My hunch agrees with the paper. Because computers operate on the rational numbers instead of the real numbers, they can never be embodied. They are always in a simulation...
This even has some concrete applications. See this: https://icfp19.sigplan.org/details/icfp-2019-papers/15/Sound...
Finally, saying that digital computers can't compute functions of the form Real -> Real is like saying that a computer can't compute functions of the form (Int -> Int) -> (Int -> Int). In other words, it's like saying that higher order functions are impossible.
Because of this, no matter how "smart" computers get, we can't trust them not to do stupid stuff. They are smart like that kid in high school who comes up with a formula to turn the world into silly putty, and is stupid enough to use it. There is more than one kind of intelligence, here the argument is that some kinds of intelligence require having skin in the game.
So that kid isn't intelligent?
Of course, geometric optics is like real numbers, and the actual world is discrete: light is a finite collection of photons. So, you can do the simulation by simply emitting a number of photons from each light source and tracing them all the way until they are all absorbed. We can still live in a simulation, but one without algorithmic shortcuts, a simulation where you simulate every single photon.
Now, I'm sure you can come up with your own version of proof that we can't live in a simulation using Nyquist's theorem. If you do, and your Friday is not too busy, please share.
[1] https://users.cs.duke.edu/~reif/paper/tygar/raytracing.pdf
- Vinyl gets dust and scratches that degrade signal.
- Dragging a needle along a surface is an inconsistent and limited mechanism for signal transfer.
- Vinyls are always derived from digital files these days anyway! Except for pre-digital prints, studio rate digital is as "pure" as it gets.
P.S. Tube amps are not better than chip amps either, it's a complete myth. Every measurement a tube amp does well at is beatable with a cheaper chip amp design. People think we can do 10 gigabit Ethernet and 4g LTE radio bandwidth with chips, but not accurately control a speaker producing audible frequencies? Please.
Audiophile products have a weird way of capturing people's hearts despite having no merit. I think it's partly because people hear their favorite music through a device and misplace their feelings for the music onto the device, and partly because they are biased towards rationalizing purchases even when they've been conned by some pseudoscience or empty marketing.
Computers are just devices that perform computations. It's perfectly possible to construct computers that operate on values that are continuous and not discrete. In fact, such computers have been constructed before. They are know as analog computers and were used for things like numerically solving differential equations.
See here for a concrete application of the theory: https://icfp19.sigplan.org/details/icfp-2019-papers/15/Sound...
Another application is the Android calculator, which computes over exact real numbers in the sense described by Computable Analysis.
Finally, it's debatable whether analog computation achieves true computation over the real numbers. The presence of physical noise, and the fact that many physical quantities (like electrical charge) are ultimately discrete at the quantum level, implies that it doesn't really work AFAICT.
However if I remember correctly continuous signals (that is functions of the reals) can be represented without loss with a finite (but sufficient number of) discrete samples.
I read the exact opposite argument yesterday but not from an AGI perspective: https://getpocket.com/explore/item/a-new-theory-explains-how...
Brains are computational devices that are embodied.