Re: Poll: Are PCs Turing Machines?

From: Stephen Harris (cyberguard1048-usenet_at_yahoo.com)
Date: 12/09/04 

Date: Thu, 09 Dec 2004 21:54:34 GMT

<luiroto@yahoo.com> wrote in message
news:1102602451.086214.230200@z14g2000cwz.googlegroups.com...
>
> Stephen Harris wrote:
>> <luiroto@yahoo.com> wrote in message
>> news:1102540245.045967.12450@z14g2000cwz.googlegroups.com...
>> >
>> > Will Twentyman wrote:
>> >> Eray Ozkural exa wrote:
>> >>
>> >> > examachine@gmail.com (Eray Ozkural exa) wrote in message
>> > news:<320e992a.0412011208.2b75bc@posting.google.com>...
>> >>> The issue is simple: a PC cannot handle *all* the data a TM can
>> > process.
>> >> Will Twentyman
>> >
>> > The issue is more simple: Turing Machines does'nt exists, only
>> > Turing's algorithms.
>> > Same: Eratosthenes Machines does'nt exists, only Eratosthenes
> Sieves.
>> > Tell me, which actual TM process has been realized that a computer
>> > could not manage?
> Ludovicus
>> >
>>
>> TMs are not physical and could compute 10^2300000000000 digits
>> of Pi and then more than that.
>> A non-physical wonder tape that magically surpasses physical
> limitations.
>> Turing imagined this tape. It has never been "realized". TMs don't
>> do physically realized computations. None at all. PCs do, and that
>> is why PCs are not Turing machines.
> Harris
>
> How a TM could *compute* 10^230000000000 digits of Pi? A computer >with
> enough time (without tape) *could compute* that chain of digits.

A TM is an abstract device. Abstract means non-physical. Turing gave
his TM a magical tape that is not physical. The tape is unending and is
not part of the physical universe. Neither is there any time involved. A
TM can compute: Suppose every tree in the world were converted
into sheets of paper. And on the first page you typed 10^2300000
and you went on to fill that page and every other existing page with more
zeros to change 10^2300000 into a power that was zillions and zillions
of zeros larger like 10^2300000000000000000000000000000000
but larger than that, filling all the zillions of pages with zillions and
zillions
of zeros written on them so that the final representation was hugely
staggeringly humongous, hugely larger than a google-googleplex. But
still finite since there are a finite number of trees making a finite number
of sheets of paper making still a finite number of zeros (000...) after the
^.
I am going to call this huge number a metazillion for later reference.

A TM can compute this huge finite number when it comes to computing
finite places of Pi (Pi has an infinite decimal expansion). Because a TM
is not physical, the computation does not occur within the universe.
There is no problem with time or physical storage because those exist
in the physical universe. But not in the imaginary place that the TM with
its imaginary powers does its computation. That is how Turing made up
the TM. It was never physical and can never be physical.

The PC on the other hand is physical. It is limited by the time left in
the universe while there is still energy to power the machine. It is
limited by the amount of matter in the universe. More matter is not
created just because the universe may expand forever. The matter
becomes less dense (it spreads out).

A PC requires matter because it needs a physical substance to store
memory. Every digit of computing Pi needs to be stored onto and
into a physical substance. There is only so much matter in the universe,
so only a finite number of digits (call it Fd) can be stored in the
physical universe if you use every particle in the universe.

The TM is not physical. Not only can it store at one time all the
digits of Pi's expansion that a PC can store (Fd) but much, much,
much, much more. The PC will run out of physical memory even
if it is using all the matter in the universe. All of the digits need
to be stored. One cannot compute some digits and then erase
them and then proceed and compute some more digits and so on.

The computation of Pi on a TM is done on a tape. The tape never
runs out because it is not a physical tape. The tape acts like memory.
Physical memory for a PC, ram, requires physical substance. There
is not enough memory in the physical universe to complete some finite
calculations with a PC. There is always enough time and memory/tape
for a TM to complete its calculation of any finite number no matter
how large, many times larger than a PC, because the TM is not
physical, is not part of the universe, has no time limits set and no
physical limits for memory set.

Turing made up his thought experiment this way. He gave the TM
an unending tape which is not part of the physical universe; the TM
thus has unending memory. It can alway calculate more digits of
some number like Pi because it never runs out of memory, because
it is not physical. The PC will run out of memory because it is physical
and there is going to be a limit to how many digits of Pi it can compute.
Not because of a different algorithm, but because the TM has more
memory given to it by the way Turing invented the TM and its tape.

PCs are not Turing machines because PCs are physical and TMs
are abstract=non-physical. The biggest difference is the TM has
unending memory=tape but the PC always has limited memory
because there is only so much matter to use for physical memory
in the universe. Therefore a PC is going to run out of memory on
some very large calculation that a TM, in principle, can perform.

Shortly, a TM can compute more digits of Pi than the hugest
PC in the universe, or all of them put together, because time is
not a factor for a TM, and memory is never a problem for a TM,
because the TM and its tape are non-physical. No restrictions
that apply to a PC which is part of the physical universe apply to
a TM which is not part of the universe because it is non-physical.
A TM is a mental creation not a real physical machine.

Because that is how Turing imagined and described the TM and
its magically powerful tape. The answer to the Subject:
Re: Poll: Are PCs Turing Machines? is NO, by definition.
There is only a question if one is ignorant of the description/definition.

The question in the Subject would have been better phrased:
Do PCs exemplify Turing Machines? The answer is still NO.

But some of the principles found in the theoretical Turing Machine
are found in the concrete/physical PC. This is sometimes recognized
by saying the TM "encodes" some ideas found in PCs. Also TM
is often used in place of UTM as a generalization.

> A computer program can also show in the screen the algorithm utilized
> by Turing for *trying to compute* that string of digits, and say :"I
> analyzed the TM method and I found that it can compute N digits of Pi"

What does the algorithm have to do with it? The PC can be using a much
more efficient algorithm than the TM to compute Pi, but that is not going to
solve the problem of the PC running out of memory/storage to hold the huge
expansion of Pi's digits, even if the PC uses all the memory in the
universe.

I doubt this (I found that it can compute N digits of Pi) because a TM
can compute N digits of Pi, where N exceeds the memory capacity of
the PC. All those many digits have to be written to physical memory and
there is always going to be an N (that the TM can compute) that is larger
than all the memory of a physical PC can hold or store, no matter how
much memory the PC has, even all the memory in the physical universe.

> A PC do not only realize numerical calculus, also realize mathematical
> demonstrations and develop algorithms. If a mathematician can utilize
> the Turing Algorithm a computer also can, and with more confidency.

There is no such thing as a Turing Algorithm. The PC could use the
same algorithm to compute Pi or a more efficient one to compute Pi.
That is not the problem. The difference is in the memory potential
between a physical PC and a non-physical TM not some algorithm.

A TM theoretically does many of the same functions as a PC. There
is quite a bit of overlap. That is not under dispute. PCs are not TMs
because they cannot do some huge calculations that a TM can perform,
and this is because the physical potential of calculation for a PC is
bounded by the physical restraints of the universe and there are no
physical restraints which limit huge calculations for TMs because they
are not physical. TMs potential for calculation is always greater than PCs.
Because sometimes they can both do the same calculations, doesn't
change the important difference of when they cannot do the same
calculation to same amount of digits. There are finite numbers big enough
that a PC cannot complete the calculation but a TM can complete the
calculation just because the TM has been given more theoretical memory.

> "There are not worse deafs than that those who don't want to hear"
> Jesus
> Ludovicus
>

Take your own advice. PCs are real and TMs are imaginary and
that is why they are not the same but different. For PCs and TMs
to be the same, they have to be the same in all ways, not some
ways or even most ways. TMs are hugely different in a very
important way. They have imaginary tapes that do calucaltions
without taking up any physical time or space; no physical resources.
PCs do not have magical memory nor can they be given unending
memory. The memory for a PC will always come to an end if
the calculation is large enough and there is no way to get around it.

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