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combined one with the other in any way; on the contrary, information and its uti-
lization are inseparable constituting, as a matter of fact, one single process.
5.31 These processes are the operations w, and they are implemented
in the structural and functional organization of nervous activity.
5.4 Let
v
i
be the signals traveling along single fibers,
i
, and
v
(1)
be the
outcome of an interaction of
N
fibers (
i
= 1,2...
N
):
[
()
()
1
()
1
(
)
∫
()
1
vFvv v Fv
N
=
,
,...
.
12
i
5.41 It is profitable to consider the activity of a subset of these fibers
as determiner for the functional interaction of the remaining ones (“inhi-
bition” changes the functional interaction of “facilitatory” signals). This can
be expressed by a formalism that specifies the functions computed on the
remaining fibers:
()
()
1
[
()
π
vf
1
=
v j
,
i
.
i
[]
v
j
The correspondence between the values n of the row vector (
v
j
) and the
appropriate functions
f
v
(1)
constitutes a functional for the class of functions
f
(1)
[
v
j
]
.
5.411 This notation makes it clear that the signals themselves may
be seen as being, in part, responsible for determining the operations being
performed on them.
5.42 The mapping that establishes this correspondence is usually
interpreted as being the “structural organization” of these operations, while
the set of functions so generated as being their “functional organization.”
5.421 This shows that the distinction between structural and func-
tional organization of cognitive processes depends on the observer's point
of view.
5.43 With
N
fibers being considered, there are 2
N
possible interpreta-
tions (the set of all subsets of
N
) of the functional and structural organiza-
tion of such operations. With all interpretations having the same likelihood,
the “uncertainty” of this system regarding its interpretability is
H
= log
2
2
N
=
N
bits.
5.5 Let
v
i
(1)
be the signals traveling along single fibers,
i
, and
v
(2)
be the
outcome of an interaction of
N
1
such fibers (
i
= 1,2,...
N
1
):
[
( )
()
()
()
2
2
1
vF
i
=
or, recursively from 5.4:
()
()
(
(
)
[
(
)
(
[]
[]
)
]
)
k
k
k
-
1
k
-
2
1
v
=
FFF
...
Fv
.
i
5.51 Since the
F
(
k
)
can be interpreted as functionals
f
(
k
)
[
v
i
]
, this leads to
a calculus of recursive functionals for the representation of cognitive
processes w.
5.511 This becomes particularly significant if
v
i
(
k
-
t
)
denotes the activ-
ity of fiber,
i
, at a time interval
t
prior to its present activity
v
i
(
k
)
. That is, the
recursion in 5.5 can be interpreted as a recursion in time.
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