Birthday: Saturday morning, August 25, 2018

These reflections are for my friend, Charles, who celebrates 70 years today.

Ode to a birthday and that simple song

It started this morning even before getting out of bed. “We have to go over this just one more time. We are all missing something.”  Thinking. “With so many years of memories, so many details, why do we have such a problem understanding the meaning and value of life?”

Yes, let’s go over this just one more time.

Because you, my friend, turn 70 today…

octahedronI write.  “Remember ten years ago? How could you ever forget that very strange 60th birthday gift? It was a clear plastic octahedron with eight triangular faces. That is, octa, the Greek root word for eight and hedron, a sister word, for face. 

A puzzle and brainteaser: What has eight sides that can define four hexagonal plates with it?”

And, your answer please. Nobody knows the answer, but every elementary school student should. It is one of the most simple geometrical models in the universe. We all should have grown up with this model, yes, way back in kindergarten, right alongside all our blocks and squares. It just so happens, however, the triangle is much more basic than a square and it appears in everything.  Here is the most simple interior parts of  one of the basic solids defined by Plato back around 350 BC (as found in his writings, Timeaus), and all we still know so little about it.

octahedronA Game. That model is a game and indeed it defines the most simple interior parts of a basic-basic solid that makes up everything. There is a lot to learn from this game. Within, it has six half-sized octahedrons, one in each corner, and eight tetrahedrons, one in each face. All fourteen pieces share the common centerpoint. Four hexagonal plates, here all outlined with a different color tape, surround that centerpoint. Each of the fourteen pieces has at least one color on an edge.  If you empty the contents and attempt to recreate the simple color configuration of those four plates, it becomes very tedious. There are so many possible combinations; and like anything taken apart, it is not easy to put it back together again. Colors do not readily match up.

Sphere to tetrahedron-octahedron couplet

Yes, by the time we turn 60, our colors do not easily match up.  Those four six-sided plates, given within every cell, every genome, and every atom of our being, represent a perfection that gives us balance and stability.  At every level, and residing even more deeply within the core of our being, simple symmetries give us balance. And nestled all around those structures are innumerable spheres from which these simple, basic shapes emerge. The spheres are the transformations between the finite and infinite.  We have to re-engage the infinite because it has become so tainted by religious beliefs and fanatical behaviors that should not follow from simple continuities and symmetries.

What? How? Huh? We are not getting something basic about the logic, the numbers, and the geometries that define who we are and why we are.  So, my friend, until our dying days which will now be sooner than later, let us be going over this one more time. Let’s examine the logic, the numbers, and the geometries that define us. Just maybe, we might truly discover who we are and the meaning and value of life.

Birthday Gifts:  There will be more unique pages coming out of this dialogue, yet for now I must refer you to these three pages:
• Numbers: On Constructing the Universe from Scratch –
• The parts: How to find the essential universe –
• The whole: The universe by the numbers –
• New (to be completed soon): What is a number? –


Google: It’s Leonard Bernstein’s 100th birthday today!

Background. I’m so old I’ve actually had a conversation with Bernstein up at Tanglewood, well behind the scenes. I had accompanied Cynthia Carpenter, the organist and choir conductor of our church. She was in Bernstein’s special conducting class that summer and they had a reception for all the students and their guests one evening so everybody might have a chance to chat.  Even at that time, I was hung up about continuity and symmetry begetting harmony. It defined the infinite, a moment of perfection. We ever-so-briefly talked about it.

Bernstein grew up in Lawrence, Massachusetts.  I grew up in Wilmington and had a home in Andover, a sequence of abutting towns, so I felt some continuity with the man. His passion for music rolled over into a passion for education and integrative systems. He could feel the atonement within the power of music, and the result was his thrust for education, Artful Learning. And, that is the thrust of and of life itself.


@brainpicker Maria Popova

I also sent a note to Maria Popova this morning.  She was in that Google mix; I said:
@brainpicker Ode to a birthday and a simple song… Writing to a dear friend who turns 70 today, I discovered Google’s 100th birtday tribute to Bernstein. I met Lenny; we talked at Tanglewood, well behind the scenes. I’ll write about it all here:  Thanks.

Life is good.  Today we have resources unimagined just years ago. In 1959, I dreamed of the web. I was twelve years old. I was in elementary school and wanted to be able to ask the smartest people questions about anything at anytime from anywhere. My father was a machinist and my mother, a cake-decorating policewoman for school patrols. We had moved out of the big city (Boston-Cambridge) to a little suburb and we had three acres to call home.


A day, a week, a month, and a year: What is time?

I really am beginning to think that we’ve got it all wrong. Sir Isaac Newton taught us that time was absolute and goes on forever. Yet, Einstein (and now many others) had a different perception. Even back in Newton’s time, he was carrying on a long-distance communication (letters) with Gottfried Leibniz and they debated the issue. Leibniz died before they finished, so Newton got the upper hand. But, I am rather sure that Leibniz was closer to the truth, “Time is a relation.” Einstein and his foremost mentor, Max Planck, defined it that way.

Time has a beginning and its end is right now, today, this very moment. The best we can determine is that first moment was defined by the Planck base units and the entire universe is based on, and defined by, these units. Here is a mathematical model that uses the Planck base units and defines a dynamically expanding, simple, logical, highly-integrated universe where music best captures the essence of its many perfections.


A year, ten years, and then every ten years

Celebrate good times, come on.  There’s a song for virtually every emotion, but there are very few analyses of the power of music and the place and power of each number and each year of our life.


Presents to you this year still under construction:

1. Music.  I am now following the work of a professor at the Sorbonne who assures me that he is at the base level of life with his understanding of sound and music. I’ll be working with him and his doctoral students to see how it all mixes with all of our numbers and geometries! You’ll be the first to receive a new chart of numbers that results from it all.

2. Refine the Octahedron.  Your 60th birthday present was the beta model. Now it is incumbent on me to make a production model for the schools. You’ll be getting one of  the first ten off that production line.

3. Charts of numbers.  You have witnessed the evolution of the charts over the years. Now, several charts will emerge for classrooms around the world. Again, you’ll be among the first to get your own signed copies to decorate your office or to donate to a school.


“Happy Birthday to you, Happy Birthday to you,
Happy Birthday, dear Charles, Happy Birthday to you