On 24/04/2017 8:05 pm, Bruno Marchal wrote:
On 24 Apr 2017, at 06:53, Bruce Kellett wrote:
On 24/04/2017 1:42 pm, Russell Standish wrote:
On Sun, Apr 23, 2017 at 09:38:26PM +1000, Bruce Kellett wrote:
On 23/04/2017 8:52 pm, Quentin Anciaux wrote:
It's you who's begging the question, first define what is a
computation with physics first, without relying on abstract
mathematical notion.
A computation with physics is what is happening in the computer I am
currently working on. I can describe this in mathematical notation
if you wish, but the process is not the notation. Any process that
takes input and produces output is a computation. All physical
objects do this. And physical objects do not know any mathematics.
That is the definition of a physical process, not a computation. If we
take the usual (mathematical) meaning of computation, then I can point
to a potential counter-example: beta-decay. Recording the arrival
times of electrons from beta decay using a clock and electron detector
gives a time series that to our best knowledge is random and hence
uncomputable. It is an undeniable physical process that is not a
computation.
Which means that the physical universe is not Turing emulable. I
thought the idea was that the physical world was not emulable because
it relies on the statistics of the infinite processes running through
our conscious state. Beta decay is not emulable because quantum
randomness is not computable (pseudo-randomness will never do in the
long run). I do not see that these reasons for non-computability are
the same.
In any case, one could include beta decay as a computation -- simply
claim a violation of the Church-Turing thesis. That might not be such
a bad idea.
Then all functions will be computable. By definition, if you can
compute a function, you can provide a mean to get the result, and such
that anybody will get the same result following that mean. That is not
the case for the beta decay.
There are a number of things that are completely reproducible in beta
decay: the lifetime of the nucleus, the statistics of the arrival times
of electrons from a large sample of nuclei, etc. So beta decay does
compute a number of things, not so different from a mathematical
function , really-- a function only computes a limited number of things.
You need different functions for different computations
Bruce
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