Information Technology Reference
In-Depth Information
change of appearance of the same object as when a cube is rotated, or a
person turns around, and we take it to be the same object (cube, person,
etc.); or when we see a tree growing, or meet an old schoolmate after a
decade or two, are they different, are they the same, or are they different
in one way and the same in another? Or when Circe changes men into
beasts, or when a friend suffers a severe stroke, in these metamorphoses,
what is invariant, what does change? Who says that these were the same
persons or objects?
From studies by Piaget 1 and others 2 we know that “object constancy” is
one of many cognitive skills that are acquired in early childhood and hence
are subject to linguistic and thus cultural bias.
Consequently, in order to make sense of terms like “biological invari-
ants,” “cultural universals,” etc., the logical properties of “invariance” and
“change” have first to be established.
As the notes procede it will become apparent that these properties
are those of descriptions (representations) rather than those of objects. In
fact, as will be seen, “objects” do owe their existence to the properties of
representations.
To this end the next four propositions are developed.
2. The logical properties of “invariance” and “change” are those of repre-
sentations. If this is ignored, paradoxes arise.
Two paradoxes that arise when the concepts “invariance” and “change” are
defined in a contextual vacuum are cited, indicating the need for a formal-
ization of representations.
3. Formalize representations R, S, regarding two sets of variables {x} and {t},
tentatively called “entities” and “instants” respectively.
Here the difficulty of beginning to talk about something which only later
makes sense so that one can begin talking about it, is pre-empted by “ten-
tatively,” giving two sets of as yet undefined variables highly meaningful
names, viz, “entities” and “instants,” which only later will be justified.
This apparent deviation from rigor has been made as a concession to
lucidity. Striking the meaningful labels from these variables does not change
the argument.
Developed under this proposition are expressions for representations
that can be compared. This circumvents the apparent difficulty to compare
an apple with itself before and after it is peeled. However, little difficulties
are encountered by comparing the peeled apple as it is seen now with the
unpeeled apple as it is remembered to have been before.
With the concept “comparison,” however an operation (“computation”)
on representations is introduced, which requires a more detailed analysis.
This is done in the next proposition. From here on the term “computation”
will be consistently applied to all operations (not necessarily numerical)
that transform, modify, re-arrange, order, etc., either symbols (in the
Search WWH ::




Custom Search