– star-shaped –
Ancient art is full of diverse starlike ornaments and it’s no wonder that many historians have come to the conclusion that ancient peoples were admirers of stars, five-pointed, six-pointed, eight-pointed – and to a somewhat lesser degree of three-pointed, seven-pointed, nine-pointed stars – yet nobody seemed to inquire why artists undertook such trying experiences to make these “ornaments”, particularly to produce them in stone. Some historians on encountering the cross in the ornaments of ancient peoples of South America cried out, “They were familiar with the cross before Christianity!” Of course none of us could have imagined the existence of a “language of geometry” or a “script that could be ‘interpreted’” and for which we will perhaps need more time to interpret it if we don’t accept that the entire ornamental range of worldwide presentations is actually a genetic coding system on which nature is based, whereas some systems of star-shaped and descriptive presentations are genetic groupings, component parts of a general system, a message that tells about the diversity of species including the human species in general, whose, it seems, basis is concordance, a measured mixture of all individual – yet again, of their own “languages” and “backgrounds” – considered, although each contains “all”. Therefore precisely with the octagon we will try to present the belonging of everything to all, and yet to being a specific part of itself; but of course always sticking to the purely geometric way. We will avoid “getting lost” in the long-past ancient cultures, but rather to those closer to our own of which to this very days three are still very much alive, three “genetic-geometrical realities” in the form of three “children”, of what we have said are all „O“ (read geometrically – a circle – a bordered space of infinity) and now further read this only as infinity – three living religions – Judaism, Islam and Christianity (of course the more distant ones are also alive), but these three have the same center that exists to this very day – Jerusalem – which in the time frame that has long been narrated by those who have conveyed the word; the time frame of the center that was “split into three parts”. Thus we can observe the time frame as well. By means of geometric interpretation and segmentation we might succeed to understand the above, somewhat philosophical and poetical, piece of writing.
So, the octagon (a double square – star-shaped)!
So – general beginning – radius – from center the arc of circumscribed circle – arc divided by circles of same radius into six natural parts.
* * *
Divided into four sections by the poles and intersections that are present. (the poles on the circle are vertically subtended and at intersections horizontally – subtended)
From there to basic circle we draw circles of same radius and the new intersections are connected by rectilinear directions that divide the basic circle into 8 sections. So, we get new rectilinear intersections on the basic circle.
Again we get four rectilinear intersections and circumscribe circles of same radius as the basic circle. New intersections are created and we begin their “differentiation”.
New circles and the first divisible ones outside of the basic circle – we circumscribe intersections of the endpoint ones. We have the scope in the compass – the new radius – and it is larger.
With that radius (truncated – only to the field of the basic circle) from 8 points of the divided basic circle we inscribe the radius from point to point and that is the radius of the octagon star-shaped polygon of the basic circle.
Outside of the circle there is one more group of intersections created only from four rectilinear intersections. We circumscribe them with their circle.
With that radius from the 8 points of the divided basic circle we circumscribe semicircles.
We circumscribe their external intersections on the semicircles. That is the new radius.
If with that radius, from the peak pole of the basic circle, we start the point-to-point division, we will get the first star-shaped 12-sided polygon.
And inside the circle the intersection of the first star-shaped octagon is described with a circle and with that radius we start the division of the basic circle from its peak pole.
Then with that radius we divide the basic circle into 9 equal segments (nonagon). (With same radius from subtended pole – 18-sided polygon – from 4 poles 36-sided polygon, from 8 – 72 etc etc.)
From the very beginning but prior to acquiring the first star-shaped 8-sided polygon, we acquired horizontal intersections (subtended). We circumscribe thm with circle. This circle is the circle of the ancient Pi, and its diagonals are (4 radii) the sides of square’s perimeter or Pi number of the basic circle.
The radius of the circle of the ancient Pi divides the basic circle into 24 segments. However, we won’t dwell on that since that is not our goal.
* * * *
According to this section one may get the impression that we are moving away from the given theme that we initiated (the pyramidal code, doubling the cube, series of measurement). On the contrary, we are just assembling the base, the colors of the genetic code, so as to understand the base like in the case when the base consists of three colors and two “gradations” and everything else is the ratio of mixture of all other individual colors. That is how millions of shades are produced (however, this might be a poor comparison) since natural coloration has many more series that bring them to life, such as the unimaginable beauty experienced by anyone who was “lucky” to see at least one of its sequences. When I cite “lucky” under quotation marks, it is because seeing and knowing are great unknowns full of questions. Certainly, the given theme was thus far just partially “interpreted“ (due to truncated drawing we left out whole series and series of radii). The thought comes to mind (in reference to the nonagon) that I should once more, after who knows how many times, demonstrate the trisection enigma; but we will skip it and move on to searching for what we spoke about at the beginning of this chapter. You probably noticed that we talk about the genetic code as if geometry is a living being. In other words, life is a strictly balanced geometrical rule. And whatever is equilibrated is ideal (we are talking about an ideal basis) and one such basis is certainly the ideal proto-genetic code. If any irregularity in it emerges, it is a degradation in a manner that makes it seem as if the “skeleton” of equilibrated ancient geometry is taking its own “flesh”. However, I would not take upon myself the qualification to talk about this, had I not seen parts of this with my own eyes and heard parts of it with my own ears. Yet I would not dare try to explain all this because I don’t know how, nor dare to convey it to anybody for fear that I might not do it correctly. I can only convey the knowledge that I acquired from this geometry along with the realization of where we took the wrong actions and how we can simply learn much more.
One day the time will certainly come when on the basis of all this a potential energy of someone or some other existing or future generation will take on a pioneering – investigative venture in search of the new and novel and will acquire the answers in the fields of natural science. However, in light of our human duality (I am aware of it) in a positive and negative sense, this depends on the nature of the individuals participating in the venture and their surroundings. This is surely permissible and left up to us, although I hold that there is no danger since I always have before my eyes a proverb that goes “Where there is evil, there is always more good”. I’m talking about the futility of many catastrophic stories about the existence of Man on earth and the outcome is always that Man will never disappear. The circumstances that are happening right now are disastrous for the human species but the mentioned circumstances are products of our own making, but likewise a search to find the road to something new. So let’s not condemn and prevent such searches, because we have “to know”, and when we do find out, we will then estimate which road to take. That is our way and who knows what we are yet to encounter. After all, we are the youngest evolutionary species on the planet and maybe beyond. It’s possible. Once I was asked for my opinion about UFOs, the appearance of an unknown phenomenon. I inadvertently replied: “That is us from the future”. Who knows how far away is that future? I think that this future is still very far away and this judgment arises from the fact that in the field of energy we are still using generators with a stator and rotor. Nobody seems to think of rotating the stator and rotor (in opposite directions), which would be a step forward – double rotation. And then how could anyone come upon the idea of static stator and static rotor, or to spin an energy field, etc. etc.. So, we have to discover many more specific things, and on the other hand we have yet to go through the inevitable clash of civilizations to rid ourselves of dogmas and find the original – the new, although there is a simpler way to go through all this faster. But as I promised in some of the previous chapters I will write about it.
But now let’s continue with the dissecting of the star-shaped octagon (doubled square).