Re:“Computer science is not about computers”
by antonvs on Sunday May 30, 2021 @09:10PM
(#27338803)
> I don't think Turing machines have any lesser status (it's literally equivalent to lambda calculus, after all!)
"Equivalence" has a specific meaning here, though. The term "Turing tarpit" was invented to point out the limits of that equivalence, and any attempts to define computations for Turing machines quickly run into that.
The sense in which I consider Turing machines to be "rather unmathematical" is closely related to this. You can write useful mathematical proofs in lambda calculus - as I've pointed out elsewhere, there are automated proof assistants based on this fact. There's no such equivalent for Turing machines. Theoretically, there could be, due to Turing equivalence, but in practice, no-one wants to exploit that.
Given one formalism that has actively been used for such mathematical purposes, and another that has been actively avoided, I call the latter rather unmathematical by comparison to the former.
People can quibble with my word choice, but it's describing a real, measurable phenomenon, the effects of which have played out predictably over the last 70 years.
"Equivalence" has a specific meaning here, though. The term "Turing tarpit" was invented to point out the limits of that equivalence, and any attempts to define computations for Turing machines quickly run into that.
The sense in which I consider Turing machines to be "rather unmathematical" is closely related to this. You can write useful mathematical proofs in lambda calculus - as I've pointed out elsewhere, there are automated proof assistants based on this fact. There's no such equivalent for Turing machines. Theoretically, there could be, due to Turing equivalence, but in practice, no-one wants to exploit that.
Given one formalism that has actively been used for such mathematical purposes, and another that has been actively avoided, I call the latter rather unmathematical by comparison to the former.
People can quibble with my word choice, but it's describing a real, measurable phenomenon, the effects of which have played out predictably over the last 70 years.