The Second Trumpet

The opening up of these different octals in all these new groups or triples poses a great problem. How can we combine all of these different octals into a single system in seven symbols? (We shall again call the possible set of 30 octals the "sea") This idea that there is a method to calculate groups of octal groups and their corresponding seven cycles will be called the "great mountain, burning with fire".

We can then hazard a guess at what will happen. If we correspond "fire" subgroups in the left-hand to the intersections between different groups (i.e. like [0,c,e,g]=a) then we might be able to find a unique association. That is, we might be able to find a product based on this intersection (as blood) so that the third part of the sea became "blood". Then we might find that we have inconsistencies, that we have no direct product within an equivalent of "grass" to the sea, (i.e., a missing product on the elements) and the equivalent of trees in the sea (ships) (one missing product of subgroups also).

It turns out that if we pick any three seven cycles arbitrarily, whilst using the same identity element (a is used here) then we may make a unique correspondence for octals that differ only in hail and fire, not in the original octal used.

as before...

a = [0,b,d,f] = [0,c,e,g]*
b = [0,c,d,g] = [0,a,e,f]
d = [0,c,e,f] = [0,a,b,g]
c = [0,a,f,g] = [0,b,d,e]
f = [0,b,e,g] = [0,a,c,d]
g = [0,a,d,e] = [0,b,c,f]
e = [0,a,b,c] = [0,d,f,g]£

a = [0,b,d,f] = [0,c,e,g]*
b = [0,c,e,f] = [0,a,d,g]
f = [0,c,d,g] = [0,a,b,e]
c = [0,a,d,e] = [0,b,f,g]
d = [0,b,e,g] = [0,a,c,f]$
e = [0,a,f,g] = [0,b,c,d]
g = [0,a,b,c] = [0,d,e,f]

It turns out that for any three chosen "fire" octals (the next I used was generated by (a,c,d,b,g,f,e)) Each octal shares one element of any of the other two. (marked here by the symbols *, $ and £. For an association the right hand elements and the fire element must be the same.

a = [0,c,d,g] = [0,b,e,f]
c = [0,b,d,f] = [0,a,e,g]
d = [0,b,e,g] = [0,a,c,f]$
b = [0,a,f,g] = [0,c,d,e]
g = [0,c,e,f] = [0,a,b,d]
f = [0,a,d,e] = [0,b,c,g]
e = [0,a,b,c] = [0,d,f,g]£

It then turns out as expected that each seven cycle has only two of three elements of each subgroup - the third is missing. So, as we can make eight sets of these associations, The third in a product becomes an intersection (as blood) based on a product made from association upon "fire" (This method "burns on "fire") the third part of the right hand elements (living creatures in the sea) - they don't show an (third part) element, and the third part (product) of the subgroups of the left hand (middle column) are not present in each of the three related octals.

Thus this "method" or mountain, if it can be called thus relates the wider set of octals (the sea) by intersection (blood) so that a third part of operations on singleton elements (creatures in the sea) and ships (subgroups) are "destroyed." I take the meaning of "destroyed" as in "never present", as the actual product of these elements is in each individual group to start with: seeking a product elsewhere based on intersections has no intuitive result or calculation behind it. In reference to the original sun octal with "life" the product is now in stark contrast to that. It shows an ability to "slip out" of one octal group into another. (yet whilst preserving a K4 subgroup in a different octal.)

Continue To Next Page

Return To Section Start

Return To Previous Page