6.3 Accuracy, Meaning, and Effect

65

D(a, a) = 0 ;

D(a, b) = D(b, a) > 0

if

b /= a ;

D(a, b) + D(b, c) ≥ D(a, c) .

Other distances can be defined (see Sect. 17.4.2).

In biology, the question of accuracy refers especially to the replication of DNA, its

transcription into RNA, and the translation of RNA into protein. It may also refer to

the accuracy with which physiological signals can be transmitted within and between

cells.

6.3.2

Meaning

Shannon’s theory is not primarily concerned with the question of semantic content

(i.e., meaning). In the simple example of measuring the length of a piece of wood,

the question of meaning scarcely enters into the discourse. In nearly all of the other

cases, where we are concerned with receiving signs, or sequences of symbols, after

we have received them accurately we can start to concern ourselves with the question

of meaning. The issues can range from simple ones of interpretation to involved and

complex ones. An example of the former is the interpretation of the order “Wait!”

heard in a workshop. It may indeed mean “pause until further notice”, but heard by an

apprentice standing by a weighing machine, may well be interpreted as “call out the

weight of the object on the weighing pan.” An example of the latter is the statement

“John Smith is departing for Paris”, which has very different connotations according

to whether it was made in an airport, a railway station, or some other place.

It is easy to show that the meaning contained in a message depends on the set of

possible messages. Ashby (1956) has constructed the following example. Suppose a

prisoner-of-war is allowed to send a message to his family. In one camp, the message

can be chosen from the following set:

I am well

I am quite well

I am not well

I am still alive,

and in another camp, only one message may be sent:

I am well.

In both cases, there is implicitly a further alternative—no message at all, which would

mean that the prisoner is dying or already dead. In the second camp, if the recipient

is aware that only one message is permitted, he or she will know that it encompasses

several alternatives, which are explicitly available in the first camp. Therefore, the

same message (I am well) can mean different things depending on the set from which

it is drawn.