I stand corrected. But that just means I chose a bad example. My point
was that consciousness doesn't require Turing completeness. You agreed
with me about the paramecium.
Brent
On 7/10/2024 7:24 AM, Jason Resch wrote:
There was a study done in the 1950s on probabilistic Turing machines (
https://www.degruyter.com/document/doi/10.1515/9781400882618-010/html?lang=en
) that found what they could compute is no different than what a
deterministic Turing machine can compute.
"The computing power of Turing machines
provided with a random number generator was
studied in the classic paper [Computability by
Probabilistic Machines]. It turned out that such
machines could compute only functions that are already computable by
ordinary Turing machines."
— Martin Davis in “The Myth of Hypercomputation” (2004)
To see why consider that programs can similarly split themselves and
run in parallel
with each of the possible values. To each instance of the split
program, the value it is provided will seem random. But importantly:
what the program can computes with this value
is the same as what it would compute had the value come from a "truly
random" quantum measurement.
It would make a difference if it were a quantum computer or not.
For us observing the program run from the outside, it would make a
difference. But the program itself has way of distinguishing if it is
receiving a value that came from a real measurement of a quantum
system, or if it was provided the result of a simulated quantum system.
And going the other way, what if it didn't have a multiply
operation. We're so accustomed the standard Turing-complete von
Neumann computer we take it for granted.
A program will crash if it's run on a hardware that it's not
compatible with. This is why you can't take a .exe from windows and
run it on a Mac. But if you run a windows emulator on the Mac you can
then run the .exe within it.
The program the has no idea it is running on a Mac, it has every
reason to believe it is running on a real windows computer, but it is
fooled by the emulation layer (this emulation layer is what I speak of
when to refer to the "Turing firewall"). That such layers can be
created is a direct consequence of the fact that all Turing machines
are capable of emulating each other.
Jason
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