> On 6 Jan 2019, at 17:10, Jason Resch <jasonre...@gmail.com> wrote:
> I am trying to make a list of what properties are comparable between two 
> universes and which properties are incomparable.

What do you mean by “universes”? If it means “physical universe”, and if 
Mechanism is postulated, I am not sure it makes sense to compare two physical 
universe, although it can make sense to talk about different digital 
approximation of a universe. 

> 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? 

All universal machine in arithmetic have the same universe, or set of physical 
laws, as they are truly machine-invariant. Only the geographies and histories 
can differ, so your question becomes is mass, energy, entropy, dimension, age, 
etc.. geographic-historical or physical?

> 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.

If we don’t notice, it is the same, except for the weigh, which depends on 
which representation emulate which experiences in arithmetic.

> 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?

I am not sure this makes sense. There is no “universe” of that kind, I would 
say (when we postulate mechanism). There is only interfering (statistically) 
histories/computations-seen-from-inside (seen by the Löbian machine supported 
by those computations). 


> 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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