Just the numbers…

References: Overview, (1) a Wiki-like working-draft, (2) Speculations, and a working paper.

The first draft of  “Just the numbers” was written in March 2012. Since that time there have been small edits and updates.

The Planck Length: What is it?   First, for over 100 years, the Planck Length was virtually ignored.   Today it is getting more and more attention.PlanckL1

Second, there is the technical definition:

Third, there is an historic perspective. Developed by Max Planck, he took the speed of light in a vacuum, his own Planck constant, and the gravitational constant to distill the smallest possible length in the universe. Conceptually, nothing could be smaller. So, it is not a point. It has a specific length. Some might say, “It’s a special kind of point.” We do not. After two years of thought on the matter, we are slowly deleting all references to a point. The academic community knows a lot about points, but not enough. For our purposes we have begun to refer to it as “the simplest possible vertex in a point-free geometry.” It is a pre-structure structure  in a point-free domain that becomes the foundation for points, lines, triangles and all three-dimensional objects. Our simple guess is that this pre-structure is the range between notations 1 and 60-to-65.

Begin at the Planck Length and simply multiply it by two over and the results by 2 and do that over and over again. Called base-2 exponential notation, it creates a scale or order of magnitude. Each doubling of that very special measurement, 1.616199(97)×10-35meters creates something. Each doubling is also referred to as a layer, notation, or step.

Powers-of-two and exponentiation based on the Planck length. Herein it is referred to as Base-2 Exponential Notation (B2EN). We will see the universe, from the smallest to the largest measurement of a length, using base-2.  It is more meaningful than using base-ten scientific notation because B2EN renders greater granularity; and, although superimposed by us on the universe, it renders a necessary relationality through nested geometries.

This project originated within five high-school geometry classes in December 2011. In looking at the five platonic solids, particularly the tetrahedron, the question was asked, “How far within could one go before hitting the Planck Length?”

Within a tetrahedron are four half-size tetrahedrons and an octahedron. Within that octahedron there are six half-size octahedrons and eight half-size tetrahedrons. Within both objects the edges can seemingly be divided in half and a new set of smaller objects observed. It would appear to be endless. Yet, unlike the limitless paradox introduced of Zeno, (ca. 490 BC – ca. 430 BC), we now have the Planck Length as a limit. Mathematically defined in and around 1899, the Planck Length was largely ignored by the scientific community and even today it has not been universally accepted.

1.616199(97)x10-35 meters: We initially started by looking at the online references to the Planck length. In March 2012, there were just 276 Google links to that number (virtually none). Over the next few years, we suspect those references will grow substantially. Our guess is that it is one of the more important concepts and physical numbers that in some special ways begin to define space and time.

Professor Laurence Eaves of the University of Nottingham in England has a delightful YouTube video that explains this length that we use to define a vertex.

In our simple exercise, we take the Planck length and multiply it by 2, until we reach something that is measurable today (the diameter of a proton), then continue multiplying. Each notation provides a range of sizes that necessarily includes everything in the known universe. Eventually we come to the largest measurement of a length, the Observable Universe. In one set of calculations, it only required 202+ notations or doublings. Yet, we have also received excellent guesses based on calculations up to 206.

The work is displayed five columns.  The first column is a Planck number based on the number of times the Planck length has been multiplied. The second column is the number of base-ten notations. The third column is the number of  vertices, the powers of two. The fourth column is for the incremental increase in size or length. And, the fifth column will be used for simple reflections.

B2EN B10SN Points, vertices or doublings Length (meters) Discussions, Examples,Information, Speculations:
0 1 2^0=1 1.616199(97)×10-35m At the Planck Length, though it is a truly just a concept, let us take it as a given and that it is a special kind of vertex that is pointlike.
1 1 2^1=2 3.23239994×10-35m At the first notation, there are two vertices. The shortest possible line,  the conceptual beginnings of a string and a simple relation. We are a long way from knowing where the strings of string theory come into this picture. It can be a two-dimensional object, a circle and a 2-D sphere. With each new doubling this notation is within its initial conditions. This is source code. Also, we are exploring in what ways it could be a type of perfection. In 1944, Max Planck in a speech in Florence, Italy, said, “All matter originates and exists only by virtue of a force which brings the particle of an atom to vibration and holds this most minute solar system of the atom together. We must assume behind this force the existence of a conscious and intelligent mind. This mind is the matrix of all matter.” (The Nature of Matter, Archiv zur Geschichte der Max-Planck-Gesellschaft, Abt. Va, Rep. 11 Planck, Nr. 1797, 1944)
2 1 2^2=4 6.46479988×10-35m At the second notation there are four vertices. The first truly three-dimensional expression. All still within their sphere, one might think there are several logical possibilities, another sphere, a longer line, a jagged line or a tetrahedron. It may be true that the tetrahedron and the first three dimensions of space are the most simple and perfect.
3 2 2^3=8 1.292959976×10-34m At the third doubling there are eight vertices. Logical possibilities seem to expand dramatically. With five vertices two abutting tetrahedrons could take shape. With six vertices an octahedron could emerge. With seven vertices, a pentastar (tetrahedral pentagon) could emerge.  With all eight vertices, a cube or hexahedron could be created. The simple tetrahedral-octahedral chain begins to manifest with just eight vertices.
4 2 2^4=16 2.585919952×10-34m At the fourth doubling there are sixteen vertices. If any one of the vertices were to become a center vertex, and 10 vertices are extended from it, a tetrahedral icosahedron emerges.  And with the icosahedron, Among the many possibilities, in another configuration, a cluster of four polytetrahedral clusters (a total of 20 tetrahedrons) begin to emerge and completes with twenty vertices (picture to be added). These vertices could also divide the edges of the internal four tetrahedrons and one octahedron. If the focus was entirely within the octahedron, the first shared center vertex of the octahedron would begin to be defined and by the 18th vertex the fourteen internal parts, eight tetrahedrons (one in each face) and the six octahedrons (one in each corner) would be defined (picture to be added).
5 2 2^5=32 5.171839904×10-34m At the fifth notation, there are 32 vertices. With twenty vertices a simple dodecahedron is possible; all five platonic solids have manifest. The tetrahedral-octahedral chain could now manifest with seven octahedrons and fourteen tetrahedrons.
6 3 2^6=64 1.0343679808×10-33m At the sixth notation, there are 64 vertices. With just 43 of those vertices a hexacontagon (or Pentakis dodecahedron) could be created. It has 12 polytetrahedral clusters on the surface with an icosahedron in the middle.
7 3 2^7=128 2.0687359616×10-33m The seventh doubling, with 128 vertices. The results are not. Simple exponential notation based on the power of two is well documented. Of course, by using base-2 exponential notation and starting at the Planck length, necessary relations might be intuited.
8 3 2^8=256 4.1374719232×10-33m Geometric complexification, morphism,  The nature of the perfect fittings. Imperfect fittings
9 3 2^9=512 8.2749438464×10-33m In that pentastar there is a 7.368 degree spread between tetrahedrons. That do not fit perfectly. That measurement is also 1.54 steradians and the effect within the icosahedron increases.
10 4 1024 1.65498876928×10-32m At the tenth doubling,  look within an optimized Pentakis Dodecahedron where there is an outer layer of sixty tetrahedrons (twelve imperfect pentastars), an inner layer of irregular tetrahedrons, and an icosahedron of 20 tetrahedrons in the center. All are imperfect. Yet, within each tetrahedron there is a little perfection. There are four half-sized tetrahedrons and an octahedron all seated perfectly together. Within that octahedron, there are six octahedra and eight tetrahedra .
11 4 2048 3.30997752836×10-32m

Finite subdivision rule

12 4 4096 6.61995505672×10-32m _
13 5 8192 1.323991011344×10-31m _
14 5 16,384 2.647982022688×10-31m _
15 5 32,768 5.295964045376×10-31m _
16 6 65,536 1.0591928090752×10-30m _
17 6 131,072 2.1183856181504×10-30m _
18 6 262,144 4.2367712363008×10-30m _
19 6 524,288 8.4735424726016×10-30m _
20 7 1,048,576 1.69470849452032×10-29m _
21 7 2,097,152 3.38941698904064×10-29m more information
22 7 4,194,304 6.77883397808128×10-29m _
23 8 8,388,608 1.355766795616256×10-28m _
24 8 16,777,216 2.711533591232512×10-28m _
25 8 33,554,432 5.423067182465024×10-28m _
26 9 67,108,864 1.0846134364930048×10-27m _
27 9 134,217,728 2.1692268729860096×10-27m
28 9 268,435,456 4.3384537459720192×10-27m _
29 9 536,870,912 8.6769074919440384×10-27m _
30 10 1,073,741,824 1.73538149438880768×10-26m _
31 10 2,147,483,648 3.47076299879961536×10-26m _
32 10 4,294,967,296 6.94152599×10-26m _
33 11 8,589,934,592 1.3883052×10-25m _
34 11 1.7179869×1011 2.7766104×10-25m Actual number: 17,179,869,184 vertices
35 11 3.4359738×1011 5.5532208×10-25m 34,359,738,368
36 12 6.8719476×1011 1.11064416×10-24m 68,719,476,736
37 12 1.3743895×1012 2.22128832×10-24m 137,438,953,472
38 12 2.7487790×1012 4.44257664×10-24m 274,877,906,944
39 12 5.4975581×1011 8.88515328×10-24m 549,755,813,888
40 13 1.0995116×1012 1.77703066×10-23m 1,099,511,627,776
41 13 2.1990232×1012 3.55406132×10-23m 2,199,023,255,552
42 13 4.3980465×1012 7.10812264×10-23m 4,398,046,511,104
43 14 8.7960930×1012 1.42162453×10-22m 8,796,093,022,208
44 14 1.7592186×1013 2.84324906×10-22m 17,592,186,044,416
45 14 3.5184372×1013 5.68649812×10-22m 35,184,372,088,832
46 15 7.0368744×1013 1.13729962×10-21m 70,368,744,177,664
47 15 1.4073748×1014 2.27459924×10-21m 140,737,488,355,328
48 15 2.8147497×1014 4.54919848×10-21m 281,474,976,710,656
49 15 5.6294995×1014 9.09839696×10-21m 562,949,953,421,312
50 16 1.12589988×1015 1.81967939×10-20m 1,125,899,906,842,624
51 16 2.25179981×1015 3.63935878×10-20m 2,251,799,813,685,248
52 16 4.50359962×1015 7.27871756×10-20m 4,503,599,627,370,496
53 17 9.00719925×1015 1.45574351×10-19m 9,007,199,254,740,992
54 17 1.80143985×1016 2.91148702×10-19m 18,014,398,509,481,984
55 17 3.60287970×1016 5.82297404×10-19m 36,028,797,018,963,968
56 18 7.205759840×1016 1.16459481×10-18m 72,057,594,037,927,936
57 18 1.44115188×1017 2.32918962×10-18m 144,115,188,075,855,872
58 18 2.88230376×10 17 4.65837924×10-18m 288,230,376,151,711,744
59 18 5.76460752×1017 9.31675848×10-18m 576,460,752,303,423,488
60 19 1.15292150×1018 1.86335169×10-17m 1,152,921,504,606,846,976
61 19 2.30584300×1018 3.72670339×10-17m 2,305,843,009,213,693,952
62 19 4.61168601×1018 7.45340678×10-17m 4,611,686,018,427,387,904 (Quarks)
63 20 9.22337203×1018 1.49068136×10-16m 9,223,372,036,854,775,808 (Quarks, Photons)
64 20 1.84467440×1019 2.98136272×10-16m 18,446,744,073,709,551,616 (Neutrinos, Quarks, Photons)
65 20 3.68934881×1019 5.96272544×10-16m 36,893,488,147,419,100,000
66 21 7.37869762×1019 1.19254509×10-15m 73,786,976,294,838,200,000 (Protons, Fermions)
67 21 1.47573952×1020 2.38509018×10-15m 147,573,952,589,676,000,000 (Neutrons)
68 21 2.95147905×1020 4.77018036×10-15m 295,147,905,179,352,000,000 (Helium)
69 21 5.90295810×1020 9.54036072×10-15m 590,295,810,358,705,000,000 (Electron)
70 22 1.18059162×1021 1.90807214×10-14m 1,180,591,620,717,410,000,000 (Aluminum)
71 22 2.36118324×1021 3.81614428×10-14m 2,361,183,241,434,820,000,000 (Gold)
72 22 4.72236648×1021 7.63228856×10-14m 4,722,366,482,869,640,000,000
73 23 9.44473296×1021 1.52645771×10-13m 9,444,732,965,739,290,000,000
74 23 1.88894659×1022 3.05291542×10-13m 18,889,465,931,478,500,000,000
75 23 3.77789318×1022 6.10583084×10-13m 37,778,931,862,957,100,000,000
76 24 7.55578637×1022 1.22116617×10-12m 75,557,863,725,914,300,000,000
77 24 1.51115727×1023 2.44233234×10-12m 151,115,727,451,828,000,000,000
78 24 3.02231454×1023 4.88466468×10-12m 302,231,454,903,657,000,000,000
79 24 6.04462909×1023 9.76932936×10-12m 604,462,909,807,314,000,000,000
80 25 1.20892581×1024 1.95386587×10-11m 1,208,925,819,614,620,000,000,000
81 25 2.41785163×1024 3.90773174×10-11m 2,417,851,639,229,250,000,000,000
82 25 4.83570327×1024 7.81546348×10-11m 4,835,703,278,458,510,000,000,000
_ _ _________________ ______________________ ________________________
83 26 9.67140655×1024 .156309264 nanometers 9,671,406,556,917,030,000,000,000
or 1.56309264×10-10m
84 26 1.93428131×1025 .312618528 nanometers 19,342,813,113,834,000,000,000,000
85 26 3.86856262×1025 .625237056 nanometers 38,685,626,227,668,100,000,000,000
_ _________________ ______________________ ________________________
86 27 7.73712524×1025 1.25047411 nanometers or 77,371,252,455,336,200,000,000,000
or 1.25047411×10-9m
87 27 1.54742504×1026 2.50094822 nanometers 154,742,504,910,672,000,000,000,000
88 27 3.09485009×1026 5.00189644 nanometers 309,485,009,821,345,000,000,000,000
_ _________________ ______________________ ________________________
89 28 6.18970019×1026 10.0037929 nanometers 618,970,019,642,690,000,000,000,000
or 1.00037929×10-8m
90 28 1.23794003×1027 20.0075858 nanometers 1,237,940,039,285,380,000,000,000,000
91 28 2.47588007×1027 40.0151716 nanometers 2,475,880,078,570,760,000,000,000,000
92 28 4.95176015×1027 80.0303432 nanometers 4,951,760,157,141,520,000,000,000,000
_ _________________ ______________________ ________________________
93 29 9.90352031×1027 160.060686 nanometers 9,903,520,314,283,042,199,192,993,792
or 1.60060686×10-7m
94 29 1.98070406×1028 320.121372 nanometers 19,807,040,628,566,000,000,000,000,000
95 29 3.96140812×1028 640.242744 nanometers 39,614,081,257,132,100,000,000,000,000
_ _________________ ______________________ ________________________
96 30 7.92281625×1028 1.28048549 microns 79,228,162,514,264,300,000,000,000,000
or 1.28048549×10-6m
97 30 1.58456325×1029 2.56097098 microns 158,456,325,028,528,000,000,000,000,000
98 30 3.16912662×1029 5.12194196 microns 316,912,650,057,057,000,000,000,000,000
_ _ _________________ ______________________ ________________________
99 31 6.33825324×1029 10.2438839 microns 633,825,300,114,114,700,748,351,602,688
or 1.02438839×10-5m
100 31 1.26765065×1030 20.4877678 microns 1,267,650,600,228,220,000,000,000,000,000
101 31 2.53530130×1030 40.9755356 microns 2,535,301,200,456,450,000,000,000,000,000
102 31 5.07060260×1030 81.9510712 microns 5,070,602,400,912,910,000,000,000,000,000
_ _ _________________ ______________________ ________________________
103 32 1.01412052×1031 .163902142 millimeters 10,141,204,801,825,800,000,000,000,000,000
or 1.63902142×10-4m
104 32 2.02824104×1031 .327804284 millimeters 20,282,409,603,651,600,000,000,000,000,000
105 32 4.05648208×1031 .655608568 millimeters 40,564,819,207,303,300,000,000,000,000,000
_ _ _________________ ______________________ ________________________
106 33 8.11296416×1031 1.31121714 millimeters 81,129,638,414,606,600,000,000,000,000,000
or 1.31121714×10-3m
107 33 1.62259276×1032 2.62243428 millimeters 162,259,276,829,213,000,000,000,000,000,000
108 33 3.24518553×1032 5.24486856 millimeters 324,518,553,658,426,000,000,000,000,000,000
_ _________________ ______________________ ________________________
109 34 6.49037107×1032 1.04897375 centimeters 649,037,107,316,853,000,000,000,000,000,000
or 1.04897375×10-2m
110 34 1.29807421×1033 2.09794742 centimeters 1,298,074,214,633,700,000,000,000,000,000,000
111 34 2.59614842×1033 4.19589484 centimeters 2,596,148,429,267,410,000,000,000,000,000,000
112 34 5.19229685×1033 8.39178968 centimeters 5,192,296,858,534,820,000,000,000,000,000,000
___ ___ _________________ ______________________ ________________________
113 35 1.03845937×1034 16.7835794 centimeters or 10,384,593,717,069,600,000,000,000,000,000,000
1.67835794×10-1m
114 35 2.0769437×1034 33.5671588 centimeters 20,769,187,434,139,300,000,000,000,000,000,000
115 35 4.1538374×1034 67.1343176 centimeters 41,538,374,868,278,600,000,000,000,000,000,000
___ ___ _________________ ______________________ _____________________
116 36 8.3076749×1034 1.3426864 meters 83,076,749,736,557,200,000,000,000,000,000,000
or 52.86 inches
117 36 1.66153499×1035 2.6853728 meters 166,153,499,473,114,000,000,000,000,000,000,000
118 36 3.32306998×1035 5.3707456 meters 332,306,998,946,228,000,000,000,000,000,000,000
119 37 6.64613997×1035 10.7414912 meters 664,613,997,892,457,000,000,000,000,000,000,000
120 37 1.32922799×1036 21.4829824 meters 1,329,227,995,784,910,000,000,000,000,000,000,000
121 37 2.65845599×1036 42.9659648 meters 2,658,455,991,569,830,000,000,000,000,000,000,000
122 37 5.31691198×1036 85.9319296 meters 5,316,911,983,139,660,000,000,000,000,000,000,000
123 38 1.06338239×1037 171.86386 meters 10,633,823,966,279,300,000,000,000,000,000,000,000
124 38 2.12676479×1037 343.72772 meters 21,267,647,932,558,600,000,000,000,000,000,000,000
125 38 4.25352958×1037 687.455439 meters 42,535,295,865,117,300,000,000,000,000,000,000,000
126 39 8.50705917×1037 1.37491087 kilometers 85,070,591,730,234,600,000,000,000,000,000,000,000
127 39 1.70141183×1038 2.74982174 kilometers 170,141,183,460,469,000,000,000,000,000,000,000,000
128 39 3.40282366×1038 5.49964348 kilometers 340,282,366,920,938,000,000,000,000,000,000,000,000
129 40 6.04462936×1038 10.999287 kilometers 680,564,733,841,876,000,000,000,000,000,000,000,000
130 40 1.36112946×1039 21.998574 kilometers 1,361,129,467,683,750,000,000,000,000,000,000,000,000
131 40 2.72225893×1039 43.997148 kilometers 2,722,258,935,367,500,000,000,000,000,000,000,000,000
132 40 5.44451787×1039 87.994296 kilometers 5,444,517,870,735,010,000,000,000,000,000,000,000,000
133 41 1.08890357×1040 175.988592 kilometers 10,889,035,741,470,000,000,000,000,000,000,000,000,000
134 41 2.17780714×1040 351.977184 kilometers 2,177,807,148,294,000,000,000,000,000,000,000,000,000
135 41 4.355614296×1040 703.954368 kilometers 43,556,142,965,880,100,000,000,000,000,000,000,000,000
136 42 8.711228593×1040 1407.90874 kilometers 87,112,285,931,760,200,000,000,000,000,000,000,000,000
137 42 1.742245718×1041 2815.81748 kilometers 174,224,571,863,520,000,000,000,000,000,000,000,000,000
138 42 3.484491437×1041 5631.63496 kilometers 348,449,143,727,040,000,000,000,000,000,000,000,000,000
139 43 6.18970044×1041 11,263.2699 kilometers 696,898,287,454,081,000,000,000,000,000,000,000,000,000
140 43 1.23794009×1042 22,526.5398 kilometers 1,393,796,574,908,160,000,000,000,000,000,000,000,000,000
141 43 2.47588018×1042 45 053.079 kilometers 2,787,593,149,816,320,000,000,000,000,000,000,000,000,000
142 43 4.95176036×1042 90 106.158 kilometers 5,575,186,299,632,650,000,000,000,000,000,000,000,000,000
143 44 1.11503726×1043 180,212.316 kilometers 11,150,372,599,265,300,000,000,000,000,000,000,000,000,000
144 44 2.23007451×1043 360,424.632 kilometers 22,300,745,198,530,600,000,000,000,000,000,000,000,000,000
145 44 4.46014903×1043 720,849.264 kilometers 44,601,490,397,061,200,000,000,000,000,000,000,000,000,000
146 45 8.9202980×1043 1,441,698.55 kilometers 89,202,980,794,122,400,000,000,000,000,000,000,000,000,000
147 45 1.78405961×1044 2,883,397.1 kilometers 178,405,961,588,244,000,000,000,000,000,000,000,000,000,000
148 45 3.56811923×1044 5,766,794.2 kilometers 3.56812E+44
149 46 7.13623846×1044 11,533,588.4 kilometers 713,623,846,352,979,940,529,142,984,724,747,568,191,373,312
150 46 1.42724769×1045 23,067,176.8 kilometers 1.42725E+45
151 46 2.85449538×1045 46,134,353.6 kilometers 2,854,495,385,411,910,000,000,000,000,000,000,000,000,000,000
152 46 5.70899077×1045 92,268,707.1 kilometers 5.70899E+45
153 47 1.14179815×1046 184,537,414 kilometers 1.1418E+46
154 47 2.28359638×1046 369,074,829 kilometers 2.2836E+46
155 47 4.56719261×1046 738,149,657 kilometers 4.56719E+46
156 48 9.13438523×1046 1.47629931×1012 meters 9.13439E+46
157 48 1.826877046×1047 2.95259863×1012 meters 1.82688E+47
158 48 3.653754093×1047 5.90519726×1012 meters 3.65375E+47
159 49 7.307508186×1047 1.18103945×1013 meters 7.30751E+47
159 49 7.307508186×1047 1.18103941 ×1013 meters 730,750,818,665,451,000,000,000,000,000,000,000,000,000,000,000
160 49 1.461501637×1048 2.36207882 ×1013m 1.4615E+48
161 49 2.923003274×1048 4.72415764 ×1013m 2.923E+48
162 49 5.846006549×1048 9.44831528 ×1013m 5.84601E+48
163 50 1.16920130×1049 1.88966306×1014m 1.1692E+49
164 50 2.33840261×1049 3.77932612×1014m 2.3384E+49
165 50 4.67680523×1049 7.55865224×1014m 4.67681E+49
166 51 9.35361047×1049 1.5117305×1015m 9.35361E+49
167 51 1.87072209×1050 3.0234609×1015m 1.87072E+50
168 51 3.74144419×1050 6.0469218×1015m 3.74144E+50
169 52 7.48288838×1050 1.20938436×1016m 7.48289E+50
170 52 1.49657767×1051 2.41876872×1016m 1.49658E+51
171 52 2.99315535×1051 4.83753744 ×1016m 2.99316E+51
172 52 5.98631070×1051 9.67507488 ×1016m 5.98631E+51
173 53 1.19726214×1052 1.93501504 ×1017m 1.19726E+52
174 53 2.39452428×1052 3.87002996 ×1017m 2.39452E+52
175 53 4.78904856×1052 7.74005992 ×1017m 4.78905E+52
176 54 9.57809713×1052 1.54801198×1018m 9.5781E+52
177 54 1.91561942×1053 3.09602396×1018m 1.91562E+53
178 54 3.83123885×1053 6.19204792×1018m 3.83124E+53
179 55 7.66247770×1053 1.23840958×1019m 7.66248E+53
180 55 1.53249554×1054 2.47681916×1019m 1.5325E+54
181 55 3.06499108×1054 4.95363832×1019m 3.06499E+54
182 55 6.12998216×1054 9.90727664×1019m 6.12998E+54
183 56 1.22599643×1055 1.981455338×1020m 1.226E+55
184 56 2.45199286×1055 3.96291068×1020m 2.45199E+55
185 56 4.90398573×1055 7.92582136×1020m 4.90399E+55
186 57 9.80797146×1055 1.58516432×1021m 9.80797E+55
187 57 1.96159429×1056 3.17032864×1021m 1.96159E+56
188 57 3.92318858×1056 6.34065727 ×1021m 3.92319E+56
189 58 7.84637716×1056 1.26813145 ×1022m 7.84638E+56
190 58 1.56927543×1057 2.53626284×1022m 1.56928E+57
191 58 3.13855086×1057 5.07252568×1022m 3.13855E+57
192 59 6.27710173×1057 1.01450514×1023m 6.2771E+57
193 59 1.25542034×1058 2.02901033×1023m 1.25542E+58
194 59 2.51084069×1058 4.05802056×1023m 2.51084E+58
195 59 5.02168138×1058 8.11604112×1023m 5.02168E+58
196 60 1.00433628×10 1.62320822×1024m 1.00434E+59
197 60 2.0086725×1059 3.24641644×1024m 2.00867E+59
198 60 4.01734511×1059 6.49283305×1024m 4.01735E+59
199 61 8.03469022×1059 1.29856658×1025m 8.03469E+59
200 61 1.60693804×1060 2.59713316×1025m 1.60694E+60
201 61 3.21387608×1060 5.19426632 ×1025m 3.21388E+60
_________________ ______________________ _____________________________________________
202 61 6.42775217×1060 1.03885326×1026 meters 6.42775E+60
203 62 1.28555043×1061 2.07770658×1026 meters 1.28555E+61
204 62 2.57110087×1061 4.15541315×1026 meters 2.5711E+61
205 62 5.14220174×1061 8.31082608×1026 meters 5.1422E+61
206 63 1.028440348×1062 1.662165216×1027 meters 1.0284E+62
_________________ ______________________ _____________________________________________
PL-EOU 1 – 205.1 From the Planck Length 8.79829142×1026 meters
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