Abstract
We would like to be able to measure the complexity (or quantity, or form, or structure) of any finite symbolic objects, such as chromosomes, texts, pictures and pieces of music. How much form does such an object have, how complex is it? We would like our measure to be uniform, so as to allow us to compare the complexity of heterogeneous objects, like genes, photos and songs.
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References
Boolos, G. and Jeffrey, R. [1980] Computability and Logic, (2nd ed.), Cambridge: Cambridge University Press.
Gödel, K. [1931] Über formal unentscheidbare Sätze der Principia Mathanatica und verwandter Systeme I, Monatshefte für Mathematik und Physik, 38, 173–198.
Hermes, H. [1971] Aufzählbarkeit, Entscheidbarkeit, Berechenbarkeit, (2nd ed.), Berlin/New York: Springer-Verlag.
Kolmogorov, A. [1968] Logical basis for information theory and probability theory, IEEE Transactions on Information Theory, vol. IT-14, 662–664.
Lebow, I. [1991] The Digital Connection, New York: Computer Science Press.
Luther, A. [1989] Digital Video in the PC Environment, New York: McGraw Hill.
Ming L. and Vitanyi, P. [1990] Kolmogorov complexity and its applications, in: J. van Leeuwen, (ed.), Handbook of Theoretical Computer Science, vol. A: Algorithms and Complexity, Amsterdam: Elsevier.
Mosterín, J. [1992] Scientific theories and the flow of information, in: Echeverría, I. and Mormann, (eds.), The Space of Mathematics. Philosophical, Epistemological and Historical Explorations, Berlin-New York: De Gruyter, pp. 366–378.
Poundstone, W. [1985] The Recursive Universe, New York: William Morrow.
Rucker, R. [1987] Mind Tools: The Mathematics of Information, London: Penguin Books.
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© 1997 Springer Science+Business Media Dordrecht
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Mosterín, J. (1997). The Natural Numbers as a Universal Library. In: Agazzi, E., Darvas, G. (eds) Philosophy of Mathematics Today. Episteme, vol 22. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5690-5_18
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