Algebraic Methods in Nonlinear Perturbation Theory
Many books have already been written about the perturbation theory of differential equations with a small parameter. Therefore, we would like to give some reasons why the reader should bother with still another book on this topic. Speaking for the present
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REMARKS ON INFORMATION AND MIND
1. CREA TURA AND PLEROMA
It was not until the forties that the existence of the world of infonnation was explicitly recognized, i.e. it was recognized that along with the world of physics, the world of forces, masses and impacts, there is the realm of communication, difference, organization and meaning, where the laws which hold sway are quite different from those of physics, and are sometimes surprising. A major contribution to the recognition of the world of infonnation came from the work of Qaude E. Shannon, an engineer and mathematician then working at Bell Laboratories, who in 1948 wrote a seminal paper on the mathematical theory of communication. That paper was important not only because it contained beautiful theorems concerning the coding of infonnation sources and transmission channels, but also because it attracted people's attention to such key concepts as entropy, redundancy, capacity etc. But Shannon's theory, so important as it is from a theoretical as well as from a practical point of view, does not exhaust all aspects of infonnation. There are many concepts which are not stated, or even used, in Shannon's theory. These limitations stem mainly from the fact that the mathematical theory of communication is only concerned with the syntactic aspects of infonnation, and deliberately neglects its semantic and pragmatic aspects. Being so clearly bounded, Shannon's theory yields a variety of important and deep theorems. At the same time, those theorems have no validity outside the scope of the theory. This is why many attempts to apply such concepts as entropy or capacity in fields different from communication engineering have led to meaningless results. In what follows I shall try to give some hints about the concept of infonnation assuming that the reader is familiar with the fundamentals of Shannon's theory. Following Gregory Bateson, Carl Gustav Jung and the Gnostics, I shall call Pleroma the world of matter and forces, and Creatura the world of infonnation and structure. In the Pleroma each thing always stands for itself, whereas in the Creatura each thing can stand for another thing, thus becoming a symbol: every thing can bear a meaning, which is not inherent in the thing itself but is 141 G. Corsi et al. (eds), Bridging the Gap: Philosophy, Mathematics, and Physics, 141-146. © 1993 Kluwer Academic Publishers.
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GIUSEPPE LONGO
given to it by man, i.e. by a meaning-giving and meaning-using being. Meaning, in tum, is strictly related to redundancy, i.e. to repetitive information. Actually it is when we perceive a redundant pattern (e.g. a circle) that we can grasp or understand its form even before we can see it all: as happens with associative memories, we can reconstruct the whole form from a part of it. The same applies to a numerical sequence: if the sequence is redundant, i.e. is not completely random, we can guess at the next term with good success and even encompass the whole (infinite) sequence in a finite recursive formula. In other words, we again know
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