Changes

<p>The archetype of all auto-graphs is perhaps the familiar model of the natural numbers <math>\mathbb{N}\!</math> as a sequence of sets, each of whose successive sets collects all and only the previous sets of the sequence:</p>

<p>The archetype of all auto-graphs is perhaps the familiar model of the natural numbers <math>\mathbb{N}\!</math> as a sequence of sets, each of whose successive sets collects all and only the previous sets of the sequence:</p>

: <p><math>\{\}, \quad \{\{\}\}, \quad \{\{\}, \{\{\}\}\}, \quad \{\{\}, \{\{\}\}, \{\{\}, \{\{\}\}\}\}, \quad \ldots\!</math></p>

| <math>\{\}, \quad \{\{\}\}, \quad \{\{\}, \{\{\}\}\}, \quad \{\{\}, \{\{\}\}, \{\{\}, \{\{\}\}\}\}, \quad \ldots\!</math>

<p>This is the purest example of a PSD developmental sequence, where each member of the sequence documents the prior history of the development.  This AG is akin to many kinds of PSD data structures that are found to be of constant use in computing.  As a natural precursor to many kinds of ''intelligent data structures'', it forms the inveterate backbone of a primitive capacity for intelligence.  That is, this sequence has the sort of developing structure that can support the initial growth of learning in many species of creature constructions with adaptive constitutions, while it remains supple enough to supply an articulate skeleton for the evolving process of reflective inquiry.  But this takes time to see.</p>

<p>This is the purest example of a PSD developmental sequence, where each member of the sequence documents the prior history of the development.  This AG is akin to many kinds of PSD data structures that are found to be of constant use in computing.  As a natural precursor to many kinds of ''intelligent data structures'', it forms the inveterate backbone of a primitive capacity for intelligence.  That is, this sequence has the sort of developing structure that can support the initial growth of learning in many species of creature constructions with adaptive constitutions, while it remains supple enough to supply an articulate skeleton for the evolving process of reflective inquiry.  But this takes time to see.</p>

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<p>For future reference, I refer to this ''model of natural numbers'' as &ldquo;MON&rdquo;.  The very familiarity of this MON means that one reflexively proceeds from reading the signs of its set notation to thinking of its sets as mathematical objects, with little awareness of the sign relation that mediates the process, or even much reflection after the fact that is independent of the reflections recorded.  Thus, even though this MON documents a process of reflective development, it need inspire no extra reflection on the acts of understanding needed to follow its directions.</p>

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<p>In order to render this MON instructive for the development of a RIF, something intended to be a deliberately ''self-conscious'' construction, it is important to remedy the excessive lucidity of this MONs reflections, the confusing mix of opacity and transparency that comes in proportion to one's very familiarity with an object and that is compounded by one's very fluency in a language.  To do this, it is incumbent on a proper analysis of the situation to slow the MON down, to interrupt one's own comprehension of its developing intent, and to articulate the details of the sign process that mediates it much more carefully than is customary.</p>

For future reference, I dub this "model of natural numbers" as "MON".  The very familiarity of this MON means that one reflexively proceeds from reading the signs of its set notation to thinking of its sets as mathematical objects, with little awareness of the sign relation that mediates the process, or even much reflection after the fact that is independent of the reflections recorded.  Thus, even though this MON documents a process of reflective develoment, it need inspire no extra reflection on the acts of understanding needed to follow its directions.

In order to render this MON instructive for the development of a RIF, something intended to be a deliberately "self conscious" construction, it is important to remedy the excessive lucidity of this MONs reflections, the confusing mix of opacity and transparency that comes in proportion to one's very familiarity with an object and that is compounded by one's very fluency in a language.  To do this, it is incumbent on a proper analysis of the situation to slow the MON down, to interrupt one's own comprehension of its developing intent, and to articulate the details of the sign process that mediates it much more carefully than is customary.

<p>These goals can be achieved by singling out the formal language that is used by this MON to denote its set theoretic objects.  This involves separating the object domain <math>O = O_\text{MON}\!</math> from the sign domain <math>S = S_\text{MON},\!</math> paying closer attention to the naive level of set notation that is actually used by this MON, and treating its primitive set theoretic expressions as a formal language all its own.</p>

Thus, I need to discuss a variety of formal languages on the following alphabet:

Thus, I need to discuss a variety of formal languages on the following alphabet: