🚀 go-pugleaf

boerncke@kirk.fmi.uni-passau.de (Frank-Roland Boernke) writes:

>So what does this mean in the end? When I introduced this subject, I asked,
>whether a Turing Machine, that handles not only bits or naturals but also 
>real numbers is more powerful, than a turing machine, that only works 
>with natural numbers. 

>My professor said, both types of Turing Machines are the same concerning
>their power of computability. I claimed that can't be true, refering to
>ideas  like the ones mentioned in the quotes at the beginning of this side.

>Who is right?

The Turing machine that puts a bit (1 or blank) in each square of its tape
and can represent the digits of \pi in base 2 and then multiplies them
does not terminate---your machine with its infinite capacity is different
from the conventional definition. Ergo, the difference is fundamentally a
philosophical difference. Hard core intuitionists would probably not accept
your machine as valid; hard core formalists would not see anything wrong.
This is an apples and oranges thing until you get some agreement on the
rules of the game.

-- 
===============================================================================
Steve (really "D. E.") Stevenson           steve@hubcap.clemson.edu
Department of Computer Science,            (803)656-5880.mabell
Clemson University, Clemson, SC 29634-1906