I am back from 'the flat of no internet', where the heat has been drying the paint before I had time to spread it evenly on the wall. And happily
@Moliere has done all the hard work for me, so I can waffle a bit on interpretations and applications. But first ...
The bits on time: we get the conclusion I was thinking of, which is interesting to me!, that there are undecidable expressions (now that we have functions that go to infinity).
One thing I'm thinking is you could just posit another space-dimension to accommodate GSB's "cross in a plane", but I'm ok with saying this is space-time instead. — Moliere
GSB tries the extra space dimension himself, with the idea of a tunnel, but it doesn't quite work, because as soon as the boundary is undermined, it becomes 'incontinent'. he still needs time to keep the distinction clear. But if we go back to switches and circuits, everything is understandable.
There is a very simple circuit that works as a buzzer or operates an electric bell, and at the heart of it is a switch that operates itself.
This is not the switch one operates to make the buzzer buzz, or the fire alarm ring, but an internal switch, that, as it operates the hammer on the bell, also switches itself off so that the hammer immediately falls back, and switches the circuit on again. The circuit cycles on and off indefinitely. We have electro-mechanical feedback; we have time, because any number of spacial dimensions cannot do the job of the same circuit being on and off - only
time as change resolves the contradiction and maintains the continence of the distinction.
But I'll go back a bit, not to all those theorems , that are just extensions of what we already have, but to this:
Indicative space
If So is the pervasive space of e, the value of e is its value to So. If e is the whole expression in So, So takes the value of e and
we can call So the indicative space of e.
In evaluating e we imagine ourselves in So with e and thus surrounded by the unwritten cross which is the boundary to S-1. — P.42
A formal system is always imaginary, but normally, one imagines oneself outside the system commanding, evaluating, operating the system from outside, that is from "
S-1". But here, that is ruled out, because outside and inside are the form of the first distinction. 'Value' is always relational, and always 'a difference that makes a difference'. To put it another way, there is no absolute value and no absolute outside, one is always
in one's world, that one creates in distinguishing.