From: Michael Wilson (firstname.lastname@example.org)
Date: Sat Aug 27 2005 - 16:21:22 MDT
Phil Goetz wrote:
>> If you're using variables that have insufficient dynamic range to
>> encompass the entire co-ordinate space, then by definition you
>> must be using some kind of system for nesting reference frames.
The diameter of your universe is X quanta and your variables have
Y states. If Y>=X, then you can parameterise the set of all possible
spatial locations into a vector of variables the same size as the
number of spatial dimensions in your universe. If Y<X, there is no
lossless mapping with a set of this size. To specify exact positions
you would need to combine vectors, e.g. a coarse vector specifying
the location of a shared reference frame combined with fine vectors
specifying the exact positions of everything in that frame. Note
that this only saves you storage space if the universe is somewhat
sparse, but it will save computation if you're prepared to round
the effects of fields such that they apply equally to everything in
a given frame.
>> If you're using true absolute co-ordinates, i.e. every particle
>> or similar ontological primitive has a position in quanta relative
>> to the universe itself, then your variables must have enough
>> range to allow speeds from 1 distance quanta/time quanta up to
>> 1 universe diameter/time quanta without any loss of precision.
Technically 1 universe radius per time quanta.
> In a Newtonian universe. Which is why it's a bad approach
> for a universe-simulator.
When I said /must/, I didn't mean 'so you must meet this onerous
condition', I meant 'so clearly you already have this capability'.
If you can state the position of anything absolutely, then you can
also state the velocity of anything absolutely as long as the
maximum possible velocity measured in distance quanta / time quanta
is smaller than the radius of the universe / desired subquantum
precision. Obviously you can use the same strategy for compressing
groups of similar velocities as you can for compressing groups of
similar positions (reference frames), but again this has nothing
to do with the question of relative time.
> I didn't say it simplified things; it reduces the storage
> and computational requirements.
/Relativity/ greatly increases computational requirements, and
will only decrease storage requirements under a generous set of
assumptions. /Relative encoding/ is a special case of removing
redundant information, which can but is not required to incorporate
lossy compression, and is a useful technique in many real world
computing applications. The two things are not closely related.
I realise you were just trying to make a humorous allusion. But
making sweeping statements about science, based on the fact that
two things the author doesn't fully understand or just hasn't taken
the time to think through seem vaugely compatible, is a bad habit
that we should all be trying to stamp out.
* Michael Wilson
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