SpiritArt: Numbers

written by Rene K. Mueller <kiwi(at)the-labs.com>, November 2000

Numbers are part of our daily life, what if behind their abstractness lies something as real, as alive, as conscious like ourselves? Numbers are fundamental quality of creation, and to honor them this page is dedicated for . . .

You may say Numbers are invention of humans, it is partially true: We defined the meaning of the figures like 2 to be two, but the amount of seeds on a corn is finite and countable, and the corn itself knows how many seeds it should grow . . . Numbers relate Aspects of Creation to each other due their nature.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, . . .

I would like to illustrate the many different notations there are to represent numbers. Let us first start as maybe an ancient tribe counted numbers with sticks:

I
I I
I I I
I I I I
I I I I I
I I I I I I
I I I I I I I
I I I I I I I I
I I I I I I I I I
I I I I I I I I I I
I I I I I I I I I I I
I I I I I I I I I I I I
I I I I I I I I I I I I I
I I I I I I I I I I I I I I
I I I I I I I I I I I I I I I

It is obvious the "stick"-notation, or -basis, or -representation of larger numbers getting hard for us humans to perceive as we immediatly start to count the sticks again when they are more than 4 or 5 sticks.

Abstraction
The roman-numbers is a further abtraction: I = 1, V = 5, X = 10, L = 50, C = 100, D = 500, M = 1000.

I, II, III, IV, V, VI, VII, VIII, IX, X, XI, XII ...

A further abstraction occured to represent with a single or two strockes a symbol which represents the first ten digits, from arabia (originally sanskrit) we got 1, 2, 3, 4, 5, 6, 7, 9, 10, 11, . . .

Why we did base our counting on ten? Because we as human specie have twice five fingers on our two hands. This means also that a physical basis of ten fingers became the basis of our number-system for writing, as we counted first with our fingers, or as children do before they can abstract numbers.

Different Count-Basis or Number-Systems
This leads now to a deeper look of the notation of numbers. Maybe you know that a computer knows only 0 and 1, on or off, this notation is known as binary-system whereas our hindu/arabic number-system (base 10) is known as decimal-system. The 'stick' counting can be considered as simplest counting- or number-system based on 1, but how look numbers for different counting or number-systems?

base:	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20
1:	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1
2:	10	2	2	2	2	2	2	2	2	2	2	2	2	2	2	2	2	2	2
3:	11	10	3	3	3	3	3	3	3	3	3	3	3	3	3	3	3	3	3
4:	100	11	10	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4	4
5:	101	12	11	10	5	5	5	5	5	5	5	5	5	5	5	5	5	5	5
6:	110	20	12	11	10	6	6	6	6	6	6	6	6	6	6	6	6	6	6
7:	111	21	13	12	11	10	7	7	7	7	7	7	7	7	7	7	7	7	7
8:	1000	22	20	13	12	11	10	8	8	8	8	8	8	8	8	8	8	8	8
9:	1001	100	21	14	13	12	11	10	9	9	9	9	9	9	9	9	9	9	9
10:	1010	101	22	20	14	13	12	11	10	A	A	A	A	A	A	A	A	A	A
11:	1011	102	23	21	15	14	13	12	11	10	B	B	B	B	B	B	B	B	B
12:	1100	110	30	22	20	15	14	13	12	11	10	C	C	C	C	C	C	C	C
13:	1101	111	31	23	21	16	15	14	13	12	11	10	D	D	D	D	D	D	D
14:	1110	112	32	24	22	20	16	15	14	13	12	11	10	E	E	E	E	E	E
15:	1111	120	33	30	23	21	17	16	15	14	13	12	11	10	F	F	F	F	F
16:	10000	121	100	31	24	22	20	17	16	15	14	13	12	11	10	G	G	G	G
17:	10001	122	101	32	25	23	21	18	17	16	15	14	13	12	11	10	H	H	H
18:	10010	200	102	33	30	24	22	20	18	17	16	15	14	13	12	11	10	I	I
19:	10011	201	103	34	31	25	23	21	19	18	17	16	15	14	13	12	11	10	J
20:	10100	202	110	40	32	26	24	22	20	19	18	17	16	15	14	13	12	11	10
21:	10101	210	111	41	33	30	25	23	21	1A	19	18	17	16	15	14	13	12	11
22:	10110	211	112	42	34	31	26	24	22	20	1A	19	18	17	16	15	14	13	12
23:	10111	212	113	43	35	32	27	25	23	21	1B	1A	19	18	17	16	15	14	13
24:	11000	220	120	44	40	33	30	26	24	22	20	1B	1A	19	18	17	16	15	14
25:	11001	221	121	100	41	34	31	27	25	23	21	1C	1B	1A	19	18	17	16	15

As you may have noticed I extended the range of digits from 0-9 and then additionally A-Z treating them as 11, 12, 13 and so on, just for illustration purposes (even though this is common in computer-science to display hexadecimal numbers this way).

Some number-systems have been named binary (base 2), ternary (base 3): quaternary (base 4), quinary (base 5), senary (base 6), septenary (base 7), octenary (or octal, base 8), nonary (base 9), denary (or decimal), undenary (base 11), duodecimal (base 12), hexadecimal (base 16), vigesimal (base 20), and sexagesimal (base 60).

Base 12
It maybe is also worth to mention that beside decimal-system also other system are still strong in our western culture embedded: the base 12 counting- or number-system, the dozen, or the way we count our time now:

5*dozen = 60 seconds -> 1 minutes,
5*dozen = 60 minutes -> 1 hour,
2*dozen = 24 hours -> 1 day.

Base 10 vs. Base 12
The main advantage to count in dozen is the better factorization, which in other words means easier divideable by integers without remainder; e.g. when you have 12 items to divide, then you have more choices to divide them as 10, which was significant when sharing the items:

12 you can divide by 2, 3, 4 and 6 without remainder,
10 you can devide only by 2, and 5 without remainder.

This made also the division of our 12-hour-clocks easier, because 12 is divideable by 4 easily, whereas 10 wouldn't be divideable without remainder by 4.

Beyond Number-Systems
Beyond counting basis would mean each integer number has its own name and symbol and not composed on any basis as such. This would express the honor and recognition the numbers in their nature more independently as our human-concepts, anatomy (10 fingers) and its derived thinking.

Unity and Numbers
Another approach could be taken that the numbers are described through their relationship to the origin, the One. In way the counting is exactly this, it honors and affirms the One as many times as the number is, e.g. one, two, three, four, and so on, each number is composed by the sum of One's, each number incarnates a multiple of One. In this regard one must mention Plotinus's Six Enneades (250 AD), famous greek mystic speaking about the 'On the good, or the one' or specially Plotinus' ennead six, sixth tractate: On Numbers (excerpt):

1. It is suggested that multiplicity is a falling away from The Unity, infinity being the complete departure, an innumerable multiplicity, and that this is why unlimit is an evil and we evil at the stage of multiplicity.
A thing, in fact, becomes a manifold when, unable to remain self-centred, it flows outward and by that dissipation takes extension: utterly losing unity it becomes a manifold since there is nothing to bind part to part; when, with all this outflowing, it becomes something definite, there is a magnitude.
But what is there so grievous in magnitude?
Given consciousness, there will be, since the thing must feel its exile, its sundrance from its essence. Everything seeks not the alien but itself; in that outward moving there is frustration or compulsion; a thing most exists not when it takes multiplicity or extension but when it holds to its own being, that is when its movement is inward. Desire towards extension is ignorance of the authentically great, a movement not on the appropriate path but towards the strange; to the possession of the self the way is inward.
Consider the thing that has taken extension; broken into so many independent items, it is now those several parts and not the thing it was; if that original is to persist, the members must stand collected to their total; in other words, a thing is itself not by being extended but by remaining, in its degree, a unity: through expansion and in the measure of the expansion, it is less itself; retaining unity, it retains its essential being.
Yet the universe has at once extension and beauty?
Yes; because it has not been allowed to slip away into the limitless but is held fast by unity; and it has beauty in virtue of Beauty not of Magnitude; it needed Beauty to parry that magnitude; in the degree of its extension it was void of beauty and to that degree ugly. Thus extension serves as Matter to Beauty since what calls for its ordering is a multiplicity. The greater the expansion, the greater the disorder and ugliness.
2. What, then, of the "Number of the Infinite"?
To begin with, how is Number consistent with infinity?
Objects of sense are not unlimited and therefore the Number applying to them cannot be so. Nor is an enumerator able to number to infinity; though we double, multiply over and over again, we still end with a finite number; though we range over past and future, and consider them, even, as a totality, we still end with the finite.
Are we then to dismiss absolute limitlessness and think merely that there is always something beyond?
No; that more is not in the reckoner's power to produce; the total stands already defined.
In the Intellectual the Beings are determined and with them Number, the number corresponding to their total; in this sphere of our own- as we make a man a multiple by counting up his various characteristics, his beauty and the rest- we take each image of Being and form a corresponding image of number; we multiply a non-existent in and so produce multiple numbers; if we number years we draw on the numbers in our own minds and apply them to the years; these numbers are still our possession.

Consider to read the complete Ennead VI, sixth tractate: On Numbers.

When I Met the Number 13
In late fall of 1999 I was doing an affirmation (prayer) in order to understand the nature of numbers better, and especially find a way of a personal approach, if not saying relationship to them, because I realized in all my spirituality I missed this part without realizing it consciously, only deep within me I had this longing to reawaken or remember what I was knowing already but could not recall and express consciously.

I must say, all my affirmations and prayers have been answered in my life, it is something most sacred to me, and I learned through all of my life, when I'm alone, then only because I separate myself from my divinity, when I'm centered within my core and soul, then I'm never alone, and so a prayer is for me the most sacred performance I do in this human-form, and I wished in a way my entire life is one constant and fiery prayer to All-That-Is/Creator/God.

So, in the 2nd week of January 2000 my affirmation/prayer was answered, in a way I did not foresee or expected it at all:

I was washing my dishes and just started to clean up all spoons, forks and knifes which were left.
So, I was starting to hear within me:
"Greetings, we are 13"
Hmm ....
"We are 13"
No, there are more spoons, forks and knifes, at least 17 or even more I thought. Sometimes I know the amount of things I look at without actually counting them, but this time it was different.
"We are 13"
No, please, I'm already enganged with a lot of mundane stuff, I can't stand now a spirit pretending being 13, or saying there are 13 spoons, knifes and so forth. "Stop it" I thought and hoped that presence or spirit, or whoever it was to stop.
"Count us"
I felt silly, I started to count, and when I saw I had 10 in my hand, and still a bunch not yet counted, I felt truly silly, because I knew there were more than 13.
So I counted 17, and I said to myself that I should remember not to open myself for entities to be channeled, because sillyness like this would occur ...
"We are 13"
"Where 13?" I asked, trying to challenge that being to confront with the obvious that there was no 13.
"We are within those 17 you just counted . . ."
Oppps ... I missed the point completely!
What happened is a conversation which I partially are able to reproduce:
"Do realize that every number is embedded within its next higher number? And all numbers are made of the 1/One?"
"It is like you humans are: everyone is an individual, but you are also part of each other".
"The question is, how do numbers relate to each other ... such as we (13) are within 17 - but when you apply another relationship ... " (refering a certain form of calculation such as division or multiplication) " ... then the relationship appears different, and maybe apart and as an individual" (such as the prime-numbers I thought for myself)
"In this sense, when you think you are an individual, then you relate yourself in a certain way where you are truly unique, and individual; but also, you always have within yourself the 1/One" (refering the Source of All Things/God)
"When you feel apart of something or even lonely, ask yourself which relation you are choosing to look at yourself and others ..."
"We are 13 and we know we are embedded in countless other numbers" and I felt their joy when they expressed this insight . . .
"You humans are very very complex numbers, we are like archetypes of yours, we are living within you"
"So next time you count, remember us, the 13, especially since you have the tendencies to negate our existance" (meant collective tendency to negate e.g. the 13th row, or 13th floor etc) And while the presence faded away, I was thinking, why 13, why not another number?
"Today is also January 13, and you counted us" . . .
I was speechless . . .
And so I pondered on this more . . .
A society which is so focused on counting time, money, and now even with a more and more computerized society, numbers, everywhere numbers.
What, if every number is a being ...
"We are" I hear immediatly ... and then I think, so what when we talk, and count, and measure ...
"This what we are for" . . .
"There is nothing which is purposeless" . . .
"We help you to relate yourself" . . .
My mind kept running asking, slowly to realize the consequence of this 'conversation' with 13 to All That Is . . . when every number is a being, alive, conscious, and existing for the purpose to create relationships between All and One . . .
Well, the day I 'met' 13, I feel almost silly writing about it, but the same moment I know also . . . I do want to understand this entire world I live in, everything . . .
And how unconscious and ignorant I have been using numbers . . .
I promise myself from this day on, Jan 13 2000, I want to honor every number I use to relate myself in this reality, may it be paying in the grocery-store, counting the days or years, or looking at the watch and seeing it's 20 past nine . . .
Everything is sacred . . . 1 2 3 4 5 6 7 8 9 10 11 12 13 . . .

One of the easiest relationships between numbers, aside the successor nature of integers, is the factorization describing the number by multiplication(s) of other numbers. These factors are prime:

2: prime
3: prime
4: 2²
5: prime
6: 2 * 3
7: prime
8: 2³
9: 3²
10: 2 * 5
11: prime
12: 2² * 3
13: prime
14: 2 * 7
15: 3 * 5
16: 2⁴
17: prime
18: 2 * 3²
19: prime
20: 2² * 5
21: 3 * 7
22: 2 * 11
23: prime
..
99997: 19² * 277
99998: 2 * 49999
99999: 3² * 41 * 271
100000: 2⁵ * 5⁵
100001: 11 * 9091
100002: 2 * 3 * 7 * 2381
100003: prime
100004: 2² * 23 * 1087
100005: 3 * 5 * 59 * 113
100006: 2 * 31 * 1613
100007: 97 * 1031
100008: 2³ * 3³ * 463
100009: 7² * 13 * 157
100010: 2 * 5 * 73 * 137
..

The factorization of 1 to 1,000,000 you can download here (20MB)

Pi The ratio of circumference of a circle to its diameter	Prime Numbers Prime numbers and their nature	Fibonacci Numbers Fibonacci numbers and their appearance in nature
Open Directory: Specific Numbers Sites dedicated to specific numbers.