silent_water [she/her]

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

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  • silent_water [she/her]@hexbear.nettoScience Memes@mander.xyztopology
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    2 months ago

    there are exactly 4 division algebras (over the field of real numbers): the real numbers, the complex numbers, the quaternions, and the octonians. you can’t add any more complex parts because you lost associativity with the octonians. I’m not entirely sure how the first domino leads to the last, though.









  • a functioning public transit system covers the whole city, nearly point to point, and it runs on a regular schedule with buses and trains arriving every few minutes.

    but who’s going to pay for it???

    it’s really a good thing no one has ever run the numbers on this and there’s absolutely no literature analyzing the costs of various forms of public infrastructure to determine which is the most cost effective. there’s no way at all anyone has ever done that.


  • have you ever been to an American city? everything is at the service of roads, cars, and space to park the cars. we have thoroughfares through residential neighborhoods, monstrous intersections that are unsafe to cross by foot, infrastructure that’s unsafe to use by any mode of transportation that isn’t a car – because the cars will run you over – and it’s all wildly more expensive and less efficient than a functioning public transportation system. think of it like this – if more people can get where they need to go by public transit, the roads won’t be so congested.


  • what’s the remainder of pi after division by 3 and 3^2? notice how the remainder is the same – i.e. there’s no 3s digit needed. and the same will be true for all higher powers of 3. this is because pi is <3^n for all n > 1. but we failed to express the fractional part of pi. if we extend to the p-adic rationals, we can express it as an infinite expansion but that’s not allowed for p-adics – they can only have a finite number of digits in the part to the right of the radix.


  • silent_water [she/her]@hexbear.nettoScience Memes@mander.xyzi and π
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    9 months ago

    yeah, the remainder of pi after p^2 for p>2 will always be the same as the remainder after division by p (p^2 if p=2), so it truncates to the left of the radix, and p-adic rationals can’t go off infinitely to the right of the radix. also, more trivially, pi isn’t algebraic so it’s not the solution to any polynomial with rational coefficients, so it’s also not the solution to any polynomial mod p^n.