Why there is no such discipline as hypercomputation
Section snippets
Hypercomputation as practice
The great day has arrived! The world’s first working hypercomputer is being unveiled. Here comes the output – guaranteed by the engineers to be a non-Turing-computable infinite sequence of natural numbers:But wait! No matter how long this goes on, we will see only a finite number of these outputs. Moreover any such finite sequence of natural numbers is the initial part of both computable and non-computable infinite sequences (in fact, infinitely many
Hypercomputation as theory
While one may justly be skeptical regarding practice, non-computability (in the Church–Turing sense of course) is an inviting subject for theoretical study. Although this may be news to some of the promoters of “hypercomputation”, this has been an extremely active field of research beginning with the work of Post and Kleene in the 1940s. In particular Post’s Theorem makes it possible to relate just how non-computable a particular problem is to its logical complexity. For example if membership
Computers and computability
Although real-world computation is finite and computability theory deals with the infinite, the latter has had an important influence on the former. It was Turing’s work that has played the key role. His universal machine and the Church-Turing explication of the notion of algorithmic process together suggested the possibility of an all-purpose computer that could execute any algorithm subject only to constraints of space and time. Furthermore, as I have remarked elsewhere:
Before Turing the
The hypercomputation community
Whatever one may think of the scientific value of the efforts of the founders of hypercomputationalism, there is no question that as promotion it has been a brilliant success. Ignoring what had been accomplished in the study of non-computability, and turning the negative into a positive by replacing the “non” by “hyper” was surely an inspired move. Examining the table of contents of this special issue suggests that although a number of the articles have little or no connection to the project of
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Cited by (56)
Nature inspired algorithms with randomized hypercomputational perspective
2022, Information SciencesCitation Excerpt :Quantum hypercomputation [21–23] etc. That said, it is worth pointing out that the role model of hypercomputation is Turing’s O-machines (O for Oracle) and the concept of hypercomputation has never been proved or refuted completely, although there are various arguments in favor of and against it [12–26]. The situation of this paper provides an excellent opportunity to empirically have some evidences against randomized hypercomputation.
Machines that perform measurements
2022, Theoretical Computer ScienceCitation Excerpt :Some arguments have been raised against the possibility of actually achieving hypercomputation. E.g. Martin Davis remarks the need for non-computable properties, a priori, to be able to “program” a hyper-machine, and the fact that no finite amount of data will be sufficient to distinguish a computable from a non-computable sequence (see [26] and [27]). Regarding machines that rely on an analogue computation to surpass the Turing barrier, it is argued in [23] that the models of hypercomputation that draw from the notions of infinite or continuous “are not materially realizable and so cannot constitute new forms of effective calculability”.
East-West paths to unconventional computing
2017, Progress in Biophysics and Molecular BiologyCitation Excerpt :However, in the controversial supposition that real numbers exist, no one knows how to engineer such parameters into a dynamic system. It is certainly impossible (see (Davis, 2006a; Davis, 2006b)). Good bye to real number based programming!
“Viral” Turing Machines, computation from noise and combinatorial hierarchies
2017, Chaos, Solitons and FractalsCitation Excerpt :Wegner has even proposed that the ICP represents an example of “Hypercomputation” or “Super-Turing Computation” that moves beyond the confines of the so called “Turing Tarpit” or the associated but as yet formally unproved “Church-Turing Thesis” [13] claiming that in general, ICP contains certain non-algorithmic aspects. This particular issue proved quite thorny and it soon became a matter of fierce debate that strongly polarized the computer science community as can be seen in Davis [14,15] as well as in the more recent rebuttal in [16]. Recently, Dodig-Crnkovic suggested an alternate epistemological interpretation of information semantics as ICP in [17], associated with info-computationalism [18].
An analogue-digital church-turing thesis
2014, International Journal of Foundations of Computer ScienceInteraction Grammars: Beyond the Imitation Game
2023, Choreomata: Performance and Performativity after AI