serious-discussion

[bright hill]

I know diff geo is really big for GR and stuff

But that's about it

[rocky shuttle]

Essentially, what I wanted to cover today is how to integrate differential forms on manifolds and Stokes' theorem, which is an extension of the fundamental theorem of calculus

[zealous garden]

hmm....

[rocky shuttle]

This requires a more theoretical approach, I think Lee is better suited for this

[bright hill]

Oh, don't worry, i dont give a crap about GR so Lee won't be necessary for now lmao

[zealous garden]

I care about GR

[rocky shuttle]

I'm not an expert in GR. I have a colleague who is doing numerical analysis in GR. The only thing I can say is perhaps that GR uses the language of differential geometry to formulate the Einstein field equations, which describes the curvature of spacetime. So mass tells spacetime how to curve and spacetime tells mass how to move.

[zealous garden]

should I skip spivak and go to Lee

[bright hill]

Spivak is a prereqs for lee, i think

[rocky shuttle]

Sure, if you want to go deep in and not only care about integration on manifolds

[zealous garden]

idk I really enjoyed Taylor's treatment of integration on manifolds

I'd be willing to go through something like that again just because it was kinda fun

[rocky shuttle]

My path to differential geometry was very messy. I started with Optimization Algorithms on Matrix Manifolds by Absil, because the course I had in my uni was quite application-oriented. Then I picked up Vector Analysis by Jänich. Then Lee, Do Carmo, and Spivak.

Ok, how to motivate it... Have you done some integration in physics? Like computing the work done along a path in some gravitational field? Or computing the flux of an electric field through a surface given some distribution of electrical charge?

[bright hill]

Nope

I don't know much physics over all lel

[mint canopy]

Clever tactic, but maybe just read #❓how-to-get-help

[zealous garden]

sorry I can't do discrete geometry yet

I'm still learning differential geometry

[surreal kindle]

newbiee, ewwww

[rocky shuttle]

Ok, so, maybe you have heard in school that the work done by lifting some mass $m$ over some height difference $Δh$ with gravitational acceleration $g$ is given by $$W = F Δh = m g Δh,$$ where $F$ is the gravitational force. Turns out, we can generalize it to arbitrary force fields by considering the line integral $$W = \int_{\Gamma}F\cdot dS,$$ where $\Gamma$ is the path we're integrating over and $F\cdot dS$ is a differential 1-form.

[fathom swallow]

Zanarcane

[rocky shuttle]

Usually, physics and engineering students memorize that the above line integral is given by $$W=\int_{\Gamma}F\cdot dS=\int_{a}^{b}F(\gamma(t))\cdot\dot\gamma(t)dt,$$ where (\gamma\colon[a,b]\to\mathbb{R}^3) is a parameterization of the path / curve / 1-dimensional manifold (\Gamma). But it's quite insightful to learn the general formulation using differential forms.

[bright hill]

Are you looking for $\mathbb{R}$?

[fathom swallow]

DarQ

[rocky shuttle]

One particular interesting thing is that if the force field F is conservative, then the work done along any path only depends on the starting and end point.

[fathom swallow]

Zanarcane

[rocky shuttle]

Oh lol, yeah, I'm used to using my macro \R

[bright hill]

I use \bR haha

You can request a preamble edit later if you want

[rocky shuttle]

Especially, if the path is also closed, i.e., starting and end point are the same, then the work done is 0, according to our intuition.

[rocky shuttle]

It's not a big deal (yet).

[rocky shuttle]

This is also similar to the fundamental theorem of calculus in 1D, if the function $f\colon[a,b]\to\mathbb{R}$ has an antiderivative $F$ with $F'(x)=f(x)$, then $$\int_{a}^{b}f(x)dx=F(b)-F(a).$$

[fathom swallow]

Zanarcane

[rocky shuttle]

You can also see the FTC as a telescoping sum in the discrete case, i.e., given a finite sequence $x_i$ for $i=0,...,n$, the sum of differences reads $$\sum_{i=1}^{n}\Delta x_i=\sum_{i=1}^{n}x_i-x_{i-1}=x_n-x_0.$$

[fathom swallow]

Zanarcane

[rocky shuttle]

I quote @zealous garden

the accumulation of the differences inside, is the same as the accumulation of the values outside

[zealous garden]

[rocky shuttle]

And this applies to the more general case, where you integrate over n-dimensional manifolds, summarized in Stokes' theorem

[bright hill]

This feels waay too wishy-washy ngl

[rocky shuttle]

Well, I'm just trying to motivate 😂 You need some work to do all of this rigorously.

[bright hill]

Fair lmao

[rocky shuttle]

I like this segment after the proof of Stokes' theorem for chains in Spivak

So the work is in defining the mathematical objects, such as differential forms, boundary of a chain, etc. properly, then Stokes' theorem follows directly from the FTC in 1D.

[bright hill]

oooo

[zealous garden]

basically

I had stokes' theorem proved as a special case of the FTGC

[bright hill]

I didn't think the proof was THAT trivial lmfao

[rocky shuttle]

G?

[zealous garden]

Geometric

[rocky shuttle]

oh right, didn't need to ask

[rocky shuttle]

tell me about that, GA lover

I assume that FTGC uses FTC in the proof?

Some people say that Stokes' theorem is a generalization of FTC, but I think extension is the better word

[zealous garden]

the way It's often introduced is that Stoke's Theorem is a generalization of FTC, and FTGC is a generalization of stokes' theorem

it doesn't look like this proof uses the FTC directly, but it does do a few telescoping sums

[rocky shuttle]

literal telescoping sums?

I can't imagine it not using FTC, hmm

[zealous garden]

it might have to do with the way Taylor chooses to phrase it

[frail lagoon]

gm

[zealous garden]

the trick with the FTGC is that the basic form looks just like stoke's theorem with forms, but apparently there are a lot of choices that go into getting that presentation

like you need to establish your orientation

[frail lagoon]

lol

yeah proving stokes has been among the most disappointing moments of my maths career

[zealous garden]

then when you have an orientation established, it has to induce an orientation on the boundary

which gives you some options

i.e. for an orientation $w$, we have the choice of $w$ and $w^{\dagger}$ for orientation, which can be taken in combination with a normal vector $n$ to the boundary to induce an orientation on the boundary by $\partial w = w n$ or $\partial w = n w$ or $\partial w = w^{\dagger} n^{\dagger}$ etc etc.

[fathom swallow]

wraithlord_kotopology

[zealous garden]

I think there are like 6-8 different choices you could make to define the way that an orientation on a boundary is induced by an orientation on the interior

[frail lagoon]

wew daggers

[zealous garden]

furthermore, when differentiating we have to decide whether we mean $\nabla = e^i \partial_i$ or $\nabla = \partial_i e^i$

[fathom swallow]

wraithlord_kotopology

[zealous garden]

and then we have to, again, make a similar choice with integration, distinguishing between $\int dx F$ and $\int F dx$

[fathom swallow]

wraithlord_kotopology

[zealous garden]

so we usually run with:

$\overrightarrow{\partial} w = n w \ \overleftarrow{\partial} w = w n$

$\overrightarrow{\nabla} = \partial_i e^i \ \overleftarrow{\nabla} = e^i \partial_i$

$\int F = \int \overleftarrow{\partial}w F$ (for Multivector Fields)

[rocky shuttle]

uhhh, alright, what does dx F mean? I'm familiar with F dx = F ∧ dx = -dx ∧ F, is it the same?

[zealous garden]

no

so

dx F means that you combine dx and F with the geometric product

oh wait

I'm mixing notations

[fathom swallow]

wraithlord_kotopology

[zealous garden]

that juxtaposition is the geometric product

[rocky shuttle]

wew

completely new language for me

[zealous garden]

dx (now replaced with del w) is a pseudoscalar of the tangent space

that is $\bigwedge_i dx^i$

[fathom swallow]

wraithlord_kotopology

[zealous garden]

this is similar

the reason we have these disagreements is because the geometric product in general fails to commute or anti commute

using this notation, the direct analogue of stoke's theorem looks like

$\oint_{\partial M} f \overrightarrow{\partial w} = \int_M \overrightarrow{\nabla} f w$ or

$\oint_{\partial M} \overleftarrow{\partial w} f = \int_M w \overleftarrow{\nabla} f$

[fathom swallow]

wraithlord_kotopology

[zealous garden]

which actually generalizes further, we can multiply on both sides of del(w) (formerly dx), this one is a doozy

$\int_{\partial M} f (\overrightarrow{\partial} w) g = \int_M \overrightarrow{\nabla} f ( w ) g + (-1)^{m - 1} \int_M f (w) \overrightarrow{\nabla} g$

[fathom swallow]

wraithlord_kotopology

[zealous garden]

with the left-handed version being what you likely expect

let g = 1 and we recover the first version I showed

the geometric derivative (nabla with the arrow on it) is a dirac operator, it's basically the exterior derivative + the codifferential

so the final bits we need to turn this into stokes' theorem are a way to translate between multivector fields and differential forms, and to integrate forms over manifolds

[rocky shuttle]

This feels a lot like partial integration (I think it is). What is m here? The dimension of M?

[zealous garden]

it suffices to identify differential forms with multivector fields that remain unchanged when projected onto the manifold, and to identify the exterior derivative with the curl (the grade-raising portion of the geometric derivative) projected onto the manifold

[zealous garden]

yes m is the dimension of the manifold M

the last tricky+gross part, is the definition of integration for these "differential forms"

$\int_M \omega = \int_M \langle w^{\dagger} f \rangle_0$

[fathom swallow]

wraithlord_kotopology

[zealous garden]

where f is the multivector field representing the differential form omega

[rocky shuttle]

ok, a lot of things I need to look up the definition of

the angle brackets mean projecting onto the 0-blade space?

[zealous garden]

in GA <F>_n means "extract the nth grade part of F"

so that means the scalar part of that geometric product

[rocky shuttle]

ok

and orientations here are just either -1 or +1?

[zealous garden]

orientations (w) are pseudoscalars, I picture them as infinitesimal pieces of the manifold

[rocky shuttle]

i guess not, since wn \neq nw

[zealous garden]

and they are unitary

so -1/+1 in 1D

then we also have that w^2 = \pm 1, depending on the dimension of w

i.e. in 1 it's 1, in 2,3 it's -1, in 4 it's 1

[rocky shuttle]

is wn = -nw?

[zealous garden]

wn = (-1)^m nw

I think

might be m-1

[rocky shuttle]

oh, yeah dependence on the dimension

[zealous garden]

now to prove stokes' theorem as a special case.
we want: $\ \int_{\partial M} \omega = \int_{M} \text{d} \omega$

which according to our definitions of integrating forms becomes

$\int_{\partial M} \langle (\overrightarrow{\partial} w)^{\dagger} f \rangle_0 = \int_{M} \langle w^{\dagger} \overleftarrow{\text{d}} f \rangle_0$

[fathom swallow]

wraithlord_kotopology

[rocky shuttle]

What happened to the codifferential?

[zealous garden]

we can simplify the (not pictured, left-handed version of the) two-sided fundamental theorem directly with f=1, g=f, and w=w^\dagger

$\int_{\partial M} \overleftarrow{\partial}(w^{\dagger})f = \int_M w^{\dagger} \overleftarrow{\nabla} f$

[fathom swallow]

wraithlord_kotopology
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[zealous garden]

well, the codifferential lowers grades, and multiplying by a pseudoscalar to your space (like our orientations) acts like the hodge dual

this means that the codifferential lowers the grade, then the orientation sends it to the opposite dimensionality, where it gets ignored because it's definitely not in the scalar part

which is what we care about

[rocky shuttle]

I see

[zealous garden]

as the next manipulation from here, we take the scalar part and basically walk through the reasoning I just outlined

along with a short lemma about projection onto manifolds

[rocky shuttle]

What's your main reference for GA?

[zealous garden]

and it shows that $\langle w^{\dagger} \overleftarrow{\nabla}f \rangle_0 = $\langle w^\dagger \overleftarrow{\text{d}} f\rangle_0$, which after substituting back in and using our definitions, yields the theorem

[fathom swallow]

wraithlord_kotopology
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[zealous garden]

I Mostly use Michael D. Taylor's book as a reference atm

it's cheaper than something like Snygg's Diff Geo with GC or Hestenes' "From Clifford Algebra to Geometric Calculus"

while being more rigorous and detailed than Alan MacDonald's LAGA and VAGC

[rocky shuttle]

Oh, there is a crash course written by Taylor

[zealous garden]

but Taylor's notation (the one I've been using up to now) is one I have strongly mixed feelings about

like where taylor has w and del w, macdonald has d^m x and d^(m-1) x

but then where taylor takes time to develop what the fuck a manifold is and how to integrate over one properly

macdonald only goes so far as to talk about open subsets of R^n

with most proofs omitted

[rocky shuttle]

Why do you think d^m x and d^(m-1) x are better? I would confuse them with the exterior derivative.

Wait, are those cross products?

or x

[zealous garden]

well macdonald chose $d^m x$, because $\text{d}^m \mathbf{x} = \text{d} x^1 \wedge \ldots \wedge \text{d} x^m$

[fathom swallow]

wraithlord_kotopology

[zealous garden]

and putting the exponent over the x just looks like the tangent vector

[rocky shuttle]

aha

I skimmed the crash course, looks quite manageable

[zealous garden]

my problem with both so far is that their material stays pretty firmly in the realm of Geometric Algebras with positive signature

which excludes things like Conformal Geometric Algebra, Spacetime Algebra, and Projective Geometric Algebra (the first two have pseudo-riemannian metrics, the last has a degenerate form)

[frigid matrix]

@zealous garden @zealous garden what is geometric algebra

also isnt the notation to do dx^I where I indexes over x^i

d^m x is not canon

[zealous garden]

Geometric Algebras are Clifford Algebras, perhaps with the stipulation that they are over the Reals

[frigid matrix]

the only correct notation is lee

[zealous garden]

Clifford called them Geometric Algebras before his death

And the people who call them Clifford Algebras usually have very different intentions than those who call it a Geometric Algebra

Like talk of Clifford algebras sometimes completely skip over the grading, but that's a central aspect to anyone doing Geometric Algebra

So in Geometric Algebras we typically care about interpretations of Clifford Algebras for representing and manipulating some Geometric space

Like in VGA (Vector Geometric Algebra), the simplest kind

Where the different k-vectors are used to represent k-dimensional subspaces, reflections, rotations, dilations, and oriented k-dim volume segments

Or in something a bit more complicated like Projective Geometric Algebra (3,0,1), where we have planes, points, lines, and translations as well

[frigid matrix]

oh cool

thanks for explanation @zealous garden

i have seen definitions of clifford algebra when looking at a gauge theory thing. but i do not know the various uses besides potentially mathematical physics. if i remember correctly it has something to do with this thing called a killing form?

and usually clifford algebras are parameterized by a field its over and a dimension?

iirc

let Q be a killing form?

then clifford algebra is n’th tensor product quotient the set of vectors that vanish with Q?

im not sure exactly but its something like this

im curious if it comes up in contexts other than physics do you know?

[zealous garden]

Ah the tensor definition yeah

So you take the tensor algebra and quotient it by the ideal generated by uv + vu - 2q(u,v) for a bilinear form q

Clifford Algebras are most used in math phys to my knowledge

Geometric Algebras are most used in physics, engineering, computer graphics and computer vision

Where they subsume things like the quaternions and dual quaternions

[zealous garden]

in math phys clifford algebras subsume things like spinors and twistors

[frigid matrix]

o

[alpine kindle]

i thought you have to quotient by (v² - q(v)) for q a quadratic form

because in char 2 they're not equivalent

or sth

[zealous garden]

A quadratic form is actually too general

And that (v^2) doesn't use all of the bilinear form like we need/want

Maybe I did get the divisor of the quotient wrong though, I'm not entirely used to that

[alpine kindle]

this is what it says on wikipedia

it says lower down that if char ≠ 2 this is equivalent to what you said

[zealous garden]

Gotchu

I see

So it turns out that is also one of the differences

Clifford Algebras generally accept a quadratic form

We prefer to restrict Geometric Algebras to bilinear forms

[alpine kindle]

can't you define a quadratic form from any bilinear form and vice versa

[zealous garden]

Idk if it goes both ways but I know bilinear forms go to quadratic forms

[alpine kindle]

if you have a quadratic form $Q$, you can define a symmetric bilinear form $B$:
$$B(u,v) = \frac{Q(u+v) - Q(u) - Q(v)}{2}$$

[fathom swallow]

Ally (ea/eam/eius)

[alpine kindle]

(also from wikipedia 😵‍💫)

this obviously doesn't work in char 2 so uhh

[static loom]

so ignore it 😎

[bright hill]

New merosity pfp less goo

Is that ai generated? Lel

[static loom]

haha no, just a wilted rose that happens to look kind of like a skull

halloween theme

[bright hill]

Cool

[neat lintel]

@ember dawn @void holly look, im not saying we need to use that here, but this isnt physics. The whole point of math to assure this sort of accuracy

If you will make a function that is partially satisfying why make it at all?

You cant just exclude 0 from the inputs

Just saying,

[ember dawn]

you excluded almost all real numbers from the inputs, without question or objection.
I'm just saying exclude one more

[void holly]

honestly, it's not about literally buying 0 books. it's about showing that there is a $3 initial fee that you will always pay for some number of books (technically must be a positive number). that's why so many of these kinds of questions exist, they're not literally saying to plug in 0 and solve for the price when someone "buys 0 books"

they're not really concerned about domain and stuff at this level

i kinda worded that weird but yeah i hope it makes sense lol

[neat lintel]

Yes its suggesting that you pay intitial fee of 3 dollars regardless, which doesnt make sense as it wasnt proppsed by the question

I get that 4th graders are not concerned with domains and piece-wise functions, but that gives no excuse to make an inaccurate question

Thats like, the whole point of mathematics

[icy crag]

#help-6

[chrome pewter]

only in ohio

[severe swallow]

wtf who says these overleaf cv templates look good? I'm browsing through them to find a good one but they all look like shit

[surreal sapphire]

moderncv looks fine?

[severe swallow]

like which one, I'm not really getting a decent result when searching for it'

[surreal sapphire]

https://en.wikibooks.org/wiki/LaTeX/Curriculum_Vitae#moderncv

its used in this overleaf template: https://www.overleaf.com/latex/templates/moderncv-and-cover-letter-template/sttkgjcysttn

though i would just learn how to use the package and not copy-paste some template

[severe swallow]

well, I really don't wanna get into studying the package but eh....

if this is considered a decent cv, I guess cvs just look really unappealing in general

[surreal sapphire]

i dont know what kind of look you want

its just a table

imo less is more

[severe swallow]

yes, I'm not looking for something that does a lot, but it still should have an aesthetic that makes an eye want to look at it.

I mean it shouldn't be something that looks like spaced out text editor file

[deep mango]

im surprised you don't think something like this looks good

https://www.latextemplates.com/template/moderncv-cv-and-cover-letter

[deep mango]

maybe, but it also shouldn't look like the instruction booklet of a complicated board game

[severe swallow]

it's certainly one of the better ones of the ones shown on overleaf

[surreal sapphire]

you can always learn like html+css and make it yourself

this is just standard moderncv

[severe swallow]

yeah exactly, that's the issue I had with most of the cvs on overleaf when searching for templates, they either went van gogh style or did the equivalent of printing hello world

[deep mango]

like this stuff is so dumb to me

i get it

but also

what do the little skill bars at the bottom mean!?

this isn't a fucking mmorpg

[surreal sapphire]

maybe if you apply for a designer job

[severe swallow]

yeah these bars are ridiculous lmao

[deep mango]

maybe this appeals to hiring managers at a tech firm or something

[severe swallow]

Algebraic Geometry: Level 1/10

[deep mango]

but if you're writing a CV, for an academic job, no one cares about things looking like this. they'll be happier if you just have it in the format everyone has it in

[surreal sapphire]

tbh i think a default moderncv one also looks good

[severe swallow]

it's not an academic job though

[surreal sapphire]

i had a cv done "professionally" a few years back

and it was done in word

it looks horrible

and my moderncv one looks way better

i assume random word one is the default and just using latex makes it look special

though maybe in academia using moderncv is standard

[surreal sapphire]

also the main issue here from a hiring perspective is not listing months, only years

this way it appears as if the person is trying to hide stuff

i know because i do the same

[severe swallow]

alright I'll try to suffer my way through this package

[severe swallow]

wym, fired after 3 months?

[deep mango]

hired december fired january

2 years experience

[surreal sapphire]

yes, hiding months of unemployment

like if you quit a job january 2020 and get a new one december 2020, you can hide that by just listing years

old job: xxxx - 2020
new job: 2020 - xxxx

this hides almost a full year of unemployment

[severe swallow]

is this really that much of an issue if you've been in academia meanwhile?

[surreal sapphire]

if you are unemployed, you arent in academia

[severe swallow]

ah..... well ok then

[surreal sapphire]

maybe replace unemployed with NEET

[severe swallow]

"trying to read hartshorne" 2020-2022

[surreal sapphire]

i mean yeah, you can explain periods of being NEET

but it doesnt look good on a glance

thanks capitalism

[severe swallow]

well, I'm still in my masters, so this I don't have to worry about yet

[bright hill]

"I am a lvl 56 communicator" 🤓 🤓

That's legit so cringe lmfao

[surreal sapphire]

tfw fishing 99

[severe swallow]

but I guess I'll have to be a nonstop hustler if I don't want awkward gaps like this in my cv

[surreal sapphire]

i mean my opinion is idc fuck them

[woven whale]

math level 69

doing calculus 17

[surreal sapphire]

but if you dont have gaps, the standard way is to list months too

[severe swallow]

I mean, I have to survive somehow though

[rocky shuttle]

I would put lorem ipsum in my cv, yes

[ember vale]

Why there aint no game theory server here?

[rancid meadow]

tech recruiters froth at the mouth when they see these

tons of tech resumes will have like a skill section w different tiers of understanding

i just list all my shit in one line bc i’m the best at everything i do but

[deep mango]

They'd better wipe off because I don't want their disgusting spittle all over my fist

[bronze pelican]

This resume sucks

So much space wasted in the left column

[deep mango]

Ikr

Put the dumb progress bars there

[rancid meadow]

the only bars on my resume are my rhymes 💯

[long matrix]

ryc is dumdum

[fair mural]

true

[covert geyser]

I have a simple logic question: if one is one and one also counts for two what does two count for

[vivid halo]

what

[covert geyser]

yes

[upbeat mesa]

Is it possible to have a circle but only have a single interior point with all its surrounding points being a boundary?

[storm sage]

what do you mean?

[upbeat mesa]

Like an infinitely small circle that goes around a single point

[storm sage]

you can't have that in euclidean geometry (the sort of geometry you do in high school), but you can define that yea

I imagine it'll have really weird properties

[upbeat mesa]

ok cool thanks, got a dumb idea cooking up and im trying to see if its even worthwhile

Considering if I should just define it as a collection of points around a point that may or may not include an object

Though not sure that would work but I can dream

[zealous garden]

Doesn't that imply that there's a "next number"

[storm sage]

wdym?

[zealous garden]

To have an interior be a single point

[storm sage]

I'm sure you can consider this set and define a topology on it

the only neighbourhood including the interior would be the whole thing, I guess

[zealous garden]

Yes

[rocky shuttle]

My intuition fails for non-metrizable spaces

[zealous garden]

But if we still think of a circle as a collection of points equidistant from another point

Then it's a circle with "smallest possible" radius

[eager reef]

I mean

The interior is open

So you’d have that singletons are open

[zealous garden]

That's not the issue, the issue is the boundary part

[alpine kindle]

that specific singleton is open

[eager reef]

I thought they meant for arbitrary points

[eager reef]

That would mean that it’s already the discrete topology

[alpine kindle]

I don't think that's possible for arbitrary points

[eager reef]

that was my point yes

i guess we could try the discrete topology

look at some point and the ball around it with radius <=1

that's the entire space

but i'm not sure rn if the interior of that ball is the ball of radius <1 rn

it's not true for every metric space

for the discrete topology on {0,1} it isn't for example

so a discrete space where this holds would be an example i guess?

actually i think that cannot work

well, whatever

[storm sage]

I was thinking it'd be the same as the metric topology except you remove the singleton set containing the center from the topology

[alpine kindle]

actually this can work as the subspace topology of R²-{x : 0 < |x| < 1}

where the disc they mention is the closed ball $\overline{B_1(0)}$

[fathom swallow]

Ally (ea/eam/eius)

[storm sage]

that's what I was thinking but it's kinda weird for the singleton center point to be an open set imo

so I excluded it

I'm p sure that's still a topology

[rocky shuttle]

the complement is closed, so...

[storm sage]

?

[rocky shuttle]

so, the singleton center is open

[storm sage]

how is the complement closed

or rather, why should be the complement be defined as closed

[rocky shuttle]

relative to R²-{x : 0 < |x| < 1}

[storm sage]

well yes but I'm not using the subspace topology

[rocky shuttle]

ah

[storm sage]

I'm using the subspace topology minus the singleton center point

[rocky shuttle]

I see

[alpine kindle]

but then the disc doesn't have an interior

and they stated that the interior was one point

[rocky shuttle]

@alpine kindle I'm curious, how did you manage to learn a lot of concepts in math at your age? When did you start?

[alpine kindle]

i mean it was a gradual increase

idk when exactly i started

or even how to quantify when i properly started

[storm sage]

oh it needs to have an interior?

I see

[alpine kindle]

they said that it has an interior of one point

[rocky shuttle]

Yeah, that's the original question.

[alpine kindle]

i will say that I've had a wikipedia addiction for a while

[storm sage]

I wonder if they meant interior in the topological sense or if it was just a casual description

[alpine kindle]

i came across rings a long time ago

[rocky shuttle]

You had a nesy phase?

[alpine kindle]

like multiple times

[alpine kindle]

nonono

more like a miz phase but for much shorter and less pronounced

[rocky shuttle]

Hm? Wdym exactly?

[alpine kindle]

like

the wikipedia page popped up in relation to something or other

and i realised i was out of my depth

but eventually I'd read around enough that i could actually understand a bit of what was being said there

[rocky shuttle]

Yeah, the wiki rabbit hole...

[alpine kindle]

and then more and more

and we eventually get to now where I'm trying to prove the inverse function theorem without much prior formal analysis experience

[rocky shuttle]

I'm a little bit jealous tbh, I never had a "proper" math education in school and only started to see the beauty in college

[alpine kindle]

the maths education in school here is pretty good

the issue is that it's all so easy

when you've already done it a million times

2 years before

[rocky shuttle]

schools tend to repeat things, is that what you mean?

[alpine kindle]

no

i mean I've done it on my own

[rocky shuttle]

oh, yeah, I misunderstood you

[alpine kindle]

like i respect the maths a level

it's a pretty good course all things considered

[rocky shuttle]

well, is there any way / are you interested in acceleration?

Or maybe just enroll in unversity?

[alpine kindle]

wdym acceleration

oh no

I don't want to skip years

for a myriad of reasons

including:

1. having a-levels is good in case I don't get a degree for whatever reason
2. i am doing cs and latin in addition to maths: these are subjects that i enjoy and won't get as much time to do once i get to uni
3. i have a ton of friends in school
4. it's harder to connect with people 2 years older than you

[alpine kindle]

to answer this

[rocky shuttle]

yeah, understandable

the only downside is then, you have to deal with all the easy stuff, which might bore you

[fair mural]

i mean, being bored because it’s too easy is better than being stressed because it’s too hard

[rocky shuttle]

yap, and there is no need to rush

[alpine kindle]

I probably won't be stressed because it's too hard
but I'll definitely be stressed about everything else

i really don't want to be "that kid"

and i suppose i already sort of am

[rocky shuttle]

unless you want a Fields Medal /s

Life is too short for math

[neat lintel]

Is there any way to get rid of this dark blue name?

I find it hard to read sometimes.

[rocky shuttle]

be very active

[neat lintel]

I'd rather not spend more time on discord than I already do.

[deep mango]

i can give you a role which makes your name white if you like

[neat lintel]

Please do.

Thanks.

[deep mango]

just dm modmail if you ever want it removed

[neat lintel]

Got it.

[rocky shuttle]

not very ppl

[deep mango]

it's the "not very ppl" role

[static loom]

lol is that what that role is for?

[deep mango]

yes

[neat lintel]

I guess this role makes me not much of a person.

[static loom]

to "not" the "very active" role haha nice

[deep mango]

i dont understand the name either

[rocky shuttle]

How do you actually get honorable?

[static loom]

[deep mango]

there is an internal nominations process, there are no set criteria besides the ones listed in #info

[haughty apex]

anyone know why the transitive reduction of a finite direct acyclic graph is unique and a subgraph

[slender rover]

https://gyazo.com/371111a295c0b4d421a9471b7d7101af
anyone?

[rocky shuttle]

𝔇

[naive solstice]

hey guysss

is it a or b?

im not sure

[woven whale]

e

[slender rover]

i think D too and cant figure out why this website says its wrong, according to it correct answer is B

[rocky shuttle]

no

[rocky shuttle]

It doesn't matter what they say.

[slender rover]

agreed. was curious if anyone else thought B so wouldve asked why and how

[bright hill]

Consistently contribute quality content to the server

[rocky shuttle]

How many are there in total rn?

[bright hill]

,whohas onor

[fathom swallow]

Members in ℌonorable (Page 3/3)
===============================
41.  Manan#0640
42.  Rijinaru#5601
43.  Lochverstärker#5585
44.  Plurmorant#1811
45.  Faye#2862
46.  nGroupoid#5061
47.  Element118#2437
48.  Moldilocks#8320
49.  washingbear#1224
50.  Chmonkey#9767
51.  zetamath#3718
52.  Moth#5340
53.  ariana#4631
54.  justAlex#0934
55.  shamrock#0598
56.  det#7067```

[bright hill]

56

Huh

I thought there'd be more

Actually there is more, they just have left the server

But only like 5 or 6 or smth

[rocky shuttle]

0.05%

[teal lion]

D

[runic holly]

How do you call recursive sequences that need the 2 previous terms, like the fibonacci one ?

[rocky shuttle]

a sequence defined by a recurrence relation

[runic holly]

I thought there was a specific name like recursive sequence order 2

[rocky shuttle]

yea, P-recursive sequences

[fervent pebble]

WQHAT

RYCIE WITHOUT BLUE NAME???????????????

WTF

[rocky shuttle]

and yellow pfp

with hat

[thorny grotto]

anyone want to chill in vc and do some math problems with me?

[storm sage]

isn't it because of the booster role "very cool ppl"

someone boosted but didn't want the color

[wooden flax]

@deep mango why did you lose mod

[deep mango]

It seems the complaint you submitted to the admins was successful. Thanks.

[wooden flax]

Np

[cold needle]

Yw

[neat lintel]

ryc is still reserved mod so he went up the ladder

[fair mural]

reserved mod is lower in the role hierarchy than mod

[neat frost]

Ryc is high on copium rn

[long matrix]

hi slurp

dont be rude to ryc

[neat frost]

Morning Shuri

[neat frost]

No.

[long matrix]

which ryc pfp u like better

now or shitting penguin

[neat frost]

Now

[long matrix]

@deep mango told u silly billy

[deep mango]

I told YOU that I knew that already doofus

[bright hill]

Good morning slurp!

[reef carbon]

@swift tide gonna say it here since your channel got closed - stupidity alone is not something to apologize for

[eager reef]

[neat frost]

Good morning!

[long matrix]

no

[devout geode]

is this just uni math

[brittle socket]

What are you referring to by "this"

There are highschool channels here, particularly, look at #❓how-to-get-help #precalculus, #prealg-and-algebra, etc

[ancient flame]

math enthusiast taking business classes

[rocky shuttle]

$i\cdot\int$

[fathom swallow]

᳄ᮐᮔᮁᮊᮨᮄᮔ᮪

[storm sage]

genius

[fair mural]

enthusiast

[neat lintel]

Set theory can predict the future.

[torn willow]

How do you think trading companies work?

[azure nymph]

Philosopher Yogi Berra lol

[alpine kindle]

where is this from

[neat lintel]

Some set theory notes. Check my post history.

[burnt dune]

quick question

why do we need countable definition

if we have denumerable?

are there infinite countable sets that are not in bijection with N

?

[surreal sapphire]

no

because i have never heard the term denumerable

[burnt dune]

denumerable means in bijection with N

countable means countable the waay we know it

a friend of mine today just told me we should get rid of countable

but i thought no waay

cuz like

surely if you have an injection to N you can fail to have as urjection too

so im asking

[fair mural]

countable also means there exists a bijection to N so

[surreal sapphire]

this is a non-issue

i never heard the term denumerable

[burnt dune]

okaay

[surreal sapphire]

countable or countably finite/infinite

[burnt dune]

if a set is infinite and cuontable

does this mean it has a bijection

with it and N

no way right?

or not no way

but no

anyone 😦

QxQ does not have a bijection to N right?

nvm

[arctic grove]

Q is countable, so it does have a bijection with N

(Products of countable sets are also countable)

just read the set chapter in any analysis book for more info on this stuff

[burnt dune]

countable for me means surjection to N

but yea

[arctic grove]

thats a weird def for countable?

i have always heard countable to mean be in bijection with N or with its subsets

i have a feeling denumerable means the same thing as what most people say when they say countable

[fair mural]

so to you, R is countable lol

[burnt dune]

injection to N im sorry

[vocal roost]

imaginary times a integral sign? What the säs is this

[burnt dune]

lmao but whyu tho

{1,2,3} does not have a bijection to N

so {1,2,3} is not countable

why would u require a bijection

[fair mural]

a bijection to N would mean countably infinite

your definition is fine for just countable

[burnt dune]

responding to this

[fair mural]

since that includes finite and infinite

i know

[burnt dune]

no how

if you have two definitions

one finite and one countably infinite

there are infinite sets that are not countable like R

which are neither

you need infinite too right

[arctic grove]

it has a bijection with a subset of N

[arctic grove]

look at the def i said

[burnt dune]

yea ur right im respomding to the bijection with N thing

[fair mural]

an injection to N is countably finite OR infinite (or just called countable), a bijection to N is countably infinite

[burnt dune]

doe snot make sense to require it to be a bijection

for me

[storm sage]

countable by itself is vague, it can either mean at most countable or countably infinite

[storm sage]

denumerable is not really used

[fervent pebble]

i have been playing some minesweeper lately and the more i play the more i realize just how fucking ridiculous the world record is

it's absolutely fucking insane

https://www.youtube.com/watch?v=GrZCWx0fnfc

this isnt even the wr

but i couldnt do this in ten years of constant play

it's ridiculous

my hs on google easy mode isn't even 10s below it

fuck

[fervent pebble]

nvm finally got it down to 12 seconds 😌

[lyric totem]

hey @lucid dust , sorry to disturb you - but, when i tried to solve for a and b,
i obtained a quadratic in terms of b which yielded two solutions
if the question asks for exact values of a and b, how can there be two solutions?

[lucid dust]

I think exact values in here means single value(not range) but it can have multiple solutions.

If you substitute back and equation hold then it should be fine

[lyric totem]

alright, thanks

[devout flame]

#help-25

[brittle socket]

@devout flame Don't advertise your help channel outside your help channel

Be patient

[ionic quarry]

if I'm graphing a function where x is the number of days since an event, do I start at zero or are negative days possible

[zealous garden]

Negative days would be before the event

You'd have to decide whether or not that's permissible for your application

[rocky shuttle]

I was just memeing about the "horizontal" integration since multiplying by i corresponds to a rotation by 90° in the complex plane.

But there is actually something called Cauchy's integral formula in complex analysis, which looks like this:

$$f(a)=\frac{1}{2\pi i}\oint_{\gamma}\frac{f(z)}{z-a},dz$$

[fathom swallow]

᳄ᮐᮔᮁᮊᮨᮄᮔ᮪

[neat lintel]

can anyone help me sending links of good videos for calculus. from basics

[rocky shuttle]

https://www.youtube.com/playlist?list=PLZHQObOWTQDMsr9K-rj53DwVRMYO3t5Yr

[neat lintel]

is it from the basics

?

[rocky shuttle]

yes

[neat lintel]

ok thx

[modest magnet]

sus

[vocal roost]

a closed line integral? this is säs

[rocky shuttle]

yeah, in the context of complex analysis, it is often called a contour integral

[iron osprey]

only on riemann surfaces

[vocal roost]

hmmm

interesting

[lament flicker]

What software/programming language do you guys recommend for creating interactive math tools? For example, I want to create one that shows phase portraits of ODEs in an interactive way (as in you can drag a point on the screen and see how that affects the phase portrait). I thought of matlab or 3b1b's manim for python, are ther other better options?

[bright hill]

Unity is a good option too, i think

[lament flicker]

I already know C# pretty well so I might consider unity

[bright hill]

I saw Sebastian lague do some really cool stuff using it

[river moon]

well all the times I tried to program some user interface in python the experience was not pleasant, perhaps manim addresses this

and I remember when I was just beginning programming c# had an accessible UI designer with lots of basic features built-in

[zealous garden]

Facts

I'm working up the motivation to program a 3D graphing calculator in C++ with OpenGL, SDL2, and Klein (a glm replacement that uses geometric algebra)

[lament flicker]

Update: I don't think desmos is the way to go considering how laggy it is lol
https://gyazo.com/3c79c81c61cfe8f7a269746b1317ec17.mp4

Also damn I just realized that if I want to see trajectories rather than vectors only that'd become like 1000x more computationally expensive

[eager crescent]

https://twitter.com/PopBase/status/1588614351308849152?s=20&t=SHWlfyp8AydJ97J0dIFWoA

Pop Base (@PopBase)

eBook site Z-Library has officially been taken down after US authorities seized its domains.

The pirate website which operated since 2009 was home to millions of books, notably college textbooks, which were available for download.

Likes

19307

Retweets

1586

Twitter · Nov 4, 2022, 7:29 PM

[storm sage]

there's mathematica too but it's not free (and therefore lame)

[lament flicker]

🏴‍☠️ yo ho, yo ho 🏴‍☠️

[burnt dune]

yoooooo

Colimits are so coooooooooooooooooo

l

[storm sage]

what's a colimit?

[storm sage]

LOL

[fair mural]

bruh

[wicked plank]

Lmaoo

You guys know any good alternatives?

[azure nymph]

I mean zlib is still up if you know where to look

[echo tundra]

Library genesis is still working

[wicked plank]

Oh

Thanks

[brittle socket]

Just use their tor domain, that still works

[leaden torrent]

pls dont discuss this here

fyi

discord doesnt like it

[tight comet]

Honestly IMO I think manim's de facto standard already.
Please not matlab.

[brave wraith]

I was thinking of a solution to counter an earthquake.

I have an idea that involves balloons, helium, and a house (reference: up)

I have researched how many balloons to get the house floating but how do i get it back down :/

I was thinking of turning the helium back to liquid but how...

[wicked plank]

gun

[brave wraith]

Ohhh

yes

shoot the balloons

but that would be kinda pricey since I would need to pop around $100.000 worth of helium

[brittle socket]

Oops yeah sorry about that

[hoary gorge]

fbi gonna break in my home to steal my virtual books

[zealous garden]

Reasoning and problem solving

You'll also often be working with the same constructs, or at least variants of them

Of course your concerns will be different

[manic ginkgo]

It makes you really understand abstraction on another level imo

[manic ginkgo]

But yeah pretty much ^

[zealous garden]

I think there are a lot of benefits that you can't really single out

The little changes in the way you think and process a problem

And in the care you take when you construct your solution

Of course there's also just having the wider tool box to choose from

With an understanding of the tools instead of copy pasting

[manic ginkgo]

Yeah the other things I noticed was it made my thinking and statements way more precise, understand why that matters and how to structure things better / more efficiently

Also this: https://en.wikipedia.org/wiki/Curry–Howard_correspondence

So I’d hope that if you get better with proofs you’d also get better with writing programs 😛

[neat lintel]

[steady portal]

I wonder how many days I can procrastinate

And end up giving up on math

[fading zealot]

Cuboctahedrons (Archimedean solid with 14 faces) seen in Taipei Confucian Temple

This is an underrated shape

[final fossil]

Any us or uk or Australia student?

I need help

Cuz name cheap offer free domain name to thos students

And i really need a domain name!

[versed geode]

t!selfrole remove

[long matrix]

mwow

@small wave whats is this

@neat frost is this u

[outer dew]

Pain

[tawdry falcon]

beautiful

[patent matrix]

Hello

I lost the channel where I got my answer. Is there a way I can get redirected?

[neat frost]

No it’s a ryc streaming alt. Mine is @still nimbus silly

[fading zealot]

You can search for your own messages using the search function

[patent matrix]

How do I do that?

[long matrix]

so why do u have streaming alts

[neat frost]

I wanted to stream my computer but the audio quality on it is shit, so I wanted to also connect through my tablet for audio

[long matrix]

silly slurp, buy a better pc

[neat frost]

I have a better laptop but it’s windows

[obtuse heart]

lain zi ler

poopoofirc

[long matrix]

wsl

[neat frost]

Why tf would I use that

When I have Linux

[long matrix]

meow

[lofty wagon]

How many ways can we climb a staircase with n steps if we can take either 1 or 2 steps at a time?
i kinda know it, but i don't understand the proof to it. please help

[brittle socket]

Please read #❓how-to-get-help

Yay I drew my first commutative diagram!

In latex

[bright hill]

Cringe

Can't believe you use that filth

[zealous garden]

I have a laptop with a throwaway hard drive in it rn that has windows installed

the linux drive is sitting in a dock on my desk

I need Windows for some certification tests so I'm forced

[bright hill]

Real OGS would use a VM

[zealous garden]

I would

that doesn't work

I guess if I was willing to do some research and put in the work I might be able to throw together a windows qemu install that could trick the software that checks if it's a VM

but that's a lot of work for a "maybe"

[neat frost]

Did you… like miss the entire conversation?

[bright hill]

You got a Windows machine...

That's all I needed to know.

[deep mango]

Windows is a lot better than Linux

[alpine kindle]

?

[inland raft]

why isnt ryc a mod anymore?

[brittle socket]

He is

[inland raft]

?

[brittle socket]

Still has the reserve mod role

[inland raft]

but thats not mod

[brittle socket]

Also, he said that he's just taking a break

[brittle socket]

That's a mod role

[inland raft]

ok

[zealous garden]

based ryc

[brittle socket]

[neat lintel]

hi

i have a list

[woven whale]

yes

[neat lintel]

and i wanna check which of the numbers in that list mod 3 returns 0 (the first match)

[frigid matrix]

you are forgetting conditionals i think

find x mod 3 you might want

[woven whale]

find (\x -> x `mod` 3 == 0) list

mod returns a specific value

[neat lintel]

what does the \x mean?

[woven whale]

lambda

[neat lintel]

ah ok

[woven whale]

it's like a function that takes in a value x

[neat lintel]

very cool

[woven whale]

when you dohaskell `mod` 3 it's essentially```haskell
\x -> x mod 3

[frigid matrix]

why cant she do find (x ‘mod’ 3) list

[woven whale]

because mod returns a value

[frigid matrix]

yes

[woven whale]

yes

the find argument must be a predicate

[frigid matrix]

if the value is nonzero its false

[woven whale]

i.e. return a bool

[frigid matrix]

oh

[woven whale]

booleans aren't numbers in haskell

[frigid matrix]

ok

[woven whale]

I haven't done haskell in like at least two years lmao

but bool is defined like this I think

[frigid matrix]

why did you do haskell at all

[woven whale]

type Bool = True | False

or something like that

[woven whale]

I was bored on a school trip

so I decided to learn it

[frigid matrix]

oh cool

[neat lintel]

based

[frigid matrix]

what do you do now

[woven whale]

aaaaa

type is type alias

it's

data Bool = True | False

[neat lintel]

where did u learn it illum

[woven whale]

http://learnyouahaskell.com/chapters

[neat lintel]

i am just reading the documentation 💀

i am exactly reading this

[frigid matrix]

i used that lol

[neat lintel]

• Hoogle

[woven whale]

math

don't have time for programming anymore sadly

[frigid matrix]

math like undergrad?

[woven whale]

yes

[frigid matrix]

this is sad

do you think ull ever use haskell again

[woven whale]

I used to do AoC in haskell

[frigid matrix]

aoc?

art of code?

[woven whale]

advent of code

[frigid matrix]

oh

[neat lintel]

lol i am on linux and got a windows-like scamming ad 🥱

[fading surge]

hi

ok, I will send the design document, the rulebook for the game, so you understand what I am talking about

[frigid matrix]

ok

[fading surge]

https://docs.google.com/document/d/1RQtL6hSnvuBFi1PB_8SWnC8Zp3z0K9W-yr3UJjW9rbI/edit

how is it @frigid matrix?

[frigid matrix]

i dont completely understand novae reactions

like when do star cards detonate

[fading surge]

ok, for instance you place Planets next to the Star, with directions facing the Star, if the total Mass Points of everything pointing at the Star is equal to or higher than the Mass Points of the Star, the Star will go Nova

[frigid matrix]

oh ok

the mass point of the star add towards your total mass points

and the star map gets reset?

[fading surge]

Planet vs Star > Deduction > Nova
Planet vs Planet >Addition > Attraction
Star vs Star > Deduction > Supernova

no, you collect the cards that went Nova, and the total Mass Points is like your Victory Points

[frigid matrix]

so ideally you want all planet cards

[fading surge]

no, you want Stars

Stars is what gives you points

actually both

you need Stars and Planets

[frigid matrix]

you said planet vs planet implies addition?

[fading surge]

yes

planets with arrows pointing at each other, add up their Mass Points

[frigid matrix]

oh

[fading surge]

so you understand?

there are still certain quirks and kinks that needs fixing

but that's the general idea

are you there bro?

so you interested in working with me on this?

can you work out how many configurations are possible, keeping in mind repeated orders based on rotation?

[frigid matrix]

im here lol

[fading surge]

ok great

so wanna work with me?

I need a mathematical mind

[frigid matrix]

i do not want to make a commitment

[fading surge]

mine is more oriented towards linguistic

I see

what if I pay you?

[frigid matrix]

but i can help with direct math questions

[fading surge]

I see

[frigid matrix]

i think this might be against rules so idk what to say here

brb

[fading surge]

ok nvm

[frigid matrix]

i would do for free but not commitment

[fading surge]

ok

what commitment?

[frigid matrix]

let me rephrase. if you ask questions here i will try to answer them but I won’t set aside time to answer them/be committed to a project

[fading surge]

ok

so wait, you looked at the rulebook?

[frigid matrix]

yeah i read it for most part

but mechanics are slightly unclear

[fading surge]

what is unclear?

ask me anything

[frigid matrix]

id like to see a play through of the game maybe

[fading surge]

I see

I got some questions
there are two Decks, the Star Deck and the Constellation Deck
can you draw from both at the same time at once?
and when your turn comes, can you pass?
just draw without putting anything down?

how about if both players pass consecutively, the next player must place a card?

You may either draw up to 2 Cards from the Star Deck or the Constellation Deck at the end of a Round, which is when both Players take their Turn in sequential order. Constellation Effects last for one Round. You may also choose to pass from placing a Card down, but if both players pass consecutively, the next player has to place a Card down.

is this understood @frigid matrix

[frigid matrix]

no lol

you cant draw from at once

i read it said either 1 constellation or 2 star

[fading surge]

ok

good idea

[frigid matrix]

wait you said this

or are you still in designing stage of rules?

[fading surge]

there are some kinks

there always are

at some level

but the game is more or less written down

[frigid matrix]

are you trying to make the game as balanced as possible

[fading surge]

yes

exactly

[frigid matrix]

because its a good idea to have a google sheets or something similar

[fading surge]

can I ask how many permutations can there be?

can we talk in DM?

if not it is ok

[frigid matrix]

yeah but atm my attention is sort of split so it might take me some time to respond as you noticed. sorry about this

[fading surge]

np

you there?

[frigid matrix]

sorta just ask the question

how many permutations of what

[fading surge]

there are 20 Stars, 14 Asteroids, 2 Moons, 24 Planets

for a grand total of 60 Cards

how many permutations are possible?

given rotation orientation?

@frigid matrix

is it ok if I ping you at times?

[frigid matrix]

yeah i dont mind

[fading surge]

ok cool

so I got 60 cards

what's the number of unique permutations?

8 directions

some 1, some 2, some 3, some 4, some 5, some 6, some 7, some 8

[frigid matrix]

yeah

[fading surge]

3 is 14

8 is 1

7 is 2

1 is 8

[frigid matrix]

i guess you are meaning to ask about combinations

[fading surge]

yea

actually permutations, not combinations

[frigid matrix]

So are you asking given a star card with 1<=x<=8 directions how many unique star cards can you have?

Okay actually you arent asking that

[fading surge]

maybe it is easier to vc?

[frigid matrix]

How many cards can you have per hand

not today sry no vc

[fading surge]

you start with 5 cards

[frigid matrix]

okay

you are saying with 5 cards how many what?

[fading surge]

erm

you don't get it?

[frigid matrix]

im not sure what you want to count

[fading surge]

there are 60 cards in total, 14 Asteroids, 2 Moons, 24 Planets, 20 Stars

[frigid matrix]

yes

[fading surge]

I want them all unique if possible

[frigid matrix]

ok

all of these card types have same number of gravity lines?

when you say unique I think you mean unique gravity line directions

Like if you have a card type with N gravity lines that can point in 8 directions then we have that you can have 8chooseN unique cards

The formula for this is https://en.m.wikipedia.org/wiki/Binomial_coefficient

[fading surge]

well, they have different number of arrows

[frigid matrix]

So some asteroid type cards have a different number of gravity lines/arrows?

[fading surge]

no, all the 14 Asteroid Cards have the same number of Gravity Lines

[frigid matrix]

Okay

[fading surge]

that's why there are 14 of them

but the Planets and Stars, that's the tricky one

Moons(MP2): Reflection – Turn one orthogonally or diagonally adjacent Card 90 degrees. You may activate this Ability anytime instead of placing a Card.
Pluto(MP3): Underworld – Turn one orthogonally or diagonally adjacent Card upside down once a Game.
Mercury(MP4): Quicksilver – May Move Mercury one Space in any direction once a Game.
Mars(MP4): God of War – Discard Planet Cards equal to its Mass Points or less, when placed next to them once a Game.
Venus(MP5): Morning Star – Mass Points with Gravity Lines directed at Venus, with its own Gravity Lines directed back, get redirected back to the Source.
Earth(MP5): The Blue Planet - Reclaim Planetary Bodies of Mass Points equal to Earth's MP, from your Opponent.
Neptune(MP6): Deep Freeze – Cause the Opponent to Miss a Turn once a Game.
Uranus(MP6):
Saturn(MP7):
Jupiter(MP8):
Varuna(MP3)
Ceres(MP3)
Sedna(MP3)
Quaoar(MP3)
Makemake(MP3)
Haumea(MP3)
Eris(MP3)
Kepler-37b(MP4)
Trappist-1e(MP4)
55 Cancri e(MP5)
Gliese 504 b(MP7)
TrES-2b(MP7)
WASP-17b(MP8)
GQ Lupi b(MP9)
HD 100546b(MP10)

2MASS J0523-1403(MP8)
Trappist 1(MP9)
Proxima Centauri(MP10)
Barnard's Star(MP11)
Teide 1(MP12)
HD 100546b(MP13)
Sun(MP14): Sunburst – Once a Game, the Sun has Gravity Lines in all directions, if triggered from another Card at an unopposed angle.
Sirius A(MP15)
Pollux(MP16)
Arcturus(MP17)
Aldebaran(MP18)
Rigel(MP19)
Deneb(MP20)
Pistol Star(MP21)
Antares(MP22)
Betelgeuse(MP23)
Mu Cephei(MP24)
VY Canis Majoris(MP25)
UY Scuti(MP26)
Stephenson 2-18(MP27)

you there? what do you suggest each orientation should be?

how many permutations are there of 2 Arrows in unique configurations?

[frigid matrix]

arrows are gravity lines right?

[fading surge]

yes

[frigid matrix]

8 choose 2

[fading surge]

so how many?

[frigid matrix]

its just this formula really

[fading surge]

I see

so how many?

[frigid matrix]

28 my calculator tells me

[fading surge]

I see

hmm

is it possible for you to help me figure out the Gravity Lines of the 20 Stars and 24 Planets, together with the two Moons?

the two Moons are Moon and Charon

is it possible?

the largest Star of 27 Mass Points will have arrows pointing in all directions

how about for Supernova, if you use a Star to initiate the Nova, that Star is not counted, you do not get it as Victory Points?

[bright hill]

Lies!

[azure nymph]

It's great at letting me kick the update can down the road until it decides to update while I'm working on my problem set for class that I forgot to save so I lose 40 minutes of progress

[fading surge]

@frigid matrix hi, you back yet?

[frigid matrix]

yea

[fading surge]

so what do you suggest?

how many permutations are there?

[frigid matrix]

moons have 8 gravity lines?

[fading surge]

all have 8

as in, 8 possible

just whether 1 to 8

[frigid matrix]

how many actual gravity lines do moons have

or does it vary

[fading surge]

hmm, no idea at the moment

there are only 2 Moons

[frigid matrix]

like you said aseteroids had 3 out of 8

[fading surge]

The Moon and Charon

[frigid matrix]

If there are only two moons and they are powerful cards maybe give them less gravity lines?

[fading surge]

they aren't powerful

they are MP2

they have Reflection though

this game is the toughest game I ever had to design

I faced a similar challenge with my Star Wars Lightsaber duelling board game

but this is way harder

what do you suggest? based on your mathematical ability and talent?

[frigid matrix]

im not sure i have decision expertise for designing a game

[fading surge]

np, we work together

I am a game designer, so I have a knack for it in the first place

I just need a little help and nudge

[fading surge]

@frigid matrix so how?

[covert siren]

Has anyone tried paperlike screen protector for the Ipad?
Thinking of switching over to taking notes, etc. on my Ipad but it's quite slippery so I saw paperlike was an option.
Has anyone used it for writing math problems, if so is it worth it? (Just finding a bunch of sponsored videos on youtube, want an unbiased opinion)

[sterile yoke]

anyone know how to use excel

[covert siren]

Thanks, will take a look at it 🙂

[hushed pagoda]

is anybody familiar with mla citation here?

[storm sage]

check purdue owl, they're such a good resource

[brittle socket]

Feels nice when you make a link between two concepts and you are correct :D

[hybrid lotus]

anyone takes calculus 1 at university?

[woven whale]

calculus is just applied real analysis

[fading surge]

@frigid matrix hi!

is there an accurate way of considering where the directions point towards for every Mass Point?

[arctic grove]

keep coping

[proud olive]

Copying what?

Is it something Linux can copy that windows can't?

Linux can copy money??

Keep copying

[arctic grove]

lmao no

coping

not copying

[brittle socket]

Hi ShyShuu

[neat lintel]

if earth revolves around the sun, does the sun revolve around something of larger mass?

[neat frost]

Indeed

[neat lintel]

what is it

[neat frost]

The galaxy spins or whatever

[neat lintel]

woah

does that mean the entire solar system shifts and moves in space?

[neat frost]

Yes

[neat lintel]

so what does it orbit?

the center of the galaxy

or is there something smaller than that that's a mid-point

[neat frost]

Yeah something like that iirc. I only know what I’ve read in popsci BS, so I don’t know shit about physics, but pretty sure it orbits the massive black hole in the middle of the galaxy

[brittle socket]

Iirc at the centre of galaxies there are supermassive blackholes

In the milky way gal its sagitaraus A* or smt I think

Yeah

[neat lintel]

interesting stuff

thank you

[zealous garden]

Yes

[brittle socket]

np : )

[zealous garden]

Galaxies have massive blackholes at the center, some even have quasars

[brittle socket]

[zealous garden]

I'm not sure if it's strictly every galaxy

I assume it is

[neat lintel]

man

I'm very tired of factoring problems in my math class

it's very tedious

$a^3-b^3=(a-b)(a^2+ab+b^2)$