The saying “Know thyself” may refer by extension to the ideal of understanding human behavior, morals, and thought, because ultimately to understand oneself is to understand other humans as well. However, the ancient Greek philosophers thought that no man can ever comprehend the human spirit and thought thoroughly, so it would have been almost inconceivable to know oneself fully. Therefore, the saying may refer to a less ambitious ideal, such as knowing one’s own habits, morals, temperament, ability to control anger, and other aspects of human behavior that we struggle with on a daily basis.
It may also have a mystical interpretation. ‘Thyself’, is not meant in reference to the egotist, but the ego within self, the I AM consciousness.
Delphi became the site of a major temple to Phoebus Apollo, as well as the Pythian Games and the famous prehistoric oracle. Even in Roman times, hundreds of votive statues remained, described by Pliny the Younger and seen by Pausanias. Supposedly carved into the temple were three phrases: γνωθι σεαυτόν (gnothi seauton = “know thyself”) and μηδέν άγαν (meden agan = “nothing in excess”), and Εγγύα πάρα δ’ατη (eggua para d’atē = “make a pledge and mischief is nigh”), as well as a large letter E. Among other things epsilon signifies the number 5. Plutarch’s essay on the meaning of the “E at Delphi” is the only literary source for the inscription. In ancient times, the origin of these phrases was attributed to one or more of the Seven Sages of Greece, though ancient as well as modern scholars have doubted the legitimacy of such ascriptions. According to one pair of scholars, “The actual authorship of the three maxims set up on the Delphian temple may be left uncertain. Most likely they were popular proverbs, which tended later to be attributed to particular sages
“Let no one destitute of geometry enter my doors.” Plato (c. 427 – 347 B.C.E.)
“[Geometry is] . . . persued for the sake of the knowledge of what eternally exists, and not of what comes for a moment into existence, and then perishes, …[it] must draw the soul towards truth and give the finishing touch to the philosophic spirit.“
Further along in the Meno occurs the celebrated case of the Geometrical Example at Meno 87, which in contrast to the previous mathematical illustration, has been twisted, tortured, and intentionally passed over for two centuries. Jebb said (loc.cit.) asven over a century ago:
The hypothesis appears to be rather trivial and to have no mathematical value. . . (which Raven echoes in 1965)
and here follow some barely intelligible geometrical details”.
Bluck however, in 1961 devotes an excursus of some sixteen pages to a complete review of views on the problem, which include an array or barely intelligible geometrical details. The passage is made more difficult of interpretation by the fact that Socrates introduces the geometrical example in a very summary manner, which some have felt was an indication or its relative unimportance.
I believe on the contrary that the almost schematic reference implies that the topic and the example were well known to the Platonic audience, and did not need explanation. Plato knows how to explain in full, and when he refrains we must understand the matter to be common knowledge. The problem as it occurs at Meno 87 a is briefly this:
We will proceed from here on like the geometer who when asked if a given triangle can be inscribed in a given circle, will say:
‘I can’t say, but let us proceed hypothetically or experimentally, draw out one leg, swing the other two and see if it falls short or exceeds the rim of the circle.’
In making this paraphrase I have added the word “experimentally” for obvious reasons, and I have taken the noun chorion correctly as area (not rectangle or a triangle, as has been said, which means nothing) in a sense very well attested. So apparently with these conditions, the words themselves are not obscure or really unintelligible, although as yet the meaning has not yet come to the surface.
You might think the loss of geometry like the loss of, say, Latin would pass virtually unnoticed. This is the thing about geometry: we no more notice it than we notice the curve of the earth. To most people, geometry is a grade school memory of fumbling with protractors and memorizing the Pythagorean theorem. Yet geometry is everywhere. Coxeter sees it in honeycombs, sunflowers, froth and sponges. It’s in the molecules of our food (the spearmint molecule is the exact geometric reaction of the caraway molecule), and in the computer-designed curves of a Mercedes-Benz. Its loss would be immeasurable, especially to the cognoscenti at the Budapest conference, who forfeit the summer sun for the somnolent glow of an overhead projector. They credit Coxeter with rescuing an art form as important as poetry or opera. Without Coxeter’s geometry as without Mozart’s symphonies or Shakespeare’s plays our culture, our understanding of the universe,would be incomplete.
See: γνώθι σεαυτόν