See also Derrida + Serpent in this journal.
* See Stoicheia (Elements) in this journal.
Tuesday, December 23, 2014
Stoicheia*
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Tuesday, October 18, 2022
Square Ice
See as well remarks here from 23 Dec. 2014
on the Greek word "stoicheia."
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Wednesday, February 28, 2007
Wednesday February 28, 2007
Elements
of Geometry
The title of Euclid’s Elements is, in Greek, Stoicheia.
From Lectures on the Science of Language,
by Max Muller, fellow of All Souls College, Oxford.
New York: Charles Scribner’s Sons, 1890, pp. 88-90 –
Stoicheia
“The question is, why were the elements, or the component primary parts of things, called stoicheia by the Greeks? It is a word which has had a long history, and has passed from Greece to almost every part of the civilized world, and deserves, therefore, some attention at the hand of the etymological genealogist.
Stoichos, from which stoicheion, means a row or file, like stix and stiches in Homer. The suffix eios is the same as the Latin eius, and expresses what belongs to or has the quality of something. Therefore, as stoichos means a row, stoicheion would be what belongs to or constitutes a row….
Hence stoichos presupposes a root stich, and this root would account in Greek for the following derivations:–
- stix, gen. stichos, a row, a line of soldiers
- stichos, a row, a line; distich, a couplet
- steicho, estichon, to march in order, step by step; to mount
- stoichos, a row, a file; stoichein, to march in a line
In German, the same root yields steigen, to step, to mount, and in Sanskrit we find stigh, to mount….
Stoicheia are the degrees or steps from one end to the other, the constituent parts of a whole, forming a complete series, whether as hours, or letters, or numbers, or parts of speech, or physical elements, provided always that such elements are held together by a systematic order.”
Example:
The Miracle Octad Generator of R. T. Curtis
For the geometry of these stoicheia, see
The Smallest Perfect Universe and
Finite Geometry of the Square and Cube.
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Saturday, July 5, 2003
Saturday July 5, 2003
Elementary,
My Dear Gropius
“What is space, how can it be understood and given a form?”
— Walter Gropius
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Stoicheia,” Elements, is the title of
Euclid’s treatise on geometry.
Stoicheia is apparently also related to a Greek verb meaning “march” or “walk.”
According to a website on St. Paul’s phrase “ta stoicheia tou kosmou,” which might be translated
“… the verbal form of the root stoicheo was used to mean, ‘to be in a line,’ ‘to march in rank and file.’ … The general meaning of the noun form (stoicheion) was ‘what belongs to a series.’ “
As noted in my previous entry, St. Paul used a form of stoicheo to say “let us also walk (stoichomen) by the Spirit.” (Galatians 5:25) The lunatic ravings* of Saul of Tarsus aside, the concepts of walking, of a spirit, and of elements may be combined if we imagine the ghost of Gropius strolling with the ghosts of Plato, Aristotle, and Euclid, and posing his question about space. Their reply might be along the following lines:
Combining stoicheia with a peripatetic peripateia (i.e., Aristotelian plot twist), we have the following diagram of Aristotle’s four stoicheia (elements),
which in turn is related, by the “Plato’s diamond” figure in the monograph Diamond Theory, to the Stoicheia, or Elements, of Euclid.
Quod erat demonstrandum.
* A phrase in memory of the Paulist Norman J. O’Connor, the “jazz priest” who died on St. Peter’s day, Sunday, June 29, 2003. Paulists are not, of course, entirely mad; the classic The Other Side of Silence: A Guide to Christian Meditation, by the Episcopal priest Morton Kelsey, was published by the Paulist Press.
Its cover (above), a different version of the four-elements theme, emphasizes the important Jungian concept of quaternity. Jung is perhaps the best guide to the bizarre world of Christian symbolism. It is perhaps ironic, although just, that the Paulist Fathers should distribute a picture of “ta stoicheia tou kosmou,” the concept that St. Paul himself railed against.
The above book by Kelsey should not be confused with another The Other Side of Silence, a work on gay history, although confusion would be understandable in light of recent ecclesiastical revelations.
Let us pray that if there is a heaven, Father O’Connor encounters there his fellow music enthusiast Cole Porter rather than the obnoxious Saul of Tarsus.
Saturday July 5, 2003
Elements
In memory of Walter Gropius, founder of the Bauhaus and head of the Harvard Graduate School of Design. Gropius died on this date in 1969. He said that
"The objective of all creative effort in the visual arts is to give form to space. … But what is space, how can it be understood and given a form?"
"Alle bildnerische Arbeit will Raum gestalten. … Was ist Raum, wie können wir ihn erfassen und gestalten?"
Gropius
— "The Theory and Organization
of the Bauhaus" (1923)
I designed the following logo for my Diamond Theory site early this morning before reading in a calendar that today is the date of Gropius's death. Hence the above quote.
"And still those voices are calling
from far away…"
from far away…"
— The Eagles
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("Stoicheia," Elements, is the title of
Euclid's treatise on geometry.)
Euclid's treatise on geometry.)