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"The Numerica Format: a numerical sequencing method"
By: Paul Allen Panks (dun...@yahoo.com)
Date: April 30, 2004
(Version 1.2 - Revised and Expanded)
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=======
Summary
=======
This is a simple encoding sequence using numbers assigned
as letters and punctuation. The sequence is comprised of an
encoding arrangement of 49 total letters, punctuation and
numerical mathematical assignments.
The resulting sequence uses the multiplication table of zero [0] through
nine [9]. Some numbers -- 11,13,17,19,22,23,26, etc. -- are not reachable
via the regular 0 through 9 multiplication tables. Such numbers must then
be added together to simulate actual values not reachable via the normal
multiplication standard.
This sequencing method is best described as the "Numerica Format".
Encoded sequences are called "Numericas". Individual sequence lines are
termed "Numeri".
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Binary Assignment
=================
To make full use of the sequence, letters, basic punctuation and numbers
are approximated through simple mathematical equations. Forty-nine total
letters, numbers and punctuation are assigned to the following numeric
values:
A = 1
B = 2
C = 3
D = 4
E = 5
F = 6
G = 7
H = 8
I = 9
J = 10
K = 11
L = 12
M = 13
N = 14
O = 15
P = 16
Q = 17
R = 18
S = 19
T = 20
U = 21
V = 22
W = 23
X = 24
Y = 25
Z = 26
Punctuation is also required, and thus is assigned to the following
numbers:
27 = .
28 = !
29 = ?
30 = ,
31 = &
32 = (space)
33 = *
34 = @
35 = %
36 = $
37 = +
38 = -
39 = #
40 = 0
41 = 1
42 = 2
43 = 3
44 = 4
45 = 5
46 = 6
47 = 7
48 = 8
49 = 9
50 = (undefined)
The sequence is straightforward and easily used. A brief explanation
(with an example of the sequence as it is normally used) will follow
later on during the course of this article.
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The Multiples Table
===================
Listed below is a standard multiplication table (used in the
Numerica Format). Note that numbers never go above 81, or below 0:
1 2 3 4 5 6 7 8 9
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0|1 2 3 4 5 6 7 8 9
1|1 2 3 4 5 6 7 8 9
2|2 4 6 8 10 12 14 16 18
3|3 6 9 12 15 18 21 24 27
4|4 8 12 16 20 24 28 32 36
5|5 10 15 20 25 30 35 40 45
6|6 12 18 24 30 36 42 48 54
7|7 14 21 28 35 42 49 56 63
8|8 16 24 32 40 48 56 64 72
9|9 18 27 36 45 54 63 72 81
------------------------------------
=====================================
How numbers are added (or multiplied)
=====================================
Some values (e.g. 11,13,17,19,22,23,26, etc.) have no possibility
of being multiplied successfully by numbers ranging from 0 through 9.
Therefore, they must be added together. In special cases, the added
numbers represent the larger numbers themselves (i.e. 2+9 will be
equal to the number "29",etc.)
In order to differentiate between multiplication of two numbers
(and addition), the sequence in which they are added together
is reversed in logical order.
The forty-nine numeric assignments are reached via the following
Simple mathematical equations (Note: Some equations arenequations; rather,
they are quite literal representations of the
numbers themselves):
0+1=1 [A]
0+2=2 [B]
0+3=3 [C]
0+4=4 [D]
0+5=5 [E]
0+6=6 [F]
0+7=7 [G]
0+8=8 [H]
0+9=9 [I]
5*2=10 [J]
5+6=11 [K]
6*2=12 [L]
6+7=13 [M]
7*2=14 [N]
5*3=15 [O]
8*2=16 [P]
8+9=17 [Q]
9*2=18 [R]
1+9=19 [S]
5*4=20 [T]
7*3=21 [U]
2+2=22 [V]
2+3=23 [W]
6*4=24 [X]
5*5=25 [Y]
2+6=26 [Z]
9*3=27 [.]
7*4=28 [!]
2+9=29 [?]
6*5=30 [,]
3+1=31 [&]
8*4=32 [ ]
3+3=33 [*]
3+4=34 [@]
7*5=35 [%]
9*4=36 [$]
3+7=37 [+]
3+8=38 [-]
3+9=39 [#]
4+0=40 [0]
4+1=41 [1]
4+2=42 [2]
4+3=43 [3]
4+4=44 [4]
4+5=45 [5]
4+6=46 [6]
4+7=47 [7]
4+8=48 [8]
4+9=49 [9]
5+0=50 [blank]
A few notes:
The 50th sequence is left undefined, thus, the Numerica Format really only
has 49. "Space", an invisible punctuation mark used to separate words from
one another in normal language, is assigned as the 32nd sequence.
Addition always has the lowest value added first, followed by the larger
value. In only a few instances, such as 2+2, are the values the same when
adding together two numbers. When multiplying, the first number is always
larger than the second, with one exception: 5*5 (the sum has no known
value reachable via numbers 0 through 9 outside of 5*5).
==========================
Example of a simple Numeri
==========================
A brief summary of a simple Numeri and the resulting sequence
follows. This is a simple Numeri consisting of 6 total words and
1 punctuation mark (a period, or .).
Example:
THE COW JUMPED OVER THE MOON.
Translated:
54 08 05 84 03 53 23 84 52 73 67 82 05 04 84 53 22 05 92 84 54 08
05 84 67 53 53 72 93
T H E C O W J U M P E D O V E R T H E M
O O N .
Or:
THE COW JUMPED OVER THE MOON.
5408058403532384527367820504845322059284540805846753537293
To the casual observer, this is just random gibberish, meaning
nothing. But to the readers of the Numerica Format, it may
mean something useful -- perhaps even informative.
===========
Limitations
===========
There are a few limitations present within the sequence described
within this article. They are briefly outlined below:
1) Unfortunately, numbers are denoted beginning with the number 4, as they
cannot be reliably sequenced by multiplication. This is a limitation
within the coding sequence itself. Therefore, it is defined as a flaw.
2) Additionally, only the most basic punctuation is included, bringing
the total coding sequence to forty-nine mathematical assignments (26
letters, 13 punctuation marks and 10 numbers). The 50th sequence is left
undefined, and may be redefined as necessary.
3) Simple Numeri (such as "THE COW JUMPED OVER THE MOON.")
require long Numericas. This may be broken down into 40 or 80-column
singular Numeri in order to increase readability. In general, Numeri
should be indented slightly to allow for footnotes. For example:
|540805840353238452736782050484532205928454080584|
|6753537293 |
(The cow jumped over the | moon.)
4) Numeri are broken down into lines which may overlap (as above). To
designate where they might overlap, select either 40 or 80-columns set
into descending rows. Then word wrap the sentence as
suggested in the example above.
5) When translating simple documents to the Numerica Format, it is not
unusual to designate the 50th sequence (which is undefined) as a line
break. Example:
|540805840353238452736782050484532205928454080584|
|6753537293505408058405720493 |
(The cow jumped over the | moon. [line break] The End.)
==========
Conclusion
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The simplicity of the Numerica Format, combined with the difficulty
in determining source data, allows it to be invaluable for encoding
brief messages to those requiring security of information. The
majority of individuals who come across messages encoded as
Numerica will confuse the data with useless or trivial
information. If data needs to be secure, but decodable, this
is an easy and fairly straightforward method of accomplishing
such a task.
Sincerely,
Paul Allen Panks
dun...@yahoo.com
Phoenix, Arizona