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3.2 The representation S of an instant t regarding the entity x
1
is distinct from
the representation of this instant regarding the entity x
2
:
St x
(
()
)
π
()
St x
(
)
1
2
3.3 However, the comparative judgment (“distinct from”) cannot be made
without a mechanism that computes these distinctions.
3.4
Abbreviate the notation by
Rx t
(
)
Æ
()
()
R
i
j
ij
(
)Æ
St x
S
kl
l
(
i, j, k, l
= 1,2,3,...)
4.
Contemplate relations Rel
m
between the representations R and S:
Rel
(
R
,
S
)
m
ij
kl
(m = 1,2,3,...)
4.1 Call the relation which obliterates the distinction x
i
π x
l
and t
j
π t
k
(i.e.,
i
=
l
;
j
=
k
) the “Equivalence Relation” and let it be represented by:
Equ R
(
,
S
)
ij
ji
4.11
This is a representation of a relation between two representations and reads:
“The representation R of an entity x
i
retarding the instant t
j
is equivalent to the rep-
resentation S of an instant t
j
regarding the entity x
i
.”
4.12 A possible linguistic metaphor for the above representation of the equiva-
lence relation between two representations is the equivalence of “thing acting”
(most Indo-European languages) with “act thinging” (some African languages)
(cognitive duality). For instance:
“The horse gallops”
¨
“The gallop horses”
4.2
The computation of the equivalence relation 4.1 has two branches:
4.21
One computes equivalences for x only
Equ R
(
,
S
)
=
()
Obj x
ij
ki
j
4.211 The computations along this branch of equivalence relation are called
“abstractions:”
Abs.
4.212 The results of this branch of computation are usually called “objects” (enti-
ties), and their invariance under various transformations (t
j
,t
k
, . . .) is indicated by
giving each object a distinct but invariant label N
i
(“Name”):
Obj x
()
Æ
N
j
j
4.22
The other branch computes equivalences for t only:
Equ R
(
,
S
)
∫
()
Eve t
ij
jl
j
4.221 The computations along this branch of equivalence relation are called
“memory:”
Mem.
4.222 The results of this branch of computation are usually called “events”
(instants), and their invariance under various transformations (x
i
,x
l
, . . .) is indicated
by associating with each event a distinct but invariant label T
j
(“Time”):
Eve t
()
Æ
T
j
j
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