Big Board – little universe

Tetra86Octa86Hexa86Dodeca86 Icosa86 Tetrahedral-Octahedral Tetrahedral chain
Introduction: Starting in the center-left column below, a unit of measurement based on the Planck Length is divided-by-two 101 times until that measurement is the Planck Length, generally considered the smallest unit of measurement within space and time. 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 that the simplest three-dimensional form defined by the fewest number of vertices is the tetrahedron.  Assume that the nesting of the basic Platonic structures within each other necessarily interrelates all structure of every manifestation within the known universe. The blanks are for students to find answers from examples within their studies, especially biology, chemistry, physics, astronomy and astrophysics and also to correct mistakes.  Go to the general overview…
Basic Questions, Basic Structures, and Form-and-Function: Could all structures be in some way derivative of the five basic solids discussed by Plato and the Greeks in and around 360 BC? If that concept is taken as a given, then questions about form and function could 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 the simplest mathematical operations can still open new paths and logic to explore.
Go to the image file of this board
 Tetra2-98Octa2 Cubocta84 PentakisDodeca2 Icosa2 TOT2
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 micronsor 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 orabout .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 ___
NANO- TECHNOLOGY 95. Range of visible light ~ 400 to 1000 nm 640.242744 nanometers 2.62243428 millimeters 107. A small ant Myrmecology
___ 94. Nanoparticles ~ 100-to-10000 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 5.00189644×108 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 and 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 SCALEPN 75 to 150 84. Diameter of a water molecule ±280 pm .312618528 nanometers or 3.12618528×10-10 meters 5.3707456 meters 118. A small bedroom PSYCHOLOGY
Picometrespm 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. ____ 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. Diameter of florine ion 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
BEGINNING 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
PN 1-TO-75 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 atom nucleus 3.81614428×10-14 m 43.997148 kilometers 131. Large cities ___
___ 70. Aluminum atom 1.90807214×10-14m 87.994296 kilometers 132. Small states ___
___ 69. Electron diameter 9.54036072×10-15m 175.988592 kilometers or 108 miles 133. Very small countries or anything within 100 miles NATIONAL POLITICS
___ 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
Femtometresfm 67. Neutron diameter Hydrogen – 1.75±×10-15m 2.38509018×10-15m 703.954368 kilometers 135. Countries ___
  66. Diameter of a proton or fermions (femtometre ) 1.19254509×10-15m 1407.90874 kilometers or about 874 miles 136. Larger countries ___
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. Over a 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. ___ 5.82297404×1019m 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. ___ BEGINNING OF
___ 51. ___ 3.63935878×10-20m 46,134,353.6 kilometers 151. ___ LARGE SCALE
___ 50. Over a quadrillion vertices 1.81967939×10-20m 92,268,707.1 kilometers 152. ___ PN 150-to-202.34
___ 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. ___ 5.68649812×1022m 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. Over 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. 34,359,738,368 vertices 5.5532208×10-25m 3.0234609×1015m 167. ___ ___
SPECULATIONS: 34. 17,179,869,184 vertices 2.7766104×10-25m 6.0469218×1016m 168. In the range of one light year (ly) (9.4×1015) 1 parsec ~ 31 trillion km or 19 trillion miles
Quantum State 33. 8,589,934,592 vertices 1.3883052×10-25m 1.20938436×1016m 169. ______ 1 parsec ~ 31 trillion km or 19 trillion miles
Machines (QSM) 32. 4,294,967,296 vertices 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 vertices 3.47076299×10-26 m 4.83753744×1016m 171. Distance to Alpha Centauri A & B (41 Pm) ___
___ 30. Over 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 vertices 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 vertices 4.3384537×10-27m 3.87002996×1017m 174. Diameter of Orion Nebula (350 Pm) ___
27. 134,217,728 vertices 2.16922687×10-27m 7.74005992 ×1017m 175. Distance to Regulus star (730 Pm) ___
Mt 26. 67,108,864 vertices 1.0846134×10-27m 1.54801198×1018m 176. Omega Centauri diameter (1.6 Em) Exametre (Em): 110 light years (ly)
___ 25. 33,554,432 vertices 5.42306718×10-28 m 3.09602396×1018m 177. Thickness of our Milky Way (2 Em) Our Galaxy
___ 24. 16,777,216 vertices 2.711533591×10-28m 6.19204792×1018m 178. Distance to Helix Nebula (6.2 Em) ___
___ 23. 8,388,608 vertices 1.35576679561×10-28m 1.23840958×1019m 179. Distance to the Orion Nebula (13 Em) 12.38 Em
QSM 22. 4,194,304 vertices 6.778833978×10-29m 2.47681916×1019m 180. Horsehead Nebula (15 Em) ___
___ 21. 2,097,152 vertices 3.3894169890×10-29m 4.95363832×1019m 181. ___ ___
EXTREMELY 20. 1,048,576 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 vertices 4.2367712×10-30m 3.96291068×1020m 184. To the center of our galaxy (260 Em) ___
PN 10-to20 17. 131,072 vertices 2.1183856181504×10-30m 7.92582136×1020m 185. ___ ___
16. 65,536 vertices 1.05919280907×10-30m 1.58516432×10921m 186. Go to Large Magellanic Cloud 1.5 Zettametre: 150,000 ly
15. 32,768 vertices 5.2959640453×10-31m 3.17032864×1021m 187. Small Magellanic Cloud (2 Zm) 3 Zettametres: 310,000 ly
14. 16,384 vertices 2.6479820226×10-31m 6.34065727×1021m 188. ___ ___
13. 8192 vertices 1.3239910113×10-31m 1.26813145×1022m 189. ___ ___
Note: Theta-Fushian functions 12. 4096 vertices 6.61995505672×10-32m 2.53626284×1022m 190. Distance to the Andromeda Galaxy 24 Zm
See: Models 11. 2048 vertices 3.30997752836×10-32m 5.07252568×1022m 191. ___ ___
SMALLEST-SCALE UNIVERSE 10. 1024 vertices
1.65498876928×10-32m 1.01450514×1023m 192. (Fill in a blank) 101 Zettametres
Cubicities 9. 512 vertices
8.2749438464×10-33m 2.02901033×1023m 193. Go to Centaurus A Galaxy (140 Zm) ___
Primary QSM 8. 256 vertices
4.1374719232×10-33m 4.05802056×1023m 194. (Fill in a blank) ___
Primary Mt 7. 128 vertices
2.0687359616×10-33m 8.11604112×1023m 195. ___ ___
Nested Geometries 6. 64 vertices
1.0343679808×10-33m 1.62320822×1024m 196.  ___ Yottametre (Ym)
Primary cubicities 5. 32 vertices
5.171839904×10-34m 3.24641644×1024m 197. Length of the Great Wall (4.7 Ym) ___
Strings & Knots 4. 16 vertices
2.585919952×10-34m 6.49283305×1024m 198. Distance to the Shapley Supercluster (6.1 Ym) ___
Primary knots 3. 8 vertices
1.292959976×10-34m 1.29856658×1025m 199. Length of Sloan Great Wall (13.7 Ym) 12.98 Ym
Cubicity or string 2. 4 vertices
6.46479988×10-35 2.59713316×1025m 200.___ ___
Primary String 1. 2 points 3.23239994×10-35 5.19426632×1025m 201.___ ___
Singularity 0. 1 point 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 Pentakis Dodecahedron Illustration 3.Pentakis
dodecahedron
32 external vertices or points, 60 external tetrahedra, a layer of 46 asymmetrical
tetrahedra and an icosahedron in the center.
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.  
 Icosahedron Illustration 2. Icosahedron20 tetrahedrons
13 points
with shared center point,
1.54 steradians
 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, LouisianaVersion 2.0.0.1 FiveTetrahedrons Illustration 1.Five Tetrahedrons,7 points7.36° gap or deviation

Gaps between faces are less than 1.5°

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

© Institute for Perfection Studies (Bruce Camber)    © My Golden Rules, Inc. (501c3) (Hattie Bryant)   © Small Business School

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