EN/NL PhD @ TU Delft CGV Loves EDM, LoL, TFT and MTG

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Joined 1 year ago
Cake day: June 1st, 2023
  • ඞmir@lemmy.mltoMemes@lemmy.ml•Math
    7·
    4 months ago

    Cursive big f: “integration”, which can be interpreted in two ways. One is “area under the curve” for some part of the curve. Other is “average value of a part of the curve multiplied by the size of that part of the curve”. Curve being the function, the graph, f(x), however you wanna call it.

    Normal d: “differentiation” (from difference), infinitely small change. Usually used in ratios: df/dx means how much does f(x) change relative to x when you change x a little bit.

    Cursive d: “partial”, same as normal d but used when working with higher dimensional data like 3D. Can also mean “boundary” of something. Example: boundary of a volume in 3D, like wrapping paper around a box. Or, boundary of such wrapping paper itself, if it’s not perfectly connecting.

    Omega: just a Greek letter used as a variable, in this case there’s a history of it being used as a sort of “density” variable in the field of differential geometry. The college row in the meme is kind of translating the high school row from a function to a 3D volume.

  • ඞmir@lemmy.mltoShowerthoughts@lemmy.world•*Permanently Deleted*
    1·
    8 months ago

    It would appear to me that there’s not really an “at rest” state in terms of movement in space. We’re on a planet orbiting a sun that orbits the central point of our galaxy, which in turn is also moving and perhaps orbiting something else even bigger. So, “at rest” is always subjective.

    Correct, that’s classical relativity, from before the notion of spacetime even existed.

    But the twin paradox says if a twin travels away at a high speed then returns, they would have aged less.

    It depends on who does the acceleration. Acceleration is key for the twin experiment, and the reason it works is because they are the one accelerating and decelerating. This requires “general” relativity to make sense, it can’t be explained by merely special relativity.

    Whatever is influencing us, there must be a 3d vector in space we, as a whole, are moving toward (probably constantly changing though). So, surely if you sent someone in the opposite of that vector, time for them would actually speed up rather than slow down.

    I don’t get what you mean here… which 3d vector are you referring to, and why should it exist? One of the important concept is that every reference frame is equally valid.

    Would they not “catch up” and be on part overall with time passing?

    From one pov the earth sped up, instead of the twin’s spaceship slowing down. These are both valid interpretations. You can always catch up by doing the opposite of what you did before, but you need to look at acceleration for it to make sense. Acceleration is what turns your 4d vector so your reference frame changes, and you can sort of arbitrarily change “passing of time” if you can induce unlimited acceleration.

    We wouldn’t see this skew on satellites and the like because they’re travelling with us on that vector but at a constant speed relative to us too. But sending away from us and back, we probably would.

    I feel like you’re rediscovering the idea of an “aether” which was disproven by Lorentz and Einstein.

    Note that I’m not a physicist, just someone who loves staying up to date with modern physics!

  • ඞmir@lemmy.mltoShowerthoughts@lemmy.world•*Permanently Deleted*
    10·
    8 months ago

    Sort of. You’re already doing it at this moment.

    Einstein showed that time is not a separate space, but is actually the same as any other dimension. However, we have not found any way to reverse our direction so far. We can only choose a direction to move forward in. In fact, you’re doing so when you get in a car; you’re experiencing a minor change in how you’re moving through time relative to those around you.