Recent content by mma

This is a mathematical statement. Can you prove it?

In Newtonian mechanics, conservation laws of momentum and angular momentum for an isolated system follow from Newton's laws plus the assumption that all forces are central. This picture tells nothing about symmetries. In contrast, in Hamiltonian mechanics, conservation laws are tightly...

I think, you mean something else of "finite propagation speed" than I. As I wrote in the OP, I define here the finite propagation speed as As far as I see, Wrobel's proof is good if we insist to this definition.

I like this nice argument that proves the statement, that continuous mass distribution is a necessary condition for the finite speed of propagation. However the sufficiency is still not quite clear to me.

speed? This question emerged in my mind while studying a discrete and continuous mathematical model of a falling slinky. In the discrete model, we suppose an instantaneous interaction between mass points at a distance, so the action propagates through the chain of mass points with infinite...

This interesting fact was new to me. I found the details in Wikipedia:

You are right. I should have told countably infinite.

>Avogadro’s number is big enough to be considered the physicists’ true infinity. I think that the notion of infinity in mathematics is quite different from "very big". If you add one mole of oxygen to one mole oxygen, the you get two mole oxygen. This is definitely more, than one mole. But if...

Or an energy losing device. If we neglect the energy dissipation, then in our world we can call height on equal right the vertial distance measured from a fixed point and the mechanical work done since started from this point (because then E = mgh). But if we take into account also the...

I meant originnaly exactly this.

@jim mcnamara Still matematicians sometimes take it seriously, see for example here. I would regard these two properties mentioned there by anon:

Perhaps this is in relation somehow with the curvature. We live in a real line bundle L. Its base space is S^2 (the surface of the Earth), and the fibers are the vertical lines. The gravitation defines a connection on this bundle, i.e. determines the horizontal subspaces of the tangent bundle...

My stairs on the torus look like this: where the the points of the opposite sites of the square are identified, so it is is a topological torus:

Penrose stairs is this impossible object: Such an object can exist locally but not globally. The point is, that walking in one direction on the stairs, we are always rising, still we can make a closed walk on it. These stairs are impossible because we cannot draw a closed curve on the surface...

Nobody mentions that Penrose stairs is possible on the torus. I wonder Why. isn't this obvious?