Principles of Labyrinth Design (Part 1 - Elements)

 There are as many kinds of labyrinth as there are dimensions in which to design them (excepting the first dimension alone, which permits only a binary and trivial variation). The 2-dimensional labyrinth is, of course, the simplest non-trivial variety. Of the 2-dimensional labyrinths, there are two kinds; linear and non-linear. 2-dimensional, linear labyrinths include only four directions; south, east, north, and west. Non-linear labyrinths are omni-directional (throughout 360 degrees). 

A 'simple labyrinth' is any 2-dimensional linear labyrinth.

A 'true labyrinth' has only one exit, and therefore one non-trivial solution.

A labyrinth's 'direction-value' (DV) is the number which denotes the total orientation of its solution. A right turn equals +1 to the DV. A left turn equals -1 to the DV. Hence, if a labyrinth's solution necessitates 5 right-turns and 3 left-turns, its DV equals 2.

An 'open labyrinth' has its exit on the periphery of the labyrinth. This kind of labyrinth always has a DV of -1, 0, or 1.

A 'closed labyrinth' has an end-point that is enclosed within the perimeter of the labyrinth. A closed labyrinth is not necessarily direction-neutral.

The fundamental, or "1st order", elements of simple labyrinths can be laid out and enumerated such that each element corresponds to a number of the hexadecimal system (fig. 1):

With this system of labeling, any simple labyrinth can be described numerically with a matrix. For example, the following simple labyrinth (fig. 2) can be described with the corresponding matrix (fig. 3). This matrix can be written as follows: 326/451/035.

Simple labyrinths are modular; that is, larger matrices can be reduced to smaller matrices, or even single numbers. For example, fig. 3 can be reduced to 'c' because fig. 2 is reducible to a north-facing dead-end. However, the DV of a given labyrinth is not affected by modular reduction: Every fundamental dead-end has a DV of zero, whereas fig. 2 has a DV of -4.

Reörienting every labyrinth so that the initial orientation is north (i.e. the entrance always faces south), and fully modulating it to its most fundamental solution, we can see that every simple open true labyrinth can be reduced to 1, 3, or 6. Every simple closed true labyrinth can be reduced to 'c'.

There are elements composed of 1st order elements, called "2nd order" elements. The 2nd order elements are 'loops' and 'trees'. Both loops and trees can be open or closed.

A loop is any pattern which leads back to its initial point. Examples are 36/75 for a closed loop and 36/b5 for a closed loop.

A tree is any pattern which diverts to multiple paths (i.e. branches) from one path. E.g. a/b.

3rd order elements are composed of 2nd order elements. The 3rd order elements are 'wheels' and 'double loops'.

A wheel is a conjunction of trees, such that there are multiple branches in all four directions from a single point. E.g. bb/bb.

A double loop is a loop circumscribed by a loop.

Commentary on Jean Daneliou's "Prayer as a Political Problem" (Part 1)

The Church of the Poor

The argument in this chapter is that Christianity is universal; its message and promise is destined to all people. The ‘poor’ does not mean simply those of meager economic power, but those of meager power in any regard. The poor lack intellectual and even spiritual means as well. If the Church is the “church of the poor” because it is universal, it cannot be an elite society. 

With this truth in mind, Danielou identifies an urgent problem: The world is inhospitable to the Faith. This is not a new revelation by any means. “The flesh lusteth against the spirit, and the spirit against the flesh” (Gal 5:17). “The lust of the flesh is of the world” and “we received not the spirit of the world” for “the world knew Him not.” We are called therefore to be “in the world but not of it.” That the Faith is not of the world, however, is a fact of its divine origin. Our mission is to be the light of the world, to spread the Gospel, and to baptize all nations, for the world belongs to Christ.

Danielou is addressing a deeper, more troubling fact about the world that is particular to modernity: “A world has come into being in which everything serves to turn men away from their spiritual calling.” The world is infested with temptations to every kind of vice, temptations that are carefully crafted for maximum effect to yield maximum profit. Not only is the man of Faith a stranger in this world, but any kind of religious activity whatsoever is alien. Christianity is a supernatural revelation and therefore will never be quite at home in the world, but religion is perfectly natural. Man is born with an impulse to revere the divine and the sacred; to conduct himself with respect to what is mightier, nobler, and more sublime than himself. Yet modern society is hostile to religion of any kind. One who seeks to sanctify the mundane with daily practices of devotion will constantly struggle against conflicting duties, social expectations, and the more pressing human needs which arise as their result. Even civic holidays and the vestigial pastiches of religious festivals like Christmas, Easter, and Halloween have been reduced to motions of mere economic expedience. For the Christian, to consider only one example, Holy Days of Obligation are observed only under tension with one’s obligations to his employer or to his family (by either “taking the day off” to hear morning mass or forfeiting his evening to hear evening mass–in either case there is no impression of a sacred festival). The seasonal patience of thaw, harvest, and solstice; the cyclical tempo of light and dark, expectation and remembrance, abundance and want, is lost. Even the pagan spirit of bacchanalia, which seems to persist in some recognizable forms, is neither ritualized nor dedicated to any god, but is rather tolerated as a useful stimulus to the most banal functions of modern life.

Such is our problem. Hence, Danielou says, “it is sufficiently clear that Christians ought to be trying to change the shape and pattern of society so as to make possible a Christian life for the whole of mankind.”