Comment on Manifolds

Droggelbecher@lemmy.world ⁨3⁩ ⁨months⁩ ago

• kogasa@programming.dev ⁨3⁩ ⁨months⁩ 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 ⁨3⁩ ⁨months⁩ 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 ⁨3⁩ ⁨months⁩ 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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    • kogasa@programming.dev ⁨3⁩ ⁨months⁩ ago

      Not really, you need to have a basic understanding at least

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      • Droggelbecher@lemmy.world ⁨3⁩ ⁨months⁩ ago

        That’s what I thought, which is why I don’t get the meme. Who is it talking about? Who has learned about GR but gets confused by manifolds? How else would they have learned GR?

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  • someacnt@sh.itjust.works ⁨3⁩ ⁨months⁩ 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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    • kogasa@programming.dev ⁨3⁩ ⁨months⁩ ago

      You might be thinking of a [connection of an affine bundle](en.wikipedia.org/wiki/Connection_(affine_bundle). You could learn it through classes (math grad programs usually have a sequence including general topology, differential topology/smooth manifolds, and differential geometry) or just read some books to get the parts you need to know.

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      • psud@aussie.zone ⁨3⁩ ⁨months⁩ ago

        You lost a bracket in your link

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• Cypher@lemmy.world ⁨3⁩ ⁨months⁩ 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 ⁨3⁩ ⁨months⁩ ago

    haaaannnn

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• Foreigner@lemmy.world ⁨3⁩ ⁨months⁩ 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 ⁨3⁩ ⁨months⁩ ago

  I definitely cannot do that

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