On 27 Nov 2017, at 23:08, John Clark wrote:
On Sun, Nov 26, 2017 at 10:04 PM, Jason Resch <jasonre...@gmail.com>
wrote:
> Richard Feynman in "The Character of Physical Law" Chapter 2
wrote:
"It always bothers me that according to the laws as we understand
them today, it takes a computing machine an infinite number of
logical operations to figure out what goes on in no matter how tiny
a region of space, and no matter how tiny a region of time. How can
all that be going on in that tiny space? Why should it take an
infinite amount of logic to figure out what one tiny piece of space/
time is going to do?"
Obviously infinite logic is not required unless infinite precision
is also required, but sometimes (and protein folding would be a
good example of this) an astronomically huge number of calculations
are required for even a very modest approximation of what is
happening in a tiny piece of spacetime, and yet nature can do it
with great precision in a fraction of a second. How come? Feynman
himself took the first first tentative steps toward answering that
question just before he died, as far as I know he was the first
person to introduce the idea of a quantum computer.
I think Feynman did much more than that. He made lecture on
computation(*), and get some contributions on quantum circuit and the
non emulability of quantum machine by probabilistic Turing machine, +
some idea on the thermodynamic of computation, not well mentioned by
some followers, according to Hey(**). He might just have ignored, as
far as I can search, the mathematical notion of universal machine.
Deutsch got it and was able to define a quantum universal machine, and
gives a clear-cut problem where a quantum machine is very plausibly
much more efficient (Of course Shor will do even much more in that
respect).
Feynman disliked philosophy, but seems to get the point that the
quantum reality was not Turing emulable in polynomial or real time.
Deustch shows also that the quantum digital universal machine does
*not* violate the Church-Turing thesis, making (trivially) very
elementary arithmetic emulating all quantum computers (obviously not
in "real time" if that needs to be said, not even in "real space", but
the "first person" can't know that ...).
... so that the question, needed to be solved to progress in the mind-
body problem, consist in showing why the quantum computer seems to win
"below the substitution level".
The answer is that the modal translation of the "certain bet" which is
in arithmetic Bp & ~Bf, on p semi-computable (sigma_1) gives a quantum
logic. This put a highly non trivial structure accessible on the
consistent extensions (in some sense slightly different from the one
use in the provability logics, to be sure).
(And thanks to the G/G* separation, which splits also the quantum
logic, we get the quanta (first person sharable (by a linear tensor
product)) and the qualia, which extend them with non communicable
personal data).
Bruno
(*) Feynman Lectures on Computation
https://www.amazon.com/Feynman-Lectures-Computation-Richard-P/dp/0738202967
(**) The book of Anthony J.G. Hey
https://www.amazon.com/Feynman-Computation-Anthony-Hey/dp/081334039X
> Does computationalism provide the answer to this question,
No natural phenomenon has ever been found where nature has solved a
NP-hard problem in polynomial time. Quantum Computer expert
Scott Aaronson actually tested this and this is what he
found:
" taking two glass plates with pegs between them, and dipping the
resulting contraption into a tub of soapy water. The idea is that
the soap bubbles that form between the pegs should trace out the
minimum Steiner tree — that is, the minimum total length of line
segments connecting the pegs, where the segments can meet at points
other than the pegs themselves. Now, this is known to be an NP-hard
optimization problem. So, it looks like Nature is solving NP-hard
problems in polynomial time!
Long story short, I went to the hardware store, bought some glass
plates, liquid soap, etc., and found that, while Nature does often
find a minimum Steiner tree with 4 or 5 pegs, it tends to get stuck
at local optima with larger numbers of pegs. Indeed, often the soap
bubbles settle down to a configuration which is not even a tree
(i.e. contains “cycles of soap”), and thus provably can’t be
optimal.
The situation is similar for protein folding. Again, people have
said that Nature seems to be solving an NP-hard optimization problem
in every cell of your body, by letting the proteins fold into their
minimum-energy configurations. But there are two problems with this
claim. The first problem is that proteins, just like soap bubbles,
sometimes get stuck in suboptimal configurations — indeed, it’s
believed that’s exactly what happens with Mad Cow Disease. The
second problem is that, to the extent that proteins do usually fold
into their optimal configurations, there’s an obvious reason why
they would: natural selection! If there were a protein that could
only be folded by proving the Riemann Hypothesis, the gene that
coded for it would quickly get weeded out of the gene pool."
For more I highly recommend Aaronson's book "Quantum Computing
since Democritus".
John K Clark
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