Problem Theory (original) (raw)
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On Turing Completeness, or Why We Are So Many
Why are we so many? Or, in other words, Why is our species so successful? The ultimate cause of our success as species is that we, Homo sapiens, are the first and the only Turing complete species. Turing completeness is the capacity of some hardware to compute by software whatever hardware can compute. To reach the answer, I propose to see evolution and computing from the problem solving point of view. Then, solving more problems is evolutionarily better, computing is for solving problems, and software is much cheaper than hardware, resulting that Turing completeness is evolutionarily disruptive. This conclusion, together with the fact that we are the only Turing complete species, is the reason that explains why we are so many. Most of our unique cognitive characteristics as humans can be derived from being Turing complete, as for example our complete language and our problem solving creativity.
Turing and the fragility and insubstantiality of evolutionary explanations
As is well known, Alan Turing drew a line, embodied in the "Turing test," between intellectual and physical abilities, and hence between cognitive and natural sciences. Less familiarly, he proposed that one way to produce a "passer" would be to educate a "child machine," equating the experimenter's improvements in the initial structure of the child machine with genetic mutations, while supposing that the experimenter might achieve improvements more expeditiously than natural selection. On the other hand, in his foundational "On the chemical basis of morphogenesis, " Turing insisted that biological explanation clearly confine itself to purely physical and chemical means, eschewing vitalist and teleological talk entirely and hewing to D'Arcy Thompson's line that "evolutionary `explanations, "' are historical and narrative in character, employing the same intentional and teleological vocabulary we use in doing human history, and hence, while perhaps on occasion of heuristic value, are not part of biology as a natural science. To apply Turing's program to recent issues, the attempt to give foundations to the social and cognitive sciences in the "real science" of evolutionary biology (as opposed to Turing's biology) is neither to give foundations, nor to achieve the unification of the social/cognitive sciences and the natural sciences.
Turing and the Development of Computational Complexity
2011
Turing's beautiful capture of the concept of computability by the "Turing machine" linked computability to a device with explicit steps of operations and use of resources. This invention led in a most natural way to build the foundations for computational complexity.
Philosophia: International Journal of Philosophy (2014) 15(1): 50-62
Due to his significant role in the development of computer technology and the discipline of artificial intelligence, Alan Turing has supposedly subscribed to the theory of mind that has been greatly inspired by the power of the said technology which has ev entually become the dominant framework for current researches in artificial intelligence and cognitive science, namely, computationalism or the computational theory of mind. In this essay, I challenge this supposition. In particular, I will try to show tha t there is no evidence in Turing's two seminal works that supports such a supposition. His 1936 paper is all about the notion of computation or computability as it applies to mathematical functions and not to the nature or workings of intelligence. On the other hand, while his 1950 work is about intelligence, it is, however, particularly concerned with the problem of whether intelligence can be attributed to computing machines and not of whether computationality can be attributed to human intelligence or to intelligence in general.
Mental Experience and the Turing Test: This Double Face is the Face of Mathematics
2012
We seem to be on the threshold of understanding the physiological basis for learning and for memory storage. But how would knowledge of events on the molecular and cellular level relate to human thought? Is complex mental behavior a large system property of the enormous numbers of units that are the brain? How is it that consciousness arises as a property of a very complex physical system? Undoubtedly, these questions are fundamental for a theory of the mind. On the other hand, there are questions of basic importance, pioneered by Turing, for his theory of the "human computer," that is, discrete state machines that "imitate" perfectly the mental processes achievable by his "human computer"; we will refer to it, although the name is only partially true to his vision, as his theory of "computational intelligence." Finding even a level of commonality to discuss both a theory of the mind with a theory of computational intelligence has been one of the grand challenges for mathematical, computational and physical sciences. The large volume of literature, following Turing's seminal work, about the computer and the brain and involving some of the greatest scientists of all time is a testimony to his genius. In this paper we discuss, in the context of the Turing test, recent developments in physics, computer science, and molecular biology at the confluence of the above two theories, inspired by two seminal questions asked by Turing. First, about the physical not reducible to computation: "Are there components of the brain mechanism not reducible to computation?" or more specifically, "Is the physical space-time of quantum mechanical process, with its so called Heisenberg uncertainty principle, compatible with a [Turing] machine model?" Second, about computing time: "[in the Turing test] To my mind this time factor is the one question which will involve all the real technical difficulty." We relate the above questions to our work, respectively, on superconductivity and quantum mechanics, and the Ising model and the proof of its computational intractability (NP-completeness) in every 3D model, and share lessons learned to discourage, under high and long-term frustration of failure, the retreat under the cover of the positivist philosophy or other evasions. Inspired by von Neumann, we relate Turing's questions and his test difficulties to von Neumann's thesis about the "peculiar duplicity" of mathematics with respect to the empirical sciences. As von Neumann put
Turing's Approaches to Computability, Mathematical Reasoning and Intelligence
2013
In this paper a distinction is made between Turing's approach to computability, on the one hand, and his approach to mathematical reasoning and intelligence, on the other hand. Unlike Church's approach to computability, which is top-down being based on the axiomatic method, Turing's approach to computability is bottom-up, being based on an analysis of the actions of a human computer. It is argued that, for this reason, Turing's approach to computability is convincing. On the other hand, his approach to mathematical reasoning and intelligence is not equally convincing, because it is based on the assumption that intelligent processes are basically mechanical processes, which however from time to time may require some decision by an external operator, based on intuition. This contrasts with the fact that intelligent processes can be better accounted for in rational terms, specifically, in terms of non-deductive inferences, rather than in term of inscrutable intuition.
The Turing Machine as a cognitive model of human computation
"Classical computationalism considers the Turing Machine to be a psychologically implausible model of human computation. In this paper, I will first elaborate on Andrew Wells' thesis that the claim of psychological implausibility derives from a wrong interpretation of the TM as originally conceived by Turing. Then, I will show how Turing's original interpretation of the TM could be useful to construct cognitive models of simple phenomena of human computation, such as counting using our fingers or performing arithmetical operations using paper and pencil."
Alan Turing and the “Hard” and “Easy” Problem of Cognition: Doing and Feeling
The" easy" problem of cognitive science is explaining how and why we can do what we can do. The" hard" problem is explaining how and why we feel. Turing's methodology for cognitive science (the Turing Test) is based on doing: Design a model that can do anything a human can do, indistinguishably from a human, to a human, and you have explained cognition. Searle has shown that the successful model cannot be solely computational.
Alan Turing and the Mathematical Objection
Minds and Machines, 2003
This paper concerns Alan Turing's ideas about machines, mathematical methods of proof, and intelligence. By the late 1930s, Kurt Gödel and other logicians, including Turing himself, had shown that no finite set of rules could be used to generate all true mathematical statements. Yet according to Turing, there was no upper bound to the number of mathematical truths provable by intelligent human beings, for they could invent new rules and methods of proof. So, the output of a human mathematician, for Turing, was not a computable sequence (i.e., one that could be generated by a Turing machine). Since computers only contained a finite number of instructions (or programs), one might argue, they could not reproduce human intelligence. Turing called this the "mathematical objection" to his view that machines can think. Logico-mathematical reasons, stemming from his own work, helped to convince Turing that it should be possible to reproduce human intelligence, and eventually compete with it, by developing the appropriate kind of digital computer. He felt it should be possible to program a computer so that it could learn or discover new rules, overcoming the limitations imposed by the incompleteness and undecidability results in the same way that human mathematicians presumably do.