6.2 Constraint

63

accounts of major events such as military victories were preserved in massive stone

monuments whose inscriptions can still be read today several thousand years later.

Military secrets are printed on paper or photographed using silver halide film and

stored in bunkers, rather than committed to magnetic media. We tend to write down

things we need to remember for a long time.

The value of information is closely related to the problem of weighing the credi-

bility that one should accord a certain received piece of information. The question of

weighting scientific data from a series of measurements was an important driver for

the development of probability theory. Daniel Bernoulli (1777) raised this issue in

the context of averaging astronomical data, where it was customary to simply reject

data deviating too far from the mean and weight all others equally. ²²

Bennett has proposed that his notion of logical depth (Sect. 11.5) provides a formal

measure of value, very much in the spirit of Eqs. (6.26) and (6.27). A sequence of

coin tosses formally contains much information that has little value; a table giving

the positions of the planets every day for several centuries hence contains no more

information than the equations of motion and initial conditions from which it was

deduced, but saves anyone consulting it the effort of calculating the positions. This

suggests that the value of a message resides not in its information per se (i.e., its

absolutely unpredictable parts) nor in any obvious redundancy (e.g., repetition), but

rather in what Bennett has suggested be called buried redundancy: parts predictable

only with considerable effort on the part of the recipient of the message. This effort

corresponds to logical depth.

The value of information is also related to the amount already possessed. The

same Bernoulli asserted that the value (utility in economic parlance) of an amount

mm of money received is proportional to log left bracket left parenthesis m plus c right parenthesis divided by c right bracketlog[(m + c)/c], where cc is the amount of

money already possessed, ²³ and a similar relationship may apply to information.

6.2.2

The Quality of Information

Quality is an attribute that brings us back to the problem posed by Bernoulli in 1777,

namely how to weight observations. If we return to our simple measurement of the

length of a piece of wood, the reliability may be affected by the physical condition

of the measuring stick, its markings, its origin (e.g., from a kindergarten or from

Sèvres), the eyesight of the measurer, and so forth.

22 See also Euler (1777).

23 Bernoulli (1738), cf. Thomas (2010).