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The Crown of Numerology

Like Geomancy, discussed on the previous page, Numerology appears to have been constructed by analogy to astrology, with the advantage of saving money on ephemerides.

I won't discuss numerology at length here, but I will note that it is usually based on assigning numerical values to the letters of the alphabet as follows:

1 2 3 4 5 6 7 8 9
-----------------
A B C D E F G H I
J K L M N O P Q R
S T U V W X Y Z

and, thus, one takes one's name:

J O H N   S M I T H
1 6 8 5   1 4 9 2 8

1+6+8+5 = 20
1+4+9+2+8 = 24

20+24=44

4+4=8

adds together the digits corresponding to the letters in one's name, and then adds together the digits of the total, repeatedly if necessary, to get a single-digit result. Sometimes the numbers 11 and 22, if obtained as intermediate totals, are taken note of as having special meaning.

Adding together the digits in a number repeatedly is a simple way to obtain the remainder when dividing that number by nine, except that when zero is the remainder, nine is obtained this way.

The scheme by which a numeric value is assigned to each letter resembles that used in gematria, based on the system used by the ancient Greeks and Hebrews for writing numbers, in which nine letters stood for the digits from 1 to 9, another nine letters stood for 10, 20, 30... 90, and another nine letters (with special letters added to supplement the 22-letter Hebrew alphabet and the 24-letter Greek alphabet) stood for 100, 200, 300... 900. This allowed numbers from 1 to 999 to be expressed easily without the need for a zero - the invention of the zero, making written numbers follow the logic of the abacus, thus making for convenient arithmetic, being a major conceptual breakthrough.

For the modern alphabet, such a system would be:

  1   2   3   4   5   6   7   8   9
  ---------------------------------
  A   B   C   D   E   F   G   H   I

 10  20  30  40  50  60  70  80  90
 ----------------------------------
  J   K   L   M   N   O   P   Q   R

100 200 300 400 500 600 700 800
-------------------------------
  S   T   U   V   W   X   Y   Z

Gambling and superstition go hand in hand. Thus, many books purporting to give the meaning of one's dreams also include lucky numbers for dreams based on numerology. The older ones gave a series of numbers from 1 to 78 for players of "policy numbers". Since this was a form of illegal gambling, eventually holding a draw became impractical, and so this form of gambling was replaced by what is known as the "numbers game", where the last three digits of published clearing-house totals either from a stock exchange or from a horse-race track were used. More recently, legal lotteries have involved drawing a three-digit number.

A three-digit number could be obtained from the name of something dreamed about using the method of gematria; if the sum is more than three digits long, the excess digits could be added to the last three:

A   1
U 300
T 200
O  60
M  40
O  60
B   2
I   9
L  30
E   5
  ---
  707

However, this scheme, if used to give numbers for every dream in a dream book, would not work well, as too many words are short and lack letters from the end of the alphabet, and so the numbers would not be randomly distributed.

If one wants random-looking three-digit numbers, one obvious thing to do would be to use ten as the basis rather than nine:

0 1 2 3 4 5 6 7 8 9
-------------------
  A B C D E F G H I
J K L M N O P Q R S
T U V W X Y Z

One could start with the digits for every letter in a word, and add them in pairs, taking the last digit of each result, going down a pyramid to form numbers of every length:

A U T O M O B I L E
1 1 0 5 3 5 2 9 2 5
 2 1 5 8 8 7 1 1 7
  3 6 3 6 5 8 2 8
   9 9 9 1 3 0 0
    8 8 0 4 3 0
     6 8 4 7 3
      4 2 1 0
       6 3 1
        9 4
         3

But this suffers from the disadvantage that 6+3+1 = 10, 1+0 = 1, and so the lucky number for "automobile" has the "vibration" of 1, while the word itself has the "vibration" of 5 by the conventional numerological system.

How can the randomness of this system be combined with adherence to the correct modulo 9 remainder of the conventional system?


Here is one scheme:


Calculate the three-digit pyramid number for the dream dictionary entry, and the three-digit gematria number as well, as shown above. Also obtain the single-digit vibration of the entry by summing the digits of the gematria number.

(Rule 1) If the pyramid number is 000, calculate the three-digit gematria number, and use that.

Calculate the vibration of the pyramid number by summing its digits, and summing the digits of the result if necessary.

(Rule 2) If that vibration is the same as that obtained from the gematria number, use the pyramid number unchanged.

(Rule 3) If the two vibrations are not equal, but the vibration of the pyramid number is nine, add the gematria number and the vibration number together (since adding something divisible to nine to a number doesn't change its remainder when divided by nine), reducing the result if necessary to three digits by adding the leading digits to the last three, repeatedly if required.


So far, a limited fraction of the cases have been accounted for. When the two numbers have different and significant vibrations, how can they be harmonized?

One complicating factor is that the digits 9 and 0 both have the same "vibration", thus leading to a clash between a system based on ten and one based on nine.

What we want to do is impose the vibration of the gematria number on the pattern of the pyramid number.

This can be done as follows:


(Rule 4) If the pyramid number contains two zeroes, replace the digit that is not zero by the vibration digit of the gematria number.

(Rule 5) If the pyramid number contains one zero, substitute for the nonzero digits of the pyramid number according to the column in the following table corresponding to the vibration numbers of the pyramid number and the gematria number:

VP VG
 1| 2 4 5 7 8  3     9     6
 2| 4 8 1 5 7    6     3     9
 3|            5 7 9 2 4 6 8 1
 4| 8 7 2 1 5  6     3     9
 5| 1 2 7 8 4    9     6     3
 6|            8 1 3 5 7 9 2 4
 7| 5 1 8 4 2  9     6     3
 8| 7 5 4 2 1    3     9     6

PD SD
 1| 2 4 5 7 8  2 3 4 5 6 7 8 9
 2| 4 8 1 5 7  3 4 5 6 7 8 9 1
 3| 6 3 6 3 6  4 5 6 7 8 9 1 2
 4| 8 7 2 1 5  5 6 7 8 9 1 2 3
 5| 1 2 7 8 4  6 7 8 9 1 2 3 4
 6| 3 6 3 6 3  7 8 9 1 2 3 4 5
 7| 5 1 8 4 2  8 9 1 2 3 4 5 6
 8| 7 5 4 2 1  9 1 2 3 4 5 6 7
 9| 9 9 9 9 9  1 2 3 4 5 6 7 8

To use this table:

Look up the vibration of the pyramid number in the column in the top half of the table marked VP; then, in the row where that number is found, in the section marked VG, look up the vibration of the gematria number.

The column in which the vibration of the gematria number is found is also the column in the bottom half of the table, in the section marked SD, where the substitutes for the nonzero digits of the pyramid number, in the column marked PD, are to be taken from.

Where both vibrations are relatively prime to nine, multiplication is used; where that is not the case, addition is resorted to. Since two is relatively prime to nine, splitting the difference up into exactly two parts is always simple.

(Rule 6) If the pyramid number contains no zeroes, substitute for the digits of the pyramid number according to the column in the table above corresponding to the vibration numbers of the pyramid number and the gematria number, substituting all three digits if the multiplication section (the first five columns) is used, and only the last two digits if the addition section (the last eight columns) is used.

There you have it; a practical scheme for assigning numbers to dreams in a lucky dream and number book!

Thus, for example:

By gematria:

C   3
A   1
T 200
  ---
  204

By pyramid:

C A T
3 1 0

Thus, the vibration of CAT is 6, but its pyramid number has vibration 4.

Since the pyramid number has one zero in it, Rule 5 applies, and we substitute:

3 1 0
-----
4 2 0

getting 420 as our result, which has the correct vibration of 6.

For the word AUTOMOBILE above, we have a vibration of 5 and a pyramid number with a vibration of 1, with no zeroes.

So we use rule 6. Going from 1 to 5 is in the multiplicative section of the table, so all three digits are substituted:

6 3 1
-----
3 6 5

with the result having the correct vibration of 5.

Another example can be the word SHOES:

By gematria:

S 100
H   8
O  60
E   5
S 100
  ---
  273

By pyramid:

S H O E S
9 8 5 5 9
 7 3 0 4
  0 3 4

Here, the vibration of SHOES is 3, and the vibration of its pyramid number is 7. The pyramid number contains one zero, so rule 5 is applied.

0 3 4
-----
0 1 2

For going from 7 to 3, note that the addition section of the table had to be used; with rule 5, unlike rule 6, this does not change the procedure of substituting for all nonzero digits.

Variations

In the case of rule 6, of course, changing just the last two digits is arbitrary. So one could instead change the first two, or the first and last. Also, the fact that three is not relatively prime to nine, so one can't add the same amount three times in all cases, doesn't preclude addressing the case where it is three or six that needs to be added. So a revised table having this form could be used:

VP VG
 1| 2 4 5 7 8         3   9   6
 2| 4 8 1 5 7           6   3   9
 3|             6 9   5 7 2 4 8 1
 4| 8 7 2 1 5         6   3   9
 5| 1 2 7 8 4           9   6   3
 6|             9 3   8 1 5 7 2 4
 7| 5 1 8 4 2         9   6   3
 8| 7 5 4 2 1           3   9   6

PD SD
 1| 2 4 5 7 8   2 3   2 3 5 6 8 9
 2| 4 8 1 5 7   3 4   3 4 6 7 9 1
 3| 6 3 6 3 6   4 5   4 5 7 8 1 2
 4| 8 7 2 1 5   5 6   5 6 8 9 2 3
 5| 1 2 7 8 4   6 7   6 7 9 1 3 4
 6| 3 6 3 6 3   7 8   7 8 1 2 4 5
 7| 5 1 8 4 2   8 9   8 9 2 3 5 6
 8| 7 5 4 2 1   9 1   9 1 3 4 6 7
 9| 9 9 9 9 9   1 2   1 2 4 5 7 8

where all three digits are substituted if either the multiplicative section or the first additive section is used, but only two digits are substituted if the second additive section is used.

A further step to reduce arbitrariness is to attempt to use the gematria number to pick which two digits are substituted in the second additive section case. For example, the rules could be:

If all three digits of the gematria number are different, apply the substitutions on the two digits of the pyramid number corresponding to the largest two digits of the gematria number.

If two of the digits of the gematria number are the same, apply the substitutions on the two digits of the pyramid number corresponding to those two digits.

This still leaves an arbitrary choice if all three digits of the gematria number are equal. One could choose to substitute the first and last digit in that case, to at least get symmetry.

A Simpler Rule

However, there is a much simpler rule that is possible.

While the system of pyramid addition is shown for decimal digits, a way of using it that preserves vibrations from 1 through 9 is also possible, using the same principle of substitution found in the rules above.

Numbers from 1 through 9 may be, in effect, halved through this substitution:

1 2 3 4 5 6 7 8 9
-----------------
5 1 6 2 7 3 8 4 9

When performing a pyramid sum, the first and last digits are added into the digits of the next row only once, but all the others are added twice. So before forming the next row, perform this substitution on all the digits except the first and last:

A U T O M O B I L E
-------------------
1+3+2+6+4+6+2+9+3+5 = 41; 4+1=5
1 6 1 3 2 3 1 9 6 5
 7+7+4+5+5+4+1+6+2  = 41; 4+1=5
 7 8 2 7 7 2 5 3 2
  6+1+9+5+9+7+8+5   = 50; 5+0=5
  6 5 9 7 9 8 4 5
   2+5+7+7+8+3+9    = 41; 4+1=5
   2 7 8 8 4 6 9
    9+6+7+3+1+6     = 32; 3+2=5
    9 3 8 6 5 6
     3+2+5+2+2      = 14; 1+4=5
     3 1 7 1 2
      4+8+8+3       = 23; 2+3=5
      4 4 4 3
       8+8+7        = 23; 2+3=5
       8 4 7
        3+2         =  5
        3 2
         5          =  5

This provides strings of digits of all lengths less than or equal to the length of the word composed of digits from 1 through 9 and having the same vibration as the word itself.

In this particular case, the three-digit number from the decimal pyramid is 631, which contains no zeroes. So 887, the three-digit number produced by this pyramid is taken.

The number from the decimal pyramid is used only to indicate the number and placement of zeroes; as long as it is not 000, in which case the gematria number is used, as above, the procedure is:

If the decimal pyramid number has no zeroes, take the three-digit number from the vibratory pyramid.

If the decimal pyramid number has one zero, replace the two nonzero digits in it with the digits of the two-digit number from the vibratory pyramid.

If the decimal pyramid number has two zeroes, replace its one nonzero digit with the vibration of the word, which can be determined from the base of the vibratory pyramid or the sum of the digits of the gematria number.

Note that the numbers to be used are always those prior to the encoding of the digits which is used as the preparation for the addition to create the next shorter number.

Thus, as another example, let us take the word SHOES, which, as we have seen above, has a decimal pyramid number of 034.

The vibratory pyramid is formed as follows:

S H O E S
1 8 6 5 1
1 4 3 7 1
 5 7 1 8
 5 8 5 8
  4 4 4
  4 2 4
   6 6
   6 6
    3

and so in this case the lucky number is 066.

Compound Rule

In addition to being used on its own as a simple rule, it can be used as an alternative to the sixth rule in the system above for those cases where a substitution cannot be applied to all three digits of the decimal pyramid number but only two of them.

That way, the vibratory pyramid is only calculated in those difficult cases of the rule above where an arbitrary choice of the digits to modify would be required.

Copyright (c) 2011 John J. G. Savard


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