Thoughts and Notes on Cognition - Understanding Understanding: Essays on Cybernetics and Cognition - page 187

c ) intent:

() ÆÆ .

w m d

z z

4.41 Since peripheral activity implies central activity

r ƨ v p

x x z

we have

w(n z )

dG

dG w(n z ) .

4.411 From this it is seen that a conceptualization of descriptions of
(the internal representation of) the environment arises from the conceptu-
alization of potential movements. This leads to the contemplation of expres-
sions having the form

[ ]

()

(

[ ]

( )

(

[]

)

)

wdw dw

n

G ,

n - 1

G ,

n - 2

... x ,

1 2

that is “descriptions of descriptions of descriptions...” or, equivalently,
“representations of representations of representations....”
5 The information associated with an event E is the formation of opera-
tions w which control this event's internal representation w(r x ) or its
description dG.
5.1 A measure of the number of choices of representations (w i [E]) or of
descriptions (dG i [E]) of this event—or of the probabilities p i of their occur-
rence—is the “amount of information” of this event with respect to the
organism W.( H [E,W] =-log 2 p i , that is, the negative mean value* of all the
[log 2 p i ]).
5.11 This shows that information is a relative concept. And so is H .
5.2 The class of different representations w∫(w i [E]) of an event E deter-
mines an equivalence class for different events (E i [w]) ∫ E. Hence, a
measure of the number of events (E i ) which constitute a cognitive unit, a
“category E” 6 —or of the probabilities p i of their occurrence—is again the
“amount of information”, H , received by an observer upon perceiving the
occurrence of one of these events.
5.21 This shows that the amount of information is a number depend-
ing on the choice of a category, that is, of a cognitive unit.
5.3 We have from a paper by Jerzy Konorski: 7

It is not so, as we would be inclined to think according to our introspection, that the
receipt of information and its utilization are two separate processes which can be

* The me an value of a set of quantities, x i , whose probability of occurrence of p i is
given by X

i =S x i · p i .