2.
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? ________________________________________________________________________________________
The simple conceptual starting points Wikipedia on the Planck length |

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.

TOUR #1. NEEDS EDITING. BENEFITS STATEMENT

REGARDING PRODUCTIVITY, INSIGHT AND OPTIMISM.

The universe is mathematically very small:

http://doublings.wordpress.com/2013/07/09/1/

TOUR #2. The very small scale universe is amazingly complex.

Assuming the Planck Length is a singularity of one vertex, consider

the expansion of vertices. By the 60th notation, of course, there are

over a quintillion vertices and at 61st notation well over 2 quintillion more

vertices. Yet, it must start most simply and here we believe the work

within cellular automaton and the principles of computational equivalence

could have a great impact. It’s mathematics of the most simple. We also

believe A.N. Whithead’s point-free geometries should have applicability.

Key references for more: http://doublings.wordpress.com/2013/04/17/60/

TOUR #3. This little universe is readily tiled by the simplest structure.

The universe can be simply and readily tiled with the four hexagonal plates

within the octahedron and by the tetrahedral-octahedral-tetrahedral chains.

Key references for more: http://bigboardlittleuniverse.wordpress.com/2013/03/29/first/

TOUR #4. And, the universe is delightfully imperfect.

In 1959, Frank/Kaspers discerned the 7.38 degree gap with a simple

construction of five tetrahedrons (seven vertices) looking a lot like the Chrysler

logo. As I said in the restaurant, we have several icosahedron models with its

20 tetrahedrons and call squishy geometry. We also call it quantum geometry

(just in our high school) and we guess, “Perhaps here is the opening to randomness.”

Key references for more: YET TO BE WRITTEN

Future tours: The Planck Length as the next big thing.

Within computational automata we might just find the early rules

that generate the infrastructures for things. Given your fermions and proton

do not show up until the 66th notation or doubling, what are we to do with those

first 65?