The first Big Board-little universe chart, December 2011

Scroll down below these basic geometries to see the listings within this original chart.
Tetrahedron Hexahedron Octahedron150 ______ Dodecahedron151 Icosahedron151 TOT151
Start in the center-left column below. All units of measurement are based on the Planck Length. On the left going down the numbers are divided 101 times by two until the measurement is the Planck Length, considered the smallest unit of a length. In the center-right column, the same measurement is multiplied by two. In 101+ steps we are out to the edges of the observable universe. Assume the simplest three-dimensional form defined by the fewest number of vertices is the tetrahedron. Notice how the the basic Platonic structures nest within each other. Necessarily all structure of every manifestation within the known universe can be interrelated. There are blanks for students to find answers from examples within their studies, especially biology, chemistry, physics, astronomy and astrophysics. Students are also invited to correct mistakes.
Basic Questions and Structures, and Form-and-Function: Could all structures be in some way derivative of the five basic solids discussed by Plato and the Greeks (circa 360 BC)? If that concept is taken as a given, then questions about form and function can be re-engaged. Perhaps base-2 exponential notation is a place to start. Though apparent throughout the sciences, these five basic solids have not been used to develop an integrative model for human knowledge. Perhaps this is a step in that direction. Most academics today cannot tell you what is most simply contained within a tetrahedron or octahedron (by dividing the edges in half and connecting the vertices). Pictures below illustrate some answers. It seems that simple mathematical operations can still open new paths and logic to explore. More…
Tetra151 Cuboctahedron151 Octahedron151 ___ Hexacontagon151 Icosahedron151b TOTINside151
GENERAL
DISCIPLINES
(and Scale)		 PLANCK NUMBER. EXAMPLES
(within ±50%)		 DECREASING IN SIZE, Get smaller, divide by 2 (Center left column) ___
INCREASING IN SIZE, Get larger, Multiply by 2 (Center right column)
PLANCK NUMBER. EXAMPLES
(within ±50%)
 GENERAL DISCIPLINES
(and Scale)
HUMAN SCALE 101. Range: Human Hair 40.9755356 microns ___ Around 40 microns 101. Thicker Hair HUMAN SCALE
BIOLOGY 100. Sperm cell diameter 20.4877678 microns 81.9510712 microns 102. Thickness of paper MANUFACTURING
Cytology 99. Diameter of average human body cells 10.2438839 microns
or 1.02438839×10-5m		 .163902142 millimeters
or 1.63902142×10-4m		 103. Egg cell diameter ___
Microbiology 98. Diameter of average human capillary 5.12194196 microns or
about .0002 inches		 .327804284 millimeters 104. This period. Got it? ___
97. Red blood cells~2.4 µm 2.56097098 microns (µm) .655608568 millimeters 105. Large bacterium Bacteriology
Bacteriology 96. Rather small bacteria and red light (1.28 µm) 1.28048549 microns or 1.2804854×10-6 m 1.31121714 millimeters or 1.3112171×10-3m 106. Large grain of sand ___
Nanotechnology 95. Range of visible light ~ 400 to 1000 nm 640.242744 nanometers 2.62243428 millimeters 107. A small ant Myrmecology
___ 94. Nanoparticles ~ 10000 to 100 nm 320.121372 nanometers 5.24486856 millimeters (around a quarter inch) 108. Very small objects that we can still handle PHYSICS
___ 93. Thickness of gold leaf ~125 nm 160.060686 nanometers 1.04897 centimeters or 1.04897375×10-2m 109. Often parts of common small objects CHEMISTRY
___ 92. Nanowires 80.0303432 nanometers 2.09794742 centimeters 110. Rather small things ELECTRONICS
___ 91. Semiconductor chip 40.0151716 nanometers 4.19589484 centimeters 111. A spoonful TECHNOLOGY
Virology 90. Virus range 20.0075858 nanometers 8.39178968 centimeters 112. Anything 3.3 inches! BIOLOGY
___ 89. Thickness of a cell wall is around 10 nm 1.00037929×10-8 meters or 10 nanometers 16.7835794 centimeters or 1.67835794×10-1m 113: Small living and manufactured things ZOOLOGY
Immunology 88. Insulin molecule 5.00189644×10–9 meters 33.5671588 centimeters 114. Objects we handle BOTANY
___ 87. DNA helix ±2 nm 2.50094822 nanometers 67.1343176 centimeters or 19.68 inches 115. Agricultural and manufactured things ANTHROPOLOGY
Chemistry 86. Glucose molecule Fullerenes diameter (Buckyballs) range: ~1.1nm 1.25474112 nanometers 1.3426864 meters or 52.86 inches 116. A child or other smaller animals SLEEP & VISIONS
Genetics 85. Distance between base pairs within DNA ±340 pm .625237056 nanometers or 6.25237056×10-10 meters 2.6853728 meters or 105.723 inches 117. A bed, a little stable or place to rest INSIGHTS & IDEAS
HUMAN SCALE
PN 67 to 134		 84. Periodic Table is complete. Diameter of a water molecule ±280 pm .312618528 nanometers or 3.12618528×10-10 meters 5.3707456 meters 118. A small bedroom PSYCHOLOGY
Picometres
pm		 83. Diameter of a carbon atom ±70 pm .156309264 nanometers or 1.56309264×10-10m 10.7414912 meters, 35.2411 feet 119. A home, a small barn or shop SOCIOLOGY
___ 82. Helium atom diameter 7.81546348×10-11 meters . 21.4829824 meters 120. Property FAMILIES
___ 81. Hydrogen atom ±25 pm 3.90773174×10-11 meters 42.9659648 meters 121. Larger properties RETAIL
___ 80. Periodic Table of Elements begins 1.95386587×10-11m 85.9319296 meters 122. Complex systems CONSTRUCTION
___ 79. Use Huang scale 9.76932936×10-12m 171.86386 meters or about 563 feet 123. Big buildings or a little neighborhood GEOLOGY
___ 78. Wavelength of an X-ray 4.88466468×10-12m 343.72772 meters or about 1128 feet 124. A huge complex or a neighborhood ARCHITECTURE
___ 77. 2.44233234×10-12 m 687.455439 meters 125. Farms and large complexes AGRICULTURE
___ 76. Gamma wavelength 1.22116617×10-12m 1.37491087 kilometers 126. Very small towns SMALL POLITICAL SYSTEMS
BEGINNINGS OF 75. Use Falstad scale 6.10583084×10-13m 2.74982174 kilometers 127. Smallest states TRANSPORTATION
SMALL SCALE 74. ___ 3.05291542×10-13m 5.49964348 kilometers 128. Towns AERONAUTICS
73.___ 1.52645771×10-13m 10.999287 kilometers or within 6.83464 miles 129. Small cities, or large towns JUDICIAL SYSTEMS
NUCLEAR PHYSICS 72. Average range of the size of atom’s nucleus 7.63228856×10-14m 21.998574 kilometers 130. Large towns LOCAL POLITICS
___ 71. Gold atomic nucleus 3.81614428×10-14 m 43.997148 kilometers 131. Large cities ___
Human Scale 70. Aluminum atom 1.90807214×10-14m 87.994296 kilometers 132. Small states ___
Beginnings of 69. Electron diameter 9.54036072×10-15m 175.988592 kilometers or 108 miles 133. Very small countries or anything within 100 miles NATIONAL POLITICS
Going up 68. Helium atom diameter 4.77018036×10-15 m 351.977184 kilometers or 218 miles 134. Within the orbital range: International Space Station SPACE POLITICS
Femtometres (fm) 67. Neutron diameter Hydrogen – 1.75±×10-15m 2.38509018×10-15m 703.954368 kilometers 135. Countries BEGINNINGS OF
Going down, beginnings of 66. Diameter of a proton or fermions (femtometre ) 1.19254509×10-15m 1407.90874 kilometers or about 874 miles 136. Larger countries LARGE SCALE

small scale 		65. 36+ quintillion vertices 5.96272544×10-16 m 2815.81748 kilometers 137. Regions of earth ___
THEORETICAL
PHYSICS		 64. Neutrinos, quarks 2.98136272×10-16m 5631.63496 kilometers 138. Largest countries ___
Attometers 63. ___ 1.49068136×10-16m 11,263.2699 kilometers or about 7000 miles 139. Diameter of the earth ___
am 62. ___ 7.45340678×10-17m 22,526.5398 kilometers 140. GPS Satellite Altitude ___
61. ___ 3.72670339×10-17m 45,053.079 kilometers 141. ___ ___
VERY-SMALL 60. 1+ quintillion vertices 1.86335169×10-17m 90,106.158 kilometers 142. ___ ___
SCALE UNIVERSE 59. Quarks 9.31675848×10-18m 180,212.316 kilometers (over 111,979 miles) 143. ___ ___
PN 40-to-60 58. ___ 4.65837924×10-18m 360,424.632 kilometers 144. Distance: Earth to Moon ___
___ 57. ___ 2.32918962×10-18m 720,849.264 kilometers 145. ___ ___
___ 56. ___ 1.16459481×10-18m 1,441,698.55 kilometers 146. Diameter of the sun ___
Zeptometers 55. ___ 5.82297404×10–19m 2,883,397.1 kilometers 147. ___ ___
zm 54. ___ 2.91148702×10-19m 5,766,794.2 kilometers 148. ___ ___
___ 53. ___ 1.45574351×10-19m 11,533,588.4 kilometers 149. ___ ___
___ 52. ___ 7.27871756×10-20m 23,067,176.8 kilometers 150. ___ ___
___ 51. ___ 3.63935878×10-20m 46,134,353.6 kilometers 151. ___ ___
___ 50. 1+ quadrillion vertices 1.81967939×10-20m 92,268,707.1 kilometers 152. ___ PN 134-to-201+
___ 49. ___ 9.09839696×10-21m 184,537,414 kilometers 153. Range: Earth to Sun ASTRONOMY
___ 48. ___ 4.54919848×10-21m 369,074,829 kilometers 154. To go to Ceres asteroid ___
___ 47. ___ 2.27459924×10-21m 738,149,657 kilometers 155. Range: Jupiter-to-Sun ___
___ 46. Pati Preons 1.13729962×10-21m 1.47629931×1012m 156. Range: Saturn-to-Sun ASTROPHYSICS
Yoctometers 45. ___ 5.68649812×10–22m 2.95259863×1012m 157.Range: Uranus-to-Sun Terametres (Tm)
ym 44. ___ 2.84324906×10-22m 5.90519726×1012m 158. Range: Pluto-to-Sun LARGE SCALE
___ 43. ___ 1.42162453×10-22m 1.18103945×1013m 159. ___ UNIVERSE
___ 42. ___ 7.10812264×10-23m 2.36207882×1013m 160. 24 hour light travel ___
___ 41. THE CHALLENGE: 3.55406132×10-23m 4.72415764×1013m 161. ___ ___
VERY-VERY, 40. 1+ trillion vertices 1.77703066×10-23m 9.44831528×1013m 162. ___ ___
SMALL-SCALE 39. 549 billion vertices 8.88515328×10-24m 1.88966306×1014m 163. 7-day light travel ___
UNIVERSE 38. 274 billion vertices 4.44257664×10-24m 3.77932612×1014m 164. ___ ___
PN 20-to-40 37. 137 billion vertices 2.22128832×10-24m 7.55865224×1014m 165. ___ ___
36. 68 billion vertices 1.11064416×10-24m 1.5117305×1015m 166. ___ Petametres (Pm)
35. 34 billion vertices 5.5532208×10-25m 3.0234609×1015m 167. ___ ___
SPECULATIONS: 34. 17,179,869,184 2.7766104×10-25m 6.0469218×1015m 168. ___
Quantum State 33. 8,589,934,592 1.3883052×10-25m 1.20938436×1016m 169. Beyond one light year (ly) (9.4×1015) 1 parsec ~ 31 trillion km or 19 trillion miles
Machines (QSM) 32. 4,294,967,296 6.94152599×10-26m 2.41876872×1016m 170. Go to Proxima Centauri (39.9 Pm) 1 parsec (3.26 light years, 30.8 Pm)
(QSM) 31. 2,147,483,648 3.47076299×10-26 m 4.83753744×1016m 171. Distance to Alpha Centauri A & B (41 Pm) ___
___ 30. 1+ billion vertices 1.735381494×10-26 m 9.67507488×1016m 172. Distance to Sirius (81 Pm, 8.6 ly) ___
Modulus for 29. 536,870,912 8.67690749×10-27 m 1.93501504 ×1017m 173. Distance to Tau Ceti (110 Pm) 100 Petametres or 11 light years (ly)
transformations (Mt) 28. 268,435,456 b2v 4.3384537×10-27m 3.87002996×1017m 174. Diameter of Orion Nebula (350 Pm) ___
27. 134,217,728 b2v 2.16922687×10-27m 7.74005992 ×1017m 175. Distance to Regulus star (730 Pm) ___
Mt 26. 67,108,864 b2v 1.0846134×10-27m 1.54801198×1018m 176. Omega Centauri diameter (1.6 Em) Exametre (Em): 110 light years (ly)
___ 25. 33,554,432 b2v 5.42306718×10-28 m 3.09602396×1018m 177. Thickness of our Milky Way (2 Em) Our Galaxy
___ 24. 16,777,216 b-2 vertices 2.711533591×10-28m 6.19204792×1018m 178. Distance to Helix Nebula (6.2 Em) ___
___ 23. 8,388,608 b-2 vertices 1.35576679×10-28m
1 barn		 1.23840958×1019m 179. Distance to the Orion Nebula (13 Em) 12.38 Em
QSM 22. 4,194,304 b-2 vertices 6.77883397×10-29m 2.47681916×1019m 180. Horsehead Nebula (15 Em) ___
___ 21. 2,097,152 b-2 vertices 3.38941698×10-29m 4.95363832×1019m 181. ___ ___
EXTREMELY 20. 1+ quintillion b-8 vertices 1.69470849×10-29m 9.90727664×1019m 182. ___ ___
SMALL-SCALE 19. 524,288 vertices 8.47354247×10-30m 1.981455338×1020m 183. Small Megellanic Cloud diameter in Milky Way (150 Em) 198.1 Exametres
UNIVERSE 18. 262,144 b-2 vertices 4.2367712×10-30m 3.96291068×1020m 184. To the center of our galaxy (260 Em) ___
PN 10-to-20 17. 281+ trillion b-8 vertices 2.11838561×10-30m 7.92582136×1020m 185. ___ ___
16. one square femtometer 1.05919280×10-30m 1.58516432×10921m 186. Go to Large Magellanic Cloud 1.5 Zettametre: 150,000 ly
15. 32,768 base-2 vertices 5.29596404×10-31m 3.17032864×1021m 187. Small Magellanic Cloud (2 Zm) 3 Zettametres: 310,000 ly
14. 4+ trillion base-8 v 2.64798202×10-31m 6.34065727×1021m 188. ___ ___
13. 8192 vertices 1.32399101×10-31m 1.26813145×1022m 189. ___ ___
Note: Theta-Fushian functions 12. 68+ billion base-8 v 6.6199550×10-32m 2.53626284×1022m 190. Distance to the Andromeda Galaxy 24 Zm
See: Models 11. 2048 base-2 vertices 3.30997752×10-32m 5.07252568×1022m 191. ___ ___
SMALLEST-SCALE
UNIVERSE		 10. 1+ billion base-8 v 1.65498876×10-32m 1.01450514×1023m 192. (Fill in a blank) 101 Zettametres
Cubicities 9. 512 base-2 vertices 8.27494384×10-33m 2.02901033×1023m 193. Go to Centaurus A Galaxy (140 Zm) ___
Primary QSM 8. 16+ million base-8 v 4.1374719232×10-33m 4.05802056×1023m 194. (Fill in a blank) ___
Primary Mt 7. 128 base-2 vertices 2.0687359616×10-33m 8.11604112×1023m 195. ___ ___
Nested Geometries 6. 262,144 base-8 v 1.03436798×10-33m 1.62320822×1024m 196. ___ Yottametre (Ym)
Primary cubicities 5. 32 base-2 vertices 5.17183990×10-34m 3.24641644×1024m 197. Length of the Great Wall (4.7 Ym) ___
Strings & Knots 4. 4096 base-8 vertices 2.58591995×10-34m 6.49283305×1024m 198. Distance (6.1 Ym) to Shapley Supercluster ___
Primary knots 3. 8 base-2 vertices 1.29295997×10-34m 1.29856658×1025m 199. Length of Sloan Great Wall (13.7 Ym) 12.98 Ym
Cubicity or string 2. 64 base-8 vertices (v) 6.46479988×10-35 2.59713316×1025m 200.___ ___
Primary String 1. 2 base-2 vertices (v) 3.23239994×10-35 5.19426632×1025m 201.___ ___
The Planck Length A vertex? 1.616199(97)x10-35m 1.03885326×1026m 202. EOU at 202.34 ___
Synopsis: This Big Board-little universe is to order data in a way to open a discussion about our basic assumptions — the universals and constants — that guide our thinking and work. An initial focus is Max Planck’s calculation in 1900 of the Planck Length.

Very Brief History: The work began by attempting to find new starting points for creative thinking, new insights, even breakthroughs, regarding the very nature of space and time. In the 1970s the following first principles were formulated as preconditions for a space-time moment at the zero-point defined by Planck, Stern and Einstein.

First principles: Deep within the fabric of life there is an energy, an abiding thrust to make things better, more perfect. That is the cornerstone of business, but much more. Simple logic tells us that there are three forms within functions that define an increasingly perfected state within an experience:
1. The first form that defines our humanity is order and its most basic function, a simple perfection, creates continuity.
2. The second form is a relation and its function creates symmetry.
3. The third form is dynamics and its perfection, a complex function, is harmony.

These three — continuity, symmetry and harmony — just might be the precursors of a space-time moment.
A Working Project:
A Big Board of
our little universe
This work is copyright
by three groups,
all of River Ridge,
PO Box 10132
New Orleans,
LA 70123 USA

Icosahedron

 Illustration 3.
Pentakis dodecahedron
32 external vertices
or points, 60 external
tetrahedra, a layer of
46 asymmetrical tetrahedral and an
icosahedron in the
center. 1.5° deviationsIllustration 2.
Icosahedron
20 tetrahedrons made
of 13 points, 1.5° deviations with
shared center point		 The challenge of four simple concepts:
1. A universal scale created by doublings.
A simple scale that starts with a point at the Planck Length (PL), assumes Planck’s logic and mathematics are OK and that the PL singularity, an actual measurement, can be doubled. At each step there is a physical measurement. It takes 202.34 doublings to go from the PL to the Edges of Observable Universe (EOU). See all of the above.2. Nested geometries.
The first doubling renders two points and the second doubling four points. With four points a tetrahedron could be rendered; it is the simplest three-dimensional form defined by the fewest number of points. The third doubling renders eight points. With just seven of those points, a pentagonal cluster of five tetrahedrons can be inscribed (Illustration 1). With the fourth doubling, now sixteen points, the icosahedron with its thirteen vertices (points) can be created. (Illustration 2). A tetrahedron within the pentagonal cluster (Illus. 1) can inscribe four smaller tetrahedra and an octahedron within itself with just six of those points (and by dividing each edge in half). More…
This project
was initiated for
the geometry classes
of Steve Curtis
at The Curtis School,
in River Ridge, Louisiana.Version 2.0.0.1		 Five Tetrahedrons Illustration 1.
Five Tetrahedrons
7 points, 1.5°
deviations		 3. Facts and Guesses.
Simple math renders simple facts. What can be done with these numbers, images and forms? What functions can be intuited? Perhaps a challenge to students could be to use buckyballs and the basic Platonic solids to build a most primitive kind of machine. More to come…This quest is a thought experiment that begins at the PL and proceeds with facts and guesses to edge of the observable universe.4. Non-commutative geometry, irrational numbers…
Another idiosyncratic application to number theory, non-commutative geometries, irrational numbers, and dimensionful numbers is to see all of these as the results of a modulus of transformation and gaps between faces of less than 1.5° (as seen in the seven-point, five-regular tetrahedra when each shares an edge). Much more to come…
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