a.k.a. We Are The Solution To The Halting Problem
There is a theory going around that we live in a simulation. Elon Musk, cofounder of PayPal and CEO of SpaceX, Tesla, and Neuralink suggests that if realistic simulations of the universe are possible, then it is highly likely (his figure was billions to one) that we are in one of the simulations, and not in the "real" universe.
Indeed, realistic simulations of the universe are possible - but not real enough for that hypothesis to hold up to scrutiny. One can make the assumption that humans are creative - in the sense that we are not confined to any one system of logic or deduction. This is a much broader assumption than that we exhibit randomness due to quantum mechanical laws: it is the assumption that we have an ability to direct the world around us, that is absolutely undetectable by physics.
Experience
For most people, it is the case that they experience. They have qualia. Some of us only dimly, like mosquitos or liberals. Others experience vividly, like buddhist masters and great artists. In any case, experience proves that this world concerns us so that we can affect it. Descartes had the right idea when he said, "I think, therefore I am". If you experience yourself thinking, then thinking is either brought about by you, or under your control. If you experience vision, then what you see is similarly either a side effect of your beingness, or otherwise under your control.
Imagine yourself as a computer program. There's not much to imagine, because computer programs operate almost entirely deterministically. Imagine yourself fast asleep, and you've got the right image. There is no experience at all, whatsoever. This is true for all programs, from chess engines to the most sophisticated AI. They operate according to laws, are confined by those laws, and can be predicted according to those laws.
Looping Problem
The Halting Problem (perhaps more aptly named the Looping Problem, since not to go on a tangent, but programs that halt can be trivially proven to halt (just letting the proof that it halts be the number of steps you must run the program before it halts), but programs that do not halt cannot so trivially be proven not to halt - it is the looping programs that cause the trouble) has no algorithmic solution. There are tons of proofs of this all over the internet, including one written in the style of Dr. Seuss.
That is, there is no combination of syntax and semantics that, allowed to run endlessly, eventually outputs a looping proof of every program that loops, and a halting proof of every program that halts.
I choose to make the assumption, nay hold the belief, that in the course of events, humans can and will eventually discover a looping proof for each program that loops, and a halting proof for each program that halts. As experiencers, we do not act according to any system of laws. We have the creative power to invent new systems of notating programs and proving whether or not they do indeed halt.
The End
If we lived in a simulation, and were governed by its algorithms, we would not be able to solve the halting problem for each algorithm. We would not be able to prove every single true theorem about the natural numbers. If we can do so, then we do not live in a simulation - we live in the real universe, and thus can draw upon its infinite complexity.
It is clear that we can solve every problem, since we do experience. Experience is the very newness, the very becoming. Where there is experience there is creativity, and where there is no experience there is formula and calculus by rote.
Because we experience, it is impossible that we should live in a simulation. I would set the odds that we do not live in a simulation as billions to one.
