I Math Ask You a Question

Your friendly neighborhood math blog. Send me all your mathy questions, whether they're about which numbers are my favorites or how to do your homework. I don't care, I'll answer them all.

[knotty-et-al]

Visualization of the Rubik's cube

[levil0vesyou]

I didn't wanna derail the other post but I still wanna spread some love for my favourite subject...

Reblog if you've ever felt genuine joy or excitement from doing and/or thinking about math

[math-wolfe]

Try telling a non-math person that there’s a difference between “positive” and “non-negative”.

[the-real-numbers-deactivated202]

The difference is literally zero  🤷‍♀️

[tydy-the-megnet]

You mean there’s zero difference?

[the-real-numbers-deactivated202]

No, that’s much different :P

[tydy-the-megnet]

But you said zero, that much is different, right?

[the-real-numbers-deactivated202]

I did say that. It’s naught.

[tydy-the-megnet]

It’s naught different?

[the-real-numbers-deactivated202]

Well, it’s not not different.

[tydy-the-megnet]

Please, I want you to tell me what’s different

[thisurlhasbeenleftasanexercise]

Confessions of a math major

I don’t know how to count.

[the-real-numbers-deactivated202]

I can’t fucking do multiplication at all

[daughterofplath]

I still count on my fingers

[complex-variable]

I can count, I just don’t know when to stop

[lockrum-deactivated20230107]

sometimes 2*(-3)= -1

[the-real-numbers-deactivated202]

Ah yes, the accidental mod n. A natural consequence of the profession, I’m afraid.

[the-real-numbers-deactivated202]

whats your option on Pascal's triangle? i as cs major am fascinated by it

Hngh numbar gud

[the-real-numbers-deactivated202]

\end{piday}

\begin{friday}

[allofthemath]

This, ladies and gentlemen and genderqueer folks, is Pascal’s tetrahedron, a three dimensional analogue of Pascal’s triangle, and it’s pretty freaking great.

[the-real-numbers-deactivated202]

Pascal’s radio tower

[catchymemes]

Lissajous curve table

[dumbass-in-a-hoodie]

i dont understand what this is but its so mesmerising

[transgirl-link]

The top row circles determine where the dot is on the X-axis, the left row detetmines where it is on the Y-axis. They’re used to show more complex harmonic motion

[salty-dracon]

@the-real-numbers

[the-real-numbers-deactivated202]

Appropriate ways to appreciate this gif:

[mathematicalmemer]

[vacuously-true]

This can’t be right. I swear every time I have a sign error so the swear jar should be at least as full as the sign error jar.

[math-suggestion]

Expand that polynomial before you take the derivative.

[thesheebsofproduction-deactivat]

Self care <3

[di--es---can-ic-ul-ar--es]

the word “proof” in exercises wrecks me every time.

it either means:

1. you’re in the movie Arrival and you and the aliens agree to abide by some specification. if you can’t write a program that compiles on both your computer and theirs then you haven’t done the exercise, period.

2. “left as an exercise for the reader” is a god damn synonym for “spend some moments minutes convincing yourself of this”. we are building intuitions out of wet sand. lol this idiot thought we actually had to write a program.

and since use of the phrase “convince yourself of” isn’t even consensus among textbook writers at this point, you have no principled means of figuring out when you should take it one way and when you should take it another way.

[the-real-numbers-deactivated202]

[I’m going to talk something adjacent to philosophy here so if you tend to get uncomfortable when I do that (because, say, you think I’m an idiot) here’s your heads up to skip this post or make sure you’re in a good enough place to read it.]

I am of the opinion that Ideal™ mathematics that is built on 100% sound reasoning is a worthwhile thing and also nearly impossible. It’s just far too impractical to expect everyone to understand and be able to prove the entire foundation of what they’re using at the drop of a hat. Some people object to my view with “that’s impractical, I don’t know how to prove everything I use, and if I did I’d never get anything done.” This is certainly true. You have to have faith that the other people who are supplying you with information are actually correct. We can choose to trust the peer review system to fix errors, but that’s not exactly an axiom of mathematics. It is an external assumption, which I think is not a guarantee but a matter of faith. Your choice to believe other academics that the proof works is a subjective value judgement and is an additional proposition to your work that has the potential to render it false. So understanding and being able to show why everything is true is both impractical and the ideal way to do things.*

I also think that “true” statements don’t have a whole lot of value without proof. Proof is what makes them distinguishable from false statements. And I do think you can understand a proof, or at least think you understand why a technique yeilds correct results.

Re: Exercises: So either you choose to trust that it’s true and merely convince yourself, or you don’t trust a single thing uttered until you can prove it all. It depends on which you value more, pragmatics or the ideal.

* - The takeaways of that paragraph can vary from “math is nearly impossible, joke’s on you for thinking it can be done” or “hey, maybe I don’t have to care about the ideal to get useful and practical results” and I’m not really sure where it should lead. I like the second takeaway better. Some people think the second takeaway is a counter-argument. It’s a justification for the status quo that sidesteps the issue entirely. It’s comforting, but like, not ideal?

[the-real-numbers-deactivated202]

Public static void on Main

[eightyonekilograms]

arg

[otome-reviews]

Heart Hunting in The Arcana: Should you gamble?

TL;DR Do you need at least two hearts to win? If so, ALWAYS GAMBLE!!

Honestly, I haven’t had the time to play The Arcana much at all, but I think its Heart Hunter mini-game is super cute. It’s also deceptively complicated! You’ve got six turns to chase around these little characters and collect at least four hearts from one of them, right? But midway through, NIGHT FALLS, STAKES RISE, and all of a sudden you have the opportunity to go all-or-nothing, getting either 2 or 0 hearts from your target character in one spin! So should you go for it??

The answer: YES (assuming you need more than one heart, that is). But how do I know this, you ask?? I asked my boyfriend, who, despite being hundreds of miles away currently, somehow managed to both understand what I was asking AND write a computer program to answer the question (!!). 

Let’s say you’re on turn 4 or 5 and you want at least 2 hearts from someone after two turns (this turn and the next). And, you’ve walked to the same spot as them! Here are the four ways you can “win” (aka get at least 2 hearts in the next 2 turns):

You don’t gamble this turn (and get 1 heart), and the next turn you manage to travel to your target’s location (nabbing another heart)

You don’t gamble this turn (and get 1 heart), and the next turn you travel to Faust’s location and she gives you your target’s heart

You try to gamble this turn and WIN (getting 2 hearts, yay!)

You try to gamble this turn and LOSE (getting 0 hearts), and the next turn you manage to travel to your target’s location, gamble, and WIN (getting 2 hearts).

Turns out, it’s possible to write a computer algorithm that can pretend to play millions of instances of Heart Hunter and guess the percentage of times you’ll successfully get two hearts! ^_^ Without further ado, here are the estimated percentage rates of “winning” if you DON’T gamble:

And here are the percentage rates of “winning” if you DO gamble: 

You see what I’m seeing, friends?! Apparently you’re almost twice as likely to get two hearts in two turns if you DO gamble! I’m also kind of surprised that your chances of winning are a little smaller if you’re in the center. I always thought that was the best location!! Haha.

To summarize, basically, you should always gamble if you need the hearts. Guess this is one instance where the house doesn’t always win! 💕

Disclaimer: everything in this post assumes:

Faust has a 25% chance each of giving you an Asra, Julian, or Nadia heart, or seeing a Goat??.

Faust has an equal chance of showing up in any location.

All other characters move 1-4 spaces in a turn, with equal chance (except they never walk backwards).

If you gamble, you have a 50% chance of winning/losing

No idea if any of this is true! ^_^

(Paging some folks who I know play The Arcana b/c your posts show up prolifically on my dash: @sakurairin-otome @pseudofaux @wingcinna @saizoswifey @madamotome @otohoe @apassingmc)

[the-real-numbers-deactivated202]

is he, y'know, *mimes insertion sort* a computer scientist?

[the-real-numbers-deactivated202]

Yes, and he’s *mimes Stephen wolfram’s adorable hairline* really into cellular automata

[the-real-numbers-deactivated202]

[smbc-comics]

[the-real-numbers-deactivated202]

i.4cdn(.) org/sci/1540378654660(.)png please look at this im losing it at this situation

Oh my god. I know nothing about superpermutations but Robin Houston appears to have one or two papers on the topic. He must feel bewildered. This is funny.

The Haruhi Problem

More formally, "what is the shortest string containing all permutations of a set of n elements?" Algorithm and Bounds

Edit: apparently it comes from 4Chan, thanks @yumantimatter 😊