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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
102/2020

Information and Complexity, or: Where is the Information?

Nihat Ay, Nils Bertschinger, Jürgen Jost, Eckehard Olbrich and Johannes Rauh

Abstract

The concepts of information and complexity seem to be intricately linked. Complexity notions are quantified in information theoretical terms, and a general principle might say that a structure is the more complex, the more information is needed to describe or build it. That principle, however, needs some qualification. One should distinguish between – usually useful – information about regularities of a structure or a process and – often useless – information about random details. The question is not only information about what?, but also where is that information?, that is, whether and how it is or can be internally stored in a system with limited capacity, at which level of a process information is needed to predict the continuation of a process, and where it can be found in a distributed system. In the latter case, we should, however, not only look for information that is exclusively located somewhere or that is shared between entities, but should also consider complementary or synergistic information, that is, information that only emerges when several sources are combined.

These lecture notes describe what is currently known about these questions, and they develop the underlying theoretical concepts and elucidate them at simple examples. Also, when we can quantify complexity concepts, we can also try to optimize the corresponding complexity measures. This will also be systematically discussed.

These notes are the result of a series of lectures that one of us (JJ) delivered at the Summer School in Como in July, 2018. They present work that we have done jointly during the last few years. JJ thanks Elisa Mastrogiacomo and Sergio Albeverio for organizing a very stimulating school, and the participants and the other lecturers, in particular Luciano Boi, Ivar Ekeland and Frank Riedel, for stimulating discussions.

Received:
29.10.20
Published:
30.10.20

Related publications

inBook
2022 Repository Open Access
Nihat Ay, Nils Bertschinger, Jürgen Jost, Eckehard Olbrich and Johannes Rauh

Information and complexity, or: Where is the information?

In: Complexity and emergence : Lake Como School of Advanced Studies, Italy, July 22-27, 2018 / Sergio Albeverio... (eds.)
Cham : Springer, 2022. - pp. 87-105
(Springer proceedings in mathematics and statistics ; 383)