As far as we know, the universe is made up of discrete units and any other type of math is an abstraction over discrete math.

I thought it was a smooth continuous manifold

To what extent are the Planck length and Planck second confirmed smallest discrete units?

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.

Where could you recommend I read more about how they are derived scales?

Wikipedia is a good start, but if it's too terse/advanced there's always simple wikipedia which seems to have an explanation as well https://simple.wikipedia.org/wiki/Planck_units

I suppose it was pointless of me to ask if what I received was a wiki link, no offense. Thanks.

you received a link to simplified wikipedia, which is not wikipedia. https://simple.wikipedia.org/wiki/Simple_English_Wikipedia

I can't tell now if you're being intentionally condescending.

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.

Is that because we see no way to bootstrap equipment down so many magnitudes of scale, not even close - or is it something else?

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.

One addendum / clarification:

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.

As far as we know, the universe is a single unity, and any discrete units and any other type of math are human distinctions overlaid upon that unity.

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 assume the post is missing its "/s".

Yes. It was a parody of yunwal's post (which I possibly should have cc'ed). . Reread yunwai's post and mine together and you will understand.

Endless "unity...discrete" discussions have arisen in both science and philosophy since the beginning.

FWIW my use of the phrase "human distinction" was merely for emphasis: I make no claims about non-humans.

In any case, any distinction I have interest in or speak of would be human, whether made by a human or otherwise.

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.

No, the discreetness comes from physical experiments. I do see a problem defining something outside of one’s mind or outside the universe though :)

Discreetness only comes from experiments carried out in secret laboritories.

Pronounce "lah-BORE-i-tories", obviously.