[Inquiry] Re: Peirce's Logic Of Information

[Jon Awbrey]

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PLOI.  Note 7

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In struggling to sketch some of the Figures that I need for the
next part of this discussion, I am finding the plaintext format
so constraining that I think it has become almost indispensable
to introduce a standard alternative form of representation for
the requisite graphs, specifically, their representation in
terms of "adjacency matrices" or "incidence matrices".

For example, consider the bigraph that we drew before:

` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `
` ` ` ` ` ` ` ` `q_1` `q_2` `q_3` `q_4` `q_5` ` ` ` ` ` ` ` `
` ` ` ` ` ` ` ` ` o ` ` o ` ` o ` ` o ` ` o ` ` ` ` ` ` ` ` `
` ` ` ` ` ` ` ` ` `\` ` |\` `/|\` `/| ` `/` ` ` ` ` ` ` ` ` `
` ` ` ` ` ` ` ` ` ` \ ` | \ / | \ / | ` / ` ` ` ` ` ` ` ` ` `
` ` ` ` ` ` ` ` ` ` `\` | `\` | `\` | `/` ` ` ` ` ` ` ` ` ` `
` ` ` ` ` ` ` ` ` ` ` \ | / \ | / \ | / ` ` ` ` ` ` ` ` ` ` `
` ` ` ` ` ` ` ` ` ` ` `\|/` `\|/` `\|/` ` ` ` ` ` ` ` ` ` ` `
` ` ` ` ` ` ` ` ` ` ` ` o ` ` o ` ` o ` ` ` ` ` ` ` ` ` ` ` `
` ` ` ` ` ` ` ` ` ` ` `e_1` `e_2` `e_3` ` ` ` ` ` ` ` ` ` ` `
` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `
` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `

This can be represented by means of the following matrix:

` ` ` ` ` ` ` ` ` ` ` `e_1` `e_2` `e_3` ` ` ` ` ` ` ` ` ` ` `
` ` ` ` ` ` ` ` ` ` o-------------------o ` ` ` ` ` ` ` ` ` `
` ` ` ` ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` `
` ` ` ` ` ` ` ` q_1 | ` 1 ` ` 0 ` ` 0 ` | ` ` ` ` ` ` ` ` ` `
` ` ` ` ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` `
` ` ` ` ` ` ` ` q_2 | ` 1 ` ` 1 ` ` 0 ` | ` ` ` ` ` ` ` ` ` `
` ` ` ` ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` `
` ` ` ` ` ` ` ` q_3 | ` 1 ` ` 1 ` ` 1 ` | ` ` ` ` ` ` ` ` ` `
` ` ` ` ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` `
` ` ` ` ` ` ` ` q_4 | ` 0 ` ` 1 ` ` 1 ` | ` ` ` ` ` ` ` ` ` `
` ` ` ` ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` `
` ` ` ` ` ` ` ` q_5 | ` 0 ` ` 0 ` ` 1 ` | ` ` ` ` ` ` ` ` ` `
` ` ` ` ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` `
` ` ` ` ` ` ` ` ` ` o-------------------o ` ` ` ` ` ` ` ` ` `
` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `

Here, the occurrence of a "1" at the intersection
of e_j street and q_k avenue indicates that there
is an edge connecting e_j and q_k, and a "0" says
otherwise.

In future, then, I'll feel free to represent a graph by means
of its matrix, especially whenever I can't easily draw it,
and safely leave the rest to the reader's imagination.

Jon Awbrey

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