Their argument is that quantum gravity can encode undecidable statements, and therefore cannot be completely computed. Of course take it with a grain of salt, since it relies on an incomplete and possibly inaccurate characterization of quantum gravity, something we don’t know anything about. Still, a cool idea.
And again, almost every statement in this paper is wrong, including the main claim
Only if you assume the law of the excluded middle, right?
Statements aren’t just true or false, they can also be malformed or undefined.
Of course the whole affair seems a little moot since you obviously only have to be accurate enough that it doesn't disrupt the ancestor simulation or whatever, but that's less fun to think about I suppose.
for the article: "the fundamental nature of reality operates in a way that no computer could ever simulate"
Yes, no computer in our universe, with our physical laws. In "a totally different level of existence", all bets are off regarding the fundamental nature of reality there. It could be utterly different. So, speculation is nonsensical, it's unfalifiable.
It’s like saying
bool isTrue = true;
bool isProvable = false;
bool isTrueAndProvable = isTrue && isProvable; // falseBut some people seemingly like to pretend with enough "can do attitude" they can prove or disprove anything in a paper, no matter how unconvincing the line of reasoning.
Basically simulation here means “is a TM”, not “is nested”.
Finding evidence is nonsensical if you assume they set everything up perfectly and have never intervened.
That is a stupendously huge "if".
In any case, here’s some food for thought: ray tracing is undecidable [1]. If something is undecidable, it is for any form of computation, classical, quantum, or anything. Does this mean we can find some “glitches in the matrix”. It simply means such glitches are there (if we are in a similation). But they might be too infinitesimal for us to identify.
[1]https://users.cs.duke.edu/~reif/paper/tygar/raytracing.pdf
Does it? Do they?
Good luck. I don't know why anyone would spend money on this but... sure, go ahead. Let's go back to the tenth century. WHy not? We burn money are far stupider shit.
The main thing I'm trying to imply is that if Jesus shows up and starts doing miracles constantly, the proof gets pretty simple. Same thing if someone sticks their digital finger into a simulation. Demonstrating the evidence would be pretty straightforward.
Yes. The halting theorem is a version of God's omnipotence paradox: if God is omnipotent, can he make a rock that's so heavy that he can't lift it? Either way, God's power is limited. Similarly, can God create a universal halting decider? If he can, then we can use that halting decider to create a program whose halting can't be decided. I won't bore you with the details, but the idea is that the "God" I used above can be anything. It can be the writers of the simulation we live in.
> Do they?
No matter who the writers of the simulation are, they are finite beings, and their devices are finite, one way or another. The set of real numbers is infinite and uncountable. So not all numbers can be represented. Any representation of real numbers will make approximations.