This discussion extends the general overview of the Big Boardlittle universe and a roughdraft for an article about it all. Of course, even this page is a workinprogress.
What is simple? A point? What do we know about a point? There are so many concepts to learn just in that one simple word. And then, how about two points? ...three points? A rather idiosyncratic access path to the simple mathematics of points, lines, triangles and objects begins at the Planck length and simply multiplies it by two over and over again..
Powersoftwo and Exponentiation based on the Planck length. Herein it is referred to as Base2 Exponential Notation, Powers of Two based on the Planck length" (abbreviated, "B2EN"). Can the universe, from the smallest to the largest, be seen in a more meaningful way than using baseten scientific notation (B10SN)? B2EN renders greater granularity, a necessary relationality, and nesting geometries. The project originated with a series of five high school geometry classes in December 2011. The smallest possible measurement within space and time was defined mathematically back in 1889 by a fellow named Max Planck. Generally accepted within the scientific community, the Planck length is so small, it is written using scientific notation.
The number is 1.616199(97)x10^{35} meters. As a starting point we looked for all 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, those references will grow substantially. As we understand it today, we believe it must be one of the most important numbers within space and time.
Professor Laurence Eaves of the University of Nottingham in England has a delightful YouTube video that explains this length. That number can be used to define a point.
In this simple exercise, take the Planck length and multiply it by 2, until we reach something that is measurable today (the diameter of a proton) and then to objects within the human scale, and finally to the edges of the observable universe. Mathematically, it will require just 202.34 notations. In five columns, the first column is the baseten notations. The second column is a Planck number based on the number of times the Planck length has been multiplied. The third column is the number of points, 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 about a notation.
Notations 57 to 116 Notations 116 to 159 Notations 159 to 205

1

0

2^0=1

Length (widthheight)meters
1.616199(97)×10^{35}m

Additional Information, Discussion, Examples:
At this first notation, there is just one point, a singularity. More...

1 
1 
2^1=2 
3.23239994×10^{35}m 
At the second notation, there are two points, the shortest possible line, possibly the beginnings of a string which opens discussions about some of the most basic questions in science. 
1 
2 
2^2=4 
6.46479988×10^{35}m 
At the third notation there are four points. There are several logical possibilities: (1) four points form a line, (2) four points form a jagged line of which four [[skew polygonskewed triangles]] could be formed, (3) three points form a triangle that define a plane with the fourth point forming a [[tetrahedron]] (imperfect or perfect) that defines the first three dimensions of space 
2 
3 
2^3=8 
1.292959976×10^{34}m 
At the fourth notation there are eight points. The logical possibilities are now expanded to include placing the points either inside the tetrahedron, on the edges of the tetrahedron or outside the tetrahedron. Here multiplying could also involve dividing any of the six edges of the tetrahedron. If the points are are equally distributed on the edges of tetrahedron, an octahedron and four tetrahedrons begin to emerge. (picture to be added) If added within, [[Closepacking of equal spherestetrahedrally closepacked structures]] emerge. If added externally, with just three additional points, a tetrahedral pentagon is created of five tetrahedrons. (picture to be added) With all eight additional points added externally,a [[cube]] or [[hexahedron]] could be created. 
2 
4 
2^4=16 
2.585919952×10^{34}m 
At the fifth notation there are sixteen points. If any one of the points were to become a center point, and 10 points are extended from it, a tetrahedral icosahedron emerges. (picture to be added) With twenty points a simple dodecahedron is possible. And with the icosahedron, all [[platonic solidsfive basic platonic solids]] are accounted. 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 points. (picture to be added) These points 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 point of the octahedron would begin to be defined and by the 18th point 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) 
2 
5 
2^5=32 
5.171839904×10^{34}m 
At the sixth notation, there are 32 points. Here there is a possibility for a cluster of eight tetrahedral pentagons to emerge and complete with 34 points. 
3 
6 
2^6=64 
1.0343679808×10^{33}m 
At the seventh notation, there are 64 points. With just 43 of those points a hexacontagon could be created. It has 12 polytetrahedral clusters with an icosahedron and many tetrahedrons in the middle. 
3 
7 
2^7=128 
2.0687359616×10^{33}m 
By the eighth notation, the progression becomes selfevident. The results are not. Simple exponential notation based on the power of two is well documented. Of course, by using the Power of two, exponentiation and starting at Planck's constant, necessary relations can be constructed. 
3 
8 
2^8=256 
4.1374719232×10^{33}m 
Geometric complexification to be discussed. 
3 
9 
2^9=512 
8.2749438464×10^{33}m 
_ 
4 
10 
1024 
1.65498876928×10^{32}m 
_ 
4 
11 
2048 
3.30997752836×10^{32}m 
_ 
4 
12 
4096 
6.61995505672×10^{32}m 
_ 
5 
13 
8192 
1.323991011344×10^{31}m 
_ 
5 
14 
16,384 
2.647982022688×10^{31}m 
_ 
5 
15 
32,768 
5.295964045376×10^{31}m 
_ 
6 
16 
65,536 
1.0591928090752×10^{30}m 
_ 
6 
17 
131,072 
2.1183856181504×10^{30}m 
_ 
6 
18 
262,144 
4.2367712363008×10^{30}m 
_ 
6 
19 
524,288 
8.4735424726016×10^{30}m 
_ 
7 
20 
1,048,576 
1.69470849452032×10^{29}m 
_ 
7 
21 
2,097,152 
3.38941698904064×10^{29}m 
more information 
7 
22 
4,194,304 
6.77883397808128×10^{29}m 
_ 
8 
23 
8,388,608 
1.355766795616256×10^{28}m 
_ 
8 
24 
16,777,216 
2.711533591232512×10^{28}m 
_ 
8 
25 
33,554,432 
5.423067182465024×10^{28}m 
_ 
9 
26 
67,108,864 
1.0846134364930048×10^{27}m 
_ 
9 
27 
134,217,728 
2.1692268729860096×10^{27}m 
9 
28 
268,435,456 
4.3384537459720192×10^{27}m 
_ 
9 
29 
536,870,912 
8.6769074919440384×10^{27}m 
_ 
10 
30 
1,073,741,824 
1.73538149438880768×10^{26}m 
_ 
10 
31 
2,147,483,648 
3.47076299879961536×10^{26}m 
_ 
10 
32 
4,294,967,296 
6.94152599×10^{26}m 
_ 
11 
33 
8,589,934,592 
1.3883052×10^{25}m 
_ 
11 
34 
1.7179869×10^{11} 
2.7766104×10^{25}m 
Actual number: 17,179,869,184 points 
11 
35 
3.4359738×10^{11} 
5.5532208×10^{25}m 
34,359,738,368 
12 
36 
6.8719476×10^{11} 
1.11064416×10^{24}m 
68,719,476,736 
12 
37 
1.3743895×10^{12} 
2.22128832×10^{24}m 
137,438,953,472 
12 
38 
2.7487790×10^{12} 
4.44257664×10^{24}m 
274,877,906,944 
12 
39 
5.4975581×10^{11} 
8.88515328×10^{24}m 
549,755,813,888 
13 
40 
1.0995116×10^{12} 
1.77703066×10^{23}m 
1,099,511,627,776 
13 
41 
2.1990232×10^{12} 
3.55406132×10^{23}m 
2,199,023,255,552 
13 
42 
4.3980465×10^{12} 
7.10812264×10^{23}m 
4,398,046,511,104 
14 
43

8.7960930×10^{12}

1.4.2162453×10^{22}m

8,796,093,022,208 
14 
44 
1.7592186×10^{13} 
2.84324906×10^{22}m 
17,592,186,044,416 
14 
45 
3.5184372×10^{13} 
5.68649812×10^{22}m 
35,184,372,088,832 
15 
46 
7.0368744×10^{13} 
1.13729962×10^{21}m 
70,368,744,177,664 
15 
47 
1.4073748×10^{14} 
2.27459924×10^{21}m 
140,737,488,355,328 
15 
48 
2.8147497×10^{14} 
4.54919848×10^{21}m 
281,474,976,710,656 
15 
49 
5.6294995×10^{14} 
9.09839696×10^{21}m 
562,949,953,421,312 
16 
50 
1.12589988×10^{15} 
1.81967939×10^{20}m 
1,125,899,906,842,624 
16 
51 
2.25179981×10^{15} 
3.63935878×10^{20}m 
2,251,799,813,685,248 
16 
52 
4.50359962×10^{15} 
7.27871756×10^{20}m 
4,503,599,627,370,496 
17 
53 
9.00719925×10^{15} 
1.45574351×10^{19}m 
9,007,199,254,740,992 
17 
54 
1.80143985×10^{16} 
2.91148702×10^{19}m 
18,014,398,509,481,984 
17 
55 
3.60287970×10^{16} 
5.82297404×10^{19}m 
36,028,797,018,963,968 
18 
56 
7.205759840×10^{16} 
1.16459481×10^{18}m 
72,057,594,037,927,936 
18 
57 
1.44115188×10^{17} 
2.32918962×10^{18}m 
144,115,188,075,855,872 
This page is Notations 0 to 57 It continues here: Notations 57 to 116 Notations 116 to 159 Notations 159 to 206
