# Scholars Pointing Us In The Right Direction**

## 1. Leonhard Euler. Can his “identity” be extended to the universe?

Euler’s insights, particularly his introduction of exponential functions and his study of infinity, make him one of our key scholars to study.

In that light, Euler’s identity from 1748 may be larger than currently understood.  Physicist Richard Feynman called it “our jewel… the most remarkable formula in mathematics.”

[1] Do we live in an exponential universe? Let us reopen historic discussions, the most enigmatic being the finite-infinite relation. More…

The most beautiful equation in mathematics:

See Nahin’s  comment about “exquisite beauty.”

We started working on our chart in 2011. It is simple, granular, natural, and symbolic.

[2]  Other scales of the universe also work, yet the most informative begins at the Planck Scale and goes to the current Age of the Universe. That creates a parts-whole simple logic. Also, if the dimensionless constants do not work within a scale of the universe, we need to examine the nature of logic and numbers. If we were to take this chart. as a given, there are many substantial observations to make. The biggest is that our physical universe is finite and derivative. Planck Time becomes the first moment of the universe. Going up to the current time, that range defines the Age of the Universe. So, I believe it is long overdue that we all revisit Sir Isaac Newton’s absolute space and time.  It has been our “commonsense” view for centuries and I believe it has been truncating our scholarship since the 1687 publication of his Principia.

I struggled with this conclusion, but this chart of simple calculations opens a new perspective.  My struggle.The chart. Why now?

## 2. Gottfried Leibniz: The relation is the primary real.

His debate with Isaac Newton was never concluded. Leibniz died; Newton got the upper hand. In our time over 300 years later, let us re-engage the old debate. Academics around the world have discounted Newton’s absolute space and time, yet it still dominates our commonsense logic. Any proposed alternative will necessarily stretch our imaginations. A discrete, finite, quantized understanding of space and time, necessarily fully configured with light throughout all 202 notations, will be a challenge for all of us.  To open up the infinite and infinity will also stretch us in ways we never imagined. We are on the edge of saying, “Everything is a mathematical relation and all mathematical relations are related.” Numbers.  Notation by notation.  The chart.  More.  And more.

## 3. Max Planck: His equation for light is the most basic.

Planck’s formula for Planck Time uniquely binds light (c) and the Planck Length. It seems more basic than e0=mc2 by Einstein because when Planck’s simple formula is extended throughout all 202 notations, it redefines space, light and time, and that necessarily calls infinity out to be redefined, too. More…  And more… And more…

## 4. Alfred North Whitehead, Austin Farrer, John Wheeler, David Bohm, John Bell and so many others help us to understand  that space-and-time are not infinite. Continuity, symmetry and harmony are.

I admit to my predispositions about the infinite. I’ve always had this thing for simple perfections within continuity, symmetry and harmony. With Frank Wilczek of MIT, I found a profoundly informed physicist with an open spirit and a touch of humility who is also enamored with those three fundamental concepts.  Yet, long before us, Alfred North Whitehead wrestled with the idea of the becoming of continuity (Process & Reality p. 68 – 9). David Bohm wrestled with the implicate order, John Wheeler with simplicity and John Bell with the inequalities of entanglement.

## 5. Contemporaries Max, Nima, and so many others are  bewildered…

Kill infinity!says one. Ditch space and time! says the other.  The next generation is revolting. My response to these hyper-intelligent, thought-leaders of their generation, “Cool your jets. Let’s first see if we can redefine space-time-and-infinity.”  Within my ignorance of so much of their physics, I cling to John Wheeler’s simplicity. Often closely associated with naïveté, I will be the first to admit that I have a long, long way to go before these concepts are clearly integrated for me. Yet, this simple structure for integration is far more satisfying than any others that I have studied.

***

The near future.  Freeman Dyson disagrees with me. He should. In our first discussion in August of 1978  (in his office at the Institute for Advanced Studies), I did not know about his work to establish the mathematics of renormalization. The whole concept will be reopened in light of the 202 notations. In so doing, our studies of the finite-infinite relation-and-dynamics can be re-engaged in what I anticipate will be significant ways. More…

My next task is to study that history to see if there could be a normalization independent of concepts of space and time yet reflective of all the work (both mathematics and physics) regarding  higher dimensions. The first 64 notations may just add new flavors and special light on some of those old discussions, i.e. superstring theory and its 10 or 11 spacetime dimensions.

A geometry of imperfection and probability come out of our studies of the pentastar (five tetrahedrons sharing a common centerpoint) and the icosahedron (twenty tetrahedrons sharing a common centerpoint). It appears that these same geometries are also responsible for quantum fluctuations. In the study of each notation and how each notation is necessarily derivative of the prior, we will continue to study the nature of these fluctuations. More…

This Quiet Expansion is a clear alternative to big bang cosmology. Although leading academics around the world have discounted the big bang theory, a clear alternative has yet to be accepted by their industry. Here is my proposed alternative based on the simplest math.  More. And more.

## For more:

### Endnotes:

[1] http://www.feynmanlectures.caltech.edu/I_22.html (Note: If this link fails to take you to his lecture 22, Algebra, please advise me. You will find the quote in section 22-6, the third paragraph from the bottom where he says, “We summarize with this, the most remarkable formula in mathematics… This is our jewel.”

[2] Currently called a hypostatic model because it stands under and is the foundation of the foundations of reality. One might assume that it is the basis of realism, isotropy-and-homogeneity and a natural inflation. Those first 64 notations seem to be a predefinition of all possible relations vis-a-vis numbers and geometries.

[3] …trying to stand on the shoulders of giants.*

* Attributed to Bernard of Chartres (12th century), used by Isaac Newton in his correspondence in 1675, and Stephen Hawking as a title of a book in 2002

**…to pursue a deeper, more basic truth and to grow as genuinely as possible in our openness, integrity, and curiosity.” Reading these two lines together expresses my sentiments well. -BEC