by Harry Teasdale
I start from the concept that numbers are to be characterized as the means of defining a value by a symbol.
Natural & Artificial Numbers
Minus Zero = Natural Numbers = f
0 – 0 = f0
1 – 0 = f1
11 – 0 = f2
111 – 0 = f3
1111 – 0 = f4
11111 – 0 = f5
111111 – 0 = f6
1111111 – 0 = f7
11111111 – 0 = f8
111111111 – 0 = f9
Plus Zero = Natural Numbers Multiplied
1 + 0 = 10
11 + 0 = 20
111 + 0 = 30
1111 + 0 = 40
11111 + 0 = 50
111111 + 0 = 60
1111111 + 0 = 70
11111111 + 0 = 80
111111111 + 0 = 90
Plus Zeros = Natural Numbers Multiplied
1 + 00 = 100
11 + 00 = 200
111 + 00 = 300
1111 + 00 = 400
11111 + 00 = 500
111111 + 00 = 600
1111111 + 00 = 700
11111111 + 00 = 800
111111111 + 00 = 900
On this chart I define numbers by the symbols 0 & 1 with these to represent the opposites from which all other numbers arise, for us humans such a system is of course unworkable so in order to make it workable I have placed alongside the numbers f1 – f9. My reason for defining these as an f number will clarify as we move forward.
The natural cycle starts out with 0 on the left to represent the negative element and 1 on the right to represent the positive element. After this the natural set of numbers become artificial and increase in value on the 0 moving to the right-hand side of the 1 – 9, first in tens, then hundreds, with this to continue indefinitely.
In number theory, a perfect number is a positive integer that is equal to the sum of its proper positive divisors, that is, the sum of its positive divisors excluding the number itself (also known as its aliquot sum). Equivalently, a perfect number is a number that is half the sum of all of its positive divisors (including itself)
i.e. (1+2+3+6)/2 = 6, 1 + 2 + 4 + 7 + 14 = 28
This definition is ancient, appearing as early as Euclid’s Elements (VII.22) where it is called perfect, ideal, or complete number.
Euclid also proved a formation rule (IX.36) whereby p(p+1)/2 is an even perfect number whenever p is what is now called a Mersenne prime.
Much later, Euler proved that all even perfect numbers are of this form. This is known as the Euclid–Euler theorem.
It is not known whether there are any odd perfect numbers, nor whether infinitely many perfect numbers exist.
Perfect Numbers Known to Greeks
First seen 15th century manuscript
After these the numbers are too large to set down, but these are a sample of number of digits they contain and the year of discovery.
with 2,663 digits
An aspect of numbers that were known to ancient man is that of a `perfect` number with this the list from the early Greeks to the present time.
Daily “f “ numbers
As brought out on this chart a day can be understood as either a single period of 1 x 24 hours, or as 4 x 6 hours, or, by an `f `number.
It is to be noted, in the context of numbers that have a natural limit of between 1 – 9, that after the 9th hour the `f` numbers restart, as they do after the 18th hour.
It is also seen that with the minutes of a day these are represented by a uniform sequence of f6, f3, f9.
Just as the final time cycle of seconds are all found to represent the highest possible `f` number, in which the 1st hour of 3600 seconds is represented by 3 + 6 + 0 +0 and so f9, the 2nd hour by 7 + 2 + 0 + 0 thus f9 and the 3rd hour by 1 + 0 + 8 + 0 = 0 therefore f9. etc. etc.
360o of the “perfect six”
Following on from a day comprised of quarters, hours, minutes in which the number of seconds = 3600 = f9, when a circle is divided into quarters and into units of 6? the same sequence of f6, f3, f9 appear, as is the cycle brought to close with the f9.
List of “perfect” Numbers
Having now recognised how the natural numbers convert as an `f` number allows a closer look to be taken of the list of `perfect` numbers to find they also convert to an `f` number – or, at least to the first set of 13 numbers. With the exception of the `perfect` six all of the numbers that follow can be understood as representing the `perfect` number of f1, (i.e. 0 + 1 = 1, 1 – 0 = 1, 1 x 0 = 1, 1 ÷ 0 = 1.) As opposed to what is considered to be the first `perfect` number of 6: because 1, 2 and 3 are its proper divisors as do 1 + 2 + 3 = 6.
With an `f` number as representing the natural time cycle, as found with a day, a circle, as well as in a list of `perfect` numbers, this would appear not to be the case when it came a priesthood that lived in a world dominated by a solar cycle of 365¼ days, as obviously such a number would not dived equally. However whilst a seasonal year of this length will not divided equally, an artificial `year` of 364 days will, so for me it became a matter of finding a means by which the priesthood could compensate for the `missing` 1¼ days – which in terms of a `perfect` number converts as 4 x 6 hours and 1 x 6 hours.
The reason for the priesthood wanting a uniform `year` was in order to comply with the fundamental Law of keeping a Sabbath in place. In Genesis we have:
“And on the seventh day God ended his work which he had made; and he rested on the seventh day from all his work which he had made. And God blessed the seventh day, and sanctified it: because that in it he had rested from all his work which God created and made”. (Gen. 2: 2-3)
However following a cycle of 365¼ days it is not possible to keep to this basic Law, whereas to follow a uniform cycle of 364 (= 13 = f4) days this will divide equally into 13 (f4) months, each of 28 (f1) days.
In my study of the Temple I was aware of two `festivals` that brought in the `perfect` six, although this is not at first apparent, as according to those who had first translated the scriptures into Greek, between 280 – 130 BC, known as the Septuagint (Latin: `Seventy`.
Supposedly because of the number of translators) seemingly the thinking was the smallest time cycle followed by the Hebrews was that of a day. However once it is accepted that the priesthood was well aware that a day was to be divided, at least, into hours then what appears in some texts as `days` for these two `festival` need to be read as hours.
The `missing` day is to be found in what is known as Passover: said to have been the 10th day of the month when Moses was to lead an enslaved Israel out of bondage from Egypt , the time of leaving is said to have followed the killing of the firstborn of the Egyptians, at `midnight`.
As seen charted (for reasons I enter into in deal in my writings) this passing over of a day took place at the end of the old year and start of a new year. (Exodus 12:1-28. In the King James Version the word day does not appear in the original text but in order to make it read `right` has been inserted.)
The same misunderstanding is found with Atonement, which is given as the 10th of the 7th month (Leviticus 16:29. )
The word day once more missing from the KJ version but is again found inserted. As brought out on the chart the 6 hours was to be absorbed by putting the `clock` back by this amount, which leaves us with a priesthood whose calendar would lose one day each year that obviously would have to be accounted for.
How they compensated for this was, as seen next, to allow the 6 hours to drop back over a time cycle of (12 x 6 =) 72 years so we are again dealing with the highest f number of 9.
Year Chart of 12 & 13 Months
Illustrated here a 364 day `year` is defined in terms of days, weeks, 13 uniform months, 12 seasonal months and Quarters.
- a) The six days of a week are defined by
- b) Sabbath as the 7th day is defined by
- c) A `year` of 13 months is represented by f4, thus the same numbers as its Quarters.
- d) A uniform `year` of 3 – 6 - 4 days represents one of 13 months. i.e. f4.
The ascending and descending seasonal cycle I define as 1 – 6 & 1 – 6 months.
Year Chart of 12 & 13 Months –Animated
Here the 364 day cycle is seen animated.
Year Chart Over 72 Years
On this illustration I have extended the circular time cycle of a day and year to one of 72 years, with this done in three stages so as to reflect the continuing cycle of f3, f6, f9 when the numbers are seen as representing these divisions: i.e. 1 x 12 = 12, 2 x 12 = 24, 3 x 24 = 72.
72 Year Cycle of “f “ Numbers
Click on this link to view All Charts ( 6A-6L) in PDF format:
On charting a uniform cycle of 13 months over a period of 72 years, the sequence is one of a repeating cycle of f6, f3, f9, and in this the `f` numbers are seen to match those of the month numbers. i.e.
f6 of the 6th year cycle,
f3 of the 12 year,
f9 of the 18th year cycle,
f6 of the 24th year,
f3 of the 30th year,
f9 of the 36th year and so on throughout the 72 year cycle.
Therefore what started out as a cycle of 364 day `year` would on reaching the end of the 6th year record as 2184 days, as would the numbers continuing to expand by the end of the 12th `year` to 4368 days, then to 6552 days at the end of the 18th `year`, until the a figure of 26208 is reached at the end of the 72nd year.
However such numbers represent but one cycle of 72 years, whereas in a Temple that stood for centuries this cycle would only be the first of many, each of which would bring an increase in numbers – as we shall see.
Abridgment of ” f “ numbers cycle
(view in PDF format)
With this abridgment the f3, f6, f9 sequence is brought out better.
Cycle of 3 x 6 Years
(click to enlarge)
On this illustration I have replaced the cycle of Fig. 3 with one in which the four segments of a year are replaced by four segments depicting a cycle of years. Each segment sub-divided into 12 units, with each of these units representing a cycle of 6 years – therefore each quarter represents the cycle of 72 years. The define the movement of 6 years I colour it red, in which it is seen that what starts out as a circle divided into four segments becomes, after the first cycle, becomes one of eight segments. Therefore the 1st cycle of 6 years = f6, the 2nd cycle of 6 years = 12 years, therefore f3, and the 3rd cycle of 6 years = 18 years, therefore f9. As will be seen this sequence is to continue throughout the 72 year cycle.
It is to be noted that in terms of degrees these segments could be defined separately, as 90? + 90? + 90? + 90?, as could they be defined as f9 + f9 + f9 + f9. Or, when the cycle is expressed in terms of ascending degrees we have 90?, 180?, 270?, 360?, which then produce the all encompassing `f` number of `f9` as with 90? = f9, 180? = f9, 270? = f9, 360? = f9.
Cycle of 6 x 6 Years
(click to enlarge)
It is to be noted that on reaching the 36th year; the halfway point through the 72 year cycle, the outline is of a diagonal cross with this symbolising the movement of an artificial time cycle, over that of the natural `fixed` cycle as defined by the solar cycle.
Cycle of 9 x 6 Years
(click to enlarge)
The cycle now three quarters the way through continues.
Cycle of 12 x 6 Years
(click to enlarge)
On reaching the limit of travel the diagonal cross and upright cross are one more in alignment, at which point the cycle restarts as on Fig. 4A.
The effect on the priesthood and local population after 72 years would be one of a gradual dropping back on the seasons towards winter – to that of a sudden return to what the older generations would remember from their youth as spring.
Applied to a Temple that was in use over centuries this cycle of 72 years would only be the starting point of the numbers as represented by 936 months or 26208 days, as after this the second cycle record as 144 years, the third as 216 years, the forth as 288 years and fifth as 360 years, and so on.
Each set of years having their own month and day numbers so would they continue to increase for as long as records were kept. If at some later stage what these numbers represented was not understood, or that what they were recording as the means by which a Sabbath was kept in place then to come across even the first set of number (936 x 28 =) 26208 in a connection with the priesthood and `service` given over a period of 72 years would have been at the very least mystifying.
Whereas to have come across numbers, defining years of `service`, that increase by a factor x 2 to and so produce 52416, or, by a factor of x 3 to 78624, or, by x 4 to 104832 and so on creates their own problems. It also means such numbers can no more be understood in terms of a Priesthood that belonged to the Temple (the House of Israel) so would have to be in some way allocated to the People of the House of Israel.
Seen in this light explanations began to emerge that would explain the implausible account in Exodus in which we have the figure of Moses as leading Israel in a mass migration, numbered in hundreds of thousands, out of Egypt into a wilderness in what is reported to have been forty years with the objective of eventually reaching a `promised land` and there build the Temple. (In another section of my Temple study, I bring out evidence that the numbers found with a time cycle based on the `perfect` six also applies to the priesthood that was itself based on twelve groups each of six priests who offered `service` over a period of six days, with the Sabbath, the 7th, a day of rest.)
Once this system of dividing a circle into sections is accepted as the means by which the ancients recorded time and numbers, it follows this system would have been passed on to others, either in the form of the detail seen on my Charts, or, by means of symbolizing it in other ways. It was from this point of view, along with the knowledge concerning the occupation of Jerusalem by the Romans, that lead me to the connection between this symbolization and what is found incorporated into the system of numbering used by the Romans.
Roman Numerals & Zero
It is said the system of numbering the Romans used had been adapted from one used by the Etruscans some centuries earlier, with this later modified during the Middle Ages. It is also claimed the Romans system was based on certain letters being given numerical values and the concept of the zero did not exist in Europe until after 1000 AD. However the numerals are set against the ascending and descending cycle of Fig. 4 and the 36 year cycle seen on Fig. 5B it becomes obvious that a zero forms the basis of the numbers and what we now have in Roman Numerals is an abridgment of a more complex image.
In outline this represents a section of what I have in my main work on Time and Numbers the end result is a new line of inquiry opens up on the extent of what was known in ancient times.
I look forward to any comments you care to make.
Copyright 2015 by Harry Teasdale