tears posted:yeah it doesnt really answer the question but i appreciate the effort

This is really something that many serious physicists have struggled with. "Is the wavefunction real?" is a question that has seen a decent amount of back and forth over the years by physicists studying quantum phenomena

toyotathon posted:yup let's do visual group theory. should i catch up to ch 6?

sounds good to me

Always inspiring to see an independent researcher come up with something new.

In this case the 'amateur' has a PHD in physics but it still gives me hope lol

It's more rigorous/theoretical than the type of linear algebra I learned in Uni, which was very much applied, whereas Friedberg covers generalized vector spaces, not just the 'spatial' ones in R^n

I'm going to go do some right now!

toyotathon posted:another's about spheres. if you're standing on a sphere, holding a compass facing forward, is it possible to walk a path on the sphere and come back to where you started, w/o the compass doing a full rotation, either its needle, or spinning around its N/S axis, or E/W axis?

just put your finger on the needle as you walk around

toyotathon posted:had a math-specific question, well 2.

first is about curvature on a 2D surface. if you take the set of normal vectors at every point on a 2D surface (call itA), and multiply them by a scalar r, it makes a new surface (call itB). could you find the radius of curvature ofA, by looking at whereBintersects itself, for a given r? if you look at my old exact constraint notes maybe you can see what i'm getting at, and why...

why would **B **necessarily intersect with itself? it sounds like you're just talking about rescaling the surface **A **by r, which wouldnt by itself introduce any sort of self-intersections that werent in **A **to begin with.

another's about spheres. if you're standing on a sphere, holding a compass facing forward, is it possible to walk a path on the sphere and come back to where you started, w/o the compass doing a full rotation, either its needle, or spinning around its N/S axis, or E/W axis?

theres nothing stopping you from holding the compass still, facing the same direction, while you walk in a very small circle. if you want to mark a point on the compass and align that with your velocity then you will always make a full rotation.

Like c-man says, B is not guaranteed to have intersections.

On which 'side' do we draw the blades of grass? The top or the bottom?

Also, imagine you have an elliptical indent. Which radius are we interested in, the minor one or the major one? What would the 'correct' radius of curvature be, as you call it?

tears posted:maths is for harry potter nerds

life finds a way