[Arisbe] Re: Epistemic Diagrams
Jon Awbrey
arisbe@stderr.org
Mon, 20 Aug 2001 22:54:01 -0400
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Howard, & All,
I pick up the story at the bottom of this deck:
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Howard Pattee wrote (HP):
Jon Awbrey wrote (JA):
JA: ... it is mostly the task of constructing software tools for the
support and extension of our humane intellects that is my main aim.
HP: Creating machine tools to support the intellect is an aim worthy of discussion.
Where in the course of inquiry, using any epistemic diagram you choose, do you
feel the inquiring mind needs the most help? Or is it more modest to ask where
we could expect technically plausible software (and hardware) to help the most?
JA: Here are some of the big problems that I see here:
JA: There is a field of activity, transected by several shifty lines:
1.a. <What people can do> Versus 1.b. <What people cannot do>
2.a. <What people do best> Versus 2.b. <What people do not do best>
3.a. <What people like to do> Versus 3.b. <What people do not like to do>
JA: The uses of technology worth having are those take some of the stuff that humans can do --
goodly, badly, or indifferently -- but out of which people no longer get much of a kick,
and shift these fardels so that machines will bear them.
JA: I am pretty much content to leave the creative stuff to people for a while,
since I have no clue how to automate it, and even if I did I would have to
ask whether it's creative stuff we like or creative stuff we dislike doing.
JA: The thing is that many activities of interest to us are cyclic or recurring processes,
and this means that we can often facilitate the whole cycle simply by identifying the
places where things are pinched a bit more than others, the points of high resistance --
no, there is no venturi flow here, it's a high viscosity current so far as I can tell --
and by loosening up these bottlenecks to whatever extent that we can. Still, not all
of the bottlenecks are ones that we can do much about, so we have to pick our bottles.
JA: In view of these things, I am mostly focused on the barriers, blocks, boondoggles,
bottlenecks, briar patches, broken fields, bulwarks, caltrops, hurdles, obstacles,
obstructions, ramparts, rough spots, sandtraps, and walls that we keep on running
into as we try to move forward in our evolving inquiry. Whenever I run into one
of these blocks I have to backtrack to a point in our common intellectual orbit
where I can see the nature of the obstruction well enough to see a way around,
beyond, or through it.
JA: Notice that this sort of work is often very different from trying to build imitation humans
or anything like that. In fact, though it is probably useless to tilt against the windmill
of a mere name like "artificial intelligence" (AI), my roots go back to the classical angle
of Ashby and others that initially disposed them to build an "intellectual amplifier" (IA).
WRA: | If this is so, and as we know that power of selection can be amplified,
| it seems to follow that intellectual power, like physical power, can be
| amplified. Let no one say that it cannot be done, for the gene-patterns
| do it every time they form a brain that grows up to be something better
| than the gene-pattern could have specified in detail. What is new is
| that we can now do it synthetically, consciously, deliberately.
|
| W. Ross Ashby,
|'An Introduction to Cybernetics',
| Chapman & Hall, London, UK, 1956,
| Methuen & Company, London, UK, 1964,
| Section 14/7, Page 272.
JA: On To The Epigenetic Algorithm!
JA: I am going to start by gathering together for comparative study
the various sorts of epistemic diagrams that we have been using,
plus those that I otherwise know about, that might conceivably
bear on this problem of building machine tools to support the
intellect, derricks or drilling platforms for exploration,
if you will, or frameworks and instruments for inquiry.
JA: Let us start with your rendition of Hertz's modeling relation:
HP, rendering Hertz:
| External Objects _____ We Form For Ourselves _____ Images or Symbols, Pictures
| | / [Signs, Brain States, Whatever]
| | / |
| | / |
| [Natural Laws] . . . Such That . . . / [Logic, Mathematical Model]
| | / |
| | / |
| | / |
| Naturally Necessary /___ Are The Same As The _____ Logically Necessary
| Consequents Consequents Of The Model
HH: | We form for ourselves images or symbols of external objects;
| and the form which we give them is such that the logically
| necessary (denknotwendigen) consequents of the images in
| thought are always the images of the necessary natural
| (naturnotwendigen) consequents of the thing pictured.
|
| For our purpose it is not necessary that they [the images] should be
| in conformity with the [external] things in any other respect whatever.
| As a matter of fact, we do not know, nor have we any means of knowing,
| whether our conception of things [our models] are in conformity with
| them [external things] in any other than this one fundamental respect.
|
| Heinrich Hertz (1857-1894),
|'The Principles of Mechanics', Dover, NY, 1984, pp. 1-2;
| original German edition, 'Prinzipien Mechanik', 1894.
JA: Abstracting a bit from the finer details, we have a commutative diagram of sorts:
| We Form For Ourselves
| External Object o---------------------------->o Image or Symbol in Thought,
| | /| Conception of the Object
| | / |
| | / |
| [Natural Laws] | . . . Such That . . . / | [Logic + Mathematical Model]
| | / |
| | / |
| Naturally Necessary v/ v Logically Necessary
| Consequents Of The o---------------------------->o Consequents Of The
| Thing Pictured Are The Same As The Model
JA: The more that I stare at this picture the more that I start to recognize it.
It is the very way that I used to explain to my students when I taught math
what the paradigmatic genre commonly known as "The Art of the Story Problem"
is all about. More than that, remembering this has given me a clue to what
some of our difficulties over Formalismism might be about. So looky here:
| Problem Formalization
| Story Problem o---------------------------->o Formula Problem
| . (Abduction, Abstraction) |
| . |
| . |
| . (Deduction, Explication) = | Formula Cranking
| . |
| . |
| v (Induction, Interpretation) v
| Story Solution o<----------------------------o Formula Solution
| Probational Application
JA: A few notes on this picture are in order:
JA: 1. What it illustrates is simply the following familiar process:
a. Starting with an informal, narrative, practical, or "story" problem.
b. Recognizing the story as a possible case under a rule or a "formula".
c. Deriving from the formula a canonical solution, an answer in "theory".
d. Warily interpreting the theoretical solution for the practical setting.
JA: 2. Although this process is based on a commutative diagram,
the directed trace of the process takes the final arrow
in a sense opposite to the "initial formulation" arrow.
JA: 3. It is terribly important to impress on ourselves the circumstance
that only certain sections of this problem solving process can be
reduced to rote, that is, delivered over to automatic habits and
unreflective routines, whether of humans or of machines. Indeed,
only the decadenza of deductive, explicative, syntactic argument
has the reasonable facsimile of any guarantee along these lines.
JA: 4. In particular, because the formulation arrow typically casts off
such a large degree of detail in the casual setting of the story,
the return interpretation arrow will of necessity have to supply
the lack on the way back to the scene of the initial application.
Because it is possible to guess wrong and to make errors at each
and every stage of this process, non-essentially so in deduction
but essentially and thus ineliminably so on the horizontal steps,
the "final" attempt at applying the "formal" solution can hardly
ever be considered truly final, but must be tested by common wit
and against the full details of the original pragmatic situation.
JA: 5. Imagine how silly it would be if some people were to imagine that
the horizontal arrows could be altogether cast out of our quivers,
but then, strangely enough, I've heard tell that "some people" do.
JA: Let me now plot how I would nudge into place this particular picture of
problem-solving method on the chart of my current pragmatic perspective.
JA: First, I would recognize that "there is nothing but text" in this picture,
that story problem, formula problem, formula solution, and story solution
are all just so many signs and symbols, that Poser or Solver have posed,
recalled, recited, uttered, or written in respect of the real, imagined,
or virtually "objective" predicament that Poser or Solver suppose to be
described, in various lights and shadows, genres and styles, by each of
their sundry texts. On the other hand, we must not permit ourselves to
imagine that the object of it all has dropped out of sight, out of what
may be called "The Big Picture", or else the whole proceeding ceases to
make sense anymore, but rather that our original object(ive) is acting
as a silent partner to the entire transaction. So let me draw it so:
| 4 Dénouer 1
| Narrative Outcome o<- - - - - - - -o Narrative Problem
| ^ |
| / | |
| / Application | | Abstraction
| Object o---- Interpretation | Induction Abduction | Insight
| \ Probation | | Recognition
| \ | |
| | Deduction v
| Formulaic Outcome o<----------------------o Formulaic Problem
| 3 Determination 2
| Clarification
| Explication
JA: I probably should explain why I have metamorphed this picture the way that I have.
Many of the names have been changed to protest the innocence of our own ignorance,
to wit, to remind us of our native fallibility at any turn where we think that we
have arrived at any answer, any bit of knowledge, any epistemic understanding, or
any solution to the problem that was set to us in the initial problem setting out.
Thus, it seems more fitting not to prejudice the status of a proposed solution by
literally calling it a "solution", but much better to denote it as the outcome of
an inquiry process. If I had drawn on three dimensions to represent this picture,
I might have sculpt it in a solid pyramidal form, with the object ascendant above
the near-plane of the inquiry process, but as it is I have elected to reflect our
common aspiration to come nearer our object by way of our inquiry by arranging it
so that the later phases are closer to the destination than are the earlier faces,
that so reflect the inchoate consternation of our first encounter with the puzzle.
JA: Speaking of puzzles, the placement of "induction" on the above board is bound to raise
an eyebrow of two, and I realize that it might be forcing the piece just a mite to try
to fit it to that particular niche, but my excuses for the nonce must go a bit like so.
Induction, properly countenanced, is a case of probable and probative reasoning, which
can only take place in a way that makes sense in the context of a prior abduction that
contingently establishes the sample space and frames the provisional statistical model.
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I am just not fond of the distortions that are caused by flattening
this pyramid out onto the plane, but I am hestitant about trying to
draw it in perspective for fear that the lines will get too crossed.
So let me try it another way, one that has the advantage of letting
the horizontal arrows fly in the customary left to right directions.
| 1 Dénouer 4
| Narrative Problem o- - - - - - - ->o Narrative Outcome
| | ^
| / | |
| / Abstraction | | Application
| Object o---- Insight | Abduction Induction | Interpretation
| \ Recognition | | Probation
| \ | |
| v Deduction |
| Formulaic Problem o---------------------->o Formulaic Outcome
| 2 Determination 3
| Clarification
| Explication
In this picture the vertical dimension is being used to suggest
something between a rough heuristic ordering and a full-fledged
hierarchy of means-ends relational complexities and situational
difficulties. Aside from the inherent or intrinsic hardness of
a problem, very often it is a particular agent's personal level
of acquaintance, experience, or familiarity with a problem that
determines how easy a particular problem will be for that agent.
In fact, if you stop to think about it, one of the main factors
that renders a problem "formulaic" in the first instance is the
measure of familiarity that somebody or another happens to have
with it, whether it is the store of experience possessed by the
agent immediately engaged or whether it is the body of cultural
experience that has sedimented over long periods of time to the
strata of epistemic bedrock, and thus becomes broadly available
to be passed on to novice agents in the traditional rote manner.
As you have probably recognized by now, we are looking at a recursive setup.
In other words, harder problems have their solutions catalyzed by recurring
to easier problems for the basic templates on which to build new extensions.
But that is the story of another day ...
Jon Awbrey
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