I'm saying whoever builds the simulation would decide its purpose and set the thresholds for shortcuts.

Is there any way we could discover the purpose of the simulation we are living in?

There has to be a catch one way or another.

I think the 'catch' is free energy consumed to perform the computation and the physical resources required to build the computer. Seems like it should be possible to write an equation that spells this out.

Now as for how we could ever know that our universe is virtual, I'm pretty sure that would be impossible.

A simulation, at least the ones performed by humans, typically have a purpose in that they either have the ability for a person to monitor some aspect of the simulation or else they sink parts of the simulation to memory to be reviewed later. Could that be detected?

It could be the case that our universe receives some kind of user input from the host universe, but to us it would just seem like utter randomness, as we would have no way of knowing the source of the input, but rather just a source that has no cause.

This really sounds almost identical to God and all the various arguments for his/her/its existence and potential influence.

We have seemingly stumbled upon some thoughts that seem to us to be useful to some extent to our own small existence.

I think the key word here is "useful". Is they theory that we live in a computer simulation useful? Is a belief in God useful? I would say "yes" if you are a priest but "no" if you are involved in building technology or practicing science. This is why I find this whole simulation argument bewildering, as its coming from people who otherwise seem to have no problem using the laws of physics to make useful stuff--like they are discovering religion but unable to see it as such.

We would need an example of simulating something vs building something.

How about this.

We basically just reorganize things in our universe in useful ways.

Yes, good distinction. Either we have the ability to change the laws of physics in some region of space or other dimension and thus create a universe, or we have to reorganize. Obviously the later is the only thing that is currently possible give what we know. Given that, is it possible to convert the free energy of our universe into a simulation of a similar universe at the level of fidelity that we are currently experiencing? What would that take? Why would we do it? If Universe A (the "real" one) simulated Universe B, which in turn simulated Universe C and so on, where does universe C get the free energy to simulate its universes and so on? Under what conditions would this not consume an infinite amount of free energy?

So, in terms of building a universe, I have no idea what that means.

The only thing I can think of is black holes, but that is speculation of course. There are theories about creating universes each with their own laws via black hole creation, but the nature of such theories are similar to the arguments about living in a simulation--unprovable speculation.

So perhaps the physical complexity we see in atoms and such are extremely over simplified in comparison to the greater universe. Sort of like pixels on a screen vs real life.

Thats interesting. The world does appear to be 'discrete'. However, I would encourage you to think not about the elements but the interactions of the elements. Take 10²³ particles floating around in space, each influencing each other via gravity. How much free energy does it take to compute their time evolution? Can you prove that the "grand programmer", (i.e. God) takes short-cuts in this computation?

Perhaps there are other ways to simulate a universe?

Yeah, perhaps we can build them instead. Or at the very least just "seed life". If you want to simulate a tree at high fidelity, how about you plant a seed?

we need to assume 100% efficiency

And that is the problem. The only 100% efficient simulation of an object is going to be the object itself. Otherwise we require the resources to build and maintain the computer, plus the free energy to power it while it simulates the object and its interactions.

But then my magic universe creating machine requires twice that.

Don't follow this. Why "twice"?

The more accurate you make the simulation, the more energy it needs and the closer it gets to a real universe.

This is false. No amount of simulation realism will make the simulated universe a real universe. It will always be a simulation, by definition. What if the the universe doing the simulating pulls the plug? Is the simulated universe suddenly not real anymore?

Any 100% accurate simulation IS a real universe, since there is no difference.

In one case there is a computer running the simulation, and in the other case there is not. Thats a pretty big difference.

Would be good to define here how one can make a quantitative comparison between a real and simulated universe. What metrics are used to say, for example, a universe is 95% real.

Theory says it takes thousands of years for photons generated in the centre of a star to reach the surface and escape. Do you need to simulate all of those interactions?

This all implies that we have a model of how stars should work according to the accepted laws of physics (the "theory"). You are saying that we can just sweep all those interactions under the rug and make an approximation to those laws, something that can only be done because we have a physical theory to begin with. Interestingly, you need to accept the validity of the original physical theory for you to even make your argument about skipping computations. Either we live in a universe that obeys physicals laws (the theory you refer to) or we do not (the case where Gods computer program can skip calculations and thus violate physical law). This is the "God in the Gaps" argument: You can say "But there is no way to prove that God is not skipping computation in the center of the sun". That is not science nor a valid argument. I could say that there is no way to prove there is not a bunch of fairies and unicorns in the center of the sun.

Furthermore, the question arises as to what is important in the simulation so that corners can be cut. Why is the luminance of the sun important but the dynamics of the suns plasma not? Are you saying that all those things that Humans think are important are the things that must be computed?

TL;DR The argument that you do not need to calculate every interaction requires the assumption that nature obeys physical laws to begin with so that approximations can be made, and thus the argument is in contradiction with itself. Also, it appears to be a human-centered religious god-in-the-gaps argument.

A simulation can take shortcuts.

Please explain how, using our reality as an example. Take two atoms somewhere in our universe. What are the conditions for when the "grand simulation" does not have to compute the interactions?

Also considering e=mc2 , the energy contained in the actual mass of each particle in the universe is going to be significantly higher than the energy used to store the value of that mass (and quantum state) for that particle.

Computation is not about storing the value of the mass. Its about computing the time evolution of all the bits of mass (and other forms of energy). So you do not have to just store the value of the mass. You have to compute the interactions between everything and then update those stored values. Try coming up with a number for the energy it would take to compute all those interactions and then get back to me. Perhaps just do it for your brain, or for a small dust cloud in interstellar space.

Prove it, or at the very least put forward an argument that does not appeal to non-existent computers or non-existent physical laws.