2. This Presentation:
Counting Mapping Imaginary Space
- Dot-row Counting The Platonic Solids
- Pyramid Counting Number Crystals
- Triangular Numbers Quantum Number
Derivation of the Number Field Marko Rodin's Vortex Math
-the Copy-Down Method
-the Coat-hanger Method The Spoke, Cylinder, Disc System of Counting
-the Algebraic Method The Three Number Highest Dies Game
Number Field 84 (Raw)
Novelty
Numbers as Strings
General 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?
3. Counting
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:
3
1
2
...but they are number symbols!
5. Pyramid Counting
- Close-Packed Circles
- Habit of the Conservation of Information
- Axonometric projection
- Capacity for a new dimension: depth - Pascals triangle etc
14. Novelty
Disc Cylinder-Disc Previous NOVELTY
Number Number Cylinder-Disc FACTOR (X)
(A) Number
(B) 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
15. Number as Strings / Beats / Sequences / Vectors
1
Binary 2,4,8,16,32 etc.
3
Primes
6
9
10
12
14
15
18
20
16. General Features of the Number Field The Habit of the
Conservation of Information
- Black cells are patterns of factors
- White cells are novel The Positive Edge, not reflected on the opposite edge
The same number can be
found at various angles
15
Primary Axes?
Repeated Single Number count
Single Numbers (1 out of phase?)
Single Number count
85/2
Bottom edge is infinite as long as 'counting' continues
19. What is the Number Field? Applications?
-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
20. The Number Fractal
- ALL NUMBERS HAVE EXACTLY THE SAME SHAPE! It's just a matter of SCALE!
35. The Spoke, Disc & Cylinder (SDC) System
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
30
100
36. Cylinder Discs
Overlapping discs produce composite discs, or 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 (1-4)
Cylinder Disc (1-5)
Cylinder Disc (1-6)
37. Cylinder Disc Numbers
1
12 2
11 3
10 4 Cylinder Disc (1-6)
9 5
8 6
7
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).
38. Novelty Factor X
Disc Cylinder-Disc Previous NOVELTY
Number Number Cylinder-Disc FACTOR (X)
(A) Number
(B) 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
39. Primality Test
n A B X n-X Prime?
1 1 0 1 0 no
Let Disc n = a test number
2 2 1 1 1 yes
counted using SDC
3 4 2 2 1 yes
4 6 4 2 2 no
If n - X = ? ... 5 10 6 4 1 yes
Disc CD 6 12 10 2 4 no
(n) (A)
7 18 12 6 1 yes
Cylinder Disc A 8 22 18 4 4 no
Cylinder A (1 to n) X = CD(A - B)
9 28 22 6 3 no
10 32 28 4 6 no
Disc CD
(n-1) (B) If n - X = 1 11 42 32 10 1 yes
then n is prime 12 46 42 4 8 no
Cylinder B (1 to n-1) Cylinder Disc B 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
40. Looking into the Nature of Cylinder Disc Numbers
Cylinder Disc Number(1-6)=12
Dotted lines are hidden spokes
Solid lines are visible spokes
Primes represent maximum novelty at the moment of their counting.
All lower numbers become repeats as higher numbers are counted, including primes.
Cylinder Disc (1-5) = ?
41. 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...
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