From: Berzerk <berzerk@xmission.xmission.com>
Date: Tue, 26 Jul 94 19:20:03 PDT
To: Jim choate <ravage@bga.com>
Subject: Re: Continum of numbers and Turing Machines
In-Reply-To: <199407262350.SAA01647@zoom.bga.com>
Message-ID: <Pine.3.89.9407262048.A6257-0100000@xmission>
MIME-Version: 1.0
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On Tue, 26 Jul 1994, Jim choate wrote:
> Seems to me that a Turing Machine can't simulate a continous section of
> R for a simple reason, computers can only work on rational numbers and 
> a continous section would have irrationals in it.
Ok, I am kicking myself for saying this, but it is not the data on the tape, 
it is the information of the machene itself.  It is at most a cardinal 
infinity, and even if there are irrational numbers there can't be a 
continum of these.  It has more to do with there being "steps" than what 
the steps are.  In a continum machene, you would not have steps or 
states.  It is not clear if the quantization of time could do anything to 
this(like make it bogus).  The quantization of spacial objects certainly 
makes a limit forbiding continum tapes.

<warning, sci fi follows, don't even start to criticize this, it is too 
easy!>
I was thinking you could get a quantum computer with an continum of 
states if you did not bind them, which could lead to :

AP nwes: Today sientists at mega labs detonated a quantum computer with 
the intent of solving the recorded history of light recieved here on the 
earth at that instant back to the distribution of mater at approximatly 
10-15 seconds after the big bang.  This complements nicely the forward 
computation done by a similar explosion of smaller magtude.
How is that for a wacky idea?