An entire external universe adds to the complexity of the model, not just how many entities the model contains.
This may not be the case if the simulation itself was produced in the universe as we know it, and our own apparent universe is only a simulated fragment. That isn’t what I thought you were asserting, but that is untenable for completely separate reasons.
What do you mean by complexity and how is it at all relevant?
Take Conway’s life for example. Tons of apparent complexity can emerge from rules simple enough to write on a bar napkin.
Was the copernican model ‘wrong’ because it made our universe-model more complex? Was the discovery of multiple galaxies wrong for similar reason? Many worlds?
The only formal definition of complexity that is well justified is algorithmic complexity and it has some justification as a quality metric for deciding between theories in terms of Solonomoff Induction.
The formal complexity of a universe-model is that of it’s simplest reduction.
The simplest reduction for any scientific model is universal physics.
So there is only one model, all complexity emerges from it, and saying things like “your premise X adds to the complexity of the model” is untrue and equivalent to saying your “premise X makes the model smell bad”.
Adding a universe external to this one doesn’t just add more stuff. To take the Conway’s Game of Life example, suppose that you simulated an entire universe inside it, from the beginning. For the inhabitants, a model that not only explained how their universe worked, but postulated the existence of our universe, would be more complex than one that merely explained their own. With evidence that their reality was a simulation, the proposition could be made more likely than the proposition that it stood alone.
In terms of minimum message length, having to describe another universe superordinate to your own adds to the information of the model, not just the entities described in it. The addition of our own universe could not be encapsulated in a model that simply describes the working of the simulated Conway universe from the inside without adding more information.
Once you have a model that includes a universe and the capacity to simulate universes you can add universes to the model without taking much more complexity because the model can be recursively defined. The minimum message length need not be increased much to add new universes, you just edit the escape clause. Where we are in the model doesn’t matter.
You seem to be thinking in terms of time complexity. Space complexity also needs to be considered. It seems axiomatic to me that an outer universe simulation can only contain nested universe simulations of lower space complexity than than itself.
If I am wrong, is there some discussion of this kind of issue online or in a well-know paper or textbook?
Once you have a model that includes a universe and the capacity to simulate universes you can add universes to the model without taking much more complexity because the model can be recursively defined.
This only follows if your universe can not only model other universes but can easily model universes that share its own rules of physics. This is a much stronger claim about the nature of a universe (for example, it seems likely that this is not true about our universe.)
Adding a universe external to this one doesn’t just add more stuff.
The SA does not ‘add’ a universe external to the model. The SA is a deduction derived from the Singularity-model. The Singularity-model does not ‘add’ the external universes either, they emerge within it naturally, just as naturally as future AI’s do.
For the inhabitants, a model that not only explained how their universe worked, but postulated the existence of our universe, would be more complex than one that merely explained their own.
That would only be true if their model was not also a full explanation of our universe, and thus isomorphic to some historical slice of our universe.
In terms of minimum message length, having to describe another universe superordinate to your own adds to the information of the model,
Not at all. The Singularity-model is a scientific extrapolation of our observed history into the future. As it is scientific, it reduces to physics (the model approximates what we believe would happen if we could simulate physics into the future).
The SA is not a model at all. It is a deduction which can be simplified down to:
If the Singularity-model is accurate.
Then most observable universes are simulations.
And thus our observable universe is a simulation.
You seem to think the minimum message length is somehow physics + extra simulations scrawled in. The physics generates everything, so it’s already minimal.
The addition of our own universe could not be encapsulated in a model that simply describes the working of the simulated Conway universe from the inside without adding more information.
No—but only because the physics differ substantially. You are right of course that if Conway beings evolved and somehow they had some singularity of their own in their future that generated simulated Conway universes, they would establish a lower prior to believing they were embedded in a String/M-theory universe like ours. (they of course could still be wrong, as complexity is just a reasonable bias measure). They’d attach higher credence to being embedded in a Conway universe.
But if the simulated universe is based on the same physics, then it reduces to exactly the same minimal program, and it absolutely describes both universes.
This is very similar to the multiverse in physics and the space of universes string/M-whatever theory can generate.
As I mentioned before, I thought you were arguing the orthodox simulation argument, rather than one where the simulations are created from within our own universe. That would not necessarily increase the complexity of the model, but it’s untenable for its own reasons.
For one thing, it’s far from given that any civilization would ever want to simulate the universe at a previous point; the reasons you provided before don’t remotely justify such a project; it’s not a practical use of computing power. For another, assuming you’re only simulating small fractions of the history of existence, the majority of all sentient beings in the universe would not be ones in a simulation. In fact, you would have to defy a number of probable assumptions about our universe to fit as much universe space and time in the simulation as existed outside it.
An entire external universe adds to the complexity of the model, not just how many entities the model contains.
This may not be the case if the simulation itself was produced in the universe as we know it, and our own apparent universe is only a simulated fragment. That isn’t what I thought you were asserting, but that is untenable for completely separate reasons.
What do you mean by complexity and how is it at all relevant?
Take Conway’s life for example. Tons of apparent complexity can emerge from rules simple enough to write on a bar napkin.
Was the copernican model ‘wrong’ because it made our universe-model more complex? Was the discovery of multiple galaxies wrong for similar reason? Many worlds?
The only formal definition of complexity that is well justified is algorithmic complexity and it has some justification as a quality metric for deciding between theories in terms of Solonomoff Induction.
The formal complexity of a universe-model is that of it’s simplest reduction.
The simplest reduction for any scientific model is universal physics.
So there is only one model, all complexity emerges from it, and saying things like “your premise X adds to the complexity of the model” is untrue and equivalent to saying your “premise X makes the model smell bad”.
Adding a universe external to this one doesn’t just add more stuff. To take the Conway’s Game of Life example, suppose that you simulated an entire universe inside it, from the beginning. For the inhabitants, a model that not only explained how their universe worked, but postulated the existence of our universe, would be more complex than one that merely explained their own. With evidence that their reality was a simulation, the proposition could be made more likely than the proposition that it stood alone.
In terms of minimum message length, having to describe another universe superordinate to your own adds to the information of the model, not just the entities described in it. The addition of our own universe could not be encapsulated in a model that simply describes the working of the simulated Conway universe from the inside without adding more information.
Once you have a model that includes a universe and the capacity to simulate universes you can add universes to the model without taking much more complexity because the model can be recursively defined. The minimum message length need not be increased much to add new universes, you just edit the escape clause. Where we are in the model doesn’t matter.
You seem to be thinking in terms of time complexity. Space complexity also needs to be considered. It seems axiomatic to me that an outer universe simulation can only contain nested universe simulations of lower space complexity than than itself.
If I am wrong, is there some discussion of this kind of issue online or in a well-know paper or textbook?
This only follows if your universe can not only model other universes but can easily model universes that share its own rules of physics. This is a much stronger claim about the nature of a universe (for example, it seems likely that this is not true about our universe.)
The SA does not ‘add’ a universe external to the model. The SA is a deduction derived from the Singularity-model. The Singularity-model does not ‘add’ the external universes either, they emerge within it naturally, just as naturally as future AI’s do.
That would only be true if their model was not also a full explanation of our universe, and thus isomorphic to some historical slice of our universe.
Not at all. The Singularity-model is a scientific extrapolation of our observed history into the future. As it is scientific, it reduces to physics (the model approximates what we believe would happen if we could simulate physics into the future).
The SA is not a model at all. It is a deduction which can be simplified down to:
If the Singularity-model is accurate.
Then most observable universes are simulations.
And thus our observable universe is a simulation.
You seem to think the minimum message length is somehow physics + extra simulations scrawled in. The physics generates everything, so it’s already minimal.
No—but only because the physics differ substantially. You are right of course that if Conway beings evolved and somehow they had some singularity of their own in their future that generated simulated Conway universes, they would establish a lower prior to believing they were embedded in a String/M-theory universe like ours. (they of course could still be wrong, as complexity is just a reasonable bias measure). They’d attach higher credence to being embedded in a Conway universe.
But if the simulated universe is based on the same physics, then it reduces to exactly the same minimal program, and it absolutely describes both universes.
This is very similar to the multiverse in physics and the space of universes string/M-whatever theory can generate.
As I mentioned before, I thought you were arguing the orthodox simulation argument, rather than one where the simulations are created from within our own universe. That would not necessarily increase the complexity of the model, but it’s untenable for its own reasons.
For one thing, it’s far from given that any civilization would ever want to simulate the universe at a previous point; the reasons you provided before don’t remotely justify such a project; it’s not a practical use of computing power. For another, assuming you’re only simulating small fractions of the history of existence, the majority of all sentient beings in the universe would not be ones in a simulation. In fact, you would have to defy a number of probable assumptions about our universe to fit as much universe space and time in the simulation as existed outside it.