I am trying to make a list of what properties are comparable between two
universes and which properties are incomparable. I think this has
applications regarding what knowledge can be extracted via simulation of
(from one's POV) other abstract realities and worlds (which may be actual
from someone else's point of view).

So far this is what I have, but would appreciate other's
insights/corrections:

Incomparable properties:

   - Sizes (e.g., how big is something in another universe, is a galaxy in
   that universe bigger or smaller than a planet in our universe?)
   - Distances (what possible meaning could a meter have in that other
   universe?)
   - Strength of forces (we could say how particles are affected by these
   forces in their universe, but not how they would translate if applied to
   our own)
   - Time (how long it takes for anything to happen in that other universe)
   - Age (when it began, how long the universe has existed)
   - Speeds (given neither distance nor time is comparable)
   - Present (what the present time is in the other universe)
   - Position (it has no relative position, or location relative to our own
   universe)

Comparable properties:

   - Information content (how many bits are needed to describe state)
   - Computational complexity (how many operations need to be computed to
   advance)
   - Dimensionality of its objects (e.g. spacetime, strings, etc.)
   - Entropy
   - Plankian/discrete units (e.g. in terms of smallest physically
   meaningful units)

Unsure:

   - Mass? (given forces are not comparable, but also related to energy)
   - Energy (given its relation to both entropy and mass)


So if we simulate some other universe, we can describe and relate it to our
own physical universe in similar terms of information content,
computational complexity, dimensionality, discrete units, etc. but many
things seem to have no meaning at all: time, distance, size.

Do these reflect limits of simulation, or are they limits that apply to our
own universe itself?  e.g., if everything in this universe was made 100X
larger, and all forces similarly scaled, would we notice?  Perhaps
incomparable properties are things that are variant (and illusory) in an
objective sense.

A final question, are they truly "causally disconnected" given we can
simulate them? E.g. if we can use computers to temporarily compel matter in
our universe to behave like things in that simulated universe, then in some
sense isn't that a causal interaction?  What things can travel through such
portals of simulation beyond information?

Jason

P.S.

It is interesting that when we consider mathematical/platonic objects, we
likewise face the same limits in terms of being able to understand them.
e.g., we can't point to the Mandlebrot set, nor compare its size in terms
of physical units.

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