silent_water [she/her]

  • 11 Posts
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Joined 3 years ago
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Cake day: October 26th, 2021

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  • they’re supposed to all be versions of that one, it’s just not always very easy to see how - joke was mainly about that. category theory calls things compact if they’re “small” in a very particular sense. algebraic compactness also has nothing to do with the topological notion, at least on the surface (abelian group that’s a direct summand of every group containing it as a pure subgroup). basically, every area of math where the topological notion makes no sense will invariably call something compact eventually, because mathematicians can’t resist.

    sometimes if you squint you can see how it relates back to the topological notion but frequently it’s anything but obvious if you don’t already understand the field - which means when you’re trying to work things out for yourself, you just have to treat it like one more definition of the same word until you finally get it one day.

    I think it’s easier if you have a prof who can just make the analogy clear from the start.


  • it’s worse than different languages. they use the same words to mean entirely different things. so you can say stuff from the same lexicon that means entirely different things to different mathematicians. there are supposed to be analogies that help you translate but jfc I swear to god if I hear one more definition of compactness I’m going to cry. no I’m not going to learn more category theory to understand how I can use a sheaf to translate the different notions because that also doesn’t mean what I think it means. shut up shut up shut up words mean things. next you’re going to tell me red is blue because color theory staaaahp

    self-teaching math is a pain in the ass


  • yes, this is true. no, this isn’t why wages haven’t kept up with productivity growth or why you must work 40 hours to sustain yourself. you have to work because profit earned must increase and paying you even one iota more than you need to be able to show up to work again tomorrow is a loss of profit. if they could make you work 80 hours a week or 160, they would in heartbeat.

    thankfully, this is outlawed because labor movements of the past fought to enshrine in law a limit on how much you can be forced to work and set a minimum bar for how much they can pay you. these laws are under fire - I explore why in the rest of this reply - and will be repealed eventually if labor does not resist collectively.

    however, the rate of profit always decreases on a long enough timescale because of dead labor (technology, machines, etc), inter-capitalist competition - capitalists will steal profit from each other if there’s more to be had - and because infinite growth is impossible so eventually externalities will always overcome the creation of new capital.

    consequently, capital accumulates in the hands of the capital-owning class - an ever-shrinking group of them, at that - and this continues until you, the worker, make so little that you cannot actually show up to work the next day - the loss of social reproduction. reproduction here doesn’t only refer to progeny but also feeding, clothing, housing, etc. yourself and your family, the meeting of the basic necessities that allow you to continue working, including your health - physical and mental. capital eternally strives to reduce what it must subsidize on your behalf as ensuring you can take better care of yourself reduces profits. a capitalist that makes more profit outcompetes and drives out of business all others who choose to make less profit, eventually.

    this is also why capitalism has cyclical recessions, a fact predicted in the 1870s and termed crises of capitalism, when capital has accumulated in too few hands, profit can no longer be made, and workers struggle to feed themselves. you’re just noticing Marx’s second law - the law of capital accumulation.