On Sat, Jul 20, 2019 at 9:41 AM Philip Thrift <[email protected]> wrote:

*> So where is there a Turing machine with an actual infinite tape?*
>

There are some things that a Turing Machine can not calculate and nothing
else can either, it's been proven that the 1919th Busy Beaver Number can
not be calculated even though it's known that the number exists and to is
finite. Even the 5th Busy Beaver is probably non computable, we only know
the first 4. For a computer to finish a calculation it must halt, so for
every Turing Machine that has ever actually performed a calculation only a
finite amount of tape has been used. If you programed a Turing Machine to
find the 1919th Busy Beaver Number it would indeed use up an infinite
amount of tape, but even then it wouldn't find that number.

John K Clark

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