1)
Spirits reveal many things about numbers. One such revelation concerns the numbers 4 and 7 and their unity ’47’. It concerns this prime itself largely as the mode of revealing.

Elphuisias said this is the number through playing cards. Research bears this out to some extent though spirits always claim more for their representatives.

4 and 7 are alternating numbers. This is revealed through squaring and cross adding.

All cross operations will be indicated by the following formalism (xy)+ (where +is an example)=x+y.

Base 10 contains this repeating pattern through squaring and can be demonstrated thus:

1*1=1
2*2=4*4=(16)+=7*7=(49)+=(13)+=4 etc.
3*3=9*9=(81)+=9 etc.
4*4 see 2
5*5=(25)+=7 see 2
6*6=(36)+=9 see etc.
7*7 see 2
8*8=(64)+=(10)+=1
9*9 see 3

2)
What is the meaning of cross addition? Given that the base of the number system used is essentially arbitrary how can cross addition really ‘do’ anything? One answer to this lies in the theory of pneuminous accretions. This being that since conceptuality as a substance (pneuma) sticks together when we use an operator to collapse numbers together we are essentially just sticking concepts together e.g. (88)+=(16)+=7 says that there is a relation between 88 and 7. Furthermore there is a way in which the uniqueness of the 88=>7 relation can be registered by a certain mathematical visualization.
That is usual numerology enacts an information reduction that is non-retrievable after the operation is performed (if one lost the original number one could not derive it from the reduced number). One way to conceive of large numbers as reduced to single numbers is to conceive of them on a series of axes. Usually, at least in telluric numerology we take a larger number like 47 and reduce it to 2 (via 11), the same process happens in the others. The other associative one is also straightforward i.e. 47 becomes 28 becomes 16 becomes 6. A nagging sensation is sometimes felt in number reduction, the sensation that we wish the trace of the bigger number was still somehow present. In their brutal form, numerological reductions eradicate more complicated structures to reveal the underlying pattern, that’s what they’re supposed to do. The idea here is not a perfect solution to informational loss, it is more just a turning round of the problem that gives an intriguing sense of quasi-visualization. It does also however give some grounds for saying that under some circumstances ~(2=2) or indeed any number, including 0. The idea is that for any numerological reduction (which necessarily involves an integer greater than 9) we can represent it as a spatialized schema. The below represents the reduction of all 2 digit integers in base 10. The highlighted figure shows the exact location of 47. 47 is not just 2, it is that 2 that occupies that position. Of course any coordinate transcription is in some sense equivalent to writing 47 and hence slightly tautologous, however 47 by itself does not give the spatialized position of its reduction. Naturally increasing the number size just adds more axes leading us into higher and higher dimensional coordinate systems to demonstrate the location of the single digit e.g. 231147 uses 6 dimensions to point to the 9 that it becomes. This can be done with the other elemental numerologies too (though aetheric / is still being processed). The below is the 2 dimensional table for mercurial operations ()
Again the 10s are on the y axis and the 1s on the x, 100s would be on z and so on. This only invites ways of thinking upon the matter. The key one being the non-identity of identical numbers which seems to have some allure that may be worth dwelling on further. The other thing that strikes me is the status of the numbers in the grid. They are not really 1s as one might assume for they only exist by virtue of the axes that identify them. They are necessarily numbers but of no definite kind. The real 1s are an axis that identifies the number in the grid by virtue of the elemental operator. There are 1s that are identical but single digit numbers derived from larger strings in numerological reductions are not strictly single integers.

The nagging question of the meaning of cross addition has an additional piece of research to it. Cross addition ((123)+=6) suggests the possibility of a relation, indeed says that under certain condition (a particular base) there is a relation between a number higher than the highest single integer and one of the single integers. As established, without accretive theory the general impression would be that this is in a sense arbitrary or at least meaningless. What has 53 e.g. got to do with 8? Very little other than the cross addition relationship.

What is quite interesting is the that the squares of 4 and 7 give numbers whose cross addition then has a demonstrable reality in a triangle comprised of units 1 at the top 3 on the next line down, then 5, 7 and so on.

Triangles of this kind of unit construction are remarkable as they also provide squares. The number that will be squared is the height of the triangle. So if I have a triangle of 2 height, the total number of units in the triangle will be 4, if 3 it will be nine and so on.

The relation to the issue of cross addition is as follows. If I have a triangle of a height of 4, necessarily it will be comprised of 16 units. The base however will be 7 units(1+6). There is one relation uncovered here for the base will always have the relation to the height 2n-1. If the height is 12 the base is 23 and so on.

The second relation that is more interesting to us here is the one concerning squares. Squares of 4s and 7s even of cross addition ones will always reduce to 7s or 4s respectively but the base seems to often (though not always) reveal a relation between the number itself, the square and the cross addition of the square.

These are the most concrete examples:

4 becomes 16 becomes 7 (the base units of 4)

7 becomes 49 becomes 13 (the base units of the 7 triangle) becomes 4

With small adjustments, these can also function.

13 becomes 169 becomes (curiously by preserving the first two digits as a whole number) 16+9=25 is the base number.

16 becomes 256 becomes 31 (by the same logic above) which is the base number and also reduces to 4.

22 becomes 484 and a similar logic derives the base. This time we extract 40 and add 8+4=12=3, re-add them and we have 43, the base number.

31 gives us 961, if we cross out the 9 for 9=0 in base 10 cross addition we immediately have the base number again.

Some have no apparent link.

25*25=625=13=4, or course the 7/4 transformation is preserved but the base relation is not. The base would be 49 and 625 does not have a relation to it. And no doubt there are others.

Deriving the Circuit.

In the course of working out the above it was observed that a circuit of numbers could be derived by taking the row of the triangle and placing it next to the corresponding base. The formula for row to base is 2n-1. Hence for a triangle 2 down the base is 3. Thus the circuit begins 2-3. Next we convert the 3 into a row and note that a triangle with 3 rows has a base of 5. Now we have 2-3-5. Proceeding in this way we get 2-3-5-9-8-6-2.

Reaccreting the Qabalah

From the circuit 2-3-5-9-8-6-2 laid out in the above way it was suggested that the remaining 1 4 7 might form a central column -with 10 at the bottom. Doing this creates a Gra tree qabalah structure (see below).

The system was felt to need a reinvigoration from its hoary Hebrew letter accretions to make the numbers and letters more cogent. To this end an abbreviated alphabet capable of dealing with all English phonetics was spread throughout the paths. Each path was resigilised and named. These names plug into tarotic precursor accretions to a greater or lesser extent. See also below.

The Great Paths

It is of note that the 2-3-5-9-8-6-2 circuit generated the two focal points upon which the 4 and 7 are generated (or is generated by the 4 and the 7). Though in terms of paths the gaps between 2-6, 6-8, 9-5 and 5-3 are each bifurcated by 4 or 7 at a deeper level each path is considered a whole. As such they are known as great paths and their unity is reflected in the complementary pairing of attributions. The circuit of the paths begins with the single path of Eris (2-3). The descending great path from 3-5 is comprised of Incest and Passion. The next descending great path is 5-9 and it is formed of Foetus and Superman/Boudica. This is the child of the previous paths union which grows to be great and powerful. The small connecting subsequent path is that of the Sun (9-8), the apex moment of this Heroes journey. The ascending great path from 8-6 is Twilight to Pneumatology. Physical power has faded and the power of spirit is laid bare. This ascends again in the next great path 6-2 which is formed of Philosopher-Url-king. Spirit has become analysis and the attempt to hold onto power by force -rigour. This untenable system is rendered apart by Eris and it all begins again.

The New Gra-Tree Qabalah

This tree then, whilst ostensibly the same as an old Gra-tree is different in its underpinning. The structure is derived from the circuit. 4 and 7 as alternating number occupy the central column as the logical place to put them. As stated above there is a sense that the motion of the circuit possible generates the 4 and the 7 though what this means of course cannot be said.

This system is perfectly functional and has been extended to a complete calendar to enable accretive connections to conceptual paths on a temporal axis. This is all accretion means -sticking pneuma (concepts) together.

On the Formation of a Hyperqabalah

What was observed however was a kind of oversight in the system. Part of the point of it was to accrete the modern alphabet to the paths with clear numerological attributions. This work was supposed to have been done by the new sigils. Each sigil itself was in turn supposed to have a number accreted to it. This of course does work, however because the sigils are single discrete symbols it means that a single symbol represents a composite in base 10. This means that the sigils themselves cannot be numerologically utilised like the base 10 numbers because they no longer are base 10 numbers. What has accidentally been formed by single sigilising the numbers is…

base 23

The realisation that base 23 had been formed prompted the following possibility:

What if the 22 sigils of the positive integers paths were translated into nodes, or sephiroth and what kind of internal circuit would such a (hyper)qabalah have?