Self-referential

The procedure illustrated here, besides containing only trivial technical calculations, lacks important features that are required in production programs. Extensive error checking and recovery must be performed. The procedure must detect the occurrence of a self-referential system of formulas, which would result in attempting endless recursive calls. Access to multiple raw material and formula databases adds power to the program, but must be implemented by complex code to allow flexible control of that access. The structural and input/output statements to support these features may greatly exceed the number of statements that perform modelling calculations. 

The notion of imparting its own rules draws an equivalence between biological autonomy and auto referentiality (Varela et al, 1991 Varela, 2000). In turn, auto-referentiality is related to the concept of operational closure. This is a process of circular and reflexive interdependency, whose primary effect is its own production. Operational closure must not be viewed as a lack of contact with the environment -as already stressed, any living system must be seen as an open system. The relation between autopoiesis, autonomy, and self referentiality is treated in the specialized literature, see for example Marks-Tarlow et al. (2001) and Weber (2002). 

This section is devoted to biological order, organization, and evolution. We have already seen in Appendix F that constructive integration of quantum and thermal correlations under appropriate conditions lead to a so-called CDS, i.e., an optimal spatiotemporal structure formed by the precise relations between time, size, and temperature scales. CDS suggests microscopic selforganization including Godel-like self-referential traits. 

E.J. Brandas, Microscopic Self-Organization and Self-Referential Systems. A Progress Report. Int. J. Quant. Chem. 109 (2009) 3500. 

This defines the levels within the CNS. The relative isolation between levels is maintained by circular operations which stabilize the structure at each level. For each level there are many entities organized at that level (for example, many neurons) and such entities prefer interaction with other entities at the same level. A chemical reaction, for example, in the retina of the eye is almost always interpreted as a signal about the outside world, not as a signal about neurochemistry. Thus isolation means that operations at any given level are primarily self-referencing (i.e., they take their own states as inputs for further processing). Coupling refers to exceptions to this "self-referential closure. ... 

Gusnard DA, Akbudak E, Shulman GL, Raichle ME. 2001. Medial prefrontal cortex and self-referential mental activity Relation to a default mode of brain function. Proc Natl Acad Sci USA 98 4259-4264. 

M. B. Sweatman (2005) Self-referential Monte Carlo method for calculating the free energy of crystalline solids. Phys. Rev. E 72, 016711... 

This is a functional equation for g(,v) and the universal scale factor a. It is self-referential g(x) is defined in terms of itself. 

For example, ZINC is a free database of small molecules for docking that are commercially available (http //blaster. docking.org/zinc/). ZINC is a self-referential acronym... 

It is well established that molecular structure and thermochemistry are inseparably related on both the research and pedagogical levels of our discipline. In self-referential documentation, for Volume 3 in this series [7] we wrote a chapter... 

Even more simple constructs such as Art is art, or A dog is a dog, or A dog is not a dog might be considered primitive examples of recursive definitions. Sometimes the term self-referential is used when referring to these constructs. 

As discussed earlier, the present interpretation of the truth table can be obtained from conventional representations with the use of a non-positive definite metric A All = —A22=1 Ai2=Ai2=0. In this picture, we can use conventional brake nomenclature, while for another selection of A, leading e.g. to a complex symmetric choice, it would require complex symmetric realisations. In both cases, the formulation is biorthogonal. With this realisation, we can make an identification between Eqs. (1.63) and (1.66), making the replacement q = /c(r), where q is related to the probability function/operator of the simple proposition Q = P. Hence, we realise a probabilistic origin combined with the nonclassical, self-referential character of gravitational interactions. Note also the analogy between the formulations, i.e. that the result of a classical measurement, i.e. the truth or... 

K6mer, E. and G. Matsumoto, 2002, Cortical architecture and self-referential control for brain-like compnta-tion, IEEE Eng. Med. Biol. Mag. 21(5) 121-133 (September/October). 

The fundamental difficulty with the concept of ALARP is that the term is inherently circular and self-referential. For example, the phrase best available technology used in the list above can be defined as that level of technology which reduces risk to an acceptable level— in other words to the ALARP level. Terms such as best operations and high standard are equally questionbegging. 

Other definitions of culture, such as Culture is the way we do things around here, may be true, but they are basically circular and self-referential. Such definitions offer httle practical help at eight o clock on Monday morning. 

Lack of knowledge to do with safe operating limits leads to the problem of circularity in which hazards are defined self-referentially. For example, a team may be discussing the guide phrase, High Pressure. Implicit in the discussion is often the following train of thought ... 

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