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