>Usually, when we say something doesn't exist in nature, we mean it's fundamentally incompatible with our 3 spatial dimensions as they exist, passes through itself, or is infinite along some dimension, requires infinitely thin surfaces, etc.
Well, that's what we're saying. The distinction lies in ideal/perfect, vs imperfect. For example, does a perfect cube shape exist? If you closely examine any cube in existence, it has small deformities if you look close enough, as the very edges and corners which make up a cube are made of atoms, which are non-cubical in shape (not to even mention quanta). A perfect cube relies on an cubical shape at infinite scale, but as you mentioned above:
>when we say something doesn't exist in nature, we mean it's fundamentally incompatible
>or is infinite along some dimension
Norton's dome requires an infinitesimal point of sorts for the math to work out. Does that exist in reality? Idk, but it certainly seems dubious.
> Well, that's what we're saying. The distinction lies in ideal/perfect, vs imperfect.
No, that's not. "Exist in nature" doesn't mean "perfect". Totally different concepts.
> Norton's dome requires an infinitesimal point of sorts for the math to work out. Does that exist in reality? Idk, but it certainly seems dubious.
A cone requires a point at the pointy end. Does that exist in reality? I've certainly seen a lot of objects we call "cones". And they were pointy.
The point is, if you say Norton's dome doesn't exist then you mean cubes don't exist. And we all agree cubes do exist. A perfect Norton's dome doesn't exist, just like a perfect cube doesn't exist. But a regular Norton's dome certainly does exist. Just like a regular cube. Again, it's not an exotic shape. But it doesn't need to be perfect to exist -- otherwise nothing would exist at all!
Well, that's what we're saying. The distinction lies in ideal/perfect, vs imperfect. For example, does a perfect cube shape exist? If you closely examine any cube in existence, it has small deformities if you look close enough, as the very edges and corners which make up a cube are made of atoms, which are non-cubical in shape (not to even mention quanta). A perfect cube relies on an cubical shape at infinite scale, but as you mentioned above:
>when we say something doesn't exist in nature, we mean it's fundamentally incompatible
>or is infinite along some dimension
Norton's dome requires an infinitesimal point of sorts for the math to work out. Does that exist in reality? Idk, but it certainly seems dubious.