Martin Rees – Astrophysicist, Astronomer, Cosmologist

As part of our effort to discern the Top Numbers of Key Importance within our little universe for The Big Board-little universe Project, we have begun to study the work of Lord Sir Martin Rees of Oxford, particularly his book of the title, Just Six Numbers: The Deep Forces That Shape the Universe, 1999, Weidenfeld & Nicolson, London (173 pages)

His six numbers are:

  1. N, the ratio of the strength of the electrical force to the gravitational force (reviewer, Peter Roberts, Visions.
  2. ε (epsilon)( definition of limits?)
  3. Ω (omega), measures the amount of material in the universe
  4.  λ (lambda) (?)
  5. Q,  the degree of structure in the universe
  6. D, the number of spatial dimensions, 3

Here is what Wikipedia says:

Martin Rees’s Six Numbers:

“Martin Rees, in his book Just Six Numbers, mulls over the following six dimensionless constants, whose values he deems fundamental to present-day physical theory and the known structure of the universe:

“N and ε govern the fundamental interactions of physics. The other constants (D excepted) govern the size, age, and expansion of the universe. These five constants must be estimated empirically. D, on the other hand, is necessarily a nonzero natural number and cannot be measured. Hence most physicists would not deem it a dimensionless physical constant of the sort discussed in this entry.

“Any plausible fundamental physical theory must be consistent with these six constants, and must either derive their values from the mathematics of the theory, or accept their values as empirical.”

“A long-sought goal of theoretical physics is to find first principles from which all of the fundamental dimensionless constants can be calculated and compared to the measured values.”

Ben Duronio & Walter Hickey’s Top Ten

As part of our effort to discern the Top Five Numbers of Key Importance within our little universe for The Big Board-little universe Project, we have begun to study the work of these two writers for Business Insider

Ben and Walter give us their very respectable listing of their Top 10:

  1. Pi: 3.1415  Archimedes’ Constant
  2. Euler’s Number: 2.7182 also known as e
  3. The Golden Ratio: 1.6180
  4. Planck’s Constant: 6.626068×10-34 m2 kg/s
  5. Avogadro’s Constant: 6.0221515 x 1023
  6. Speed of Light: 186,282 miles per second or 299,792,458 meters per second
  7. Gravitational Constant (G): 6.67300 x 10-11 m3 kg-1 s-2
  8. Boltzmann’s Constant: 1.380650 x 1023 joule per kelvin
  9. Imaginary Unit: i
  10. Euler’s Identity: e^(i*pi) = -1

David Pegg’s Top 25 Numbers

As part of our effort to discern the Top Numbers of Key Importance within our little universe for The Big Board-little universe Project, we studied the top 25 list of David Pegg, a reporter at The Guardian in England.

Twitter:  @davidtpegg   PGP key from MIT is here.

Of all his top 25 numbers only these are considered:

25.  Pi
Irrational, non-repeating and non-terminating number

24. Euler’s number:  2.718
Irrational, non-repeating and non-terminating number

23. Euler constant

22. Feigenbaum constant: 4.6692
Mitchell Feigenbaum in 1975

19.  0

18.  1

16. The Golden Ratio: 1.6180339887

15.  About number “5”  he says, “According to Pythagoras, the number 5 was the perfect number of human microcosm. Aristotle also added a 5th element to the 4 elements of ancient Greek studies and called it Ether, which has become the basis for most of the spiritual practices of the ancient alchemists. It also has some spiritual significance and symbolism in other cultures, including the Chinese and Japanese Buddhists. This number has also become the basis of discordianism, a jocular pseudo religion popularized by Robert Anton Wilson, which believed that everything that happens in the universe has a connection to 5 or a multiple of five.”

Extremely-Small and Extremely-Large Numbers

Let us start with the two key numbers:
1. The Planck Length: 1.61619926×10-35 meters which is 0.0000000000000000000000000000000000161619926 meters

2. The Observable Universe: 8.79829142×1026meters or 879,829,142,000,000,000,000,000,000 meters

There are many numbers in between the two. Each “0” represents a major base-10 transformation; and within each base-10, there are three or four base-2 notations. Though some say that the Planck Length is a special type of singularity, it has a specific length. Yet, that length is so small, for about 100 years, it was virtually ignored by the entire scientific community. Perhaps a better way of looking at the Planck Length is through the lenses of geometry. If we make it one of Alfred North Whitehead’s point-free vertices of a specific length, each time we multiply by two we grow the size as well as the number of vertices.

The Numbers of Vertices at Key Notations Between 1 and 65. When you assume that the Planck Length is a vertex, unusual concepts flow. First, consider the generation of vertices just by multiplying by 2, then each result by two, over and over again. By the tenth doubling there are 1024 vertices. By the 20th doubling, over a million more are added. On the 30th, another billion+ are added. Then, comes another trillion+ at the 40th, a quadrillion+ at the 50th notation and a quintillion+ at the 60th. At the 61st there are another 2+ quintillion vertices added. These vast arrays and systems of vertices cannot be observed.

This is the domain of postulations and hypostatizations. Consider this concept: going within from about the 65th notation, the domains begin to be shared. More and more is shared by everything as the Planck Length approaches. Each notation organizes uniquely, yet within groups. And these natural groupings reflect all the diversity within all the notations 65 and higher. It seems that the mathematics of cellular automaton may figure into the first 20 or 30 notations. We start with the most basic Forms, then Structures, which become the pre-structure for Substances, archetypes for Qualities, then Relations, then the Mind. We turn to systems theory, group theory, and set theory to discern the order of things.

Perhaps there are five hot spots for immediate research:
* Notations 1-20 and the foundations of cellular automaton and fractal geometries by using the functions created by more than one million vertices
* Notations 50-60 and the foundations of the Mind, logic, psychology, memory, thought, epistemology and learning with over 500 trillion vertices at the 59th notation and then another quintillion+ vertices within the 60th notation.
* Notations 60-80, the emergence of the particles and atoms and the most basic structures of all physical matter
* Notations 100-103, the emergence of the human life and most all life as we know it
* Notations 135-138, the transition to the Large-Scale Universe with the possibilities of uncovering pathways to the Einstein-Rosen bridges and tunnels also known as wormholes.
Key references for more: The numbers

Facts & Guesses. The Facts are what is measurable and what fits within each domain. The Guesses are about what goes on with those domains (aka steps, notations, layers or doublings) especially those that remain blank. Is there a pattern, especially a cyclic pattern that manifests in another notation? We followed Max Planck where he took the constants of nature, starting with the speed of light to calculate the smallest number. We took the age of the universe, with some help from scientists, to learn the largest calculation of a length, the Observable Universe. Making sense of these numbers is another story. So, over the forthcoming weeks, months and years, we will be looking even deeper. Would you help us now and take the little survey?

More notes about the how these charts came to be:
1Three downloads authored by Prof. Dr. Frank Wilczek: Scaling Mt. Planck (from Columbia University), C. Alden Mead’s letter and Wilczek’s response in Physics Today, and Wilczek’s August 2013 Lecture notes on units and magnitude (If you like this paper, also read this one).

The simple conceptual starting points
An article (unpublished) to attempt to analyze this simple model. There are pictures of a tetrahedron and octahedron.
A background story: It started in a high school geometry class on December 19, 2011.
The sequel: Almost two years later, a student stimulates the creation of this little tour.

Wikipedia on the Planck length
Wikipedia on the Observable Universe

Take it as a given that it is also a vertex. By the second doubling, there are four vertices, just enough for a tetrahedron. By the tenth doubling there are 1024 vertices. The number doubles each notation. By the 20th doubling, over a million more are added. On the 30th, another billion+ are added. Then, comes a trillion+ at the 40th, a quadrillion+ at the 50th notation and a quintillion+ at the 60th. At the 61st there are another 2+ quintillion vertices. What does it mean?

The simplest geometries yield a deep-seated order and symmetries throughout the universe. Those same simple geometries also appear to provide the basis for asymmetry and the foundations of quantum fluctuations and perhaps even human will.