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atoms. On the other hand, radioactive decay is a statistical law which is subject to the probability theorems, and cannot be applied to individual atoms, but in all practical cases, the number of atoms is so immense that an "exact" formulation can be used, namely n(t) = n 0 x e -k x t . The decay constant k does not depend on temperature, nor on pressure, nor on any possible chemical bond. The half-life T is given by the formula T = ln 2/k; this indicates the time required for any given quantity n 0 to diminish to half as much, n 0 /2. Since we are dealing with statistical events, one might expect that less than half the number of atoms or appreciably more then half could have decayed at time T. However, the probability of deviation from this law is so close to zero that we could regard it as statistically impossible. It should be clear that impossible events are neither observable nor recognizable nor measurable. Possible events have in general either been observed, or they are observable. However, there are other possible events about which it can be said that they
– cannot or cannot yet be observed (e.g., processes taking place in the sun’s interior)
– are in principle observable, but have never been observed
    Thus far, we have only discussed natural events, but now we can apply these concepts to technological processes (in the widest sense of the word, comprising everything that can be made by human beings). The following categories are now apparent:
    1. possible processes
    1.1 already implemented
    1.2 not yet implemented, but realizable in principle
    2. impossible processes: proposed processes of this kind are fundamentally unrealizable, because they are precluded by laws of nature.
    The distinctions illustrated in Figure 7 follow from a comparison of possible events in nature and in technology, namely:
    a) processes which occur only in nature, but have not (yet) been realized technologically (e.g., photosynthesis, the storage of information on DNA molecules, and life functions);
    b) processes occurring in nature which are also technologically realizable (e.g., industrial synthesis of organic substances);
    c) processes which have been technologically implemented, but do not occur in nature (e.g., synthesis of artificial materials).
Figure 7: Possible and impossible events in nature and in technological processes.

Part 2
     
    Information
     

Chapter 3
     
    Information Is a Fundamental Entity
     
    3.1 Information: A Fundamental Quantity
     
    The trail-blazing discoveries about the nature of energy in the 19th century caused the first technological revolution, when manual labor was replaced on a large scale by technological appliances — machines which could convert energy. In the same way, knowledge concerning the nature of information in our time initiated the second technological revolution where mental "labor" is saved through the use of technological appliances — namely, data processing machines. The concept "information" is not only of prime importance for informatics theories and communication techniques, but it is a fundamental quantity in such wide-ranging sciences as cybernetics, linguistics, biology, history, and theology. Many scientists therefore justly regard information as the third fundamental entity alongside matter and energy.
    Claude E. Shannon was the first researcher who tried to define information mathematically. The theory based on his findings had the advantages that different methods of communication could be compared and that their performance could be evaluated. In addition, the introduction of the bit as a unit of information made it possible to describe the storage requirements of information quantitatively. The main disadvantage of Shannon’s definition of information is that the actual contents and impact of messages were not investigated. Shannon’s theory of information, which describes information from a statistical viewpoint only, is discussed fully in the appendix (chapter