The introduction concerned an analogy in the field of infinite mathematics. The concept of set was discussed being a simple collection of objects. A distinction was drawn between the notion of finite sets and infinite sets. Finite Sets are simply sets which are not infinite. Whereas infinite sets, "go on forever". Please note that any form of definition of the infinite is pointless (ha!) but we shall rely on an intuitive notion of understanding. An additional distinction was drawn between notions of countable (able to be counted) and un-countable (not able to be counted).
The relations of numbers systems to be related to any paradigm of thought. Now there is a method for showing that two sets have the same number of elements, that is, they have the same cardinality. Two sets are said to have the same cardinality if we can match up every element of some set A with a natural number, that is, if we can establish a one-to-one relation with every element in set A with a proper or improper subset of the natural numbers then set A will be of the given cardinality. The natural numbers are the numbers starting at 1 then 2, 3, 4 etc. The natural numbers themselves being an infinite set, and by definition it is countable.
Now various number systems (paradigms) can be placed into 1-1 correspondence with the natural numbers (the functional relations themselves of 1-1 establish analogical gateways making it, "all the same shit"). The integers, the even and odd integers, even the rational numbers. When approaching the cardinality of infinite sets in order for us to get a grasp on infinity we deem the cardinality of the natural numbers to be 0, (note this audacious notion to begin with falls in the realm of magic). Omitting the proofs themselves (which were shown at the seminar), which are really quite trivial once, we have a well ordering principal (that is a way to logically convey data). We now approach the concept of an uncountable infinite set, namely there exists paradigms which are not equivalent to those discussed before. When dealing with the real number system we find that the real numbers cannot. This proof was illustrated for the unit interval [0, 1] (See Cantors Diagonal proof not supplied here). Note while purveying the proof that we need only consider the unit interval for establishing the paradox necessary to create the needed contradiction. So what is the cardinality of the Real Line
Now introducing the notion of power set denoting the number of possible combinations to take a set A. If a has n elements then the power set of A is 2^n. We can easily see this relating logical truth tables. We have 2 statements p and q with possible on/ off values. So p(A) = 2^2 with the specific elements being(TT, TF, FT, FF) with FF being analogous to the null set. There was now presented the Continuum Hypothesis namely that:
What does this mean? Namely that once we leave the notions of paradigms which can be put into 1-1 correspondence with one another there exists an infinite jump which must be made. We can successively take power sets of power sets to arrive at different continuums of infinity. It was at this point that I realized that most of the math itself was not going over too well so I branched to a Cabbalistic analogy, although the main premise of the discussion was related in the above statements.
The parable of Lamion is about the surpassment of the tree of life by the process of quenching the ineffable breath. While the star struggles to realize its nature across the tree there comes a point, which it comes into contact with a more elaborate form being the HGA. Guided by voice the point of the abyss is reached and the annihilation of the Angel with Choronzon dissolves the Horizon of the Magicians Universe to a point of view, the first approach of the Crown. Now the essence of life is first distilled from the waters of creation being born into life with flesh. Throughout the beings existence, personality constructs in the form of Shells coalesce about the waters forming the very nature of what we are. Knowledge and Conversation of the HGA relate the shells attempts (as well as the angels to reach outward towards one another ~ the Sistine chapel).
Acquiring the nature of the supernals is the first infinite jump. The crown itself is the point (of breathless depth) which itself is a mathematically non-existent object as such the Ippissimus does not exist, but the tree itself is distilled from the void and there are regions beyond that require further jumps. As the star acquires the crown various possibilities occur which were not visible before. With the required momentum the nature of the tree inverts. Filtering through the inverse spaces the descending star achieves a grand momentum grounding all of what is becomes requisite. With enough velocity the daughter ascends to the throne of Malkuth and crashes through the pit of qlipphoth (consciousness) from which the entire tree is constructed.
This represents the ascent to the consciousness of Lamion. The word is the particular refraction of light through the individual water droplet. Much of what was to be discussed in the seminar was not gone over, such as the Scarlet Brotherhood/ The Scarlet Gash. The Aeon of Ir as well as sorcerous applications of this paradigm. I touched on at the end of a particular class of servitor created and placed into tunnel Azapheme for the purpose of inverting magickal currents. This tunnel itself which is an aspect of the word of HORIZON as well as all of the particulars of everything mentioned here as well as Goetia/ Tunnels pictures shall be gone over in my next work which should be completed by 2007. The title of this text is the LAMION GOETICON ~ The Howling Ecstasy; also called "Scribbles".