Manifolds

Comments

• Droggelbecher@lemmy.world ⁨5⁩ ⁨days⁩ ago

  Can someone explain this to my physics grad student ass please?

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  • kogasa@programming.dev ⁨5⁩ ⁨days⁩ ago

    Manifolds and differential forms are foundational concepts of differential topology, and connections are a foundational concept of differential geometry. They are mathematical building blocks used in modern physics, essentially enabling the transfer of multivariable calculus to arbitrary curved surfaces. I think the joke is that physics students don’t typically learn the details of these building blocks, rather just the relevant results, and get confused when they’re emphasized.

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    • niktemadur@lemmy.world ⁨4⁩ ⁨days⁩ ago

      The existence of a connection on a manifold enables one to reason consistently about geometric concepts on the whole manifold.

      The geometry of the cosmos itself. Tracing good ol’ fashioned circles and triangles with the full extent of the visible universe and even beyond. This stuff blows my mind, even just the mere fact that we’re doing it, let alone the fact that we’re getting such incredible, counter-intuitive results.

      Picture yourself having a time machine, going back to visit Euclid or Pythagoras, or even Kepler or Galileo, and blowing their mind with four words: The Geometry Of Spacetime.

      Not only does time itself has a geometry, it must curve and contract to accommodate the absolute speed of light… nuts I tell ya.

      Then there are at least four spatial dimensions, but there may be as many as eleven. To think that Copernicus thought epicycles were weird, wait till he gets a load of THIS!

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    • Droggelbecher@lemmy.world ⁨4⁩ ⁨days⁩ ago

      Is there a way to learn general relativity WITHOUT those concepts? My curriculum made sure to introduce all that before going into GR, didn’t know that wasn’t common. Guess that was my point of confusion.

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    • someacnt@sh.itjust.works ⁨5⁩ ⁨days⁩ ago

      I do not recall well, but connections are sections of a suitable bundle, right? I have to eventually learn this but eh, seems too tedious.

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  • Cypher@lemmy.world ⁨5⁩ ⁨days⁩ ago

    I can only explain the image portion, Koalas eat eucalyptus leaves but cannot recognise them as food when they are off the branch.

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    • Hadriscus@lemm.ee ⁨5⁩ ⁨days⁩ ago

      haaaannnn

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  • Foreigner@lemmy.world ⁨5⁩ ⁨days⁩ ago

    I don’t know about the physics part, but the picture is taken from this video:

    youtube.com/shorts/9IZ410VrikQ?feature=shared

    I highly recommend this channel, they have a bunch of funny videos with animal facts.

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  • skulblaka@sh.itjust.works ⁨5⁩ ⁨days⁩ ago

    I definitely cannot do that

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• Engywuck@lemm.ee ⁨5⁩ ⁨days⁩ ago

  Actually, manifolds and differential geometry was the best part of my undergrad studies and it applied nicely to GR.

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• Reddfugee42@lemmy.world ⁨4⁩ ⁨days⁩ ago

  Thank god for NeurotypicalGPT 😅

  chatgpt.com/…/67b2f3fb-0950-8013-ae65-28078af011b…

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