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.
I don’t think this understanding will be related to the structure of reality but instead the structure of discrete math. Math is not an observed property of reality it’s a system of describing quantities and relations between them, often with plenty of practical application. Math is applied philosophy and physics is applied math.
The very notion of discreteness depends on subjective definitions of "objects". We take concepts of objects for granted because they make interacting with the world tractable, but it's really hard to define them outside of minds.
No, discrete math is exactly the same regardless of your definition of "object". It is completely independent of that. Discrete math is important to any theoretical beings that have any concept of "objects" whatsoever. It would be mostly irrelevant to entities that have no such conception, but those entities are not writing math papers.
Which is exactly why I initially suggested that the structure of primes has more to do with how theoretical beings count than with how the universe propagates state.
Can you explain what you mean here? I mean yes there’s a universe so it can be see as a unit. There’s also quantum mechanics, telling us we can only distinguish discrete objects at the bottom of the scale. Can you give an example of a non-human distinction, or explain what you mean by that concept?
I was referring to spacetime in GR is modeled as smooth continuous manifold. In case you're serious though, planck length are not some fine-grained pixels/voxels in the cartesian 3d world, at least not confirmed; in-fact planck units are derived scales.
I'm not a physicist, but I think those are the smallest units in the sense that they are the smallest units we could theoretically interact with/measure, not some hard limit. It's just that it's moot to consider anything smaller because there's no way for us to ever know.
Any given model has less fidelity than reality. An atlas map of the US has less detail than the actual terrain. The Planck constants represent the maximal fidelity possible with the standard model of physics. We can’t model shorter timeframes or smaller sizes, so we can’t predict what happens at scales that small. Building equipment the can measure something so small is difficult too… how do you measure something when you don’t know what to look for?
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.
If I handed you 1 apple, and then handed you another apple, you wouldn't be surprised to find that you had 2 apples. The same trick works with oranges and pears.
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.
Personally, I suffer from whatever it is that drives a person to think about what numbers mean.
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.
There are no virtual things! Every computer / imaginary apple is represented by real electrons on a drive / chemicals in a brain. Even if we are a simulation, we also have to ultimately be represented by something real.
It seems that there are no real things either. As far as we know, every real thing is represented by another real thing. Even electrons are made of quarks, which are probably made of other things we don't know yet.
Addition is abstract phenomena based on math, which itself is abstract, so it can only function in abstract setup.
It’s a huge refrain that shows up again every 20 years or so. Wolfram wrote a huge book with this premise, but I don’t think it’s gone anywhere even though it’s surely 25 years old by now.
It's arguably ~2500 years old, dating back to the Pythagoreans, who believed that "all is number" and had a very large and complex system of musical rituals.
The modern manifestation is mostly the intellectual product of Konrad Zuse, who wrote "digital physics" in 1969.
Wolfram came to our evolutionary biology department to preach that book about 20 years ago. We all got our heads into cellular automata for a while, but in the end they just don't have the claimed profound explanatory power in real biological systems.
GEB was similar in a cycle prior. It's cool to dream but the limits of accepted knowledge requires the hard work of assembling data, evidence, and reasoning.
Wouldn't it be fun if someone out there already knows a simple way to determine if a number is prime without factoring, but to them it is so obvious that they didn't even consider others may be interested.
Well I have a really elegant proof for this but I don't have enough space in the HN reply box to write it out -- but it is trivial, I am sure you will work it out.
Since 2002 this has been known, and it's one of the least intuitive things in modern math. (versions with probability of 1-\epsilon have existed since Miller-Rabin in 1976)
I had a similar feeling.
But I think this is indeed a glimpse to the intrinsic structure of reality itself, not just a promise of seeing reality. Like we can have a blink of turning around in Plato's cave.
I think the patterns of the Mandelbrot set is a similar thing. And there are only a handful of other things that shows the very basic structure of reality. And the encouraging thing is that it seems the core of reality is not an infinite void.
