🚀 go-pugleaf

In article <1992Dec16.095412.19570@tom.rz.uni-passau.de> boerncke@kirk.fmi.uni-passau.de (Frank-Roland Boernke) writes:
>In lectures we talked about the RAM, a formal machine-model that is proved
>to be as powerful as turing-machines(TM) and vice versa, according to the
>Church-Turing-Thesis. This seems to be ok until you say, that the RAM allows
>only natural numbers in its registers (or rational-numbers, since they are 
>countable). Our professor told us, that RAMs are allowed to store REAL numbers
>too AND they are  still as powerful as an ordinary turing machine. I claimed, this
>can`t be true, since there isn`t any possibility to work with irrational 
>numbers in TMs. 
>
>Of course, e.g. you can compute Pi up to as many digits as you want, but in every
>step  of computation you only have an approximation - a rational number.
>
>Therefore, a machine-model, that allows real numbers, must be more powerful
>than another one that does not. My professor said, that isn`t a problem but
>I don`t agree. Who is right?
>
>If I am wrong, please let me know where the fault is.

How about this: 
Maybe the model could conceivably represent the reals, but how would any
irrational number get into the machine in the first place?  There are 
uncountably many irrationals, so a table look-up won't do.  You could
try to calculate them, but how do you calculate, say, pi, with only 
Turing-machine-like operations?

So, at first glance, it looks like this machine is equivalent to the RAM
model with rationals plus a finite number of irrationals you could have in
a table.  This is equivalent to a Turing machine.

Anybody buy that?
-- 
Daniel Jimenez                     djimenez@ringer.cs.utsa.edu
"I've so much music in my head" -- Maurice Ravel, shortly before his death.
"                             " -- John Cage