Pythagoras of Samos (c.600BC) very likely gleaned megalithic number science on his travels around the “Mysteries” of the ancient world. His father, operating from the island of Samos, became a rich merchant, trading by sea and naming his child Pythagoras; after the god of Delphi who had “killed” the Python snake beneath Delphi’s oracular chasm, now a place of Apollo. The eventual disciples of Pythagoras were reclusive and secretive, threatening death on anybody who would openly speak of mysteries, such as the square root of two, to the uninitiated. It can be seen from the previous post that many such “mysteries” were natural discoveries made by the megalithic astronomers, when learning how to manipulate number without arithmetic, through a metrological geometry unfamiliar to the romantic sacred geometry of “straight edge and compass”.
Continue reading “The Megalithic Pythagoras”Month: August 2022
Seven, Eleven and Equal Perimeters
above: image of applications involving sacred geometry based upon pi as 22/7 and a circle of equal perimeter to a square, from a previous post.
The geometrical and other relationships between different numbers are easily found to be useful through simple experiments. The earliest approximations to pi (22/7) was key in the megalithic and later ancient cultures, for making circles of a known diameter and circumference, the foremost using the numbers 7 and 11 doubled twice. A staked rope of length seven will create a circumference of 44, to a high degree of accuracy.
But what is pi? it actually connects two different worlds, of extensive linear measure and of intensive rotational measure. As the radius rope is made larger the circle expands from its center but it remains a whole circle, except that its circumference is made up of more “units” all according to the ratio pi = 22/7, in a good approximation.
But measuring a circumference is fiddly, it is circular! In contrast, it is very much easier to work with squares since their perimeter is four times their side length. And in many cases, one does not really need to measure the perimeter. Because of this, the megalithic looked for and discovered an easier procedure in which one could know the circumference of a circle if one could generate the square that has the same circumference now called the equal perimeter model. This was surprisingly simple to grasp and implement.
Continue reading “Seven, Eleven and Equal Perimeters”The Megalithic Numberspace
above: counting 37 lunar months six times to reach 222,
one month short of 223: the strong Saros eclipse period.
There is an interesting relationship between the multiple interpretations of a number as to its meaning, and the modern concept of namespace. In a namespace, one declares a space in which no two names will be identical and therefore each name is unique and this has to be so that, in computer namespaces such as web domain names, the routes to a domain can be variable but the destination needs to be a unique URL.
If sacred numbers had unique meanings then they would be like a namespace. Instead, being far more limited in variety, sacred numbers have more meanings, or interpretations, just as one might say that London has many linkages to other cities. In an ordinal number set, there are many relationships of a number to all the other numbers. This means whilst their are infinite numbers in the set of positive whole numbers, there are more than an infinity of relationships between the members of that set, such as shared number factors or squares, cubes, etc. of a number.
The mathematician Georg Cantor saw “doubly infinite” sets. Sets of relationships between members of an already infinite set, must themselves be more than infinite. He called infinite sets as aleph-zero and the sets of relationships within an infinite set (worlds of networking), he called aleph-one.
Originally, Cantor’s theory of transfinite numbers was regarded as counter-intuitive – even shocking.
Wikipedia
However, in the world of sacred numbers, although there can be large numbers, in the megalithic the numbers were quite small; partly due to the difficulty that numbers-as-lengths were physically real while later numeracy abstracted numbers into symbols and, using powers of ten, modern integers are a series of place ordered numbers (not factors) in base 10, as with 12,960,000 – possible for the ancient Babylonians but, I believe, not expected for the early megalithic.
Continue reading “The Megalithic Numberspace”Knowing Time in the Megalithic
The human viewpoint is from the day being lived through and, as weeks and months pass, the larger phenomenon of the year moves the sun in the sky causing seasons. Time to us is stored as a calendar or year diary, and the human present moment conceives of a whole week, a whole month or a whole year. Initially, the stone age had a very rudimentary calendar, the early megalith builders counting the moon over two months as taking around 59 days, giving them the beginning of an astronomy based upon time events on the horizon, at the rising or setting of the moon or sun. Having counted time, only then could formerly unnoticed facts start to emerge, for example the variation of (a) sun rise and setting in the year on the horizon (b) the similar variations in moon rise and set over many years, (c) the geocentric periods of the planets between oppositions to the sun, and (d) the regularity between the periods when eclipses take place. These were the major types of time measured by megalithic astronomy.
The categories of astronomical time most visible to the megalithic were also four-fold as: 1. the day, 2. the month, 3. the year, and 4. cycles longer than the year (long counts).
Continue reading “Knowing Time in the Megalithic”