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My computer is very much a Turing machine since each time it runs out of disk space I can buy more disks. The fact you think a Turing machine has infinite memor

My computer is very much a Turing machine since each time it runs out of disk space I can buy more disks. The fact you think a Turing machine has infinite memory rather than finite but arbitrarily large memory tells me all I need to know about the sorry state of your theoretical education.

rrobukef 4y ago
A Turing machine is a mathematical concept. It has, by definition, infinite memory. A computer is just a real machine that can do similar things as a Linear Bounded Automaton, a Turing machine's little brother who'll never do quite the same things.
- thrown123098 4y ago
  Wrong: https://en.wikipedia.org/wiki/Arbitrarily_large https://en.wikipedia.org/wiki/Arbitrarily_large
  - rrobukef 4y ago
    There is a physical limit to the number of disks you can add to your CPU. There is a physical limit to the memory you can address in your CPU (48-bits). It is not arbitrarily large. Also wrong for Turing Machines, it really is infinite. That's a big difference to arbitrarily large. The halting problem is undecidable for TM's but not for arbitrarily large (you'll need precise definitions though).
    - thrown123098 4y ago
      It is left as an exercise to the reader to find a natural number which isn't arbitrarily large but calculable.
      - rrobukef 3y ago
        The tape size needed for a Turing machine is incalculable. Here's a reference to a proof: https://scottaaronson.blog/?p=2725 https://scottaaronson.blog/?p=2725. The machine with 7918-states, Z, stops (well, Z cannot be proven to run infinitly long) iff. ZFC is consistent. For this it needs a finite amount of space but we cannot calculate how much. If we could calculate an upper bound we've proven ZFC is consistent.
        thrown123098 3y ago
        Yes which is why the size if strictly finite but arbitrarily large.
dgb23 4y ago
How much does an infinite amount of disk space cost?
- thrown123098 4y ago
  [flagged]
- oriolid 4y ago
  Nothing, if it's your users who buy it instead of you.
bigbillheck 4y ago
> each time it runs out of disk space I can buy more disks. There's only so many that you can buy.

rrobukef 4y ago

A Turing machine is a mathematical concept. It has, by definition, infinite memory. A computer is just a real machine that can do similar things as a Linear Bounded Automaton, a Turing machine's little brother who'll never do quite the same things.

thrown123098 4y ago
Wrong: https://en.wikipedia.org/wiki/Arbitrarily_large https://en.wikipedia.org/wiki/Arbitrarily_large
- rrobukef 4y ago
  There is a physical limit to the number of disks you can add to your CPU. There is a physical limit to the memory you can address in your CPU (48-bits). It is not arbitrarily large. Also wrong for Turing Machines, it really is infinite. That's a big difference to arbitrarily large. The halting problem is undecidable for TM's but not for arbitrarily large (you'll need precise definitions though).
  - thrown123098 4y ago
    It is left as an exercise to the reader to find a natural number which isn't arbitrarily large but calculable.
    - rrobukef 3y ago
      The tape size needed for a Turing machine is incalculable. Here's a reference to a proof: https://scottaaronson.blog/?p=2725 https://scottaaronson.blog/?p=2725. The machine with 7918-states, Z, stops (well, Z cannot be proven to run infinitly long) iff. ZFC is consistent. For this it needs a finite amount of space but we cannot calculate how much. If we could calculate an upper bound we've proven ZFC is consistent.
      - thrown123098 3y ago
        Yes which is why the size if strictly finite but arbitrarily large.

dgb23 4y ago

How much does an infinite amount of disk space cost?

thrown123098 4y ago
[flagged]
oriolid 4y ago
Nothing, if it's your users who buy it instead of you.

bigbillheck 4y ago

> each time it runs out of disk space I can buy more disks. There's only so many that you can buy.