Some more on chapter 2 --
For 2 I think we could use brackets, thus:
[ ], [[ ]], [[ ] [ ]], [a], [[[a] [[b] [c]] [ ]] Not very clear, and it might be better to alternate square and curly by depth, thus:
[{ } { }], [{[a] [{b} {c}] { }] — unenlightened
So, following along with the axioms in chapter 2...
[][] = []
and axiom 2
[{}] = .
?
I tried messing with
's bit of code and looking for tutorials but got lost in the information web. If there's a easy link to figuring out how to embed multiple crosses,
@jgill, I'd be happy if you could pass it along because it
does look prettier, and if I can figure out the syntax it's probably not that hard to embed multiple crosses.
Part of me is wondering if we can read Axiom 1 as the line above, and axiom 2 as the crossing of the line above. So when we, while using the form of the meta-language to parse order, draw a segment from left to right that is the law of calling. And when we draw a segment perpendicular to the calling that is a crossing. So if we cross again we negate, but it's easier to see that when we embed the original cross within a series of crosses rather than a series of lines coming off of the original calling.
This makes sense at a purely formal level because they complement one another -- the calling and the crossing are perpendicular but simultaneously need one another in order to be a calling or a crossing. In a sense the perpendicularity of the crossing removes some of the form of space of the meta-language, but not quite because the space of this formal system is defined by the cross rather than by a set of axioms describing space. Perpendicularity can be defined by reference to the cross, rather than the other way about, and from that we can name the space "Cartesian" if we take space to have an infinite series of crosses. (not Euclidean, that would be harder, or at least different, I think) (a bit speculative here.... just trying to think through the ideas towards something familiar) ((Also -- it'd probably have to be two orthogonal and infinite cross-spaces to define the Cartesian plane))
Then Chapter 2 is the use of the axioms to draw a distinction -- a form taken out of the original form of calling-crossing. Which, from chapter 1, is perfect continence.
Is it right to read "construction" as what's happening in the rest of the chapter? That's the impression I get -- if distinction is perfect continence then drawing a distinction will accord with what is given -- distinction and indication. (interestingly, comparing 1 and 2, we can interpret the cross as a kind of circle, but with the space-properties of this formal, rather than a geometric, system)
But what we get is the space cloven by the first distinction is* the form, and that all others are following this form. The space is cleaved by a cross indicating/distinguishing, but distinction is the form by which we can indicate an inside or an outside. In a way we could look at the cross as a mere mark rather than an intent. It would have content but it would not be a* used signal.
The notion of "value" is really interesting to me. The value is marked/unmarked, at the most simple. The name indicates the state, and the state is its value insofar that an expression indicates it. And then with equivalence we are able to compare states through the axioms. At this point I think we can only hold equivalence between the basic axioms, which turns out to have an inside and an outside, and gives a rule for "condensation" and "cancellation". So in a way the value is just what is named at this point, but there's still a distinction to be had between marked and unmarked due to the law of crossing canceling rather than reducing to the original name.
Then the end of the chapter is what follows from everything before. "The end" as I'm reading it starts at "Operation" -- this is where we can now draw a distinction, having constructed everything prior, and it entails some properties about the system being built such as depth, shallowness, and a need to define space in relation to the cross.
*added in as an edit, was confusing upon a re-read