On 27 Mar 2014, at 18:05, meekerdb wrote:
On 3/27/2014 1:11 AM, Bruno Marchal wrote:
On 26 Mar 2014, at 22:30, Stathis Papaioannou wrote:
On Thursday, March 27, 2014, Russell Standish
<li...@hpcoders.com.au> wrote:
On Wed, Mar 26, 2014 at 05:06:46PM +1100, Stathis Papaioannou wrote:
>
> The engineering tolerance of the brain must be finite (and far
higher than the Planck level) if we are to survive from moment to
moment, and that implies there are only a finite number of
possible brains and hence mental states.
>
Steady on, I don't think it does that at all, unless you constrain
the
physical world to be bounded somehow in both space and time.
I think you were just trying to say that the space of brains (and
mental states) is discrete, something I could agree with.
Unless you allow brains to grow infinitely big, there are only a
finite number of possible brains even in an infinite universe.
Assuming comp. If the brain is defined by its "material" quantum
state, and assuming electron position is a continuous observable,
then we can have an infinity of brains, even when limiting their
size.
Why "observable"? Why not just "variable" - which it is in current
formulations of QM.
?
Position, in QM, is represented by an observable (some operator in a
Hilbert space). Its eigenvalue are the "variable" which can be
instantiated by a measurement. I am not sure I grasp the remark, nor
that it would change anything. If some physical data are actually
infinite, a non-computationalist can argue that you can "emulate" an
infinity of mind states in a finite portion of some physical-space-time.
But with real valued variables can't there be hypercomputation?
Yes. But you can have "hypercomputation" also when working with only
natural numbers, like a machine computing functions from N to N with
the help of the Halting Oracle, or with any pi_i or sigma_i oracles.
We know this enlarge properly a lot the class of computable functions.
I am not convinced by the argument of Kent, but perhaps an improvement
can be made. Von Neumann wrote a paper where he estimated that the
probability of self-duplication machines apparition on Earth is very
low. I am not convinced, but this still suggests that the theory of
evolution, when precise enough, might "see" the trace of the
multiverse, in case that probability is so low that the origin of life
involves non trivial quantum computations.
Gödel also suggested that science might have to admit a "God" in case
the speed of evolution violates the (known) physical laws. Apparently
Godel didn't see the "Many-world" alternative to God, for that function.
Godel and Einstein missed the "many-thing" idea, and I see people
resist. Yet, I think that with mechanism, we just cannot avoid that
multiplication when we believe statements like "Goldbach conjecture is
true or false".
Bruno
Brent
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