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Information and Life pp 11–32Cite as

What is Information?

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Abstract

Chapter 2 examines how the most current use of the word ‘information’ can lead to outline an axiomatic definition of information. Its most specific features are that it has no existence unless it is physically inscribed as a sequence of symbols on some medium, which however has no influence on it besides ensuring its existence, and that it can be defined only as an equivalence class, with respect to transformations like alphabet change and coding. It is thus an abstract entity which resides in the physical world. An information meets Barbieri’s concept of ‘nominable entity’, which refers to a singular object. This concept is explicated and illustrated. A natural number can be used, besides its usual meanings of representing a quantity (cardinal number) or a rank in a sequence (ordinal number), as a label uniquely representing a nominable entity. The uniqueness of nominable entities entails that their representatives do not suffer any change and thus must be protected against any perturbation. A short history of communication engineering, which developed the means of such a protection referred to as ‘error-correcting codes’, is briefly presented. It is also stated that the theoretical tools needed in order to deal with communication at a distance can be used as well for communication over time such as biological heredity.

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Notes

  1. 1.

    A symbol is an element of some given finite set of distinct objects, referred to as an alphabet.

  2. 2.

    In the information-theoretic literature. Physicists do not even ask the question whether information is a physical entity but deal with it as such, following Schrödinger and Brillouin.

  3. 3.

    In any possible meaning of the word: there should not be a causal relation between them and, if they are random, they should be mutually independent in the probabilistic meaning of the word, i.e., their joint probability should be the product of their individual probabilities.

  4. 4.

    The progress of mathematics has refuted Zeno’s paradoxes like that of Achilles and the tortoise.

  5. 5.

    It is redundant: fortunately, less than \(10^{13}\) people live in France.

  6. 6.

    An error probability of 1/2 prevents any communication by means of the binary alphabet; see Sect. 5.2.2.

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  1. E.N.S.T., Paris, France (retired), La Chanatte, le Guimand, 26120, Chabeuil, France

    Gérard Battail

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  1. Gérard Battail
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Battail, G. (2014). What is Information?. In: Information and Life. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-7040-9_2

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