Bruno,
As I have already mentioned, I am not that far to follow your theorem. I
will do it presumably the next year.
I have been working for the last ten year with engineers and my
consideration is so far at the engineering level. After all, if we know
something, we should be able to employ it in practice. And if this does
not work in practice, then how do we know that our knowledge is correct.
Said that, I understand the importance of theory and appreciate the work
of theoreticians. After all, if we say A, then we must say B as well.
Hence it is on my list to follow your theorem (but not right now).
At present, I am just trying to figure out our beliefs that make the
simulation hypothesis possible. After all, "Human brain is similar to
the Nelder-Mead simplex method. It often gets stuck in local optima."
Best wishes,
Evgenii
On 13.09.2011 10:58 Bruno Marchal said the following:
On 12 Sep 2011, at 21:07, Evgenii Rudnyi wrote:
On 9/12/2011 8:06 AM Jason Resch said the following:
...
What about of dumb water molecules, can they not form a wave?
Complex things can result from very simple rules, when you have
a huge number of those simple things interacting with each
other.
I will use this example to continue my thoughts about
Simulation Hypothesis and Simulation Technology
http://blog.rudnyi.ru/2011/09/simulation-hypothesis-and-simulation-technology.html
I will change the original question as follows. Can we simulate a
wave starting from water molecules?
I am not sure it makes sense a priori to talk about the simulation of
something physical, if only because those are not well defined. Now
if you accept QM, then, the answer is YES. A quantum computer can
simulate any physical process, even in polynomial time. Just compute
the heisenberg matrix, with some rational approximations. The quantum
errors will not grow, thanks to linearity, so you will get your water
wave rather well simulated, and then you can simulate that quantum
water wave with a classical computer, but you will have an
exponential slow down (which is of no concern for the simulated
entities which might be there).
I will consider it not in principle, but rather in the objective
reality given to us in sensation. (This what I have learned in the
USSR: Vladimir Il'ich Lenin: "Matter is the objective reality
given to us in sensation")
The USSR was a religious state. That matter is the objective reality
is the gross Aristotelian extrapolation from sensations programmed by
billions of years of evolution.
If we imagine brute-force simulation, then the answer is definite
no.
Due to the real numbers, but with the quantum equation, we can limit
ourselves to rational (complex) numbers.
Even if we consider a level of molecular simulation when the water
molecules are considered classically with a given force field,
then it is definitely out of reach, also for foreseeable future.
The Moore law just does not help.
In what sense then do we usually say "Yes, we can do it"?
Presumably this means that we do not have to simulate each molecule
to simulate a wave. The laws of continuum mechanics actually
suffice. If we consider this numerically, then there is nice way to
come to continuum mechanics through coarse-graining. One can think
for example of dissipative particle dynamics (DPD, some equivalent
of molecular dynamics) where we simulate not water molecules but
rather bigger pseudo-particles. Funny enough DPD is pretty similar
to smooth particle hydrodynamics (SPH), an alternative method to
discretize the Navier-Stokes equations. In this sense a
pseudo-particle is some equivalent of a cell in finite
elements/finite volumes. In a way, molecular dynamics is also could
be considered as a course-graining scheme. First we use quantum
chemistry to evaluate the force field and then we use it at the
next level.
In this sense, an interesting question is how simulation hypothesis
is supposed to work. As brute-force simulation? Or along the second
way?
The second way, with rational approximation of the waves (quantum or
classical). But all this is not relevant for mechanism, which
assumes that the brain is already a simulator. So it has already make
the comp truncation, so it might be simulable, even if its material
components are not simulable (as it needs to be the case: I recall
that if *I* am a machine, then the physical reality (which emerge)
cannot be simulable by a computer, but is given as a limiting process
pertaining on *all* computations). To sum up: if I am a machine, the
physical universe is not a machine, nor is the appearance of the
primary matter.
Bruno
http://iridia.ulb.ac.be/~marchal/
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