Regarding the simulation hypothesis

There appears to be a lot of bad arguments against the simulation hypothesis. As an example, once I read someone saying that simulated realities should be of lower complexity than the reality which is simulating them. I think it is not true, and that self-replication is only one example. There is also this Von Neumann universal constructor which not only can reproduce itself but it can also grow in complexity with time.

I went to wikipedia to read more about the simulation hypothesis and found a list of "However"'s that surprised me a lot. I will comment them all:

- "The assumption of this theorem is very far from being complete [...]"

Not very good for the first one: a negative-proof fallacy.

- "Arguments against simulation realism: Gravitational singularity, any of scientifical singularities [...]"

I don't see why an implementation of gravitation could not return Infinity for a certain combination of space and time coordinates.

- "[...] Weak helpfulness of Weather simulation, weak helpfulness of Earthquake prediction [...]"

I don't quite understand this one. The fact that current weather simulators could improve doesn't seem to say nothing against or in favour of the simulation hypothesis.

- "[...] Butterfly effect [...]"

Is this saying that simulations have to be linear? Aren't non-linear systems allowed?

- "Simulations are sometimes modified during their lifespan, but Physical constants (exact), Mathematical constants (exact), Exact trigonometric constants are stable (not to be confused with programming constants which are changeable)"

This one is a bit blurry. First of all, programming constants are not generally changed once the program is compiled. All programs have some exact constants declared whose value doesn't change unless a hacker modifies the exact byte of the constant in the compiled code. Secondly, this argument is a fallacy; the fact that some simulations are modified during their lifespan doesn't mean that there can't be simulations whose foundations don't change at all.

- "Simulations are temporal ("can be turned off", "restarted"), so the longer we (mankind and/or a person) live, the less likely it is that we are part of a simulation"

That is assuming that: "If a simulation is turned off or restarted, agents inside the simulation will notice it". I don't think that needs to be true. Maybe the universe just restarted now after being applied a patch and we didn't notice.

- "Simulation that is undetectable for scientists (for instance both astronomer and at the same time quantum physicist) would have to be very large and detailed, and hard to motivate with mankind ethic."

This is a misunderstood in complexity. Complexity doesn't only arise from very large and detailed systems, it can arise from very simple ones. Exact examples for this are fractals and, in general, any non-linear system.

- "Theory about simulation undetectable by scientists is not approved by ockham razor principle."

As if the Ockham Razor was a dictator who says what is true and what is not! Even though, it is the best argument in the list.

I think there isn't any reason why a system could not be simulated. Universally accepted Church-Turing hypothesis says Turing machines can execute any algorithm, and any digital computer is already a Turing machine given that it had unlimited resources. And in practice, none algorithm needs unlimited resources.

However, is the number of available computational resources going to become a singularity ever?