An Esoteric Guide to Spencer Brown’s Laws of Form #4
Moving on, GSB indicates that:
LoF p. 53
- The initials of the primary algebra are in dependent.
Remember the initials are the two equations we discussed above. The point is that these are not derivable from each other (or they would reduce to a single equation and thus not be “initial”). This means that all possible logics require a distinction of distinctions. This is to say that the form of any logic (its second order nature, N+1) requires its first act to be the realization of this form, which is its content (its first order nature N).
In other words, the foundation and generation of all logics is recursive, taking the form in which the second and first orders are mutually generative (i.e. the distinction of distinction). You may think that somehow this obviates the very principle of independence, because they are mutually generative. Not so, and this is the heart of the matter. It is precisely this type of recursion, between N and N+1, that maintains the distinction. They are mutually generative, not simply generative; this means that they require each other distinctly, in order for their own separation. They cannot be reduced to each other, and both are required. We have a complex unity, not a simple one.
Now, GSB gets into some fascinating territory with respect to “re-entry into the form”. He describes re-entry in this way:
LoF p. 56
- The key is to see that the crossed part of the expression at every even depth is identical with the whole expression, which can thus be regarded as re-entering its own inner space at any even depth.
We can see that he has just described the taijitu. What is important about GSB’s work is that it provides a way to stop the recursion at any given point, and to then look around to see what’s going on. This is to say, it can be used to calculate, to situate with directness towards one state (knowing that the states are infinitely transformable).
Most importantly, the necessity of re-entry (recursion), which we have seen lies even at the root of the root of GSB’s work (even though he didn’t point this out himself), leads him directly to something that was implicit in the form but which can be itself brought out in a calculable way. I am referring here to the generation of the imaginary realm (the home of imaginary numbers, which are found as necessary roots to the regular algebraic equation x^2 = -1).
What is important, esoterically, has to do with what GSB points out as the key feature of the imaginary numbers: they are oscillatory. Let me explain… next time.