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The Number 153
An old and dear friend wrote the following to me:
The last chapter of John, John 21 is a strange chapter. It makes the impression of an afterthought, an addendum. And it contains some very strange things as well. First of all the story of the 153 fish. John 21:3-11. Why is the number of fishes exactly 153? What is the significance of that?
I found that 153 is a special number, a triangular number, the sum of the numbers 1 thru 17. And also the sum of the first 5 faculties, 1! thorugh 5!. And the 3rd powers of the digits 1, 5 and 3. But I doubt that latter explanation because the positional number system was not yet in use. But apparently 153 was also known in antiquity as part of the ratio 265/153 which is very close to the square root of three.
Apparently Pythagoras traveled once from Sybaris to Croton where he lived. And along the coast he met a few fisherman who were just busy hauling in their nets. Pythagoras could predict the exact number of the fishes in the net: 153. And this number proved to be right.
But what is the significance of the square root of three? It appears that that is the ratio of the length and the width of the vesica piscis, the intersection of two circles from which the circumference of the one circle cuts through the center of the other and vice versa. And a slightly extended version of this vesica piscis is the famous christian fish, the secret recognition symbol of the early christians, the 'ichthus' symbol.
But I cannot find the text of Pythagoras in Iamblichus 'Life of Pythagoras'. There is that story, allright, but the exact number is not given. Plato and Archemedes should have used this number 153 as well, but so far I have not been able to locate it. I would like to find the references.
My response, such as it is, follows:
I read somewhere that Archimedes referred to the ratio 265:153 as "the measure of the fish" in his work "On Measuring the Circle". I have found a translation of his work online: http://www.math.ubc.ca/~cass/archimedes/circle.html. I found no such
reference in the few pages reproduced online. However, I found a point in this treatise interesting. 265:153 is not only an approximation of the square root of 3 but also the ratio of the circumference of any circle to its diameter (proposition 3). See also http://www.harmonictheory.com/files/geometry/fishes.pdf.
Before we started our correspondence many years ago, I used to get
books from an American publishing house affiliated with the
Theosophists--Quest Books. One such early purchase dealt exclusively
with gemetria and was over my head--although very interesting: "Jesus
Christ, Son of God" by David Fideler. It the best book on the topic I
have ever seen and recommend it. Anyway, he has a whole chapter (#6)
on the gospel of John but neglects to delve into the 153 fishes for
some reason in this chapter. But he touches on the 265:153 subject
(also the square root of 3) in an earlier chapter discussing Plato.
Here is a quote from Plato's Timaeus:
"But two things cannot be rightly put together without a third; there
must be some bond of union between them. And the fairest bond is that
which makes the most complete fusion of itself and the things which it
combines; and proportion is best adapted to effect such a union. For
whenever in any three numbers, whether cube or square, there is a
mean, which is to the last term what the first term is to it; and
again, when the mean is to the first term as the last term is to the
mean -- then the mean becoming first and last, and the first and last
both becoming means, they will all of them of necessity come to be the
same, and having become the same with one another will be all one."
According to Fideler, this means "in the proportion A:B:C, A is to B
in exactly the same ratio as B is to C. In this proportion, the
middle term B is the so-called Geometric Mean, the point of mediation
between A and C. The mathematical formula for finding the Geometric
mean between any two numbers is a simple: take the two extremes,
multiply them together, and find their square root." In my copy of
Fideler, I wrote many years ago (over a dozen) the example 2:4:8. 4
is the geometric mean as it is the square root of 2 x 8. Fideler,
without delving further, points out that the square root of 3 (i.e.,
265/153) is the geometric mean of 1 and 3.
Thought. If, as Plato posits, "two things cannot be rightly put
together without a third" and that third which binds them perfectly is
the geometric mean, then there are greater implications for the square
root of 3. Three refers to the trinity. 1 and 3 could be the first
and second elements of the trinity. What perfectly binds the first
and second elements of the trinity? Their geometric mean which is
itself the third element of the divine trinity. Is 265/153 the
geometric ratio representing the logos? If so, it would have held
power for the ancients and been part of the eastern mystery cults.
Could explain why Pythagoras does not give the number (153) and, also,
why Archimedes never explains where he gets this ratio from (he
learned it during a secret initiation). FN1.
Interesting subject. I've though more about the subject and attempted to organize the above together with new thoughts into a post on one of my blogs.
JJR
11-18-2007
Footnote 1. Porphyry write of Pythagoras: "Meeting with some fishermen who were drawing in their nets heavily laden with fishes from the deep, he predicted the exact number of fish they had caught. The fishermen said that if his estimate was accurate they would do whatever he recommended. They counted them accurately, and found the number correct, he then bade them to return the fish alive into the sea; and, what is more wonderful, not one of them died although they had been out of the water a considerable time." Footnote 97, Chapter 3, The Jesus Mysteries, by Timothy Freke and Pater Gandy (1999). The number of fish in the catch predicted by Pythagoras is not recorded. If the number were 153 (a sacred number), it helps explain why Porphyry did not record it coming from Pythagoras' lips.
Update: Additional links germane to this topic:
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