On 05 Jan 2015, at 19:44, John Clark wrote:
On Mon, Jan 5, 2015 Russell Standish <[email protected]> wrote:
> My personal opinion is that measured values are constrained to be
rational
If that is true (and it may be) and if mathematics is a language and
the irrational numbers play no role in physics then perhaps they are
a fantasy, the equivalent of a Harry Potter novel. Or perhaps not,
there are lots of ways to write a sequel to a Harry Potter novel but
only one way a new story about the irrationals could go. A story
about the irrational numbers is unique, a story about Harry Potter
is not, would that be enough to say the irrationals are not a
fantasy? I don't know.
> there can only ever be a countable number of distinct observer
moments.
I wonder if countable is good enough, I wonder if it must also be
finite.
Even with computationalism, I can conceive a non-countable set of
observer moments, although only a countable equivalent class would be
distinguishable by a machine (yet this could change the FPI measure).
Finite would not make sense with computationalism: the number of
possible experience is infinite, for machine or number in arithmetic.
Bruno
> Yet this down not imply space is "quantised" or discrete in any
way. It is quite possible there is no lower bound to the difference
between two measurements. So it doesn't surprise me that space ends
up being smooth at scales far smaller than the planck length. I
would be more suprised at the opposite conclusion, as it implies a
lack of symmetry (grids are not rotationally symmetric, except at
specific angles).
I don't think that by itself would necessarily be a deal breaker,
electric, magnetic and gravitational fields need not be rotationally
symmetric. And lots of interesting stuff happens when symmetry is
broken, water is rotationally symmetric but ice is not, and most
(but not all) lifeforms on this planet have no rotational symmetry.
John K Clark
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