هاوي رياضيات

@hhaammmaadd

pauca sed matura

Vrijeme pridruživanja: siječanj 2012.
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  1. prije 6 sati

    مع شهرة مبرهنة بايز Bayes’ theorem إلا انه لم يشاركها مع أحد ظنًا منه أنها لم تكن بتلك الأهمية ووجدت بعد موته في اوراقه ونشرت.

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  2. proslijedio/la je Tweet
    prije 11 sati

    You can read his paper, translated into English, here: It's short and sweet. Equation 6) contains the new formula for momentum, built into the new relativistic version of Newton's F = dp/dt. (5/n, n = 5)

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    prije 11 sati

    Planck wrote: "However, in view of the complicated theory of these experiments I would not completely exclude the possibility, that the principle of relativity on closer elaboration might just prove compatible with the observations." And so he went ahead and published! (4/n)

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    Odgovor korisniku/ci

    It’s closely related to motivic cohomology/chow groups, for example. That is, loosely speaking, it is (conjecturally) the most “geometric” “cohomology theory.”

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    prije 11 sati

    Planck published his paper "The Principle of Relativity and the Fundamental Equations of Mechanics" shortly after a physicist named Walter Kaufmann had done experiments that seemed to confirm a *different* formula for momentum, due to Max Abraham! (3/n)

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    prije 12 sati

    Planck's formula for momentum almost matches Newton's for speeds much slower than light. But it gives dramatically different answers at high speeds! (2/n)

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    prije 12 sati

    Max Planck was the first established physicist to embrace Einstein's work on special relativity. He worked out some important consequences! Later, in 1914, Planck helped Einstein get a research position in Berlin. (1/n)

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    Robert Wald mentions (in his General Relativity) an interesting partial order relation on the set of spacetimes (M,g), with metric g, and citing Zorn's Lemma. It is: (M,g) ≤ (M',g') if M can be isometrically embedded in M' with their Cauchy surfaces preserved.

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    Useful theorem: if f_n: [a,b] → R is a sequence of differentiable functions which converge at one point, and their derivatives df_n/dx converge uniformly on [a,b], then f_n converge uniformly to a differentiable function f and f'_n(x) → f'(x).

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    Odgovor korisniku/ci

    Sometimes complete info in one dimension gives you complete info in other dim. Adjoints are only half of the story, norm, or canonical form is the other. Together them make inverse. inv(x) = adjoint(x)/norm(x). I've been writing something up, it's very WIP

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    Odgovor korisnicima

    Yes, Brendan also talks about products and coproducts, and then he constructs monads by following the double arrow both ways, which gives arrows in A: A(a,RLa) It is all very delightful!

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    All this stuff is very nice. One cool thing is that cartesian product, disjoint union, "and", "or", "implies", and universal and existential quantifiers can all be defined using adjoints.

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    Odgovor korisnicima i sljedećem broju korisnika:

    I'm glad to spend some time in an ivory tower, but I'm not going to stay awake all night worrying how to polish the walls.

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    Odgovor korisnicima i sljedećem broju korisnika:

    Isn't this what scientists always did in times of trouble: retreat to the ivory tower?

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    Odgovor korisnicima i sljedećem broju korisnika:

    It's also funny how people work hard to make everything perfect in pure mathematics, while more important issues are left to the decision procedures of Trump, Putin and Xi Jinping. It seems the quest for tidy perfection is just a game to distract us from real life.

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  16. proslijedio/la je Tweet
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    We can write this like so: C(a✕b,c) <=> C(a,c^b) where L = _✕b, and R = _^b. What I just said I got straight from Brendan Fong from this cool lecture where he and each give a complete lecture about adjunctions! 3/end

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    The <=> means that there's a pair of arrows, one in each direction, that these two hom-sets are isomorphic. The first example given is currying: a function in two arguments is equivalent to a function of one argument returning another function in the remaining argument. 2/n

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    An adjunction is a way to relate two objects a and c, but not directly: C(a,c) Instead, we get two maps, (L)eft and (R)ight, which allow to relate them: C(L(a),c) <=> A(a,R(c)) 1/n

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  19. 2. velj

    quantum field theory: the study of quantum-mechanical systems with infinitely many degrees of freedom.

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