PRELIMINARY REMARKS
The present approach to Plato's dialogues does not attempt to suggest
what Plato thought, meant, or implied. Instead, the material is presented
here in the form of mathematical problems for the readers to solve for
themselves, should they wish to, for in the final analysis it is what the
reader understands that is important, not what is proposed by others, however
erudite they might be. What is required is a modicum of mathematical skill,
fundamental scientific concepts and an open mind. This is not a "Royal
Road" to the "Philosopher's Stone," it is astronomy and mathematics pure and simple to
provide a useful and necessary starting point. The end will ultimately
remain with the reader and the reckoner, for this matter increases in both
scope and complexity as it develops.
INTRODUCTION
Plato's Republic is an enduring and much admired work, but the two
mathematical problems presented here have nonetheless confuted hundreds,
if not thousands of inquiring minds since Plato's time [ 427 to 347 BC].
So, be forewarned, this is not a simple matter. Nor is it a matter of simple
arithmetic, either. Clues abound everywhere, but watch for phantoms and
misdirections nevertheless. You may find that you have wandered down a
lightly trodden pathway here; one that cuts across both space and time.
Few know where or when it began, and fewer still know where it will end.
Galileo and Kepler passed this way in their time too, although neither
were able to go the full distance. This is hardly surprising; among other
things Plato states in Laws VII (818-819) [translation by A.E.Taylor]
6
that: "ciphering and arithmetic make one subject." But he also says
much of relevance in the Epinomis (991-992)
too, including the observation that:6
To the man who pursues his studies in the proper way, all geometric constructions, all systems of numbers, all duly constituted melodic progressions, the single ordered scheme of all celestial revolutions, should disclose themselves, and disclose themselves they will, if, as I say, a man pursues his studies aright with his mind's eye fixed on their single end. As such a man reflects, he will receive the revelation of a single bond of natural interconnection between all these problems.Those already familiar with this material will no doubt demand to know who says the Tyrant's Number is 9 in the first place, who says the two problems are related in the second, and who is empowered to make such claims in the third. The answer to the first two questions is simple enough - I do. The Tyrant's Number might be considered to be 3, or even 27, but for present purposes I for one prefer 9 (Phaedrus 248c-249c); if you go the full distance you may make your own choice. The third question cannot be explained in a few sentences; the difficulty lies in prevailing attitudes towards the contents of the Dialogues themselves.
A word of caution: there is an unsuspected fork in this timeless pathway. One branch moves forward to new and dangerous territory, the other leads back to the comforting familiarity of the old. Perhaps you have begun to suspect that there may be more to this golden treasury of Dialogues; perhaps you have already dismissed that possibility; but either way, remember your choice if you attempt to connect these problems. Remember also that much space is given over to "names" in the Dialogues, e.g., Statesman (258c-259c), Laws, Theaetetus, The Republic, and especially the Cratylus. Moreover, be aware that all manner of devices tend to be applied in Plato's dialogues to inform the initiated and confute the uninitiated alike. At times this problem can be exacerbated by differences between translations; by all means consult other sources and alternate interpretations. But in doing so, recognize that this is not necessarily an either/or scenario, and that Plato presents these matters so skillfully and artfully that conventional meanings remain applicable.
Note:. The understanding of the Number of the Tyrant comes first; do not become overly concerned with harmony in the musical sense, at least initially; it is the third meaning which predominates here, not the second, or the first. Connect the two problems and find the second number, or better, all three. You need not explain anything else -- not the diagram, not the pempad, nor the basal four-thirds or any of the rest. But human nature being what it is, what is to stop you from trying? There is much work to be done with this massive compendium of knowledge. Moreover, moving forward a little distance in time, what was it that motivated the last of the great Platonists, Proclus [410 to 485 AD] to say:
"If I had it in my power, out of all the ancient books I would suffer to be current only the Oracles 4and the Timaeus.8 "What is so important about either one, and why are they so paired?
THE NUMBER OF THE TYRANT
THE NUMBER OF THE BRIDE
John_Harris @telus.net