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That's not true - even if the computer is Turing equivalent, it's not necessarily a Turing machine. https://en.wikipedia.org/wiki/Turing_completeness#Formal_de

by yarg 3y ago

That's not true - even if the computer is Turing equivalent, it's not necessarily a Turing machine. https://en.wikipedia.org/wiki/Turing_completeness#Formal_definitions https://en.wikipedia.org/wiki/Turing_completeness#Formal_def... > Turing equivalence: A Turing-complete system is called Turing-equivalent if every function it can compute is also Turing-computable; i.e., it computes precisely the same class of functions as do Turing machines.

leroy-is-here 3y ago
Our machines _can_ compute any Turing-computable function, except only up to some finite point because we must exist in this reality. Our numbers are infinite, but we do not argue they are not because someone was not able to count up to 999999999999999999999999999!
- yarg 3y ago
  That's not even the point - the Turing machine is a specific abstraction. > Turing machines, first described by Alan Turing in Turing 1936–7, are simple abstract computational devices intended to help investigate the extent and limitations of what can be computed. https://plato.stanford.edu/entries/turing-machine/ https://plato.stanford.edu/entries/turing-machine/ Even if we had infinite memory, our computers would be closer to those of the Von Neumann architecture than to Turing machines. > The Von-Neumann architecture is an architecture for constructing actual computers (which implement what the Turing machine describes theoretically). https://stackoverflow.com/questions/2782014/turing-machine-vs-von-neuman-machine https://stackoverflow.com/questions/2782014/turing-machine-v... This is not simple pedantry - Turing never intended for the machine to be built, it was only ever a device intended to explain computability. The theoretical Turing machine can accept a tape for any definable program, but the architecture cannot possibly run efficiently. It was never intended to.
  - leroy-is-here 3y ago
    The Von Neumann architecture is just a Turing Machine, simply a physical manifestation of one, a physical abstraction. My computer has a “tape” which is 64GB wide because I have 64GB of RAM. If we had infinite memory and infinite symbols (instead of only 2^64), we could build a universal Turing Machine. But that doesn’t mean our physical computers aren’t Turing Machines executing Turing-complete programs that just happen to be in the space of programs executable in a finite time and within the limitations of our current physical realities. I’m not sure who told you that Turing never intended for the machine to be built. He knew that he could not build a machine with infinite tape, as we both know too. But when he built the machine to crack the Enigma Machine, he did this _after_ writing his paper, “On Computable Numbers.” So, he was in effect making a Turing Machine (but he called them a-machines). We literally didn’t have computers before Turing formalized a way to execute them, instruction by instruction, and in detail. Once we had some kind of formal method to do this, physical machines could start being built. Edit: My comments have not shown misunderstanding. There seems to be this consensus that our mathematics here came _after_ our machines. But this is wrong and the implications are tremendous. Our computers we have really are machines which execute other machines. What is the only class of machine that can do that? The Turing Machine. Edit2: I suppose this is an argument of semantics. I didn’t realize. Yes, perhaps our computers are “Turing-equivalent”. I still think the “tape” and “symbol” and all of those things are merely mental variables, which is why I called these things a Form earlier. We built a physical tape, it just took the form of RAM and has much detail that electrical engineers can talk about. We also built symbols, we just called them instructions and placed them into a CPU. All of our physical devices have come from theoretical findings, not vice-versa. https://en.m.wikipedia.org/wiki/The_Treachery_of_Images https://en.m.wikipedia.org/wiki/The_Treachery_of_Images
    - yarg 3y ago
      God damn it. https://xkcd.com/386/ https://xkcd.com/386/ No, it's not a Turing machine - it's Turing equivalent. Turing equivalent, say it with me: Turing equivalent. No, it is not the same damned thing. No, my memory pool is not a fucking tape. If I claimed that a Ryzen CPU is still and Intel machine, I would be wrong (I'd be less wrong than you are, they're a hell of a lot closer than Von Neumann and Turing). There's a whole lot of nuance in this discussion that you are either unwilling or unable to understand. Every comment you've left in this thread has shown some misunderstanding of the topic at hand - you might try listening to what people are saying to you. And no, it's not pure pedantry - the machine architectures serve very different purposes.

by yarg 3y ago

leroy-is-here 3y ago

Our machines _can_ compute any Turing-computable function, except only up to some finite point because we must exist in this reality. Our numbers are infinite, but we do not argue they are not because someone was not able to count up to 999999999999999999999999999!

yarg 3y ago
That's not even the point - the Turing machine is a specific abstraction. > Turing machines, first described by Alan Turing in Turing 1936–7, are simple abstract computational devices intended to help investigate the extent and limitations of what can be computed. https://plato.stanford.edu/entries/turing-machine/ https://plato.stanford.edu/entries/turing-machine/ Even if we had infinite memory, our computers would be closer to those of the Von Neumann architecture than to Turing machines. > The Von-Neumann architecture is an architecture for constructing actual computers (which implement what the Turing machine describes theoretically). https://stackoverflow.com/questions/2782014/turing-machine-vs-von-neuman-machine https://stackoverflow.com/questions/2782014/turing-machine-v... This is not simple pedantry - Turing never intended for the machine to be built, it was only ever a device intended to explain computability. The theoretical Turing machine can accept a tape for any definable program, but the architecture cannot possibly run efficiently. It was never intended to.
- leroy-is-here 3y ago
  The Von Neumann architecture is just a Turing Machine, simply a physical manifestation of one, a physical abstraction. My computer has a “tape” which is 64GB wide because I have 64GB of RAM. If we had infinite memory and infinite symbols (instead of only 2^64), we could build a universal Turing Machine. But that doesn’t mean our physical computers aren’t Turing Machines executing Turing-complete programs that just happen to be in the space of programs executable in a finite time and within the limitations of our current physical realities. I’m not sure who told you that Turing never intended for the machine to be built. He knew that he could not build a machine with infinite tape, as we both know too. But when he built the machine to crack the Enigma Machine, he did this _after_ writing his paper, “On Computable Numbers.” So, he was in effect making a Turing Machine (but he called them a-machines). We literally didn’t have computers before Turing formalized a way to execute them, instruction by instruction, and in detail. Once we had some kind of formal method to do this, physical machines could start being built. Edit: My comments have not shown misunderstanding. There seems to be this consensus that our mathematics here came _after_ our machines. But this is wrong and the implications are tremendous. Our computers we have really are machines which execute other machines. What is the only class of machine that can do that? The Turing Machine. Edit2: I suppose this is an argument of semantics. I didn’t realize. Yes, perhaps our computers are “Turing-equivalent”. I still think the “tape” and “symbol” and all of those things are merely mental variables, which is why I called these things a Form earlier. We built a physical tape, it just took the form of RAM and has much detail that electrical engineers can talk about. We also built symbols, we just called them instructions and placed them into a CPU. All of our physical devices have come from theoretical findings, not vice-versa. https://en.m.wikipedia.org/wiki/The_Treachery_of_Images https://en.m.wikipedia.org/wiki/The_Treachery_of_Images
  - yarg 3y ago
    God damn it. https://xkcd.com/386/ https://xkcd.com/386/ No, it's not a Turing machine - it's Turing equivalent. Turing equivalent, say it with me: Turing equivalent. No, it is not the same damned thing. No, my memory pool is not a fucking tape. If I claimed that a Ryzen CPU is still and Intel machine, I would be wrong (I'd be less wrong than you are, they're a hell of a lot closer than Von Neumann and Turing). There's a whole lot of nuance in this discussion that you are either unwilling or unable to understand. Every comment you've left in this thread has shown some misunderstanding of the topic at hand - you might try listening to what people are saying to you. And no, it's not pure pedantry - the machine architectures serve very different purposes.