Abstract
This paper explores the problem of knowledge in computational informational organisms, i.e. organisms that include a computing machinery at the artifact side. Although information can be understood in many ways, from the second half of the past century information is getting more and more digitised, von Neumann machines becoming dominant. Computational information is a challenge for the act of measuring, as neither purely quantitative nor totally qualitative approaches satisfy the need to explain the interplay among the agents producing and managing computational information. In this paper, Floridi’s method of levels of abstraction is applied to the analysis of computational information, with a chief interest in the concepts of information measure, quantification and quality.
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Notes
The term is used in this paper in the generic sense, not in its logical meaning, as it does not refer to quantifiers.
Here and elsewhere, we use the common expression “the LoA of some object”: this is a short way to express the right concept of “the LoA associated to some object as in the mind of the describer/writer/observer/agent” where the context identifies the human being involved.
Mathematically, this structure is the one of integers modulo 2n, represented in the binary notation. The usual integers do not possess the structure of vectors of Booleans, and the reals are not even representable, as discussed in Sect. 4.3.
An interesting remark posed by an anonymous reviewer is whether a LoA is needed for the VNM to compute. Here, is evident that a LoA is strictly needed: the computation really performed by a VNM has no meaning unless understood as the result of the encoding of the abstract LoA into the “real machine”. For example, the operation x + 32 at the VNM level increments the number x by 32, while, in a LoA which codes characters using the ASCII table, the same operation converts upper case letters into lower-case (this example comes from the standard library of the C language, so it refers to real code)—and it is “correct” only when x is an upper-case letter, otherwise one has to accept, e.g., that the lower-case form of 1 is Q, and that the lower-case form of z does not exist.
We are illustrating the most widely studied notion, the one of worst-case analysis: there are also studies about average performances, but they are outside the scope of this paper.
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Acknowledgments
We would like to thank all participants of the Fifth Workshop of the Philosophy of Information for their useful feedbacks to our work, and the reviewers for their compelling and interesting remarks. Also, Dr. Benini has been supported in this research by the project “Correctness by Construction” (CORCON), EU 7th framework programme, grant n. PIRSES-GA-2013-612638, and by the project “Abstract Mathematics for Actual Computation: Hilbert′s Program in the 21st Century” from the John Templeton Foundation. Dr. Gobbo holds the Special Chair in Interlinguistics and Esperanto at the University of Amsterdam (UvA), Faculty of Humanities, on behalf of the Universal Esperanto Association (UEA, Rotterdam). The content and opinions expressed in this article are the authors′ and they do not necessarily reflect the opinions of the institutions supporting them.
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Gobbo, F., Benini, M. What Can We Know of Computational Information? Measuring, Quantity, and Quality at Work in Programmable Artifacts. Topoi 35, 203–212 (2016). https://doi.org/10.1007/s11245-014-9248-5
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DOI: https://doi.org/10.1007/s11245-014-9248-5