7 March 2013
Counting- Dot-row Counting- Pyramid Counting- Triangular Numbers
Derivation of the Number Field-the Copy-Down Method -the Coat-hanger Method-the Algebraic Method
Number Field 84 (Raw)NoveltyNumbers as StringsGeneral Features of the Number Field
-the Habit of Conservation of Information-Introducing the Negative Edge (necessity?)
Number Field 84 (Complete?)What is the Number Field?What are the Applications?
This Presentation:Mapping Imaginary SpaceThe Platonic SolidsNumber CrystalsQuantum NumberMarko Rodin's Vortex Math
The Spoke, Cylinder, Disc System of CountingThe Three Number Highest Dies Game
CountingCounting
What is counting?
My definition is: The process of symbolising number.
Remember, numbers are purely mental objects, whilst symbols can be both physical and mental objects. Put together this means:
The accuracy of our number symbols determines our understanding of number.
These are not numbers:
13
2
...but they are number symbols!
Dot-Row Counting
-When large, strings or scratches or rows of dots become unhandleable until the recursive age.
Pyramid Counting
- Close-Packed Circles- Habit of the Conservation of Information - Axonometric projection- Capacity for a new dimension: depth - Pascals triangle etc
The First 100
Triangular Numbers
9
84
-Copying-Down
-Coat-hanger
-Algebraic?
-Axial?
Derivation of the Number Field:
Copying-Down
1918
16
1413
1211
109
87
65
43
21
15
17
3736
3534
3332
3130
2928
2726
2524
2221
20
23
Copying-Down
Choice point
The Coat-hanger
-The next number appears as two halves before it is counted
8
6
5
9
The Coat-hanger
11
12
22
13
23
33
14
24
34
44
15
25
35
45
55
16
26
36
46
56
66
17
27
37
47
57
67
77
18
28
38
48
58
68
78
88
19
29
39
49
59
69
79
89
99
The Algebraic Derivation
- 3 Number Highest Dies method
X X>Y? Then let X=X-YY Y>X? Then let X=Y and Y=X
Results: 1/1 = +ve (white, one, novel) Other = -ve (black, zero, repeat)
22
33
24
44
55
26
36
46
66
77
28
48
68
88
39
69
99
Take any two different numbers, Create a third using the difference,Delete the highest number of the three, Begin again.
1 / 1 = Novel (choice point)
Number Field 84
Novelty
Disc Number
Cylinder-Disc Number(A)
Previous Cylinder-Disc Number(B)
NOVELTY FACTOR (X)
X = A - B
1 1 0 1
2 2 1 1
3 4 2 2
4 6 4 2
5 10 6 4
6 12 10 2
Number as Strings / Beats / Sequences / Vectors1
Binary 2,4,8,16,32 etc.
3
Primes
6
9
10
12
14
15
18
20
General Features of the Number Field
The Positive Edge, not reflected on the opposite edge
- Black cells are patterns of factors- White cells are novel
Bottom edge is infinite as long as 'counting' continues
Single Number count
Repeated Single Numbers
Single Number count (1 out of phase?)
Primary Axes?
The same number can befound at various angles
85/2
15
The Habit of the Conservation of Information
General Features - Axes½ ? ½ ?
1/3 1/4 1/5 Etc.
Offset
The Negative Edge
Neg
. Edg
e
-Universal Imaginary Shape?
-the same in all cultures, all places,, all times?
-the 'hard-copy' or static version of the process of counting?
-a teaching aid ?
-A FRACTAL?
- COUNTING
What is the Number Field? Applications?
The Number Fractal
- ALL NUMBERS HAVE EXACTLY THE SAME SHAPE! It's just a matter of SCALE!
Mapping Imaginary Space Using Number Crystals
- zero point in grey
Platonic Solids
Number 2 in 3-space
Number 2 in 3-space
Snap to grid ? ;-)
Single circuit
Knight's Move
Number 2 in 3-space
Number 2 in 3-space
Number Crystals compare well to Nassim Haramein's Physics
Quantum Number 9
-Multiplication Tables
54 nodes
Quantum negative edge a little different to the field
1 22
44
88
7 5 1
Quantum #9 Octave Circuit
1 2 4 8 16 32 1
64 128 256 512 1024 2048 4096
0.015625 0.03125 0.0625 0.125 0.25 0.5 1
Doubling Halving
Quantum Number 9 Doubling Circuit (Basic Form)
The doubling circuit can work like this in Q#9, but to crystallise Q#9 we need the negative edge
43 steps on the circuit, including 12 reflections
Quantum Doubling Axis
Quantum Number 9 Doubling Circuit
Quantum Number Crystal 9
Better Understanding Doubling Circuits
Better Understanding Doubling Circuits
Static Dynamic Schematic
Vector Marko Rodin
30
The number of spokes symbolises the number.The disc represents the one full revolution required to count the full number of spokes.A cylinder is a number of overlapping discs.
1
12
Single numbers are symbolised with spokes equidistant
The Spoke, Disc & Cylinder (SDC) System
100
Overlapping discs produce composite discs, or Cylinder Discs
Cylinder Discs
Discs 1 and 2 overlapped produce a Cylinder Disc identical to disc 2.
Discs 1,2, and 3 produce this Cylinder Disc(1-3)
Cylinder Disc (1-5)
Cylinder Disc (1-4)
Cylinder Disc (1-6)
Cylinder Disc (1-6)
1 + 2 + 3 + 4 + 5 + 6 = 21 1 x 2 x 3 x 4 x 5 x 6 = 720
And yet the Cylinder Disc (1-6) has a count of 12
I don't know what to call these Cylinder Disc numbers, but they are not sums (additions) or factorials (multiplications).
Cylinder Disc Numbers
1
23
4
5
67
8
9
10
1112
Disc Number
Cylinder-Disc Number(A)
Previous Cylinder-Disc Number(B)
NOVELTY FACTOR (X)
X = A - B
1 1 0 1
2 2 1 1
3 4 2 2
4 6 4 2
5 10 6 4
6 12 10 2
Novelty Factor X
Primality Testn A B X n - X Prime?
1 1 0 1 0 no
2 2 1 1 1 yes
3 4 2 2 1 yes
4 6 4 2 2 no
5 10 6 4 1 yes
6 12 10 2 4 no
7 18 12 6 1 yes
8 22 18 4 4 no
9 28 22 6 3 no
10 32 28 4 6 no
11 42 32 10 1 yes
12 46 42 4 8 no
13 58 46 12 1 yes
14 64 58 6 8 no
15 72 64 8 7 no
16 80 72 8 8 no
17 96 80 16 1 yes
18 102 96 6 12 no
19 120 102 18 1 yes
20 128 120 8 12 no
21 140 128 12 9 no
22 150 140 10 12 no
23 172 150 22 1 yes
Let Disc n = a test number counted using SDC
Cylinder Disc B
Cylinder A (1 to n) X = CD(A - B)
If n - X = 1then n is prime
Cylinder B (1 to n-1)
Cylinder Disc A
Disc(n)
Disc(n-1)
CD(A)
CD(B)
If n - X = ? ...
Looking into the Nature of Cylinder Disc Numbers
Cylinder Disc Number(1-6)=12
Cylinder Disc (1-5) = ?
Primes represent maximum novelty at the moment of their counting.
All lower numbers become repeats as higher numbers are counted, including primes.
Dotted lines are hidden spokesSolid lines are visible spokes
Conclusions
1. There seems to be such a thing (object) as the Number Field
2. This object evolves from counting correctly
3. Counting Correctly will involve information about which parts of number are novel and which are repeated
4. Basic Exploration of the above concepts yields...
END