jmd
In a post by John Meador & Namadev in the thread Lazzarelli: a Pythagorean diversion, mention is made of the sequence 1 2 3 4 9 8 27 and Plato's Timaeus.
The sequence (already highlighted in that thread) is important to Plato for a number of reasons, especially related to both music and the Soul.
The two sequences are usually arranged on the two sides of the letter Lambda (an inverted 'V', from which our 'L' derives, approximately: '/\'), with 1 at the top, thus:
One can see that the left-hand side descends by a doubling, and the right-hand side by a tripling principle. It is of course informative and significant that the addition of all smaller numbers add to the largest (as already mentioned in the thread previously linked).
More than this, however, each sequence (1, 2, 4, 8 and 1, 3, 9, 27) together form 55, which is the tenth triangular number (and the number of depicted pips in each suit).
From a pythagorean perspective, neither the musical importance, nor the importance of the tenth triangular number depicted by those numbers upon a Lambda form would have been lost.
Likewise, the similarity (but incompleteness of the first) between the Lambda and the Delta would have been noted.
Delta (written as a triangle) is especially significant: it is a triangle with a value of four, being the fourth letter in the alphabet. As a triangle with a value of four, it virtually implies both seven (3 & 4) and ten (a triangle of base four).
...but what is also important, and something I remember from the late 1970s but do not recall where else it may have been reproduced (it was from a book on mediæval magic located in the Centre Pompidou library on Paris) is that if one takes these same numbers (transposing the 8 and 9) and place them in a clockwise sequence upon the points of a six pointed star, definite triangles emerge:
Here one can see that the base of each triangle is also significant, with the descent into Earth (4) being from the Divine (10), and the rise to unity having a base in the stars (12).
The centre, 27, being altered to 26 by removing the value of the non-number '1', giving the equivalent to the value of the Tetragrammaton (YHVH).
The sequence (already highlighted in that thread) is important to Plato for a number of reasons, especially related to both music and the Soul.
The two sequences are usually arranged on the two sides of the letter Lambda (an inverted 'V', from which our 'L' derives, approximately: '/\'), with 1 at the top, thus:
1
2...3
4......9
8........27
2...3
4......9
8........27
One can see that the left-hand side descends by a doubling, and the right-hand side by a tripling principle. It is of course informative and significant that the addition of all smaller numbers add to the largest (as already mentioned in the thread previously linked).
More than this, however, each sequence (1, 2, 4, 8 and 1, 3, 9, 27) together form 55, which is the tenth triangular number (and the number of depicted pips in each suit).
From a pythagorean perspective, neither the musical importance, nor the importance of the tenth triangular number depicted by those numbers upon a Lambda form would have been lost.
Likewise, the similarity (but incompleteness of the first) between the Lambda and the Delta would have been noted.
Delta (written as a triangle) is especially significant: it is a triangle with a value of four, being the fourth letter in the alphabet. As a triangle with a value of four, it virtually implies both seven (3 & 4) and ten (a triangle of base four).
...but what is also important, and something I remember from the late 1970s but do not recall where else it may have been reproduced (it was from a book on mediæval magic located in the Centre Pompidou library on Paris) is that if one takes these same numbers (transposing the 8 and 9) and place them in a clockwise sequence upon the points of a six pointed star, definite triangles emerge:
1
8.....2
27
9.....3
4
8.....2
27
9.....3
4
Here one can see that the base of each triangle is also significant, with the descent into Earth (4) being from the Divine (10), and the rise to unity having a base in the stars (12).
The centre, 27, being altered to 26 by removing the value of the non-number '1', giving the equivalent to the value of the Tetragrammaton (YHVH).
