This sort of thing makes me feel there is some deep understanding of reality only inches away from us, we glimpse it through these patterns but the secret remains hidden.
Pronounce "lah-BORE-i-tories", obviously.
In any case, any distinction I have interest in or speak of would be human, whether made by a human or otherwise.
Endless "unity...discrete" discussions have arisen in both science and philosophy since the beginning.
It may be that one day we come up with a more refined model. But as of today, it’s not clear how that would happen or if it’s even possible.
Imagine going from 4K to 8k to 16k resolution and then beyond. At some point a “pixel” to represent part of an image doesn’t make sense anymore, but what do you use instead? Nobody currently knows.
It may also be that "space" and "time" are emergent properties, much like an "apple" is "just" a description of a particular conglomeration of molecules. If we get past Planck scales it may turn that out that there are no such things as "space" and "time" and the Planck constants are irrelevant. We currently don't know but there _are_ a few theoretical frameworks that have yet to be empirically verified, like string theory.
At this point I hold one object that we agree to label "apple". Note that even seeing it as a single object is a layer of abstraction. In reality it's a clump of fundamental particles temporarily banding together
> and then handed you another apple,
What's "another apple"? What does it have in common with the thing I'm already holding? We label this thing to be also an apple, but it's a totally different set of atoms, from a different tree, perhaps from the other side of the planet. Perhaps the atoms formed in stellar processes light years away from that of the other apple.
Calling both of these things "apple" is a required first step to having two of them, but that is an of abstraction, a mental trick we use to simplify the world so we can represent it in our minds.
I'm not a particle physicist but I hear electrons *can* be counted without any unwitting help from our lower-level neural circuitry.
The numbers themselves aren't a problem, I'm just pointing out that our cognition involves many overlapping layers of abstraction, and we're doing mathematics and every other mental activity in one or more of those layers.
That this seems to correlate strongly to real-world phenomena speaks well of the types of abstraction that nature has equipped us with.
However, what about virtual things, e.g. apples in a computer game.
Addition is abstract phenomena based on math, which itself is abstract, so it can only function in abstract setup.
You are differentiating, classifying, etc.
The modern manifestation is mostly the intellectual product of Konrad Zuse, who wrote "digital physics" in 1969.
> https://en.wikipedia.org/wiki/Digital_physics
Wolfram, Tegmark, Bostrom, etc. are mostly downstream of Zuse.
That...? Ah, yes, that Konrad Zuse.
That’s fine for GIMPS, which only searches for Mersenne primes, but doesn’t work in general.
https://en.wikipedia.org/wiki/Primality_test#Fast_determinis... mentions several tests that do not require factorization, though.
Fermat Reincarnation. > Fermat Reincarnation.