ONT Re: Inquiry Driven Systems
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| "What are moon-letters?" asked the hobbit full of excitement.
| He loved maps, as I have told you before; and he also liked
| runes and letters and cunning handwriting, though when he
| wrote himself it was a bit thin and spidery.
|
| "Moon-letters are rune-letters, but you cannot see them",
| said Elrond, "not when you look straight at them. They
| can only be seen when the moon shines behind them, and
| what is more, with the more cunning sort it must be a
| moon of the same shape and season as the day when they
| were written. The dwarves invented them and wrote them
| with silver pens, as your friends could tell you. These
| must have been written on a midsummer's eve in a crescent
| moon, a long while ago."
|
| J.R.R. Tolkien, 'The Hobbit, or There and Back Again',
| revised ed., Ballantine, New York, NY, 1982, p. 53.
let us turn to the not so quickly moving picture
of what i hope will eventually turn out to be
a gradually increasingly up clearing muddle:
o-----------------------------o-----------------------------o
| Objective Framework | Interpretive Framework |
o-----------------------------o-----------------------------o
| |
| s^1 |
| · |
| · |
| · |
| · |
| p · · · · s^2 |
| · · |
| · · |
| · · |
| · · |
| q · · · · s^3 |
| · |
| · |
| · |
| · |
| s^4 |
| |
o-----------------------------------------------------------o
imagine that we continue our measurements and observations
within the boundaries of this miniscule field of phenomena,
persisting in the fashion of our preliminary survey of its
so-called 'geometry'. but let me now abstract from all of
the picturesque detail of its discreet geometry, recording
facts of the form F in hieroglyphs of the genus G, like so:
F. there is a point of view L from which the turning of v into w about u
appears to describe the same angle as the turning of y into z about x.
G. there is a relation L such that <u, v, w> and <x, y, z> are both in L.
equivalently, and perhaps less confusingly, we could say it in this style:
G. there is a relation L that includes the elements <u, v, w>, <x, y, z>.
let's say that we discover a collection of facts in the following wise:
from either one of the points of view, P or Q,
the following circumstances appear to be true:
| the turning of s^1 into s^1 about p
| appears to convey the same angle as
| the turning of s^4 into s^4 about q.
according to the conversion outlined above,
we can record that more briefly as follows:
| P and Q both include these two elements:
|
| <p, s^1, s^1>
| <q, s^4, s^4>
continuing in this way, we arrive at complete lists
of the apparent factual circumstances, as seen from
the viewpoints of P and Q, respectively, given here:
| P comprises the following elements:
|
| <p, s^1, s^1>
| <p, s^1, s^2>
| <p, s^2, s^1>
| <p, s^2, s^2>
|
| <q, s^4, s^4>
| <q, s^4, s^3>
| <q, s^3, s^4>
| <q, s^3, s^3>
| Q comprises the following elements:
|
| <p, s^1, s^1>
| <p, s^1, s^3>
| <p, s^3, s^1>
| <p, s^3, s^3>
|
| <q, s^4, s^4>
| <q, s^4, s^2>
| <q, s^2, s^4>
| <q, s^2, s^2>
if the shape and the season of the moon is right,
i think that you are verging on seeing the light.
jon awbrey
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