b·log(X)~N(μ,σ²)

A blog for cool maths things, uncool maths things and cool non-maths things (but not uncool non-maths things)  

[blog-normal-distribution]

she brownian on my loop till i soup

[blog-normal-distribution]

he liouville on my gravity till i quantum

[blog-normal-distribution]

they schramm on my loewner till i evolve

[blog-normal-distribution]

she brownian on my loop till i soup

[blog-normal-distribution]

he liouville on my gravity till i quantum

[blog-normal-distribution]

she brownian on my loop till i soup

[plastichenbit]

screw it. biblically accurate angle

[bayesic-bitch]

Mathematicians be like:

Def 1.1: A function f is fucked-up iff it is not Lebesgue measurable

Def 1.2: A function is evil iff its graph has non-integer Hausdorff dimension.

Exercise 1: Prove that there exist fucked-up and evil functions

[thoodleoo]

you know what? fuck you *replaces all the boards in your ship with different boards until you aren't sure whether it's the same ship anymore*

[postilionstruckbylightning]

You know what? Fuck you back *builds exact replica of the ship with the discarded original boards*

[thoodleoo]

[math-memes]

[unknought]

new personality test I guess

[fun-o-physics]

[blog-normal-distribution]

u tellin me a brain ate these amoebas? 🤨

[blog-normal-distribution]

*buys a box of hagomoro chalk* *eats a stick of hagomoro chalk* *eats a stick of hagomoro chalk* *eats a stick of hagomoro chalk* *eats a stick of hagomoro chalk* *eats a stick of hagomoro chalk* *eats a stick of ha

[vacuously-true]

HAGOROMO Fullstomach Chalk

[blog-normal-distribution]

Wow I've really just been spelling it wrong this entire time and yall just let me huh

[vacuously-true]

Oh wow I didn't even notice you spelled it wrong. My coworkers over the summer mostly spelled it HAGAROMO so when I looked at your post, I checked the vowels, they were right, I moved on.

[blog-normal-distribution]

I used to spell it 'Hagamoro', when I noticed it was spelt with an o instead of an a I stopped paying attention and never noticed the other spelling mistake I made 🤷🏻‍♂️

[vacuously-true]

Isn't Hagamoro this guy?

[blog-normal-distribution]

I was wondering what I should put on my new chalkboard, and My Neighbour Hagamoro is the perfect candidate!

[vacuously-true]

I'm Love Him.

[the-real-numbers-deactivated202]

I'm me as well

[vacuously-true]

This took longer than I expected it to. Oops.

[blog-normal-distribution]

I've never loved anything more in my entire life

[girlactionfigure]

Link / Link

[lemonsharks]

“How would a chicken wear pants?”

- Richard Beale, 1784

[vbartilucci]

Thank you, Richard Beale, for making our opinion of the past slightly more ridiculous.

[without-ado]

Saturn's rings via @astrophosnap[1st: digital CGI]& @bitsofsaturn

[brightereyes]

(observes you)

[brightereyes]

(you behave like a particle)

[justcallmespike-deactivated2022]

(behaves like a wave while you’re not looking)

[blog-normal-distribution]

I'll be continuing on to a maths masters next year!!! It's been a primary goal of mine for a long time to do Part III and after an entire day stressing about results day (the department gave a six and a half hour window in which results could've come out and they were still released 15 minutes AFTER the upper bound) I can safely say I qualified for the 4th year!!

Luckily this means that I'll be able to post more now, now that exams are done and results are out xoxo (but I probably still won't post that regularly oops)

[7jungri]

Astronomical photographs, Harvard College Observatory, Cambridge, 1890-1920

[vacuously-true]

Fun (infuriating) fact. If a dictator has an infinite number of mathematicians imprisoned, and places a red or blue cap on each one's head, and requires them all to guess what color their hat is at the same time without communicating, and will free them only if finitely many of them guess wrong, and will execute them otherwise, it's possible for them to come up with a strategy beforehand which guarantees they can go free.

[blog-normal-distribution]

This is a really great puzzle and I recommend that anyone who hasn't seen a solution before try and solve it! As a hint, you'll need to use the axiom of choice, and equivalence relations. You'll also need to assume that everyone can see all the hats except their own.

Anyways here's the solution:

Assign each person a natural number* 1, 2, 3, 4,... and consider all possible 'colourings' of the naturals* (that is, ways to assign red and blue to each number). We define an equivalence relation on these colourings, where two colourings are equivalent if they differ at only finitely many numbers. This equivalence relation splits the set of colourings into disjoint equivalence classes. Now, the mathematicians use the axiom of choice to pick a representative colouring from each equivalence class.

Now, when the dictator comes along and puts a coloured hat on everyone, get all of the mathematicians to stand in order, and look at everyone else's hats. Since the only hat they can't see is their own, they'll be able to deduce which equivalence class of colourings they're in. Then each mathematician just says the colour assigned to their number from the representative of this class!

*the variation I had seen of the puzzle had countably many people. But upon consideration, since we're already using the axiom of choice, I do beleive we can extend this to an arbitrary infinity of people just by invoking the well ordering principle to well-order all the mathematicians, indexing with ordinals.

This is one of my favourite puzzles and was in a problem sheet I had in my first year of uni! It was an optional question and was on an entirely different calibre to the ones we were expected to be able to figure out, and I personally never knew the solution until I had my friend explain it to me two years later.