A Point Is That Which Has No Part

Etymology of the Greek word semeioun
the Greek word semeioun
derived from the Greek word semeion, σημεῖον (an indication, especially ceremonially or supernaturally)
derived from the Greek word sema, σῆμα

Etymology of the Greek word semeiotikos (σημειωτικός)
the Greek word semeiotikos, σημειωτικός
derived from the Greek word semeiosis, σημείωσις
derived from the Greek word semeioun
derived from the Greek word semeion, σημεῖον (an indication, especially ceremonially or supernaturally)
derived from the Greek word sema, σῆμα
derived from the Greek word semeioo, σημειόω (to distinguish; mark (for avoidance))

A point is that which has no part.

What is "that which has noo part"?

Etymology of the Greek word meros (μέρος)
the Greek word meros, μέρος (portion; thigh; a thigh; a division or share (literally or figuratively, in a wide application))

That is clearly a demonstrative, a representation of pointing at , or picking out by inclining towards a "thing" or an activity. A thing and or an activity are clearly perceivable, even if not initially perceived by the recipient of the communication.

The predicate must provide further information or description "which" is a relative, and it is the relative of choice. thus the reader has a choice from all perceivable forms or activities.

"Has" is a active verb of possession of constitution and the communicator is therefore emphasising a dynamic activity rather than a state of affairs

What then is a "part"?

A part is a resultant of any physical or perceptual activity of dividing off, splitting, segmenting, cutting into pieces, shattering into smaller forms etc etc

Thus to negate the activity at once requires a form or activity to be whole , to produce no resultant part, to be integral, or to be nothing, to be not a thing.

Whoever wrote this definition had thought about a lot of things before it was written.It clearly allows for individual interpretation, but sits right on the border of subjective and objective constructions of the experiential continuum. It is in every way equivalent to the notion of Shunya. As such the geometry of the Greeks and the Indians are collapsed into each other like the aspects of a reality that is derivable from a pregnant void, an infinite possibility space.

The Monad of All Things. The atom or atem. This is the spiritual significance of the point. It is a contact between the natural and supernatural worlds , the entrance into an infinite possibility, the exit into out natural cosmos from the gods, the point that our souls attach to which connects it to the divine. It is the source of the divine spark, It is Shunya,the creator and the destroyer of all things. It has no part in this world, and our world has no part in the divine world to which it is linked through a point.

Etymology of the Greek word gramma (γράμμα)
the Greek word gramma, γράμμα (mark; a writing; a letter, note, epistle, book, etc.; plural learning)
derived from the Proto-Indo-European root *gerbh-

A line however, has a part or rather is a part. It is a part of a form. It is that part of a form that excludes it breadth. Therefore the communicator makes reference to an already existing theory or description of form which includes breadth. It is the theory of topos. The particular form he applies it to is a drawn form, a representation of a substantial form. In applying it he inherently implies a limiting process for topos. The limit is a line. He does not imply a straight line, thus any shaped topos has a line as its limit or outer edge. This is its perimeter, boundary or edge. He defines these later. in relation to surface form, representation of substantial surface form..

http://farside.ph.utexas.edu/euclid.html

1. A point is that of which there is no part.
2. And a line is a length without breadth.
3. And the extremities of a line are points.
4. A straight-line is (any) one which lies evenly with
points on itself.
5. And a surface is that which has length and breadth
only.
6. And the extremities of a surface are lines.

As subtle as it is Euclid implies blueptints, plans, drawings, sketches, graphic representations of substantial forms, of spaciometric forms. The theory of topos deduces a congruency between the substantive form and the graphical image, between the form in space and the surface oriented in space. The graphic is a representation of a space, a place in space. A place is more specific in informational content and processing requirements than space. It has a greater gravitas that distinguishes it as real, and makes it the referent while space is the conceptual representation of place, moe fluid and flexible and portable. Space , as a representation of place is drawable, perceivable, but its meaning is bound to place, and has no import unless it is referential to place and realiseable in a place, Thus semantically the notions of geometry, being abstracted from place have no value if they do not result in modifications to place, they have no beauty if they have no form in place.

However, it was possible to imagine an ideal place where all these representations have a perfect form, and such a place is inhabited by the gods.

Many mystical and religious sentiments surround these drawn forms. Their graphic quality is symbolic , a kind of window into a perfect ideal place. Certain constraints on pragmatic action therefore arise. The more pragmatic the less ideal. Yet between the 2 worlds the drawn image, the artisan's sketch the artists representation holds a special and pivotal place.

The poetry of the opening stanzas of Euclid's elements are only apparent in the Greek text. It is lost in thedissection of it in translation.

The Stoics were a movement of Greeks who did not shy away from the empirical experiences of life. The fundamentals of existence and consciousness. Euclid's stoiceioon are the fundamental empirical experiences of consciousness, artisans experiences, that present themselves to the pragmatic individual who acts on the objective world subjectively.

It is this subjective objective dualism which is mediated by the drawn image on a surface. The impress of reality on the subjective inner world leaves a drawn imprint, and he subjective study of these elemental imprints effects changes in the objective reality.

The theory of Topos is a theory of surfaces. The surfaces may be drawn in space, on a sheet of paper, or on another surface, but the drawings inform the subjective processing of the individual.The individual distinguishes 2 cuts of space" length and breadth. The effect of that processing is an action on a place reflecting that insight.

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