Recent content by Feynstein100

Ah okay but isn't that literally the definition of the harmonic mean? Not sure what we'd get by proving it. I mean, I'm trying to find a relationship between HM and σ, not HM and E. Also, in the example, the E remained constant whereas the HM kept decreasing, exactly illustrating my point...

Sounds interesting. But what exactly is E in this case? 😅

I was doing a thought experiment on the harmonic mean. Let's say we have a sequence of 4 numbers: 100, 110, 90, 100 The arithmetic mean (AM) of this sequence is 100 but the harmonic mean (HM) is 99.4975. Let's imagine that the initial and final values remain constant but the middle ones get...

Just when I thought I was done, they pull me back in 😁

I give up. This is too difficult 😥

This seems to be in direct opposition to what you say here: This just keeps getting more confusing 😅 So it's the 3D portion of the 4D curvature that's actually flat? This seems unnecessarily confusing. Why not just refer to the 4D curvature as a whole to get the full picture?

Ah I get it now. I thought the overall curvature of the universe was a function of only the stress-energy density i.e. C = f(ρ), hence the problem. But turns out, C = f(ρ,H) with H being the Hubble constant. And while ρ decreases with time, H increases, canceling out the overall effect and...

That's kind of what I'm having problem with. Does that mean the curvature of the universe changes with time too? i.e. It went from being closed/finite to being open/infinite? Which does not seem logically possible to me. I still don't get it 😕

I'm sorry, I don't understand. What does that mean? 😅 Damn, I don't understand that either. I thought we were talking about the curvature of 4D spacetime? I mean, what other kinds of curvature are there?

Thank you for the correction. It looks like I misunderstood what GR being local really means 😅. It is applicable to the entire universe. I learned something new 😀 However, the second point still kind of stands. Just replace matter density with stress-energy density. My problem is still that this...

So I've often heard that when GR is applied to the entire observable universe to calculate its curvature, we get a value of zero, meaning that the entire universe is flat. I've got 2 problems with this. The first is that I thought GR was a local theory i.e. it only applies locally. Trying to...

Damn, that's a lot of homework lol. I'll get back to you when I've read them all.

Eh......what does that mean?

There is? I'd like to learn more 🤔

So it is actually arbitrary and random 😅 But that's good. Now I can begin my search for the Feynsteinian 😁