Information, The Hidden Side of Life

4Can We Define Information?

The previous chapters showed how pervasive the notion of information is in many aspects of life, from DNA molecules to ecosystems and human language. When seen from an informational perspective, these facets of life join in some form of unity that we will discuss in Chapter 5. Before that, we should manage to get a definition of information that covers the variety of situations that were evoked previously. Information is a rather recent scientific concept: it dates back to the middle of last century. Contrary to other well-established notions, information has not yet found its definitive definition. This chapter relies on some recent theoretical developments in algorithmic information theory that allow us to propose a common framework to describe the various situations we mentioned in which the word “information” occurred spontaneously.

4.1. Information as surprise

Any sign does not carry information. The oil level sensor in my car may invariably indicate level 7. If it could show only this value, the information associated with it would be zero. As we know that other values are possible, but are rare, the information attached to level 7 is very small. If the sensor indicates level 3 one day, the corresponding information that day will have a significant value.

In this example, one has clearly in mind what is at stake: the oil may be leaking. Let us forget about this for a while and concentrate on the sole probabilities. This is precisely what Claude ...