Re: Poll: Are PCs Turing Machines?

From: Stephen Harris (cyberguard1048-usenet_at_yahoo.com)
Date: 12/06/04 

Date: Mon, 06 Dec 2004 17:33:31 GMT

"Will Twentyman" <wtwentyman@read.my.sig> wrote in message
news:41b457b2$1_2@newsfeed.slurp.net...
> Eray Ozkural exa wrote:
>> Will Twentyman <wtwentyman@read.my.sig> wrote in message
>> news:<41af81f6$1_5@newsfeed.slurp.net>...
>>
>>>Eray Ozkural exa wrote:
>>>
>>>
>>>>examachine@gmail.com (Eray Ozkural exa) wrote in message
>>>>news:<320e992a.0412011208.2b75bc@posting.google.com>...
>>>>
>>>>
>>>>>I wonder what people really think about this.
>>>>>
>>>>>Are PCs physical examples to Turing Machines? [*]
>>>>>Please write only Yes/No to avoid discussion.
>>>>
>>>>
>>>>A clarification is in order.
>>>>
>>>>As far as I can understand from the replies, there are alternative
>>>>readings of my question, which is imprecision on my part.
>>>>
>>>>We usually consider equivalence in computability to be a sufficient
>>>>condition for being a physical example to a model of computation,
>>>>essentially covering the capabilities of "causal mechanism" involved.
>>>
>>>The problem is that a TM does not have limits on the size of the data it
>>>works with, as long as it remains finite. *EVERY* PC has a limit on the
>>>data it can process. The abstract notion of a PC is equivalent to a TM,
>>>but we have no abstract PCs, just the real deal with their limitations.
>>>
>>>The issue is simple: a PC cannot handle *all* the data a TM can process.
>>
>>
>> Will, what makes you think that the input tape has to be mapped to
>> spatial dimensions?
>
> Who said anything to do with spatial dimensions? I'm just talking about
> how many digits of input a particular machine can accept.
>

Eray has been told dozens of times that TMs are abstract ideas that have
no physical existence. No part of the TM has a spatio-temporal dimension.
The tape is a theorettical/fictional device which has nothing to do with
fitting
inside the boundaries of a physical universe because it is not physical.

The PC is physical and thus has spatio-temporal dimension. The PC requires
a real physical substance for memory. This substance has a similar function
to the tape of a TM; output of a computation can be stored.

There is a limited amount (finite) of physical substance which is called
"matter"
in the physical universe. If all the matter in the universe were used for
memory
storage, every particle in the universe stored one digit of Pi, then Pi
could be
computed to zillions and zillions of places and written to memory.

But at some point in this physical process (PC), all the matter in the
universe
is exhausted (the universe expanding does not create new matter) and more
digits of Pi cannot be written to physical memory.

But because a TM is an abstract (non-physical) device with a tape that
doesn't run out of memory/tape to write digits of Pi, it can store more
digits of Pi than any physical device (PC). Whatever the finite max of
digits that can be stored in PC memory, a TM can store twice as many,
and still be storing a finite number of digits. The TM can store more
digits because it is not physical, it has no physical memory constraints
imposed upon it by the universe; unlike the PC which is physical and
thus does have physical constraints imposed upon it by the universe.

It is a complete mistake to think that Turing defined a TM as a physical
device that could exist within physical reality. Turing described an
abstract,
non-physical, theoretical device. TMs _encode_ some properties that can
be physically actualized in a real computer. TMs do not _exemplify_ PCs.
A TM is not a physical example of a PC, a PC is not a physical example
of a TM. Because by definition, TMs are not physical and PCs are not
abstract, but physical. This is a fact of definition. Because some people
do not understand the definition and others have never even read the
definition does not change this fact. That is why people are saying there
is no such question as are all pcs turing machines?

There are 3 feet in a yard. No more no less. A yard is not a meter.
That is a definitional fact. People might ask if there are 36 inches in a
yard
if they are uneducated. They cannot change the reality of the defintion
because they harbor a delusion that a yard has 39.37 inches. All they
can do is display their ignorance or confusion regarding the definitions
of a yard and a meter. I am making an analogy between a yard and a meter
and a PC and a TM. They have different definitions. A TM is a non-physical
device and a PC is a physical device; they have different definitions.

Relevant Pages

  • Re: Poll: Are PCs Turing Machines?
    ... > Who said anything to do with spatial dimensions? ... > how many digits of input a particular machine can accept. ... inside the boundaries of a physical universe because it is not physical. ... a real physical substance for memory. ...
    (sci.math)
  • Re: Poll: Are PCs Turing Machines?
    ... the computation does not occur within the universe. ... so only a finite number of digits can be stored in the ... The PC will run out of physical memory even ... PCs are not Turing machines because PCs are physical and TMs ...
    (comp.theory)
  • Re: Poll: Are PCs Turing Machines?
    ... the computation does not occur within the universe. ... so only a finite number of digits can be stored in the ... The PC will run out of physical memory even ... PCs are not Turing machines because PCs are physical and TMs ...
    (sci.math)
  • Re: Poll: Are PCs Turing Machines?
    ... There isn't enough matter in the universe ... Emits significant digits of product and revises them ... equivalent to just making the PC's memory bigger. ...
    (comp.theory)
  • Re: Poll: Are PCs Turing Machines?
    ... There isn't enough matter in the universe ... Emits significant digits of product and revises them ... equivalent to just making the PC's memory bigger. ...
    (sci.math)