Mathematics

Using mathematics is an absolute necessity to trade the stock or commodities

Mathematics is the basis of all forecasting in the markets.

Using mathematics is an absolute necessity to trade stocks and commodities in the

markets successfully. The traders who master the art of trading the

markets with mathematics will be successful. Those who don’t will fail. It’s

as simple as that. Traders who rely on tips and rumors will eventually lose. By

taking this page you are showing the desire to succeed by going beyond the

what the normal trader will do. You are showing your desire to study, understand

and apply mathematics to the market. It will take a lot of study for you

to succeed, but you are on the right course. Those traders who think they can

use computer trading programs alone with simple oscillators will fail. Many

of these traders spend hundreds of hours of their valuable study time trying to

make some definite pattern or way to use oscillators. They won't be able to do

it. You need mathematics to succeed in the markets.

It looks so easy to trade with oscillators when you look back on past

charts. You just sell when the stochastics is at the top and buy when it's on the

bottom. It works some of the time, but sometimes it sets you up for a blood

bath. For example, sometimes when the stochastics gets to the top, in an apparent

sell mode, the market will take off and explode, leaving you with big

losses if you shorted the market. The same thing happens when the stochastics

gets to the bottom. If you buy when the stochastics is at the bottom, sometimes

the market will fall out of bed giving you huge losses. Traders who

follow only oscillators don’t know when the market is approaching major or

minor geometric angles or timing cycles. They have no idea of where the

market might be heading. They will short the market when the stochastics

oscillator is at the top and not know that the market is resting on a major

geometric angle or time cycle. The market will then explode giving them

huge loses. Check around with traders that use oscillators. You will find that

they generally loose money in the markets. The only traders who consistently

make money in the markets are traders who use mathematical methods

of trading. These are based on the true mathematics behind the market caused

by the vibration of numbers. Prior highs and lows and their interactive harmony

waves and geometric angles are the real cause behind market movements.

Oscillators can be used to successfully trade with, but only if they are

used with other time and price trading techniques to support them. In this

course we go over how displaced moving averages, stochastics and MACD

can be used to trade the market mathematically. It is the only my only way to use

oscillators. 

 For me, Technical Indicators  such as MACD, Moving Averages , RSI and etc...
is only as good as trading the present market movement and to spot the right timing to enter
and exit the market. To know the current standing of the market, which demands constant attention to the trader.  However,  data are all based on historic past 100 and 200 day
 average prices, 52 weeks average and others more. just to define our current
situation of the market  or to know if we are having positive momentum or not?,
 if the market are oversold or overbought ? and others more.

Similarly, its  just like taking a picture on that specific time at that specific day, 
month or year. Its also synonymous to  like in finance where we write our financial statement, 
where it is just a picture of our financial standing at that point in time.  The mindset behind
this is the thinking that past action and momentum draws our future market actions.  
With this premise, I would partialy agree at some point and dissagree at others. 
 I may say that Yes i agree, that markets builds positive and negative momentum that
 you can trade to. But this factor is just one of the many factors involve in market movement
 and the psychology of the masses. Those Traders who use only Technical Indicators, 
will find them selves in a blood bath and will have a hard time to profit.
 These Traders famous motto would be." I knew it when I saw it ". " We'll cross
the bridge when we get there"  Or their famous preposition word  " IF".in their analysis.

 But  bottomline, I think  it does not really tells us a clear indication about the future direction
of the market.  Or in other words, doesn't tells us what will happen tomorrow, or the next day or
 the next wk or years.In this field of speculation, the future is more important than the past,
while indicators basing their data on historic prices is a very risky and dangerous game.

It’s a puzzle why most traders don’t use mathematics to buy and sell

stocks and commodities and to forecast trends in the markets. It’s very easy

after you learn the mathematical trading techniques and it’s 100% more reliable

than using other techniques. It’s also much more consistent. Mathematics

is something that you can depend on. In this course, after you learn the

principles of trading market mathematics you will never want to hear tips or

rumors again. You will find that if someone offers their view of the market to

you, you’ll want to shut them out and not let them influence you. After you

know the rules of mathematics behind the market you will find your sixth

sense develops and many of the techniques you learned in this course will

start relating to each other. Your mind will have a unique sense of where the

market is headed.

In using mathematics for trading the markets, it is important to know that

the market can go only two directions. It can go up or down or it can just

move sideways. Prices can increase or decrease or just stay the same. They

can do nothing else. We will use mathematics to figure out if the markets will

go up or down. There are various methods to use to determine this. They

involve the use of mathematical trend analysis and timing techniques.

NUMEROLOGY 
THE VIBRATION NUMBER

Every stock or commodity will have its own vibration number that it trades

by. It will trade within the square of that number. The number is based on one

of several factors. The most common is the birthday or incorporation of the

stock or commodity. If the stock was incorporated on December 21, 1945 its

number would be 3 determined from adding 2 + 1. This is usually hard to

find, but can be found in exchange or corporation records. The next possible

basis for the vibration number is the first day of trade on the exchange. It is

also possible the number might be found from the all time high or low of the

stock or commodity. It is necessary to experiment with several of the possible

numbers that one finds using the above basis. Use trial and error with several

numbers until you find the one that fits best. Once you find it, it will be clear

that it works in all cases. See Exhibit 11.14.

Stocks or commodities that started trading the following dates of the month

are ruled by the numbers indicated. They generally will be strongest during

their dates or the periods of the year indicated.

IMPORTANT NOTE:  THE VIBRATION NUMBER IS PLOTTED ON THE PRICE AND TIME SQUARE CHARTS LAYOUT IN PREDICTING FUTURE PRICE AND TIME  POINTS.

-Gtrader

How to find the vibration number of a stock or commodity?

NUMBERS GIVEN TO DATES OF THE PERIODS OF THE YEAR

COMPOUND NUMBERS AND THEIR MEANINGS

Here is a way to tell whether a day will be favorable or unfavorable for a

stock or commodity. It should be of great value to anyone who uses it. Now

give your attention and concentration to the following system which I will try

to explain as briefly as possible. To find whether a day in the month is favorable

or unfavorable to a commodity the simplest rule is to work out the numeric

value of the name of the stock or commodity. Determine that value by

assigning a numeric value to each letter of the name the commodity is referred

to. Add to this number its vibration number and the date of the month

and check to see it is a good or bad number. Follow the below charts and

example to guide you.

In this example Corn is figured this way.

C = 3, O = 7, R = 2, N = 5 (add 3, 7, 2 and 5 = 17, and 1 + 7 = 8)

Corn = 8

Vibration number = 3

Total = 11

COMPOUND NUMBER CHART

FAVORABLE + AND UNFAVORABLE -

10 +, 11 -, 12-, 13 0, 14 +, 15 +, 16 -, 17 0, 18 -, 19 +, 20 0, 21 +, 22 -, 23 +,

24 +, 25 +, 26 -, 27+, 28 +, 29 +, 30 0, 31 0, 32 +, 34 +, 35 -, 36 +, 37 +, 38 +,

39 0, 40 0, 41 +, 42 +, 43 -, 44 -, 45 +, 46 +, 47 +, 48 0, 49 0, 50 +, 51 +, 51 -

Corn +Vibration Number +Date= Total Expectation

8 3 13th 24 Favorable

8 3 14th 25 Favorable

8 3 15th 26 Unfavorable

THE VIBRATION NUMBER

1st, 10th, 19th, 28th 1 Mar 21 - Apr 19th

2nd, 11th, 20th, 29th 2 Jun 20 - Jul 20th

3rd, 12, 21st, 30th 3 Feb 19th-Mar 27th, Nov 21-Dec 27

4th, 13th, 22nd, 31st 4 Jun 21 - Jul 27, Jul 21 - Aug 27

5th, 14th, 23rd 5 May 21 - Jun 27, Aug 21, Sep 27

6th, 15th, 24th 6 Apr 20th, May 27, Sep 21, Oct 27

7th, 16th, 25th 7 Jun 21 - Jul 27

8th, 17th, 26th 8 Dec 31 - Jan 27, Feb 19 - Feb 26

9th, 18th, 27th 9 Mar 21 - Apr 26, Oct 21 - Nov 27

NUMBERS GIVEN TO DAYS OF THE WEEK

The following are vibration numbers given to the days of the week. Stocks or

commodities will be strongest on the day that vibrates their number.

Day Number

Sunday 1, 4

Monday 2, 7

Tuesday 9

Wednesday 5

Thursday 3

Friday 6

Saturday 8


SAME NUMBER OF YEARS, MONTHS, WEEKS AND DAYS

You should check back in the record of both stocks and commodities and you

will find that they advance and decline on the same number years many times

up to 3 to 6 to 9 years at a time. For example if a stock advanced during the

year of 1915. Add the number 3, 6, and 9 to that data to see if the stock

advanced during those years. The dates would be 1918, 1921 and 1924. Some

time the market will follow those years exactly to the day, week or month.

Sometimes you will have a cycle inversion and the market will do the opposite

of those years. You can keep going back 3,6, and 9 years back to 100

years if you have the necessary data. Using this method you can forecast

months, weeks and days ahead of time. From this method you can many times

determine the weak and strong points of the years based on months, weeks

and even days.

Year

1915 + 3 = 1918 + 3 = 1921 + 3 = 1924

+ 3 = 1927 + 3 = 1930 + 3 = 1933

+ 3 = 1936 + 3 = 1939 + 3 = 1942

Using this method you should print out the charts and overlay them on top of

each other to see if you can find similiar trend pattern between the years.

Sometimes you will find a slight shift of time. Sometime it will be exact.

Anniversary days of major highs and lows many times will come out to the

day.

VIBRATION

BASE NUMBERS 1-9

ALL TIME LOW PRICE 21 = VIBRATION NUMBER OF 3

EXHIBIT 11.14 Vibration base number example

Pythagorean Mathematics

CONCERNING the secret significance of numbers there has been much speculation. Though many
interesting discoveries have been made, it may be safely said that with the death of Pythagoras the great
key to this science was lost. For nearly 2500 years philosophers of all nations have attempted to unravel
the Pythagorean skein, but apparently none has been successful. Notwithstanding attempts made to
obliterate all records of the teachings of Pythagoras, fragments have survived which give clues to some
of the simpler parts of his philosophy. The major secrets were never committed to writing, but were
communicated orally to a few chosen disciples. These apparently dated not divulge their secrets to the
profane, the result being that when death sealed their lips the arcana died with diem.
Certain of the secret schools in the world today are perpetuations of the ancient Mysteries, and although
it is quite possible that they may possess some of the original numerical formulæ, there is no evidence of
it in the voluminous writings which have issued from these groups during the last five hundred years.
These writings, while frequently discussing Pythagoras, show no indication of a more complete
knowledge of his intricate doctrines than the post-Pythagorean Greek speculators had, who talked much,
wrote little, knew less, and concealed their ignorance under a series of mysterious hints and promises.
Here and there among the literary products of early writers are found enigmatic statements which they
made no effort: to interpret. The following example is quoted from Plutarch:
"The Pythagoreans indeed go farther than this, and honour even numbers and geometrical diagrams with
the names and titles of the gods. Thus they call the equilateral triangle head-born Minerva and
Tritogenia, because it may be equally divided by three perpendiculars drawn from each of the angles. So
the unit they term Apollo, as to the number two they have affixed the name of strife and audaciousness,
and to that of three, justice. For, as doing an injury is an extreme on the one side, and suffering one is an
extreme on the on the one side, and suffering in the middle between them. In like manner the number
thirty-six, their Tetractys, or sacred Quaternion, being composed of the first four odd numbers added to
the first four even ones, as is commonly reported, is looked upon by them as the most solemn oath they
can take, and called Kosmos." (Isis and Osiris.)
Earlier in the same work, Plutarch also notes: "For as the power of the triangle is expressive of the
nature of Pluto, Bacchus, and Mars; and the properties of the square of Rhea, Venus, Ceres, Vesta, and
Juno; of the Dodecahedron of Jupiter; so, as we are informed by Eudoxus, is the figure of fifty-six
angles expressive of the nature of Typhon." Plutarch did not pretend to explain the inner significance of
the symbols, but believed that the relationship which Pythagoras established between the geometrical
solids and the gods was the result of images the great sage had seen in the Egyptian temples.
Albert Pike, the great Masonic symbolist, admitted that there were many points concerning which he
could secure no reliable information. In his Symbolism, for the 32° and 33°, he wrote: "I do not
understand why the 7 should be called Minerva, or the cube, Neptune." Further on he added:
"Undoubtedly the names given by the Pythagoreans to the different numbers were themselves
enigmatical and symbolic-and there is little doubt that in the time of Plutarch the meanings these names
concealed were lost. Pythagoras had succeeded too well in concealing his symbols with a veil that was
from the first impenetrable, without his oral explanation * * *."
This uncertainty shared by all true students of the subject proves conclusively that it is unwise to make
definite statements founded on the indefinite and fragmentary information available concerning the
Pythagorean system of mathematical philosophy. The material which follows represents an effort to
collect a few salient points from the scattered records preserved by disciples of Pythagoras and others
who have since contacted his philosophy.


INTRODUCTION  TO THE PYTHAGOREAN THEORY OF NUMBERS
(The following outline of Pythagorean mathematics is a paraphrase of the opening chapters of Thomas
Taylor's Theoretic Arithmetic, the rarest and most important compilation of Pythagorean mathematical
fragments extant.)


The Pythagoreans declared arithmetic to be the mother of the mathematical sciences. This is proved by

the fact that geometry, music, and astronomy are dependent upon it but it is not dependent upon them.
Thus, geometry may be removed but arithmetic will remain; but if arithmetic be removed, geometry is
eliminated. In the same manner music depends upon arithmetic, but the elimination of music affects
arithmetic only by limiting one of its expressions. The Pythagoreans also demonstrated arithmetic to be
prior to astronomy, for the latter is dependent upon both geometry and music. The size, form, and
motion of the celestial bodies is determined by the use of geometry; their harmony and rhythm by the
use of music. If astronomy be removed, neither geometry nor music is injured; but if geometry and
music be eliminated, astronomy is destroyed. The priority of both geometry and music to astronomy is
therefore established. Arithmetic, however, is prior to all; it is primary and fundamental.
Pythagoras instructed his disciples that the science of mathematics is divided into two major parts. The
first is concerned with the multitude, or the constituent parts of a thing, and the second with the
magnitude, or the relative size or density of a thing.
Magnitude is divided into two parts--magnitude which is stationary and magnitude which is movable,
the stationary pare having priority. Multitude is also divided into two parts, for it is related both to itself
and to other things, the first relationship having priority. Pythagoras assigned the science of arithmetic to
multitude related to itself, and the art of music to multitude related to other things. Geometry likewise
was assigned to stationary magnitude, and spherics (used partly in the sense of astronomy) to movable
magnitude. Both multitude and magnitude were circumscribed by the circumference of mind. The
atomic theory has proved size to be the result of number, for a mass is made up of minute units though
mistaken by the uninformed for a single simple substance.


Owing to the fragmentary condition of existing Pythagorean records, it is difficult to arrive at exact

definitions of terms. Before it is possible, however, to unfold the subject further some light must he cast
upon the meanings of the words number, monad, and one.
The monad signifies (a) the all-including ONE. The Pythagoreans called the monad the "noble number,
Sire of Gods and men." The monad also signifies (b) the sum of any combination of numbers considered
as a whole. Thus, the universe is considered as a monad, but the individual parts of the universe (such as
the planets and elements) are monads in relation to the parts of which they themselves are composed,
though they, in turn, are parts of the greater monad formed of their sum. The monad may also be likened
(c) to the seed of a tree which, when it has grown, has many branches (the numbers). In other words, the
numbers are to the monad what the branches of the tree are to the seed of the tree. From the study of the
mysterious Pythagorean monad, Leibnitz evolved his magnificent theory of the world atoms--a theory in
perfect accord with the ancient teachings of the Mysteries, for Leibnitz himself was an initiate of a secret
school. By some Pythagoreans the monad is also considered (d) synonymous with the one.
Number is the term applied to all numerals and their combinations. (A strict interpretation of the term
number by certain of the Pythagoreans excludes 1 and 2.) Pythagoras defines number to be the extension
and energy of the spermatic reasons contained in the monad. The followers of Hippasus declared
number to be the first pattern used by the Demiurgus in the formation of the universe.
The one was defined by the Platonists as "the summit of the many." The one differs from the monad in
that the term monad is used to designate the sum of the parts considered as a unit, whereas the one is the
term applied to each of its integral parts.
There are two orders of number: odd and even. Because unity, or 1, always remains indivisible, the odd
number cannot be divided equally. Thus, 9 is 4+1+4, the unity in the center being indivisible.
Furthermore, if any odd number be divided into two parts, one part will always be odd and the other
even. Thus, 9 may be 5+4, 3+6, 7+2, or 8+1. The Pythagoreans considered the odd number--of which
the monad was the prototype--to be definite and masculine. They were not all agreed, however, as to the
nature of unity, or 1. Some declared it to be positive, because if added to an even (negative) number, it
produces an odd (positive) number. Others demonstrated that if unity be added to an odd number, the
latter becomes even, thereby making the masculine to be feminine. Unity, or 1, therefore, was
considered an androgynous number, partaking of both the masculine and the feminine attributes;
consequently both odd and even. For this reason the Pythagoreans called it evenly-odd. It was customary
for the Pythagoreans to offer sacrifices of an uneven number of objects to the superior gods, while to the
goddesses and subterranean spirits an even number was offered.
Any even number may be divided into two equal parts, which are always either both odd or both even.
Thus, 10 by equal division gives 5+5, both odd numbers. The same principle holds true if the 10 be
unequally divided. For example, in 6+4, both parts are even; in 7+3, both parts are odd; in 8+2, both
parts are again even; and in 9+1, both parts are again odd. Thus, in the even number, however it may be
divided, the parts will always be both odd or both even. The Pythagoreans considered the even numberof
which the duad was the prototype--to be indefinite and feminine.
The odd numbers are divided by a mathematical contrivance--called "the Sieve of Eratosthenes"--into
three general classes: incomposite, composite, and incomposite-composite.
The incomposite numbers are those which have no divisor other than themselves and unity, such as 3, 5,
7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, and so forth. For example, 7 is divisible only by 7, which
goes into itself once, and unity, which goes into 7 seven times.
The composite numbers are those which are divisible not only by themselves and unity but also by some
other number, such as 9, 15, 21, 25, 27, 33, 39, 45, 51, 57, and so forth. For example, 21 is divisible not
only by itself and by unity, but also by 3 and by 7.
The incomposite-composite numbers are those which have no common divisor, although each of itself is
capable of division, such as 9 and 25. For example, 9 is divisible by 3 and 25 by 5, but neither is
divisible by the divisor of the other; thus they have no common divisor. Because they have individual
divisors, they are called composite; and because they have no common divisor, they are called in,
composite. Accordingly, the term incomposite-composite was created to describe their properties.
Even numbers are divided into three classes: evenly-even, evenly-odd, and oddly-odd.
The evenly-even numbers are all in duple ratio from unity; thus: 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, and
1,024. The proof of the perfect evenly-even number is that it can be halved and the halves again halved
back to unity, as 1/2 of 64 = 32; 1/2 of 32 = 16; 1/2 of 16 = 8; 1/2 of 8 = 4; 1/2 of 4 = 2; 1/2 of 2 = 1;
beyond unity it is impossible to go.
The evenly-even numbers possess certain unique properties. The sum of any number of terms but the last
term is always equal to the last term minus one. For example: the sum of the first and second terms (1
+2) equals the third term (4) minus one; or, the sum of the first, second, third, and fourth terms (1+2+4
+8) equals the fifth term (16) minus one.
In a series of evenly-even numbers, the first multiplied by the last equals the last, the second multiplied
by the second from the last equals the last, and so on until in an odd series one number remains, which
multiplied by itself equals the last number of the series; or, in an even series two numbers remain, which
multiplied by each other give the last number of the series. For example: 1, 2, 4, 8, 16 is an odd series.
The first number (1) multiplied by the last number (16) equals the last number (16). The second number
(2) multiplied by the second from the last number (8) equals the last number (16). Being an odd series,
the 4 is left in the center, and this multiplied by itself also equals the last number (16).
The evenly-odd numbers are those which, when halved, are incapable of further division by halving.
They are formed by taking the odd numbers in sequential order and multiplying them by 2. By this
process the odd numbers 1, 3, 5, 7, 9, 11 produce the evenly-odd numbers, 2, 6, 10, 14, 18, 22. Thus,
every fourth number is evenly-odd. Each of the even-odd numbers may be divided once, as 2, which
becomes two 1's and cannot be divided further; or 6, which becomes two 3's and cannot be divided
further.
Another peculiarity of the evenly-odd numbers is that if the divisor be odd the quotient is always even,
and if the divisor be even the quotient is always odd. For example: if 18 be divided by 2 (an even
divisor) the quotient is 9 (an odd number); if 18 be divided by 3 (an odd divisor) the quotient is 6 (an
even number).
The evenly-odd numbers are also remarkable in that each term is one-half of the sum of the terms on
either side of it. For example: [paragraph continues]

This sieve is a mathematical device originated by Eratosthenes about 230 B.C. far the purpose of segregating the
composite and incomposite odd numbers. Its use is extremely simple after the theory has once been mastered. All
the odd numbers are first arranged in their natural order as shown in the second panel from the bottom,
designated Odd Numbers. It will then be seen that every third number (beginning with 3) is divisible by 3, every
fifth number (beginning with 5;) is divisible by 5, every seventh number (beginning with 7) is divisible by 7,
every ninth number (beginning with 9) is divisible by 9, every eleventh number (beginning with 11) is divisible
by 11, and so on to infinity. This system finally sifts out what the Pythagoreans called the "incomposite"
numbers, or those having no divisor other than themselves and unity. These will be found in the lowest panel,
designated Primary and Incomposite Numbers. In his History of Mathematics, David Eugene Smith states that
Eratosthenes was one of the greatest scholars of Alexandria and was called by his admirers "the second Plato."
Eratosthenes was educated at Athens, and is renowned not only for his sieve but for having computed, by a very
ingenious method, the circumference and diameter of the earth. His estimate of the earth's diameter was only 50
miles less than the polar diameter accepted by modern scientists. This and other mathematical achievements of
Eratosthenes, are indisputable evidence that in the third century before Christ the Greeks not only knew the earth
to be spherical in farm but could also approximate, with amazing accuracy, its actual size and distance from both
the sun and the moon. Aristarchus of Samos, another great Greek astronomer and mathematician, who lived
about 250 B.C., established by philosophical deduction and a few simple scientific instruments that the earth
revolved around the sun. While Copernicus actually believed himself to be the discoverer of this fact, he but
restated the findings advanced by Aristarchus seventeen hundred years earlier.







continues] 10 is one-half of the sum of 6 and 14; 18 is one-half the sum of 14 and 22; and 6 is onehalf
the sum of 2 and 10.
The oddly-odd, or unevenly-even, numbers are a compromise between the evenly-even and the evenlyodd
numbers. Unlike the evenly-even, they cannot be halved back to unity; and unlike the evenly-odd,
they are capable of more than one division by halving. The oddly-odd numbers are formed by
multiplying the evenly-even numbers above 2 by the odd numbers above one. The odd numbers above
one are 3, 5, 7, 9, 11, and so forth. The evenly-even numbers above 2 are 4, 8, 16, 32, 64, and soon. The
first odd number of the series (3) multiplied by 4 (the first evenly-even number of the series) gives 12,
the first oddly-odd number. By multiplying 5, 7, 9, 11, and so forth, by 4, oddly-odd numbers are found.
The other oddly-odd numbers are produced by multiplying 3, 5, 7, 9, 11, and so forth, in turn, by the
other evenly-even numbers (8, 16, 32, 64, and so forth). An example of the halving of the oddly-odd
number is as follows: 1/2 of 12 = 6; 1/2 of 6 = 3, which cannot be halved further because the
Pythagoreans did not divide unity.
Even numbers are also divided into three other classes: superperfect, deficient, and perfect.
Superperfect or superabundant numbers are such as have the sum of their fractional parts greater than
themselves. For example: 1/2 of 24 = 12; 1/4 = 6; 1/3 = 8; 1/6 = 4; 1/12 = 2; and 1/24 = 1. The sum of
these parts (12+6+8+4+2+1) is 33, which is in excess of 24, the original number.
Deficient numbers are such as have the sum of their fractional parts less than themselves. For example:
1/2 of 14 = 7; 1/7 = 2; and 1/14 = 1. The sum of these parts (7+2+1) is 10, which is less than 14, the
original number.
Perfect numbers are such as have the sum of their fractional parts equal to themselves. For example: 1/2
of 28 = 14; 1/4 = 7; 1/7 = 4; 1/14 = 2; and 1/28 = 1. The sum of these parts (14+7+4+2+1) is equal to 28.
The perfect numbers are extremely rare. There is only one between 1 and 10, namely, 6; one between 10
and 100, namely, 28; one between 100 and 1,000, namely, 496; and one between 1,000 and 10,000,
namely, 8,128. The perfect numbers are found by the following rule: The first number of the evenlyeven
series of numbers (1, 2, 4, 8, 16, 32, and so forth) is added to the second number of the series, and
if an incomposite number results it is multiplied by the last number of the series of evenly-even numbers
whose sum produced it. The product is the first perfect number. For example: the first and second
evenly-even numbers are 1 and 2. Their sum is 3, an incomposite number. If 3 be multiplied by 2, the
last number of the series of evenly-even numbers used to produce it, the product is 6, the first perfect
number. If the addition of the evenly-even numbers does not result in an incomposite number, the next
evenly-even number of the series must be added until an incomposite number results. The second perfect
number is found in the following manner: The sum of the evenly-even numbers 1, 2, and 4 is 7, an
incomposite number. If 7 be multiplied by 4 (the last of the series of evenly-even numbers used to
produce it) the product is 28, the second perfect number. This method of calculation may be continued to
infinity.
Perfect numbers when multiplied by 2 produce superabundant numbers, and when divided by 2 produce
deficient numbers.
The Pythagoreans evolved their philosophy from the science of numbers. The following quotation from
Theoretic Arithmetic is an excellent example of this practice:
"Perfect numbers, therefore, are beautiful images of the virtues which are certain media between excess
and defect, and are not summits, as by some of the ancients they were supposed to be. And evil indeed is
opposed to evil, but both are opposed to one good. Good, however, is never opposed to good, but to two
evils at one and the same time. Thus timidity is opposed to audacity, to both [of] which the want of true
courage is common; but both timidity and audacity are opposed to fortitude. Craft also is opposed to
fatuity, to both [of] which the want of intellect is common; and both these are opposed to prudence.
Thus, too, profusion is opposed to avarice, to both [of] which illiberality is common; and both these are
opposed to liberality. And in a similar manner in the other virtues; by all [of] which it is evident that
perfect numbers have a great similitude to the virtues. But they also resemble the virtues on another
account; for they are rarely found, as being few, and they are generated in a very constant order. On the
contrary, an infinite multitude of superabundant and diminished numbers may be found, nor are they
disposed in any orderly series, nor generated from any certain end; and hence they have a great
similitude to the vices, which are numerous, inordinate, and indefinite."

THE TABLE OF THE TEN NUMBERS

(The following outline of the Pythagorean numbers is a paraphrase of the writings of Nicomachus,
Theon of Smyrna, Proclus, Porphyry, Plutarch, Clement of Alexandria, Aristotle, and other early
authorities.)
Monad--1--is so called because it remains always in the same condition--that is, separate from multitude. Its
attributes are as follows: It is called mind, because the mind is stable and has preeminence; hermaphrodism,
because it is both male and female; odd and even, for being added to the even it makes odd, and to the odd, even;
God, because it is the beginning and end of all, but itself has neither beginning nor end; good, for such is the
nature of God; the receptacle of matter, because it produces the duad, which is essentially material.
By the Pythagoreans monad was called chaos, obscurity, chasm, Tartarus, Styx, abyss, Lethe, Atlas, Axis,
Morpho (a name for Venus), and Tower or Throne of Jupiter, because of the great power which abides in the
center of the universe and controls the circular motion of the planers about itself. Monad is also called germinal
reason, because it is the origin of all the thoughts in the universe. Other names given to it were: Apollo, because
of its relation to the sun; Prometheus, because he brought man light; Pyralios, one who exists in fire; geniture,
because without it no number can exist; substance, because substance is primary; cause of truth; and constitution
of symphony: all these because it is the primordial one.
Between greater and lesser the monad is equal; between intention and remission it is middle; in multitude it is
mean; and in time it is now, because
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eternity knows neither past nor future. It is called Jupiter, because he is Father and head of the gods; Vesta, the
fire of the home, because it is located in the midst of the universe and remains there inclining to no side as a dot
in a circle; form, because it circumscribes, comprehends, and terminates; love, concord, and piety, because it is
indivisible. Other symbolic names for the monad are ship, chariot, Proteus (a god capable of changing his form),
Mnemosyne, and Polyonymous (having many names).
The following symbolic names were given to the duad--2--because it has been divided, and is two rather than
one; and when there are two, each is opposed to the other: genius, evil, darkness, inequality, instability,
movability, boldness, fortitude, contention, matter, dissimilarity, partition between multitude and monad, defect,
shapelessness, indefiniteness, indeterminate ness, harmony, tolerance, root, feet of fountain-abounding idea, top,
Phanes, opinion, fallacy, alterity, diffidence, impulse, death, motion, generation, mutation, division, longitude,
augmentation, composition, communion, misfortune, sustentation, imposition, marriage, soul, and science.
In his book, Numbers, W. Wynn Westcott says of the duad: "it was called 'Audacity,' from its being the earliest
number to separate itself from the Divine One; from the 'Adytum of God-nourished Silence,' as the Chaldean
oracles say."
As the monad is the father, so the duad is the mother; therefore, the duad has certain points in common with the
goddesses Isis, Rhea (Jove's mother), Phrygia, Lydia, Dindymene (Cybele), and Ceres; Erato (one of the Muses);
Diana, because the moon is forked; Dictynna, Venus, Dione, Cytherea; Juno, because she is both wife and sister
of Jupiter; and Maia, the mother of Mercury.
While the monad is the symbol of wisdom, the duad is the symbol of ignorance, for in it exists the sense of
separateness--which sense is the beginning of ignorance. The duad, however, is also the mother of wisdom, for
ignorance--out of the nature of itself--invariably gives birth to wisdom.
The Pythagoreans revered the monad but despised the duad, because it was the symbol of polarity. By the power
of the duad the deep was created in contradistinction to the heavens. The deep mirrored the heavens and became
the symbol of illusion, for the below was merely a reflection of the above. The below was called maya, the
illusion, the sea, the Great Void, and to symbolize it the Magi of Persia carried mirrors. From the duad arose
disputes and contentions, until by bringing the monad between the duad, equilibrium was reestablished by the
Savior-God, who took upon Himself the form of a number and was crucified between two thieves for the sins of
men.
The triad--3--is the first number actually odd (monad not always being considered a number). It is the first
equilibrium of unities; therefore, Pythagoras said that Apollo gave oracles from a tripod, and advised offer of
libation three times. The keywords to the qualities of the triad are friendship, peace, justice, prudence, piety,
temperance, and virtue. The following deities partake of the principles of the triad: Saturn (ruler of time), Latona,
Cornucopiæ, Ophion (the great serpent), Thetis, Hecate, Polyhymnia (a Muse), Pluto, Triton, President of the
Sea, Tritogenia, Achelous, and the Faces, Furies, and Graces. This number is called wisdom, because men
organize the present, foresee the future, and benefit by the experiences of the fast. It is cause of wisdom and
understanding. The triad is the number of knowledge--music, geometry, and astronomy, and the science of the
celestials and terrestrials. Pythagoras taught that the cube of this number had the power of the lunar circle.
The sacredness of the triad and its symbol--the triangle--is derived from the fact that it is made up of the monad
and the duad. The monad is the symbol of the Divine Father and the duad of the Great Mother. The triad being
made of these two is therefore androgynous and is symbolic of the fact that God gave birth to His worlds out of
Himself, who in His creative aspect is always symbolized by the triangle. The monad passing into the duad was
thus capable of becoming the parent of progeny, for the duad was the womb of Meru, within which the world was
incubated and within which it still exists in embryo.
The tetrad--4--was esteemed by the Pythagoreans as the primogenial number, the root of all things, the fountain
of Nature and the most perfect number. All tetrads are intellectual; they have an emergent order and encircle the
world as the Empyreum passes through it. Why the Pythagoreans expressed God as a tetrad is explained in a
sacred discourse ascribed to Pythagoras, wherein God is called the Number of Numbers. This is because the
decad, or 10, is composed of 1, 2, 3, and 4. The number 4 is symbolic of God because it is symbolic of the first
four numbers. Moreover, the tetrad is the center of the week, being halfway between 1 and 7. The tetrad is also
the first geometric solid.
Pythagoras maintained that the soul of man consists of a tetrad, the four powers of the soul being mind, science,
opinion, and sense. The tetrad connects all beings, elements, numbers, and seasons; nor can anything be named
which does not depend upon the tetractys. It is the Cause and Maker of all things, the intelligible God, Author of
celestial and sensible good, Plutarch interprets this tetractys, which he said was also called the world, to be 36,
consisting of the first four odd numbers added to the first four even numbers, thus:
1 + 3 +5 +7 = 16
2 + 4 + 6 + 8 = 20
36
Keywords given to the tetrad are impetuosity, strength, virility, two-mothered, and the key keeper of Nature,
because the universal constitution cannot be without it. It is also called harmony and the first profundity. The
following deities partook of the nature of the tetrad: Hercules, Mercury, Vulcan, Bacchus, and Urania (one of the
Muses).
The triad represents the primary colors and the major planets, while the tetrad represents the secondary colors and
the minor planets. From the first triangle come forth the seven spirits, symbolized by a triangle and a square.
These together form the Masonic apron.
The pentad--5--is the union of an odd and an even number (3 and 2). Among the Greeks, the pentagram was a
sacred symbol of light, health, and vitality. It also symbolized the fifth element--ether--because it is free from the
disturbances of the four lower elements. It is called equilibrium, because it divides the perfect number 10 into
two equal parts.
The pentad is symbolic of Nature, for, when multiplied by itself it returns into itself, just as grains of wheat,
starting in the form of seed, pass through Nature's processes and reproduce the seed of the wheat as the ultimate
form of their own growth. Other numbers multiplied by themselves produce other numbers, but only 5 and 6
multiplied by themselves represent and retain their original number as the last figure in their products.
The pentad represents all the superior and inferior beings. It is sometimes referred to as the hierophant, or the
priest of the Mysteries, because of its connection with the spiritual ethers, by means of which mystic
development is attained. Keywords of the pentad are reconciliation, alternation, marriage, immortality, cordiality,
Providence, and sound. Among the deities who partook of the nature of the pentad were Pallas, Nemesis,
Bubastia (Bast), Venus, Androgynia, Cytherea, and the messengers of Jupiter.
The tetrad (the elements) plus the monad equals the pentad. The Pythagoreans taught that the elements of earth,
fire, air, and water were permeated by a substance called ether--the basis of vitality and life. Therefore, they
chose the five-pointed star, or pentagram, as the symbol of vitality, health, and interpenetration.
It was customary for the philosophers to conceal the element of earth under the symbol of a dragon, and many of
the heroes of antiquity were told to go forth and slay the dragon. Hence, they drove their sword (the monad) into
the body of the dragon (the tetrad). This resulted in the formation of the pentad, a symbol of the victory of the
spiritual nature over the material nature. The four elements are symbolized in the early Biblical writings as the
four rivers that poured out of Garden of Eden. The elements themselves are under the control of the composite
Cherubim of Ezekiel.
The Pythagoreans held the hexad--6--to represent, as Clement of Alexandria conceived, the creation of the world
according to both the prophets and the ancient Mysteries. It was called by the Pythagoreans the perfection of all
the parts. This number was particularly sacred to Orpheus, and also to the Fate, Lachesis, and the Muse, Thalia. It
was called the form of forms, the articulation of the universe, and the maker of the soul.
Among the Greeks, harmony and the soul were considered to be similar in nature, because all souls are harmonic.
The hexad is also the symbol of marriage, because it is formed by the union of two triangles, one masculine and
the other feminine. Among the keywords given to the hexad are: time, for it is the measure of duration; panacea,
because health is equilibrium, and the hexad is a balance number; the world, because the world, like the hexad, is
often seen to consist of contraries by harmony; omnisufficient, because its parts are sufficient for totality (3 +2 +
1 = 6); unwearied, because it contains the elements of immortality.
By the Pythagoreans the heptad--7--was called "worthy of veneration." It was held to be the number of religion,
because man is controlled by seven celestial spirits to whom it is proper for him to make offerings. It was called
the number of life, because it was believed that human creatures born in the seventh month of embryonic life
usually lived, but those born in the eighth month often died. One author called it the Motherless Virgin, Minerva,
because it was nor born of a mother but out of the crown, or the head of the Father, the monad. Keywords of the
heptad are fortune, occasion, custody, control, government, judgment, dreams, voices, sounds, and that which
leads all things to their end. Deities whose attributes were expressed by the heptad were Ægis, Osiris, Mars, and
Cleo (one of the Muses).
Among many ancient nations the heptad is a sacred number. The Elohim of the Jews were supposedly seven in
number. They were the Spirits of the Dawn, more commonly known as the Archangels controlling the planets.
The seven Archangels, with the three spirits controlling the sun in its threefold aspect, constitute the 10, the
sacred Pythagorean decad. The mysterious Pythagorean tetractys, or four rows of dots, increasing from 1 to 4,
was symbolic of the stages of creation. The great Pythagorean truth that all things in Nature are regenerated
through the decad, or 10, is subtly preserved in Freemasonry through these grips being effected by the uniting of
10 fingers, five on the hand of each person.
The 3 (spirit, mind, and soul) descend into the 4 (the world), the sum being the 7, or the mystic nature of man,
consisting of a threefold spiritual body and a fourfold material form. These are symbolized by the cube, which
has six surfaces and a mysterious seventh point within. The six surfaces are the directions: north, east, south,
west, up, and down; or, front, back, right, left, above, and below; or again, earth, fire, air, water, spirit, and
matter. In the midst of these stands the 1, which is the upright figure of man, from whose center in the cube
radiate six pyramids. From this comes the great occult axiom: "The center is the father of the directions, the
dimensions, and the distances."
The heptad is the number of the law, because it is the number of the Makers of Cosmic law, the Seven Spirits
before the Throne.
The ogdoad--8--was sacred because it was the number of the first cube, which form had eight corners, and was
the only evenly-even number under 10 (1-2-4-8-4-2-1). Thus, the 8 is divided into two 4's, each 4 is divided into
two 2's, and each 2 is divided into two 1's, thereby reestablishing the monad. Among the keywords of the ogdoad
are love, counsel, prudence, law, and convenience. Among the divinities partaking of its nature were Panarmonia,
Rhea, Cibele, Cadmæa, Dindymene, Orcia, Neptune, Themis, and Euterpe (a Muse).
The ogdoad was a mysterious number associated with the Eleusinian Mysteries of Greece and the Cabiri. It was
called the little holy number. It derived its form partly from the twisted snakes on the Caduceus of Hermes and
partly from the serpentine motion of the celestial bodies; possibly also from the moon's nodes.
The ennead--9--was the first square of an odd number (3x3). It was associated with failure and shortcoming
because it fell short of the perfect number 10 by one. It was called the called the number of man, because of the
nine months of his embryonic life. Among its keywords are ocean and horizon, because to the ancients these
were boundless. The ennead is the limitless number because there is nothing beyond it but the infinite 10. It was
called boundary and limitation, because it gathered all numbers within itself. It was called the sphere of the air,
because it surrounded the numbers as air surrounds the earth, Among the gods and goddesses who partook in
greater or less degree of its nature were Prometheus, Vulcan, Juno, the sister and wife of Jupiter, Pæan, and
Aglaia, Tritogenia, Curetes, Proserpine, Hyperion, and Terpsichore (a Muse).
The 9 was looked upon as evil, because it was an inverted 6. According to the Eleusinian Mysteries, it was the
number of the spheres through which the consciousness passed on its way to birth. Because of its close
resemblance to the spermatozoon, the 9 has been associated with germinal life.
The decad--10--according to the Pythagoreans, is the greatest of numbers, not only because it is the tetractys (the
10 dots) but because it comprehends all arithmetic and harmonic proportions. Pythagoras said that 10 is the
nature of number, because all nations reckon to it and when they arrive at it they return to the monad. The decad
was called both heaven and the world, because the former includes the latter. Being a perfect number, the decad
was applied by the Pythagoreans to those things relating to age, power, faith, necessity, and the power of
memory. It was also called unwearied, because, like God, it was tireless. The Pythagoreans divided the heavenly
bodies into ten orders. They also stated that the decad perfected all numbers and comprehended within itself the
nature of odd and even, moved and unmoved, good and ill. They associated its power with the following deities:
Atlas (for it carried the numbers on its shoulders), Urania, Mnemosyne, the Sun, Phanes, and the One God.
The decimal system can probably be traced back to the time when it was customary to reckon on the fingers,
these being among the most primitive of calculating devices and still in use among many aboriginal peoples.


source: Except from The Secret teachings of the Ages
by Manly P.Hall
33deg Master Mason,1928

To be continued....