Non-Abelian Theories and Spacetimes Ontology--论文代写范文精选

51Due论文代写网精选essay代写范文：“Non-Abelian Theories and Spacetimes Ontology”  任何综合分类本体理论，在人类思维和本体论层面，我们的观点是,模型由范畴论和高维代数对创造更高的潜在应用科学,从一个描述性的意义上说,能够映射富有想象力的主体性，超越传统的复杂关系。其中一个可能强烈考虑广义概念，我们的目标是进一步讨论先决条件，对所有严格的数学定义进行说明。有趣的是,在最近文献中，阿贝耳分类本体(ACO)也获得一些新的含义和实际效用。

结构相关的量子理论的一个例子是,量子可观测的角度不同。此外,微观量子的物理现实似乎没有受到阿贝尔的影响，自然性条件的数学理论也存在差异。下面的essay代写范文进行阐述。

Abstract
Any comprehensive Categorical Ontology theory is a fortiori non-Abelian, and thus recursively non-computable, on account of both the quantum level (which is generally accepted as being non-commutative), and the top ontological level of the human mind– which also operates in a non-commutative manner, albeit with a different, multi-valued logic than Quantum Logic. To sum it up, the operating/operational logics at both the top and the fundamental levels are non-commutative (the ‘invisible’ actor (s) who– behind the visible scene– make(s) both the action and play possible!). At the fundamental level, spacetime events occur according to a quantum logic (QL), or Q-logic, whereas at the top level of human consciousness, a different, non-commutative Higher Dimensional Logic Algebra prevails akin to the many-valued (ÃLukasiewicz - Moisil, or LM) logics of genetic networks which were shown previously to exhibit non-linear, and also non-commutative/non-computable, biodynamics (Baianu, 1977, 1987; Baianu, Brown, Georgescu and Glazebrook, 2006). 

Our viewpoint is that models constructed from category theory and higher dimensional algebra have potential applications towards creating a higher science of analogies which, in a descriptive sense, is capable of mapping imaginative subjectivity beyond conventional relations of complex systems. Of these, one may strongly consider a generalized chronoidal–topos notion that transcends the concepts of spatial–temporal geometry by incorporating non-commutative multi–valued logic. Current trends in the fundamentally new areas of quantum– gravity theories appear to endorse taking such a direction. 

We aim further to discuss some prerequisite algebraic–topological and categorical ontology tools for this endeavor, again relegating all rigorous mathematical definitions to the Brown, Glazebrook and Baianu (2007). It is interesting that Abelian categorical ontology (ACO) is also acquiring several new meanings and practical usefulness in the recent literature related to computer-aided (ontic/ontologic) classification, as in the case of: neural network categorical ontology (Baianu, 1972; Ehresmann and Vanbremeersch, 1987, Healy, 2006), Genetic Ontology, Biological Ontology, Environmental representations by categories and functors (Levich and Solovy’ov., 1999), or ultra-complex societies.

An example of a non-commutative structure relevant to Quantum Theory is that of the Clifford algebra of quantum observable operators (Dirac, 1962; see also Plymen and Robinson, 1994). Yet another- more recent and popularexample in the same QT context is that of C ∗–algebras of (quantum) Hilbert spaces. Furthermore, the microscopic, or quantum, ‘first’ level of physical reality does not appear to be subject to the categorical naturality conditions of Abelian TC-FNT– the ‘standard’ mathematical theory of categories (functors and natural transformations). It would seem therefore that the commutative hierarchy discussed above is not sufficient for the purpose of a General, Categorical Ontology which considers all items, at all levels of reality, including those on the ‘first’, quantum level, which is non–commutative. 

On the other hand, the mathematical, Non-Abelian Algebraic Topology (Brown, Higgins and Sivera, 2007), the Non-Abelian Quantum Algebraic Topology (NA-QAT; Baianu et al., 2005), and the physical, Non-Abelian Gauge theories (NAGT) may provide the ingredients for a proper foundation for Non-Abelian, hierarchical multi-level theories of a super-complex system dynamics in a General Categorical Ontology (GCO). Furthermore, it was recently pointed out (Baianu et al., 2005, 2006) that the current and future development of both NA-QAT and of a quantum-based Complex Systems Biology, a fortiori, involve non-commutative, many-valued logics of quantum events, such as a modified ÃLukasiewicz–Moisil (LMQ) logic algebra (Baianu, Brown, Georgescu and Glazebrook, 2006), complete with a fully-developed, novel probability measure theory grounded in the LM-logic algebra (Georgescu, 2006b). Such recent developments point towards a paradigm shift in Categorical Ontology and to its extension to more general, Non-Abelian theories, well beyond the bounds of commutative structures/spaces and also free from the logical restrictions and limitations imposed by set theory.

As defined in Baianu and Poli (2008), a system is a dynamical (whole) entity able to maintain its working conditions; the system definition is here spelt out in detail by the following, general definition, D1. D1. A simple system is in general a bounded, but not necessarily closed, entity– here represented as a category of stable, interacting components with inputs and outputs from the system’s environment, or as a supercategory for a complex system consisting of subsystems, or components, with internal boundaries among such subsystems. As proposed by Baianu and Poli (2008) in order to define a system one therefore needs specify the following data: (1) components or subsystems, (2) mutual interactions or links; (3) a separation of the selected system by some boundary which distinguishes the system from its environment, without 138 necessarily ‘closing’ the system to material exchange with its environment; (4) the specification of the system’s environment; (5a) the specification of the system’s categorical structure and dynamics; (5b) a supercategory will be required only when either the components or subsystems need be themselves considered as represented by a category , i.e. the system is in fact a supersystem of (sub)systems, as it is the case of all emergent super-complex systems or organisms.

As discussed by Baianu and Poli (2008), “the most general and fundamental property of a system is the inter-dependence of parts/components/sub-systems or variables.” ; inter-dependence is the presence of a certain organizational order in the relationship among the components or subsystems which make up the system. It can be shown that such organizational order must either result in a stable attractor or else it should occupy a stable spacetime domain, which is generally expressed in closed systems by the concept of equilibrium. On the other hand, in non-equilibrium, open systems, one cannot have a static but only a dynamic self-maintenance in a ’state-space region’ of the open system – which cannot degenerate to either an equilibrium state or a single attractor spacetime region. 

Thus, non-equilibrium, open systems that are capable of selfmaintenance (seen as a form of autopoiesis) will also be generic, or structurallystable: their arbitrary, small perturbation from a homeostatic maintenance regime does not result either in completely chaotic dynamics with a single attractor or the loss of their stability. It may however involve an ordered process of changes - a process that follows a determinate pattern rather than random variation relative to the starting point. Systems are usually conceived as ‘objects’, or things, rather than processes even though at the core of their definition there are dynamic laws of evolution. Spencer (1898) championed such evolutionary ideas/laws/principles not only in the biosphere but also in psychology and human societies. Furthermore, the usual meaning of ‘dynamic systems’ is associated with their treatments by a ‘system’ (array) of differential equations (either exact, ordinary or partial); note also that the latter case also includes ‘complex’ chaotic systems whose solutions cannot be obtained by recursive computation, for example with a digital computer or supercomputer. Boundaries are especially relevant to closed systems, although they also exist in many open systems. 

According to Poli (2008): “they serve to distinguish what is internal to the system from what is external to it”, thus defining the fixed, overall structural topology of a closed system. By virtue of possessing boundaries, “a whole (entity) is something on the basis of which there is an interior and an exterior...which enables a difference to be established between the whole closed system and environment.” (cf. Baianu and Poli, 2008). As proposed by Baianu and Poli (2008), an essential feature of boundaries in open systems is that they can be crossed by matter. The boundaries of closed systems, however, cannot be crossed by molecules or larger particles. On the contrary, a horizon is something that one cannot reach. 

In other words, a horizon is not a boundary. This difference between horizon and boundary appears to be useful in distinguishing between systems and their environment. Organisms, in general, are open systems with variable topology that incorporate both the valve and the selectively permeable membrane boundaries –albeit much more sophisticated and dynamic than the simple/fixed topology cellophane membrane–in order to maintain their stability and also control their internal structural order, or low microscopic entropy. The formal definition of this important concept of ‘variable topology’ was introduced in our recent paper (Baianu et al 2007a) in the context of the spacetime evolution of organisms, populations and species. Interestingly, for many multi-cellular organisms, including man, the overall morphological symmetry (but not the internal organizational topology) is retained from the beginning of ontogenetic development is externally bilateral–just one plane of mirror symmetry– from Planaria to humans. The presence of the head-to-tail asymmetry introduces increasingly marked differences among the various areas of the head, middle, or tail regions as the organism develops. 

There is however in man– as in other mammals– an internal bilateral asymmetry (e.g., only one heart on the left side), as well as a front to back, both external and internal anatomical asymmetry. In the case of the brain, however, only humans seem to have a significant bilateral, internal asymmetry between the two brain hemispheres that interestingly relates to the speech-related ‘centers’ (located in the majority of humans in the left brain hemisphere). The multiplicity of boundaries, and the dynamics that derive from it, generate interesting phenomena. Boundaries tend to reinforce each other, as in the case of dissipative structures formed through coupled chemical, chaotic reactions. According to Poli (2008), ”this somewhat astonishing regularity of nature has not been sufficiently emphasized in perception philosophy.”（essay代写)

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