User:Jon Awbrey/SCRATCHPAD

Greek

  ἐν ἀρχῇ

  Ἐν ἀρχῇ ἦν ὁ λόγος  

Πάτερ ἡμῶν ὁ ἐν τοῖς οὐρανοῖς· ἁγιασθήτω τὸ ὄνομά σου·

ἐλθέτω ἡ βασιλεία σου·

LOGOS

Epigraph Formats

	Out of the dimness opposite equals advance . . . .      Always substance and increase, Always a knit of identity . . . . always distinction . . . .      always a breed of life.
	— Walt Whitman, Leaves of Grass, [Whi, 28]

On either side the river lie
Long fields of barley and of rye,
That clothe the wold and meet the sky;
And thro' the field the road runs by
	To many-tower'd Camelot;
And up and down the people go,
Gazing where the lilies blow
Round an island there below,
	The island of Shalott.
		— Tennyson, The Lady of Shalott, [Ten, 17]

The most valuable insights are arrived at last; but the most valuable insights are methods.

— Nietzsche, The Will to Power, [Nie, S469, 261]

The power of form, the will to give form to oneself. "Happiness" admitted as a goal. Much strength and energy behind the emphasis on forms. The delight in looking at a life that seems so easy. — To the French, the Greeks looked like children.

— Nietzsche, The Will to Power, [Nie, S94, 58]

In every sort of project there are two things to consider: first, the absolute goodness of the project; in the second place, the facility of execution.           In the first respect it suffices that the project be acceptable and practicable in itself, that what is good in it be in the nature of the thing; here, for example, that the proposed education be suitable for man and well adapted to the human heart.           The second consideration depends on relations given in certain situations — relations accidental to the thing, which consequently are not necessary and admit of infinite variety.

— Rousseau, Emile, or On Education, [Rou-1, 34–35]

Blockquote Formats

Now, I ask, how is it that anything can be done with a symbol, without reflecting upon the conception, much less imagining the object that belongs to it? It is simply because the symbol has acquired a nature, which may be described thus, that when it is brought before the mind certain principles of its use — whether reflected on or not — by association immediately regulate the action of the mind; and these may be regarded as laws of the symbol itself which it cannot as a symbol transgress. (Peirce, CE 1, 173).

The information of a term is the measure of its superfluous comprehension. That is to say that the proper office of the comprehension is to determine the extension of the term. …           Every addition to the comprehension of a term, lessens its extension up to a certain point, after that further additions increase the information instead. …           And therefore as every term must have information, every term has superfluous comprehension. And, hence, whenever we make a symbol to express any thing or any attribute we cannot make it so empty that it shall have no superfluous comprehension.           I am going, next, to show that inference is symbolization and that the puzzle of the validity of scientific inference lies merely in this superfluous comprehension and is therefore entirely removed by a consideration of the laws of information.

(Peirce, CE 1, 467).

Outline Form

1. Item 1
1. Item a
1. Item i
2. Item ii
3. Item iii
2. Item b
3. Item c
2. Item 2
3. Item 3

Mathematical Symbols

\(\lessdot\)	\lessdot
\(\gtrdot\)	\gtrdot
\(:\!\lessdot\)	:\!\lessdot
\(:\!\gtrdot\)	:\!\gtrdot
\(\colon\!\lessdot\)	\colon\!\lessdot
\(\colon\!\gtrdot\)	\colon\!\gtrdot

Cactus TeX

\[X = \{\ (\!|u|\!)(\!|v|\!),\ (\!|u|\!) v,\ u (\!|v|\!),\ u v\ \} \cong \mathbb{B}^2.\]

\[X = \{\ \underline{(u)(v)},\ \underline{(u)~v},\ \underline{u~(v)},\ \underline{u~v}\ \} \cong \mathbb{B}^2.\]

\[X = \{\!\] (u)(v)\(,\) (u)v\(,\) u(v)\(,\) uv \(\} \cong \mathbb{B}^2.\)

\[X = \{\!\] (u)(v) \(,\) (u)v \(,\) u(v) \(,\) uv \(\} \cong \mathbb{B}^2.\)

\(X = \{\!\) (u)(v) \(,\) (u)v \(,\) u(v) \(,\) uv \(\} \cong \mathbb{B}^2.\)

\(X = \{\!\) (u)(v) , (u)v ,  u(v) , uv \(\} \cong \mathbb{B}^2.\)