written by Rene K. Mueller <kiwi(at)thelabs.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 romannumbers 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 numbersystem for writing,
as we counted first with our fingers, or as children do before they can
abstract numbers.
Different CountBasis or NumberSystems
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 binarysystem whereas our hindu/arabic numbersystem (base 10)
is known as decimalsystem. The 'stick' counting can be considered
as simplest counting or numbersystem based on 1, but how look
numbers for different counting or numbersystems?
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 09 and
then additionally AZ treating them as 11, 12, 13 and so on, just for
illustration purposes (even though this is common in computerscience
to display hexadecimal numbers this way).
Some numbersystems 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 decimalsystem
also other system are still strong in our western culture embedded:
the base 12 counting or numbersystem, 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 12hourclocks easier,
because 12 is divideable by 4 easily, whereas 10 wouldn't be divideable
without remainder by 4.
Beyond NumberSystems
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 humanconcepts, 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
selfcentred, 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
nonexistent 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 humanform, and I wished in a way my entire life is one constant
and fiery prayer to AllThatIs/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 primenumbers 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
grocerystore, 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: 2^{2 }
5: prime
6: 2 * 3
7: prime
8: 2^{3 }
9: 3^{2 }
10: 2 * 5
11: prime
12: 2^{2 } * 3
13: prime
14: 2 * 7
15: 3 * 5
16: 2^{4 }
17: prime
18: 2 * 3^{2 }
19: prime
20: 2^{2 } * 5
21: 3 * 7
22: 2 * 11
23: prime
..
99997: 19^{2} * 277
99998: 2 * 49999
99999: 3^{2} * 41 * 271
100000: 2^{5} * 5^{5}
100001: 11 * 9091
100002: 2 * 3 * 7 * 2381
100003: prime
100004: 2^{2} * 23 * 1087
100005: 3 * 5 * 59 * 113
100006: 2 * 31 * 1613
100007: 97 * 1031
100008: 2^{3} * 3^{3} * 463
100009: 7^{2} * 13 * 157
100010: 2 * 5 * 73 * 137
..
The factorization of 1 to 1,000,000 you can download here (20MB)
  