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  • Kogasa@programming.devtoMemes@lemmy.mlMath
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    18 days ago

    Stokes’ theorem. Almost the same thing as the high school one. It generalizes the fundamental theorem of calculus to arbitrary smooth manifolds. In the case that M is the interval [a, x] and ω is the differential 1-form f(t)dt on M, one has dω = f’(t)dt and ∂M is the oriented tuple {+x, -a}. Integrating f(t)dt over a finite set of oriented points is the same as evaluating at each point and summing, with negatively-oriented points getting a negative sign. Then Stokes’ theorem as written says that f(x) - f(a) = integral from a to x of f’(t) dt.




  • This already exists. https://libraryofbabel.info/

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  • Geometry is a bit tricky. A lot of “obvious” facts about geometry are less obvious to prove from a given collection of axioms forming a model of geometry, because their “obviousness” stems from our natural facilities for understanding space and position. Sometimes, historically, things that are “obviously” true in geometry turn out to be false, or depend on unwritten assumptions, for complex reasons. It may be surprising in this light if current AI can beat humans’ intuition plus logic using purely analytic tools.






  • YouTube is only one section of an entire corporation.

    It’s a corporation, not a charity. They don’t spend tens of billions per year out of good will.

    Ads were fine, the ads now are not fine.

    Ads were not making enough money to justify continued operation.

    They were successful when they were less intrusive, why do they need to do things this way and break up the videos when they have grown an empire on what was previously done?

    Because “what was previously done” is not sustainable.


  • They had paid for it for years.

    Yes. With the intent of making a profit eventually. Or they wouldn’t have.

    They combat this with the price of add on devices, wall mounts, hdmi cables, etc.

    What is YouTube going to “combat” with if not advertising or subscriptions…?

    This is where my brain says fuck you. One billon means you’ve won. Stop being a greedy dick.

    One billion means nothing if you’re spending tens of billions per year to continue operating. I’m not suggesting the CEO of YouTube deserves to get richer. I’m saying the company has operational expenses and investments that require some level of profitability, and “free for everyone forever” is literally just not a viable option.