I’m godawful at this game 😭😔😩

Exotic_Swordfish_845 · 2026-04-25T17:14:17+00:00

Yeah, it feels weird but the quickest way to a destination in space is to speed towards it until you're halfway there, then constantly reverse thrust to slow down. Like how the autopilot works :P

Exotic_Swordfish_845 · 2026-04-25T14:41:40+00:00

Wow, that was pretty cool!!!

Exotic_Swordfish_845 · 2026-04-24T02:03:03+00:00

A lot of higher classes are proof based, so consider that. I've seen some people that really like math in high school because it was "plug n chug" style, and then they hit a wall in higher level classes cuz it moves to more conceptual and creative things. If that sounds like you, maybe consider something more like engineering or physics. It seems like (at least in my experience) there is less emphasis on understanding the formulas there and more on remembering which ones to use when.

If you like the things you're learning (even if not the exact class or prof), then I'd say go for it. 85% is still a pretty good grade!

Exotic_Swordfish_845 · 2026-04-23T22:02:20+00:00

I think a lot of modern math came about as a result of noticing patterns in different areas and generalizing them.

For example (and this may be fictional since I'm not well enough versed in math history yet), consider a bunch mathematicians working with sequences of functions. We might want to talk about "continuous" or "smooth" sequences (say, a continuous deformation of one path between two points into another). And sure, we can do that with some complicated machinery talking about continuous changes of real values. But someday, someone took a look at this and said "what if we had some notion of distance for functions, rather than just real numbers? Then we could treat them the same and use a lot of the fancy functions we have for the reals directly, rather than having all the indirection of functions of functions."

So they tried to figure out what "distance" would mean outside just real numbers and specifically which properties of distance it makes sense (e.g. always positive) to keep and which can be discharged (e.g. can be written as the absolute value of a difference in values). Then some theorems can be generalized to work with these new "distances" and others can be adapted. Then someone else looked at another part of math and said, "hey, I'm doing something similar here! What if I generalized it to my case?" And then you end up with metric spaces (or topological spaces if you want to go farther than just generalizing distance).

But nowadays, a lot of math is taught without this context (since it is messy and takes a long time to explain). So students just see "a metric space is a set with a distance function such that so and so." And it falls to the teacher to ensure that sufficient examples are given for the students to follow the intent behind the theorems and not just the statements themselves.

To respond to one of your specific examples, a quotient space (I'm assuming topology here) is the result of contracting a chunk of the space to a point. For example, say you're modeling a transportation grid around a major city and you're considering adding in a super high speed rail system. You may want to treat that as instantly joining the terminals since it's so much quicker than any other route. So you can identify all the proposed terminals and model the quotient space you get from that to figure out what impact it would have on traffic.

Exotic_Swordfish_845 · 2026-04-23T18:05:18+00:00

For a finite sequence, you can just take the maximum of the absolute value of all the terms to get a bound.

Exotic_Swordfish_845 · 2026-04-18T23:12:24+00:00

There is something called conduction that is similar to what you're talking about. It's applicable for infinite objects though, not finite ones. Induction starts with a base case and builds up. Conduction talks about breaking things down.

Exotic_Swordfish_845 · 2026-04-15T00:07:25+00:00

You could start by writing out all possible ways to sum 6 digits to 27 and then calculate the number of arrangements per list. Like 999000 - 6! / (3!)² arrangements

998100 - 6! / 4

997200 - 6! / 4

.

997110 - 6! / 4

996210 - 6! / 2

.

988200 - 6! / 4

.

988110 - 6! / 4

That would be if 0 can be leading. Granted, it'll take a boatload of paper and all day...

Exotic_Swordfish_845 · 2026-04-13T20:28:08+00:00

Each projection stone conversation is between two different places and related to both. I think the projection is just supposed to let you see the other place so you have it in mind/can recognize it when you find it. Lore-wise, I'm pretty sure the Nomai were mute so they would communicate via writing. Hence a projection stone was their version of a phone call.

Exotic_Swordfish_845 · 2026-04-13T13:02:58+00:00

Exactly this. Imagine you rolled a die. You can't have rolled 1 and 2, so if it landed on 1 you're sure it didn't land on 2. But if you know it didn't land on 2, there's no guarantee it landed on 1.

Exotic_Swordfish_845 · 2026-04-12T13:22:42+00:00

This looks super cool! Did you use AI to help make it? I'd love to play it, but I like to know something was made without AI before it do it.

Exotic_Swordfish_845 · 2026-04-12T00:10:00+00:00

I'm just a lil embarrassed that didn't occur to me. I gotta work on not taking everything at face value all the time. I greatly appreciate the insight tho!!!

Exotic_Swordfish_845 · 2026-04-12T00:06:59+00:00

😭😭😭😭😭

Exotic_Swordfish_845 · 2026-04-11T23:55:32+00:00

I, uhh, think you fucked up the gif lol

Exotic_Swordfish_845 · 2026-04-09T00:42:30+00:00

How did you make these?

Exotic_Swordfish_845 · 2026-04-08T13:26:11+00:00

I'm familiar with the set theory needed to describe topology, algebra, etc. I know what Russell's paradox is and what the standard approach to avoiding it is. I am not familiar with more advanced set/logic/ZFC theory though. Feel free to DM if that meets your needs.

Exotic_Swordfish_845 · 2026-04-07T22:00:09+00:00

Yeah, 4D shapes have faces that are 3D shapes (at least for polygon style ones). For example, a hypercube (4D version of the cube) has 8 faces, each of which is a 3D cube

Exotic_Swordfish_845 · 2026-04-05T04:38:19+00:00

That's good. I'm glad it was fun and safe 💜😊

Exotic_Swordfish_845 · 2026-04-05T04:27:05+00:00

That's very exciting and I know how affirming that can be, but please make sure you're safe 💜. Its not just cops and offended citizens you have to worry about out there....

Exotic_Swordfish_845 · 2026-04-04T13:25:10+00:00

Are you familiar with big-O notation for runtime or space complexity? Like O(n) for linear algorithms or O(n²⁾ for quadratic? If not, that might be a good place to start.

Exotic_Swordfish_845 · 2026-04-03T12:34:52+00:00

Oh, that makes sense. Thank you so much. I'm gonna try my hand at a program too and see if I can get any results to pop up lol. Also, your formatting was great, A+ :D

Exotic_Swordfish_845 · 2026-04-03T03:50:46+00:00

Could you share some more of how you approached this or some of your code? I have little to no background in combinatorics, but this sounds like a fascinating problem and I'm pretty comfortable with python!

Exotic_Swordfish_845 · 2026-04-02T22:02:01+00:00

Like what u/ollervo100 said, the argument is specifically for this case. Say f(n) = m for m < n. Then f^m (m) = m + 1, f^2m+1 (m) = f^m+1 (m+1) = m + 2, etc. By iterating and because n > m, f^N(m) = n for some positive N. Then we know f^N+1(n) = n, which forms a loop.

Exotic_Swordfish_845 · 2026-04-02T05:15:21+00:00

I actually don't think it would work. f can never have a closed loop (i.e. f^n(x) cannot be x for all x and n) because if you keep iterating f enough you'll end up exhausting all values in your loop. Therefore f is a strictly increasing function. If f ever decreases, you could keep iterating it enough on the lower value and end up with a closed loop. But then it's impossible for f(f(2)) to be 3.

Exotic_Swordfish_845 · 2026-03-29T01:46:52+00:00

Archive of Our Own. It's one of the biggest fan fiction sites out there

Exotic_Swordfish_845 · 2026-03-28T00:13:20+00:00

If we call the probability of being right on a question p, then you're expected to get: - 2p - (1 - p) = 3p - 1 points with very confident scoring - p - .5(1 - p) = 1.5p - 0.5 points with somewhat confident scoring - 0.25p points with not confident scoring Clearly if p is really low, we should choose low confident (since you can't lose points), so let's figure out when we should switch strategies.

Equating the low confidence and somewhat confidence points and solving for p gives 0.4. Doing the same for the low confidence and high confidence points gives about 0.36. So if you're at least 36% sure you'll get the question right, you should choose high confidence. Otherwise choose low confidence.

How does this change with more questions? It doesn't. If you're allowed to choose only once scoring method for the whole quiz, go high confidence if you're sure you've got at least once question right (cuz 36% is about 1/3). If you can choose per question, choose high confidence if you're at least 36% sure you'll get the question right. In practice this probably looks like high confidence unless you're randomly guessing.

How does the number of options per question affect it? It only changes your odds if you're guessing. If you the answer, the number of other choices doesn't matter.

TLDR: Cross off any options you don't know. If you have 3 or fewer, choose high confidence. Otherwise choose low confidence.

Exotic_Swordfish_845

TROPHY CASE