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Volumn 30, Issue 1, 2005, Pages 69-88

Evolution as context-driven actualisation of potential: Toward an interdisciplinary theory of change of state

Author keywords

[No Author keywords available]

Indexed keywords

BIOLOGICAL CHANGE; CONVERGENT PRESSURES; RANDOM VARIATION; UNIFYING FRAMEWORK;

EID: 17044435408     PISSN: 03080188     EISSN: None     Source Type: Journal    
DOI: 10.1179/030801805X25873     Document Type: Article
Times cited : (50)

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    • A complex Hilbert space is a vector space over the field of complex numbers.
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    • note
    • A measurement is described by a self-adjoint operator, which is a linear function on the Hilubert space.
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    • note
    • For mathematical completeness, we mention that this is only the case when the operator has a point spectrum. Measurements described by operators without a point spectrum must be treated in a more sophisticated way. However, this is of no relevance to the points made here.
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    • There are, however, quantum theories that do not involve collapse.
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    • Kolmogorov's axioms, and hence Kolmogorovian probability theories, are named after Andrei Nikolaevich Kolmogorov, who first formulated the axiomatic system for classical probability theory (see A. N. Kolmogorov: Grundbegriffe der Wahrscheinlichkeitrechnung; 1933, Berlin, Springer). The theory had in fact existed since the time of Laplace (Théorie Analytique des Probabilités, 1812) and had been worked out by various mathematicians, but in a rather informal way. It is well known that the probability calculus of quantum mechanics is non-classical, in the sense that it does not satisfy Kolmogorov's axioms (A. Wilce: 'Quantum logic and probability theory', in Stanford Encyclopedia of Philosophy, (ed. E. N. Zalta), Spring 2003 edn, plato.stanford.edu/archives/spr2003/entries/qt-quandog).
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    • Kolmogorov's axioms, and hence Kolmogorovian probability theories, are named after Andrei Nikolaevich Kolmogorov, who first formulated the axiomatic system for classical probability theory (see A. N. Kolmogorov: Grundbegriffe der Wahrscheinlichkeitrechnung; 1933, Berlin, Springer). The theory had in fact existed since the time of Laplace (Théorie Analytique des Probabilités, 1812) and had been worked out by various mathematicians, but in a rather informal way. It is well known that the probability calculus of quantum mechanics is non-classical, in the sense that it does not satisfy Kolmogorov's axioms (A. Wilce: 'Quantum logic and probability theory', in Stanford Encyclopedia of Philosophy, (ed. E. N. Zalta), Spring 2003 edn, plato.stanford.edu/archives/spr2003/entries/qt-quandog).
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    • Yet another possibility is that the non-determinism is ontological, i.e. the universe is intrinsically non-deterministic at bottom. In this case, it can be shown that the mathematical structure necessary to model the situation would be equivalent to the mathematical structure needed to model the situation where the non-determinism arises through lack of knowledge of the context. (For details see D. Aerts: 'Quantum structures, separated physical entities and probability', Foundations of Physics, 1994, 24, 1227-1259.) Thus, ontological non-determinism can also be described in this framework.
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    • note
    • This story has a precedent. The same problem arose in physics in the last century, Classical mechanics could describe situations where the effect of the measurement was negligible, but not situations where the measurement intrinsically influenced the evolution of an entity. This is because it does not provide a way of coping with contextuality (except in the initial conditions or in an ad hoc way, by introducing an additional model of perturbation). Modern classical theories, such as chaos and complexity, though they provide a means of transcending reductionism, still have this limitation.
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    • note
    • In the SCOP formalism, an entity is described using a state space the algebraic structure of which is given by the set of atoms of a complete lattice (this plays the role of the rays of a complex Hilbert space in quantum mechanics). Measurements ate described by Boolean morphisms on the lattice (which play the role of the self-adjoint operators in quantum mechanics).
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    • note
    • An affordance is a possibility offered by the environment. Thus the presence of food affords the possibil-. ity of eating.
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    • For example Bayes's formula for conditional probability is not satisfied
    • For example Bayes's formula for conditional probability is not satisfied.


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.