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Nobody claims that Turing machines in particular are well-suited to the task. What we claim is something more open-ended: Turing-complete languages can simulate

Nobody claims that Turing machines in particular are well-suited to the task. What we claim is something more open-ended: Turing-complete languages can simulate each other given a universal encoding (a program we typically call an "emulator") and the simulation is only polynomially slower and larger. To the details: We don't want just one tape on the Turing machine. It's fine but slow, like using unary Church numerals instead of binary Cantor numerals. We usually assume at least two tapes. Similarly, we often ignore tapes and use a random-access memory instead. Edit: I guess that this is how we're talking today? From the article: > It is common to summarize CCTM through the slogan “the mind is a Turing machine”. This slogan is also somewhat misleading, because no one regards Turing’s precise formalism as a plausible model of mental activity. The formalism seems too restrictive in several ways. The article then lists senses, finite memory, concurrency, and determinism as four ways in which the brain might differ from idealized Turing machines.

joe_the_user 7y ago
Nobody claims that Turing machines in particular are well-suited to the task. What we claim is something more open-ended: Turing-complete languages can simulate each other given a universal encoding (a program we typically call an "emulator") and the simulation is only polynomially slower and larger. Well, that's the Church-Turing Thesis, which most people accept but isn't being discussed by me or the OP - the topic being "theories of the mind", I think.
it 7y ago
Finite memory just means a limited subset of what a Turing machine can do. Concurrency doesn't make Turing computable processes capable of anything beyond what they can already do. At best it buys them speed, maybe some expressiveness for the programmer, and bugs. Nondeterminism is useful for some algorithms but it also doesn't make it possible for Turing computable processes to go beyond Turing computability. See for example https://arxiv.org/pdf/cs/0401019.pdf https://arxiv.org/pdf/cs/0401019.pdf. The most interesting item in that list would be the senses of organisms, as some of those might indeed involve processes that are not computable. Also, some aspects of the brain's activity may not be computable. See Roger Penrose's books for details, such as p. 377 of Shadows of the Mind (a section about possible noncomputability in some physical processes).

joe_the_user 7y ago

it 7y ago

Finite memory just means a limited subset of what a Turing machine can do. Concurrency doesn't make Turing computable processes capable of anything beyond what they can already do. At best it buys them speed, maybe some expressiveness for the programmer, and bugs. Nondeterminism is useful for some algorithms but it also doesn't make it possible for Turing computable processes to go beyond Turing computability. See for example https://arxiv.org/pdf/cs/0401019.pdf https://arxiv.org/pdf/cs/0401019.pdf. The most interesting item in that list would be the senses of organisms, as some of those might indeed involve processes that are not computable. Also, some aspects of the brain's activity may not be computable. See Roger Penrose's books for details, such as p. 377 of Shadows of the Mind (a section about possible noncomputability in some physical processes).