[Inquiry] Re: Futures Of Logical Graphs

[Jon Awbrey]

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FOLG.  Note 3

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Cybernetics List, Peirce List,

The "parse graphs" that we've been looking at so far are one step toward
the "pointer graphs" that it takes to make trees live in computer memory,
but they are still a couple of steps too abstract to properly suggest in
much concrete detail the species of dynamic data structures that we need.
I now proceed to flesh out the skeleton that I've drawn up to this point.

Nodes in a graph depict "records" in computer memory.
A record is a collection of data that can be thought
to reside at a specific "address".  For semioticians,
an address can be recognized as a type of index, and
is commonly spoken of, on analogy with demonstrative
pronouns, as a "pointer", even among programmers who
otherwise innocent of semiotics.

At the next level of concretion, a record/node can be represented as follows:

` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `
` ` ` ` ` o-----------------------------o ` ` ` ` ` ` ` ` ` `
` ` ` ` ` | datum_1 datum_2 datum_3 ... | ` ` ` ` ` ` ` ` ` `
` ` ` ` ` o-----------------------------o ` ` ` ` ` ` ` ` ` `
` ` ` ` ` ^ ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `
` ` ` ` ` | index_0 ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `
` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `
` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `

This depicts the circumstance that index_0 is the address
of the record in question, which record contains the data:
datum_1, datum_2, datum_3, ..., and so on.

What makes it possible to represent graph-theoretical structures
as data structures in computer memory is the fact that an address
is just another datum, and so we can have a circumstance like this:

` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `
` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` o-----o o-----o ` ` ` ` ` ` `
` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | ... | | ... | ` ` ` ` ` ` `
` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` o-----o o-----o ` ` ` ` ` ` `
` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ^ ` ` ` ^ ` ` ` ` ` ` ` ` ` `
` ` ` ` ` o---------------------|-------|-----------o ` ` ` `
` ` ` ` ` | datum_1 datum_2 ... index_1 index_2 ... | ` ` ` `
` ` ` ` ` o-----------------------------------------o ` ` ` `
` ` ` ` ` ^ ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `
` ` ` ` ` | index_0 ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `
` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `
` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `

Back at the abstract level, it takes three nodes to represent the
three data records, with a root node connected to two other nodes.
The ordinary bits of data are then treated as labels on the nodes:

` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `
` ` ` ` ` o ` o ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `
` ` ` ` ` | `/` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `
` ` ` ` ` | / ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `
` ` ` ` ` |/` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `
` ` ` ` ` O datum_1 datum_2 ... ` ` ` ` ` ` ` ` ` ` ` ` ` ` `
` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `

Notice that, with rooted trees like these, drawing the arrows is optional,
since singling out a unique node as the root induces a unique orientation
on all the edges of the tree, "up" being the same as "away from the root".

Jon Awbery

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inquiry e-lab: http://stderr.org/pipermail/inquiry/
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