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"Any who doubt that the musical ratios are all of greater inequality, i.e., that the antecedent or first term in each is greater than the consequent or second term, should consult Archytas DK 47 B 2. This Fragment requires that the ratios be of this form if the assertions about the three means [arithmetic, harmonic and geometric] are to be true. Accordingly, the ratios assigned to the octave, fifth, fourth and minor sixth, must be 2:1, 3:2, 4:3 and 8:5, and not 1:2, 2:3, 3:4 and 5:8, respectively, as Mosshammer and others would have them. Indeed, there is early proof deriving from the Pythagorean school that intervals, such as the fifths, which are represented by superparticular ratios cannot be partitioned into any number of equal subintervals because the terms of these ratios admit no number of geometric means. Consider now the question of the status of the ratio (8:5) in the Pythagorean harmonic science that dates from the late fifth century B.C. to the time of Apollodorus. One should not expect that this ratio was recognized as melodic by every school of Pythagorean musical theory. For example those who sought to derive all the musical ratios from the Tetrad of the decad by compounding and dividing the ratios of the primary and most familiar intervals, the concords of the octave, fifth and fourth, would find the minor sixth unascertainable. There is reason to believe that these were supplied by Archytas in the early fourth century B.C."
Originally posted by LeoVirgo
My idea of thinking for the spiral being so important to the ancients is from observing the stars in the northern sky.
If you watch over time, the north star seems to be a center that all the rest of the sky revolve around.
This would be like a spiral that stars with the north star and then spans outward more and more.
Just a thought...they could of noticed that the sky seems to spiral out...from the north.
Originally posted by stereologist
reply to post by King Loki
Can you post a link to one of these statues. I looked all over the place and saw nothing to indicate man's hand on this supposed underwater pyramid. It looks natural to me. Graham Hancock's ideas appear to have no academic backing. It seems that he is another Velikovsky, Berlitz, Sitchin, Von Daniken, etc. I would prefer to begin research at the wikipedia and not end there. It certainly is going to start with more validity than Hancock's work.
As far as the wikipedia goes, my comment was directed at your point that maybe the wikipedia was old news. Well it has recent information. Lots of people have been getting steamed up because the guy in Bosnia has reported their affiliation with the project to lend it some sort of authenticity. The place is a hill and a fraud is being committed using respectable people's names.
Thanks for the trolling comment. I've also been accused of being a paid disinfo officer, a member of the NWO, and maybe other things as well. It's the sort of comment that comes up right before someone plays their last card and bows out.
I hope you stay in there because I am looking forward to seeing the turtle statue links and photos.
I just wanted to add that at first I did not realize that Hancock was the ECD guy.
[edit on 25-4-2010 by stereologist]
Though the Commission found some unfairness in our treatment of one aspect of the debate, this cannot be interpreted as support for Mr Hancock's or Mr Bauval's theories. The Commission made no judgement on the evidence for and against those theories, and did not cast doubt on Horizon's scientific assessment of it.
Originally posted by stereologist
reply to post by bigfatfurrytexan
As I said before the Fibonacci spiral is a solution to the problem of logarithmic spirals. It is not the general solution which are logarithmic spirals. A moth approaches on a logarithmic spiral. It would be a daunting task to find a moth approaching on a Fibonacci spiral. Here's why. Of all the possible angles to maintain, what is the chance of the moth maintaining the angle for that spiral which is 17 degrees. Any other angle and its a logarithmic spiral.
Originally posted by stereologist
reply to post by bigfatfurrytexan
It's splitting hairs to claim that a specific solution is the solution to a problem in which a moth maintains a constant angle with a point source of light. Splitting hairs would be more like when you said the moth uses Fibonacci sequence and the solution was a Fibonacci spiral. The F. spiral is a construction based on using F. sequence to form a spiral. That construction does not tell how a moth comes to a light.
Originally posted by stereologist
reply to post by King Loki
Can you post a link to one of these statues. I looked all over the place and saw nothing to indicate man's hand on this supposed underwater pyramid. It looks natural to me. Graham Hancock's ideas appear to have no academic backing. It seems that he is another Velikovsky, Berlitz, Sitchin, Von Daniken, etc. I would prefer to begin research at the wikipedia and not end there. It certainly is going to start with more validity than Hancock's work.
As far as the wikipedia goes, my comment was directed at your point that maybe the wikipedia was old news. Well it has recent information. Lots of people have been getting steamed up because the guy in Bosnia has reported their affiliation with the project to lend it some sort of authenticity. The place is a hill and a fraud is being committed using respectable people's names.
Originally posted by stereologist
reply to post by bigfatfurrytexan
A construction and a sequence are not synonymous terms.
Originally posted by Mahasamadhi
As a symbol spirals (or any other symbol really) doesn't simply represent any single meaning, they could or probably do/did represent a multitude of different meanings (subjected to variations through time of course) - all utilized depending on the different circumstances or contexts.