Re: Symbol Grounding Problem
- From: Stephen Harris <cyberguard-1048@xxxxxxxxx>
- Date: Fri, 11 May 2007 14:51:56 GMT
Daryl McCullough wrote:
Don Geddis says...
Neil W Rickert <rickert+nn@xxxxxxxxxx> wrote on Thu, 10 May 2007:A TM cannot run Windows.You think this is a serious problem? Surely you could just record all userWhy not?That should be obvious. A TM requires that all of the data be
on the tape before execution begins. But Windows is interactive,
regularly prompting the user for input.
input for a period (an hour, a day, a year). And then replay that input
for a PC running Windows, or for a Turing Machine emulating a PC running
Windows, and you'll get the exact same output.
The problem here is that a Turing machine is an *abstract* description
of computation. The abstraction throws away details such as memory
limitations, real-time, interrupts, etc.
So the question isn't: can a Turing machine run windows? An abstraction
can't do anything in the real world. The question is whether the Turing
machine abstraction can be applied to a computer running Windows. Certainly
it can, although it's probably not the best abstraction to use.
You can model a real modern computer as a Turing machine with oracles
in the following way: Have one read-only input tape to represent the
sequence of key presses. Have another read-only input tape to represent
the sequence of mouse movements and button presses. Have a write-only
output tape to represent the output to the screen. This could be
represented in a number of ways, but one possibility is to to dedicate
one million squares per screen image, with each square holding the
information about the color and brightness of one pixel. Another
alternative is to let three squares represent an update to the
screen: the first square giving the x-coordinate of the pixel
modified, the second giving the y-coordinate, the third giving
the new color and brightness level for that pixel.
In addition to these tapes representing inputs and outputs, there
would be a read-write tape representing the hard drive, and another
read-write tape representing internal memory.
The forward march of time is only represented by the position on
the input tapes. The first square represents the first input, the
second square represents the second input, etc. What's harder to
represent using a Turing machine is the notion of an "interrupt".
It's also hard to represent the notion of relative timing of different
inputs or outputs. It can be done, but only at the cost of making
the Turing machine description a lot more complicated.
The issue along the way was whether TMs are non-trivially different
than PCs with an operating system. Neil said they are different
because they are interactive. Don responded that a TM could after
the fact display the interactive behavior. Daryl said that a TM
with an oracle could simulate an interactive TM in "real-time".
Neil did not claim that PCs have greater power which Don thought
he might be suggesting.
Oracles are not Turing-computable and are not machines. Thus, no
PC can run the equivalent of an oracle, as they are not physically
realizable. Then, is a PC running an OS with human interactive input
the same as a TM with an oracle?
If the human (brain functions) are equivalent to an oracle then that brain is non-computable and cannot be simulated by a TM. Thus the
Computationalism thesis would be false:
(C)= The functions whose values are generated by brains are Turing-computable. [C = Computationalism]
If the Computationalism thesis is true, then a PC with an OS
which is interactive is not equivalent to a TM with an oracle,
but is equivalent to a human. PCs do not have any greater power
than TMs. The TM with an oracle, although it could produce the
same output as the PC with human interaction, is not the same
because it has a greater potential, it can answer questions the
PC with OS and human, cannot.
The Oracle Turing Machine has more power than: either the interactive
PC or TM without oracle, or human, who supposedly all share the same
power according to the assumption of Computationalism.
So the Turing Machine equipped with an oracle is _not_ the same as
a PC with interactive OS, because it can provide more than all the
interactive PC events; it has more power, thus is not a solution in
the same category as normal TMs and interactive PCs, which do have
the same power in terms of what is their shared computable domain.
Interactive PCs and TMs vary within the same category, whereas the
OTMs will fix this variation, but not from within the same category
of Turing equivalence or power as the PCs and TMs under discussion.
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