Nick @internic@social.cleverlibre.org

@futurebird Well, as far as I can tell, in my specific case (which may be quite unusual for all I know) it's less a question of understanding than the ability to physically execute on that understanding.

I think if the utility of the things you're making depends on the precision with which you make them, that's where someone like me would struggle. But as you said, using software is always an option, as is constructing things from modular pieces, where no free-hand precision is required.

As an example of the latter, when learning non-Euclidean geometry, I think that polyhedra can be a good stepping stone to thinking about smooth surfaces (e.g. Euler number), and having physical models could be really helpful. You could imagine, for example, cutting out paper polygons and building polyhedra, but someone like me would struggle to cut straight sides and the proper angles (which then messes things up when you try to get the polyhedron to close on itself properly). However, a colleague had a set of magnetic building pieces (magnetic cylinders and ferromagnetic ball bearings) that could be naturally pieced together to form polygons, so with that I was able to build every platonic solid in no time. It worked fine for me because it didn't depend on the fine accuracy of placement. So even for people like me, it is possible.

I only commented because I know for many people arts and crafts are a happy carefree space, and they may forget that there are also people who view them with as much fear and loathing as some people have for math.

@MichaelPorter

4. You're right that it's not as though every mass is a multiple of the Planck mass (obviously); it's not a smallest unit of mass. It's perhaps more reasonable to think of it as a dividing line between the least massive black hole it makes sense to consider and the largest non-black-hole, point-like particle it makes sense to consider based on our current understanding of physics. So if you give single point-like particle (like an electron) that much energy then whatever happens requires new physics to describe, since it's at the boundary where two incompatible concepts meet.
5. There are other places where we see inconsistencies are that not directly related related to the Planck scale. The example of this I'm most familiar with are questions that arise from the black hole information paradox and related problems. Here the fundamental issue is that stuff falling into a black hole seems to be an irreversible process that destroys information whereas quantum mechanics demands that all processes are reversible and conserve information. Unfortunately, since the questions here relate to what happens at the event horizon of a black hole and what happens when it evaporates (something that would only happen in the very late universe for ordinary black holes), these are also not very accessible to experiment/observation. Some apparent, purely theoretical progress has been made in this area, though.

@catselbow @futurebird

@MichaelPorter @catselbow @futurebird Oh yeah, no issue with your questions at all. Actually, the only problem is that most of my professional work in Physics was in non-relativistic quantum physics/quantum information, so this topic isn't entirely in my wheelhouse. If we're lucky, someone better prepared may chime in.

So without getting myself into too much trouble speaking on things I haven't thought enough about, I'd make a few points:

1. AFAIK, Planck originally just came up with these as a set of natural units, ones that arise from only fundamental constants, not reference to specific objects, etc. And I think he came up with these before general relativity was formulated, so the phenomena that are now discussed in relation to them are not ones he would have known about.
2. OTOH, you might reasonably expect that if these ratios make quantities with these specific dimensionalities there would be at least *some* physical phenomenon that would be characterized by that scale, but not necessarily that it should be especially interesting.
3. We haven't measured phenomena anywhere close to these Planck scales (length, time, or single-particle energies), so our theories could easily be wrong way before you get there, but these correspond to places we're pretty sure there *must* be something else because our existing theories don't make sensible, internally-consistent predictions there at all.

@catselbow @futurebird

@MichaelPorter @catselbow @futurebird Yeah, but in the case of the Planck mass this is the mass of a single fundamental, point-like particle at which our theoretical understanding breaks down (because you need to apply both quantum field theory and general relativity at the same time, which we don't really know how to do). Viewed in that lens it is huge, compared to something like an electron.