can frame my questions most carefully in light of your joint work with Paul Wesson. Would you object to another email sometime soon? Thank you.

Most sincerely,


PS. I’m working to tighten up (at least a little) this article: