Jiri
Critical Thinker
- Joined
- Mar 5, 2007
- Messages
- 387
Methodology of extrapolating geometrical elements out of graphical artwork
The algorithm will differ depending on who does the research, a computer program, or a human. A program works by mechanical methods (described below) of extracting geometrical elements from an image. Then it compares those elements in various combinations to its extensive database, to see if it finds them there. If yes, it starts with this new branch. It catalogues all its positive results for human inspection.
Forcing extrapolation
An engraved line can force a straight line, when the straight line bounces off its edges on both sides without protruding.
An engraved line can also force a circle in the same manner. In both cases, the longer the engraved line the better.
A bowed line forces a straight line that snaps onto its ends.
Two or more bows force a straight line, when it is tangential to both bows.
Any picture forces its outer frame, unless it is oval The points of the frame can be connected, but also be cross-connected to other points of the enclosure. Are there angular regularities between any of the lines?
If we have an orientation, such as square's axes, we can frame any area between lines of that orientation.
Multi-point lines and circles:
In this area, computers are bound to excel over people Any two points give a line, any three a circle. There will be a lot of those in any image, however computers can find the ones with the most points, something difficult for humans to do. The multi-point lines and circles, which meet the minimum number are incorporated into the database as such.
Symmetry of two circles
A human experiences what geometrical form strikes the eye in any given image, and can take it from there. The Athena engraving drew my geometrical attention by apparent symmetries, which stood out. The first was the torso, which looked to me like the overlap of two same-size circles. Then it doesn't take long to see crossing lines form points, where the circles could have their centers. We have in fact discovered an abstract geometrical concept in the image. Drawing the circles from the marked points precipitates more developments. The two points, where the cirles intersect form a square with the circles' centers. This is a surprise. So, we draw in the square's sides. and diagonals. Everything seems to fit in. Especially, the diagonals pass through a lot of points. And that's just the start.. We can see all the initial constructions in http://www.vejprty.com/Seat1.htm
So, to implant a geometrical system into seeming free-hand, and make it discoverable later, some of its elements must stand out during just normal scrutiny- like our Square.
Symmetry on one circle:
The problem of precision faced the designer, too. How to best maintain precision of implied design on apparent free-hand work? The so called "Key circle of the Cone" shows us at once two solutions. The Key-circle comes from another readily apparent symmetry between two arcs. Do the two arcs have a common center? Here, the designers give us a hand, The arcs force two lines, cross-connecting their ends. The point, at which they cross is the center of the arcs. In fact, this is another abstract system. The two arcs are parts of the same circle, and they are symmetrical through the center. The center itself is given with definitive precision, in this manner. It also happens to be right on the edge of an engraved line. We see this in the engraving a lot - distinct points move to the edges of lines, rather than being lost somewhere within the multi-pixel lines.
Third readily apparent symmetry was on the human figure's hip.Two arcs of different length appear to have the same radius.
Symmetry of three circles:
When we put these three initial geometrical figures together, we can see systematic relationships between them. The solution, however, requires reconstruction of the so called Cone, first. The Cone is also about symmetry, this time between three circles, one of which is the Key-circle of the Cone, already mentioned above.
Fitting versus Causing
You have appreciated George Markowsky a little too much, I believe. This guy is obviously dishonest, when he says that the Parthenon as shown does not fit a Phi rectangle. True, it does not fit it, because of protruding stairs. On the other hand, it is just as true that the main lines do produce a Phi (Golden) rectangle - the height, the base, and the width. There is a fine difference here, which could unduly influence research results. Remember it. Remember - there is a witch-hunt atmosphere, when it comes to any ancient science, not allowed for by the consensus.
Markowsky is a piranha, which loves these murky waters. Look at his title "Misconception: the Great Pyramid was designed to conform to Phi", for one of the sections in his article "Misconceptions about the Golden Ratio". The title tells you it's a misconception in BOLD print, but the small print later tells you that the ratio checks out to 1.62, close enough for his acceptance limits. Because the pyramid fits physically the notion of Phi, poor Markowsky resorts to bashing Herodotus under the same heading, and the work as well as the payoff grow handsomely. In a word, it's bad pseudo-science, yet you loved it. If you fall under the sway of such partisan theories, how can I believe that this discussion is in earnest?
The discovery of a system in the Athena engraving came relatively quick and easy. I've since looked at a couple of other complete engravings from La Marche, but I was unable to find anything there like the system from the Athena engraving. Still, the images bear telltale marks of a planned, measured construction. The Athena engraving is different in that it facilitates recognition, it is a beacon for attention, so really, and it teaches its system for all the practical purposes. This situation resembles Nazca, whose monkey figure displays the Cone & Square formation as well, but the other figures and lines there are far less obvious. It seems that the Cone & Square formation might hold the clue to a grand solution of both Nazca and La Marche. It gives us some definite orientations at Nazca (one is self-same with the world compass, and one the same as the Cone) to compare the other lines to, and it gives us distance units. One could do things like checking, if the square found by Daniken at Palpa directly integrates into our system.
A couple of notes on accuracy:
When drawing geometrical figures on the engraving in lifesize, the points of the square seem accurate. When the image is blown up, suddenly there is only one way to insert an exact square to these points, which are by then transformed into quadrangles. The points themselves fall upon line edges. This fact really forces the Square's position and size. Whoever tries to duplicate my results will agree, I hope.
We heard a lot of doubt expressed here regarding my measurement of the Frame. In all the excitement, one important fact got lost, namely that the measurements are now internally generated. This means that the system including the distance units had been regenerated from the image in CAD. This was quite a test then, and it worked..
So, it seems that the image did not suffer too much, when photocopied from an issue of the Bulletin of the French Prehistorical Society. Let's see, Lwoff gave the Bulletin his best copy of the engraving, and inordinate care was taken to produce the best copies possible. The printers working with the usual high resolution for finely printed publications had made Lwoff's copy smaller, but still accurate for our preliminary research purposes. So, the issue is mainly in photocopying the bulletin, and then blowing it up again. Whatever damage had been done wasn't serious enough.
You are the mathematician, and I will not argue these figures. Instead, thank you for providing interesting insights into the matter. It was obvious that the number will be a lot more than just a factorial. While you are thinking in 13-D, I am only trying to visualize the body of all solutions in 3-D
BTW, did you account for the fact that while order matters, it does not really matter, when identical values interchange order. All these permutations would count as one, reducing the total, I think.
As to you saying that I took liberties in counting the Frame's segments, I dispute it. You must be speaking of the segment K-L. While it strikes several points in a row, it remains as one straight line segment, and keeps to the rules. It is also a fact that this segment could be subdivided. For the purposes of the Frame, however, it is perfect, just like all the other segments. I don't know why you try to make a weakness out of the Frame's strength, namely that all the segments are already ideally suited for its communicational purposes. You yourself are powerless, when it comes to improving the Frame from this viewpoint.
It is also tautological to say that if the Frame made sense in another way then I would have presented it in that way. But, of course, I would have..
Finally, sorry for late reply, I was too busy.
Jiri said:
.
The algorithm will differ depending on who does the research, a computer program, or a human. A program works by mechanical methods (described below) of extracting geometrical elements from an image. Then it compares those elements in various combinations to its extensive database, to see if it finds them there. If yes, it starts with this new branch. It catalogues all its positive results for human inspection.
Forcing extrapolation
An engraved line can force a straight line, when the straight line bounces off its edges on both sides without protruding.
An engraved line can also force a circle in the same manner. In both cases, the longer the engraved line the better.
A bowed line forces a straight line that snaps onto its ends.
Two or more bows force a straight line, when it is tangential to both bows.
Any picture forces its outer frame, unless it is oval The points of the frame can be connected, but also be cross-connected to other points of the enclosure. Are there angular regularities between any of the lines?
If we have an orientation, such as square's axes, we can frame any area between lines of that orientation.
Multi-point lines and circles:
In this area, computers are bound to excel over people Any two points give a line, any three a circle. There will be a lot of those in any image, however computers can find the ones with the most points, something difficult for humans to do. The multi-point lines and circles, which meet the minimum number are incorporated into the database as such.
Symmetry of two circles
A human experiences what geometrical form strikes the eye in any given image, and can take it from there. The Athena engraving drew my geometrical attention by apparent symmetries, which stood out. The first was the torso, which looked to me like the overlap of two same-size circles. Then it doesn't take long to see crossing lines form points, where the circles could have their centers. We have in fact discovered an abstract geometrical concept in the image. Drawing the circles from the marked points precipitates more developments. The two points, where the cirles intersect form a square with the circles' centers. This is a surprise. So, we draw in the square's sides. and diagonals. Everything seems to fit in. Especially, the diagonals pass through a lot of points. And that's just the start.. We can see all the initial constructions in http://www.vejprty.com/Seat1.htm
So, to implant a geometrical system into seeming free-hand, and make it discoverable later, some of its elements must stand out during just normal scrutiny- like our Square.
Symmetry on one circle:
The problem of precision faced the designer, too. How to best maintain precision of implied design on apparent free-hand work? The so called "Key circle of the Cone" shows us at once two solutions. The Key-circle comes from another readily apparent symmetry between two arcs. Do the two arcs have a common center? Here, the designers give us a hand, The arcs force two lines, cross-connecting their ends. The point, at which they cross is the center of the arcs. In fact, this is another abstract system. The two arcs are parts of the same circle, and they are symmetrical through the center. The center itself is given with definitive precision, in this manner. It also happens to be right on the edge of an engraved line. We see this in the engraving a lot - distinct points move to the edges of lines, rather than being lost somewhere within the multi-pixel lines.
Third readily apparent symmetry was on the human figure's hip.Two arcs of different length appear to have the same radius.
Symmetry of three circles:
When we put these three initial geometrical figures together, we can see systematic relationships between them. The solution, however, requires reconstruction of the so called Cone, first. The Cone is also about symmetry, this time between three circles, one of which is the Key-circle of the Cone, already mentioned above.
Fitting versus Causing
You have appreciated George Markowsky a little too much, I believe. This guy is obviously dishonest, when he says that the Parthenon as shown does not fit a Phi rectangle. True, it does not fit it, because of protruding stairs. On the other hand, it is just as true that the main lines do produce a Phi (Golden) rectangle - the height, the base, and the width. There is a fine difference here, which could unduly influence research results. Remember it. Remember - there is a witch-hunt atmosphere, when it comes to any ancient science, not allowed for by the consensus.
Markowsky is a piranha, which loves these murky waters. Look at his title "Misconception: the Great Pyramid was designed to conform to Phi", for one of the sections in his article "Misconceptions about the Golden Ratio". The title tells you it's a misconception in BOLD print, but the small print later tells you that the ratio checks out to 1.62, close enough for his acceptance limits. Because the pyramid fits physically the notion of Phi, poor Markowsky resorts to bashing Herodotus under the same heading, and the work as well as the payoff grow handsomely. In a word, it's bad pseudo-science, yet you loved it. If you fall under the sway of such partisan theories, how can I believe that this discussion is in earnest?
The discovery of a system in the Athena engraving came relatively quick and easy. I've since looked at a couple of other complete engravings from La Marche, but I was unable to find anything there like the system from the Athena engraving. Still, the images bear telltale marks of a planned, measured construction. The Athena engraving is different in that it facilitates recognition, it is a beacon for attention, so really, and it teaches its system for all the practical purposes. This situation resembles Nazca, whose monkey figure displays the Cone & Square formation as well, but the other figures and lines there are far less obvious. It seems that the Cone & Square formation might hold the clue to a grand solution of both Nazca and La Marche. It gives us some definite orientations at Nazca (one is self-same with the world compass, and one the same as the Cone) to compare the other lines to, and it gives us distance units. One could do things like checking, if the square found by Daniken at Palpa directly integrates into our system.
A couple of notes on accuracy:
When drawing geometrical figures on the engraving in lifesize, the points of the square seem accurate. When the image is blown up, suddenly there is only one way to insert an exact square to these points, which are by then transformed into quadrangles. The points themselves fall upon line edges. This fact really forces the Square's position and size. Whoever tries to duplicate my results will agree, I hope.
We heard a lot of doubt expressed here regarding my measurement of the Frame. In all the excitement, one important fact got lost, namely that the measurements are now internally generated. This means that the system including the distance units had been regenerated from the image in CAD. This was quite a test then, and it worked..
So, it seems that the image did not suffer too much, when photocopied from an issue of the Bulletin of the French Prehistorical Society. Let's see, Lwoff gave the Bulletin his best copy of the engraving, and inordinate care was taken to produce the best copies possible. The printers working with the usual high resolution for finely printed publications had made Lwoff's copy smaller, but still accurate for our preliminary research purposes. So, the issue is mainly in photocopying the bulletin, and then blowing it up again. Whatever damage had been done wasn't serious enough.
JSF said:
You are the mathematician, and I will not argue these figures. Instead, thank you for providing interesting insights into the matter. It was obvious that the number will be a lot more than just a factorial. While you are thinking in 13-D, I am only trying to visualize the body of all solutions in 3-D
BTW, did you account for the fact that while order matters, it does not really matter, when identical values interchange order. All these permutations would count as one, reducing the total, I think.
As to you saying that I took liberties in counting the Frame's segments, I dispute it. You must be speaking of the segment K-L. While it strikes several points in a row, it remains as one straight line segment, and keeps to the rules. It is also a fact that this segment could be subdivided. For the purposes of the Frame, however, it is perfect, just like all the other segments. I don't know why you try to make a weakness out of the Frame's strength, namely that all the segments are already ideally suited for its communicational purposes. You yourself are powerless, when it comes to improving the Frame from this viewpoint.
It is also tautological to say that if the Frame made sense in another way then I would have presented it in that way. But, of course, I would have..
Finally, sorry for late reply, I was too busy.
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