A Note on the Reality of Incomputable Real Numbers and Its Systemic Significance

Minati, Gianfranco

doi:10.3390/systems9020044

Cited by 4 publications

(1 citation statement)

References 62 publications

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“…Here, we term this incomputability as non-Turing computability. Furthermore, there are forms of non-explicit computability, that is non-symbolic computability, such as for artificial neural networks (ANN) and cellular automata (CA) performing emergent computation [19] and dealing with the reality of incomputable real numbers [20]. We consider here the incomputability of imaginary numbers as theoretical incomputability, for which no resolutive procedure is conceivable/admissible, much less a Turing machine.…”

Section: Incomputabilitymentioning

confidence: 99%

The Vacuum as Imaginary Space. The Unreasonable Effectiveness of Complex Numbers

Minati¹

2022

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The background to the article is the classic and quantum understandings of the vacuum and the use of imaginary numbers in quantum models. The purpose of the article is to outline the possible understanding of the vacuum as imaginary space always coupled with the real space in the complex space of complex numbers. This understanding relates to the duality real-potential, collapsed–collapsible, and superimpositions of waves-phenomena as in quantum mechanics. The incomputability of the imaginary parts may represent the physical meaning of the permanent potential pending nature of the vacuum. The presence of imaginary numbers in models may be intended as warranty that it is not possible to compute definitive results, but it is possible to have pending multiple equivalences and superimpositions as in quantum physics and emergent collective processes in complexity. We consider how much the complexity (i.e., the study of emergence and chaos) may be considered related to and represented by complex numbers (i.e., properties of their dual variables and their collapsibility in real numbers). The usage of imaginary numbers may also be intended as the expression or manifestation of something we do not understand yet, as it was for the indemonstrability of the fifth Euclidian postulate and the unavailability of a distribution law for prime numbers. We conclude that a new global understanding is necessary and capable of explaining what we understand as the unreasonable effectiveness of complex numbers.

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Section: Incomputabilitymentioning

confidence: 99%

The Vacuum as Imaginary Space. The Unreasonable Effectiveness of Complex Numbers

Minati¹

2022

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The Role of the Excluded

Minati¹

2022

Philosophies

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We consider the peculiarity of unique events, such as those of a natural, evolutionary, and social nature. In particular, we consider unique social events that have had either the claim or the vocation of being salvific for humanity, such as the introduction over time of the Torah, Hinduism, Buddhism, Christianity, and Islam. We question how the claimed, general salvific vocation contrasts, or is inconsistent with, the non-retroactive temporality and locality of such events, which could not have happened otherwise. This undeclared and philosophically unsolved inconsistency then reappears in subsequent cultural contradictions and inadequacies, political and social allowances such as, for instance, homo-centrism and a pathological relation with Nature. In the case of Christianity, this inconsistency is represented by the painting reproduced in the article, a work in which the excluded humans and other living beings are represented as astonished by the occurrence in this moment, and in such an unnatural context. Furthermore, we consider the original understanding as related to concepts of classical physics, or of such concepts naively adopted within the texts considered sacred. However, in some religions, such as Christianity, the inconsistency is theologically solved. We stress the need to update the ancient original elementary, naïve, pre-classic philosophical and conceptual frameworks used so that these alleged inconsistencies and contradictions may be not only theologically solved, but also conceptually solved in more complex understandings of the world, for example, considering relativistic time, long-range interdependence, quantum entanglement, and theories of the universe. Without this update, the unique saving events can affect only religiously, that is, optionally, on the scientific and philosophical conceptions used. Without this adjustment, homo-centrist illusion and egoism prevail as the natural, linear consequential attitude without raising these questions. It rather assumes that the intervention is for involved human beings, and moreover for those who have had and are lucky enough to receive and practice it, ignoring the enormous inconsistency within the message itself, and its presumed general and available salvific nature. This requires theological, philosophical, and scientific interdisciplinarity. The theme concerns inconsistencies within and superficiality of the narratives and their treatment of the unique, salvific events, without any reference to possible general and retroactive effects of how these events are represented in the painting. We conclude that the subject should be debated by taking into account contemporary understandings, such as relativistic space and time, quantum physics, and of the universe, with new philosophical and anthropological approaches. This should be a matter of responsible philosophical and theological interdisciplinary debate involving science, suitable to establish new understandings.

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Systems, Complex Systems, and Intelligence: an Educational Overview

Minati¹

2022

WSEAS TRANSACTIONS ON ADVANCES in ENGINEERING EDUCATION

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This contribution examines, for didactic purposes, the peculiarities of systems that have the ability to acquire, maintain and deactivate properties that cannot be deduced from those of their components. We evaluate complex systems that can acquire, lose, recover, vary the predominance of property sequences, characterized by their predominant coherence and variability, through the processes of self-organization and emergence, when coherence replaces organization. We consider correspondingly systemic epistemology as opposed to the classical analytic approach and to forms of reductionism. We outline aspects of the science of complexity such as coherence, incompleteness, quasiness and issues related to its modeling. We list and consider properties and types of complex systems. Then we are dealing with forms of correspondence that concern the original conception of intelligence of primitive artificial intelligence, which was substantially based on the high ability to manipulate symbols, and of those of a complex nature that consider emergent processes, such as inference, the learning, reasoning and memory. Finally, the recognition and acquisition of forms of intelligence in nature is explored, with particular reference to its emerging systemic processes.

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A Note on the Reality of Incomputable Real Numbers and Its Systemic Significance

Cited by 4 publications

References 62 publications

The Vacuum as Imaginary Space. The Unreasonable Effectiveness of Complex Numbers

The Vacuum as Imaginary Space. The Unreasonable Effectiveness of Complex Numbers

The Role of the Excluded

Systems, Complex Systems, and Intelligence: an Educational Overview

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