serious-discussion

[untold sapphire]

also what kind of math do you know. do you know abstract proof based linear algebra at all

like what a vector space is

yeah functors are part of category theory, one of the most important parts.

[mint patio]

yes I know what a VS is and I’ve taken LA but not a proper proofs based one lol just computational

[untold sapphire]

in the beginning category theory wasn't really thought of as a "theory"

more of a language

and grothendieck called it "the functorial language"

[mint patio]

He’s a guy who has a group named after him big man

[untold sapphire]

Well a functor is like a function except that instead of eating elements of a small mathematical object like elements of a set or vectors in a vector space

and spitting out like, idk, numbers

it eats entire mathematical objects themselves, like it would eat a vector space like R^3 or R^4, and spit out another entire mathematical object. lots of constructions on mathematical objects are functorial

like

[mint patio]

what the fuck

[untold sapphire]

do you know what a linear functional on a vector space is

[mint patio]

LOL

[untold sapphire]

yeah functors are like

big

[mint patio]

no 😭 I know what a linear transformation on a vector space is

[untold sapphire]

sizewise

ok

so a linear functional is just a special name we give to the linear transformations from V to the real line, R

like

[toxic schooner]

the thing that takes in multiple inputs and spits out a single output?

[untold sapphire]

often we study V by looking at maps from V into other vector spaces,

and like

[leaden torrent]

[untold sapphire]

one vector space we always have around is the real numbers R

so yeah

[cold needle]

is today's topic the dual space

[untold sapphire]

so you can add two linear transformations together

[cold needle]

[untold sapphire]

yeah.

right? you can add them pointwise

like

(f+g)(v) = f(v) + g(v)

and this sum is again a linear transformation, as is easy to check

similarly for any real number r and linear transformation T, you can define a linear transformation rT by (rT)(v) = r*(T(v))

does that make sense

[mint patio]

Yes

These are just the rules for something to be classified as a linear transformation anyways no?

[untold sapphire]

nooooooooooooo

those rules are

f(v+w) = f(v) + f(w)

and

T(r(v)) = r*T(v)

which are slightly diferent than what i said

[mint patio]

Oh yes okay lol

[untold sapphire]

also, i'm not stating axioms i'm more giving a definition of what i mean to add or scale linear transformations themselves

Right. so if V is a fixed vector space, then the set of linear transformations from V to R is itself a vector space

this is called the "dual space" of V, and it's denoted V*

with a little star

so this construction on vector spaces is an example of a functor. it's a function at the level of entire mathematical objects, that eats a vector space V and spits out the vector space V*

we might denote it like

$V\mapsto V^{\ast}$

or just

[fathom swallow]

diligentClerk

[untold sapphire]

$(-)^\ast$

[fathom swallow]

diligentClerk

[mint patio]

Okay…

big big thing

[untold sapphire]

or $\mathcal{L}(_, \mathbb{R})$, if $\mathcal{L}(V,\mathbb{R})$ represents the set of linear transformations from $V$ to $\mathbb{R}$

ok

[fathom swallow]

diligentClerk

[untold sapphire]

so i haven't really told you the trippiest part yet

[mint patio]

[untold sapphire]

so the perspective of category theory is that we don't just care about the objects themselves, but also the maps between them.

Category theory is by definition the study of the collection of all mathematical objects of a certain form, regarded as a network of objects and maps. The network is the thing, both nodes and arrows of the graph

And functors don't just operate on objects, they operate on arrows of the graph as well.

So let me tell you what i mean.

Let $V$ and $W$ be two vector spaces.

[fathom swallow]

diligentClerk

[untold sapphire]

Let $T : V\to W$ be a linear transformation, which we view as a kind of arrow in our category (an edge in our graph)

[fathom swallow]

diligentClerk

[untold sapphire]

The interesting thing is that we can naturally associate to $T$ a map from $W^\ast \to V^\ast$, called the dual map of $T$.

[fathom swallow]

diligentClerk

[untold sapphire]

So the functor doesn't just eat vector spaces and spit out vector spaces, it also eats linear transformations and spits out linear transformations

Here the definition of $T^{\ast} : W^{\ast}\to V^\ast$ is given as follows:

[fathom swallow]

diligentClerk

[untold sapphire]

let $f \in W^{\ast}$ be a linear transformation from $W$ to $\mathbb{R}$. I need to tell you what $T^\ast(f)$ is. It must be some element of $V^\ast$, that is, $T^\ast(f)$ is a linear transformation $V\to \mathbb{R}$. Given $v$ in $V$, how can I use $T$ and $f$ to give a real number $T^\ast(f)(v)$ in $\mathbb{R}$?

[fathom swallow]

diligentClerk

[untold sapphire]

Well, if I apply $T$ to $v$, this carries it into $W$; and then I can apply $f$ to $T(v)$ to send it into $\mathbb{R}$.

So I can define

[fathom swallow]

diligentClerk

[untold sapphire]

$$(T^\ast(f))(v) := f(T(v))$

[fathom swallow]

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

[untold sapphire]

which is to say that $$T^\ast(f) = f\circ T$$

[fathom swallow]

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

diligentClerk

[untold sapphire]

and you can check that this actually a linear transformation of vector spaces $T^\ast : W^\ast \to V^\ast$

[fathom swallow]

diligentClerk

[untold sapphire]

that's a functor. it's a machine that eats mathematical objects and maps between them, and spits out other mathematical objects and maps between them.

In this example, our functor ate a vector space and spat out a vector space. But in general the input and output of the functor can be totally different types of things.

Like, there are functors from a category of geometric spaces like manifolds or topological spaces into the category of vector spaces, and these can be used to translate problems in geometry or topology into problems into linear algebra.

which was hugely influential, this is essentially the main idea behind algebraic topology.

[mint patio]

But I’m assuming you wouldn’t learn about any of that in a general topology or AT course

Or at least not in terms of functors

[untold sapphire]

Maybe not in general topology but definitely in algebraic topology you would learn about categories and functors

It would be a very bad algebraic topology course if it didn't use categorical language lol

do you know what a homeomorphism is?

[mint patio]

I have been slowly drifting away from math because of being burnt out from school and stressing over how the fuck I’m going to pass next semester (it’s full of all the mech major weed out classes) and every time I come back into this server someone always says some cool shit that reignites my passion but I know I’ll never be able to continue with it because I do not have enough willpower, discipline, or time management skills to find the time to self study + actually study with good rigor

anyways

I just know it’s a type of map that people care a lot about in topology. I think I’ve read it’s a cont map w an inverse?

or smth like that

[untold sapphire]

yeah. that's the right definition

do you know what a bijection is

[mint patio]

Yes

[untold sapphire]

so like

suppose X and Y are topological spaces. what precisely is a topological space? The precise definition doesn't matter, what matters is this: A topological space is any kind of geometric space where it makes sense to talk about a function from
f : X -> Y
being continuous.
So, the real line is a topological space, R^n is a topological space. A sphere, a torus, a figure 8 loop, a Mobius strip, and so on, in all of these cases we know intuitively what it means to say that a function between them is continuous, it doesn't make any jumps or tears

there are no sudden leaps

where the value of the function changes instantaneously

Two spaces are said to be homeomorphic if you can put their points in bijection between them using a map that's continuous in both dimensions

for example,

$\tan : (-\pi/2, \pi/2) \to \mathbb{R}$ and $\arctan :\mathbb{R}\to(-\pi/2,\pi/2)$

[fathom swallow]

diligentClerk

[untold sapphire]

these two functions are mutually inverse to each other and they're both continuous on their domain

so they establish a bijection between $\mathbb{R}$ and $(-\pi/2,\pi/2)$ which is continuous in both directions

[fathom swallow]

diligentClerk

[untold sapphire]

we say these spaces are homeomorphic.

Does that make sense?

[mint patio]

Yes, and tan and arctan are the homeomorphisms?

[untold sapphire]

yes

So, it's a really really difficult problem in topology to answer the question of whether two given spaces are homeomorphic. If they are homeomorphic you have a pretty good shot at proving they are homeomorphic; you just construct the homeomorphisms between them, you just come up with the definition like i just did with tan and arctan

if they are not homeomorphic and you want to prove they are not homeomorphic

that's a whole nother story

it's not at all obvious how to try and prove that there doesn't exist any homeomorphism at all between two topological spaces.

and in the wake of theorems like this

https://en.wikipedia.org/wiki/Space-filling_curve

people were kind of freaking out that we couldn't just take for granted that two spaces were not homeomorphic

because somebody who is clever enough might construct a very pathological and bizarre continuous map between them

against all intuition to the contrary

so how do you do it??

well

here is a cool theorem about functors

and this basically follows immediately from the definition of a functor once you understand what it is

If $F$ is a functor from the category of topological spaces to the category of vector spaces

[fathom swallow]

diligentClerk

[untold sapphire]

in other words if $F$ is a machine that eats topological spaces and spits out vector spaces, and eats continuous maps between topological spaces and spits out linear transformations between vector spaces

[fathom swallow]

diligentClerk

[untold sapphire]

then if $X, Y$ are two topological spaces, and $X$ and $Y$ are homeomorphic by a homeomorphism $\tau : X\cong Y$

[fathom swallow]

diligentClerk

[untold sapphire]

then $F(X), F(Y)$ are isomorphic vector spaces by the isomorphism $F(\tau)$

[fathom swallow]

diligentClerk

[untold sapphire]

that's the theorem.

does that roughly make sense? i know i'm using a lot of stuff you don't have the background to follow but i hope that intuitioni s enough here

[mint patio]

Yes. If we have a functor between the categories of top spaces & vector spaces, X and Y being homeomorphic topological spaces implies F(X), F(Y) are isomorphic VS (I understand the intuition for sure)

So could you prove they’re not homeomorphic by assuming they are and finding a contradiction using the functor? Which I’m assuming is a lot easier

Or something along that line

[untold sapphire]

exactly - and the contradiction is in the conclusion that F(X) and F(Y) are isomorphic

because it's really easy to prove that two vector spaces aren't isomorphic

you just count their dimensions

[mint patio]

Oh wait

LMFAO

Shit

[untold sapphire]

if F(X) is 3-dimensional and F(Y) is 5-dimensional they can't be isomorphic

[mint patio]

Right right

That’s OP

[untold sapphire]

so like, back before we had this categorical language we had these numbers which we associated to geometric spaces called "Betti numbers"

and today we understand that like, they're the dimensions of these spaces F(X)

but back then it was like damn we can just prove that two spaces aren't the same by figuring out their betti numbers

and it's like

you just compute these numbers and it tells you a weird amount of useful information about the space

anyway that's the rant

[mint patio]

Thank you for that. Do you need much algebra background to continue (by you I mean like me or someone learning)?

[untold sapphire]

you don't need much algebra at all to start studying topology, just general knowledge of proof based mathematics. analysis is most helpful for topology imo, you actually learn a lot of topology in analysis

algebraic topology still doesn't require that much algebra, you need most of munkres under your belt but in terms of algebra you can read chapter 1 of hatcher with literally just knowing what a group is

of course you'll need more as you go deeper into it but you don't need much to get started.

you can pick up more as you go

[mint patio]

Yeah but it’s the boring stuff

point set zzzzz

[mint patio]

This is something I like to think I’m decent at

Learning on the fly (at least for what knowledge I have)

[untold sapphire]

eh point set is kinda boring i guess, it's not that boring imo. like compactness is a very powerful property, it's kinda crazy how much you can derive with it

compactness is a purely topological property that kind of captures being closed and bounded like [0,1] is

and if X is a compact topological space, every continuous map from X into the real numbers R is bounded

just like every continuous function on [0,1] is boudned

[mint patio]

Was the most boring part for me when I took the class 😭 that’s as far as my higher math experience has gone unfortunately, just haven’t found the time for more. Idk why I find it boring, ig I just didn’t like working in arbitrary metric spaces that much

where’s my R^n

[untold sapphire]

R^n is a nice space for sure

you know what you could try

if you want something a bit more geometric and less just like, focused on separation properties

read Lee's Introduction to Topological Manifolds

[mint patio]

If I ever find time…I want to review real analysis once winter break finally starts first since that’s what I’m more interested in, then probably move onto complex analysis. Would this book do anything for someone learning DG?

Cause that’s also pretty high priority on my to-do list

Thank you for your time earlier by the way!

[untold sapphire]

yes i'd say this is a prerequisite for DG and probably a pretty high priority prerequisite at that

[mint patio]

Oh sweet

Cool

Alright thank you for everything then, I think I’ll call it a night here

[neat lintel]

float high like a feather

float high like a rock

[inner finch]

benadrussy

[jovial ember]

Mirzussy

[neat lintel]

does anyone speak dutch in this server?

[primal crater]

dutch

[neat lintel]

bruh xd

[pale orchid]

there's a few people that speak dutch, i think

[neat lintel]

my statistic textbook is in dutch.

there are some assignments in the book that has some long text in dutch

and I have to use google translate to translate it in english

[pale orchid]

you can use this instead, it works a lot better

https://www.deepl.com/en/translator

and i think you can upload text files

[neat lintel]

nice

I have like these type of texts in my book

[pale orchid]

[neat lintel]

oog = eye?

[pale orchid]

it's a meme form of the interjection "oof"

so it says the burning duration of some kind of lamp can be modeled as a random variable with normal distribution

with mean 1600 hours and standard deviation of 100 hours

[surreal sapphire]

i found another umfahren edd: ich lass meine haare wachsen, du lässt deine haare wachsen

[pale orchid]

how large is the chance that one lamp lasts more than 1800 hrs

i never realized the word for waxing was the same as for growing lol

though i guess in english too

though "waxing moon" is kinda arcane

[neat lintel]

$z = \frac{1800 - 1600}{100} = 2$ so $P(2 > 0) $ .....

[surreal sapphire]

oh nice, its probably remnant of german origin of the language

[fathom swallow]

Bleidorb

[pale orchid]

i'm not sure that is quite right

P(z > 2) maybe?

[neat lintel]

this is the answer from the book

[pale orchid]

i haven't used these normalized distributions in a while

yeah

P(z>2) seems right

mind you, i can only KINDA read the stuff because i KINDA know german, not even dutch, so it's better if soemone that knows german or dutch well helps you out lol

[neat lintel]

$P(\underline{x} > 1800) = P(z > 2) = 0,0228$

[pale orchid]

not P(2>0)

P(2>0) = 1 lol

[fathom swallow]

Bleidorb

[pale orchid]

yes

you probably have to look up that value in a table or something

[neat lintel]

2>0 = always true, so 100% = 1

tweede decimaal van z = second decimal of z

it really sucks, when I have to find P(1550 < probabily variable z < 1700)

the mean is 1600
so I have to use the area of the left side and the right side of the bell shaped graph

[last elbow]

Alright

So

@night tree

I have something

And anyone honestly

I have believe I have a proof that that there is always a prime between p(n)^2 and p(n)*p(n+1)

Where p(n) is the nth prime

And I wonder if anything like this has ever between proven

It would be nice to know before I formalize it

[neat lintel]

atm, I have to use these.

[neat lintel]

Look at nature of numbers and you can prove distributivity

[leaden skiff]

hey do you thinks maths has like changed? like, it's not possible to be a euler or gauss today anymore

like as i learn more about physics or math, it feels like we're at a turning point or something

maybe i just don't know enough

but it feels like we're starting to hit the end of all the "easy" questions and all future progress is gonna be much harder

[neat lintel]

those "easy" questions, were extremely difficult for the past

and I think there's a lot of Eulers and Gausses today we just don't really consider them yet since we don't declare them as revolutionary for what they did now anyways

in my opinion

ofc the questions of today are of much higher standards and are much deeper so the rise of difficulty is pretty much inevitable, but I think it requires people who are on a much higher level then people back then

hell with years of learning you can easily learn stuff by revolutionary scientists and then some but you might not think like them though

[mortal igloo]

Also, Euler and Gauss did pretty foundational stuff while a lot of the current new math being done is on the edges and we have no idea exactly whether they will be foundational or not in the future. Maybe what Euler and Gauss did was also on the edges during their time

[neat lintel]

^^

[surreal sapphire]

did people before the time of euler and gauss think the same but about the ancient greeks

[leaden skiff]

maybe

[velvet dagger]

To be fair the ancient Greeks actually just had so much low hanging fruit

Socrates literally becoming a huge name for asking "But y tho" a lot

[sick burrow]

Also Plato was annoying as shit

[wild lantern]

The more I take philosophy courses the more I feel that those kinds of things are just part of philosophy.

Tons of philosophy papers are basically just "but y tho" or "well akschually"

[sick burrow]

Only the annoying ones

[wild lantern]

So all of them?

Jk

[sick burrow]

Read Zhuangzi

[wild lantern]

Who dat?

[sick burrow]

Ancient Chinese philosopher

Basically the founder of Daoism

[wild lantern]

Hmm I see

I will look into that.

[sick burrow]

The fish trap exists because of the fish. Once you've gotten the fish you can forget the trap. The rabbit snare exists because of the rabbit. Once you've gotten the rabbit, you can forget the snare. Words exist because of meaning. Once you've gotten the meaning, you can forget the words. Where can I find a man who has forgotten words so I can talk with him?

He was also the guy with the "dreamt I was a butterfly" quote

The actual gigachad philosopher is Judith Butler though

Ok there is more than one gigachad philosopher but Butler is one of them

[neat lintel]

3+i>2+i i guess

[fair mural]

i feel like that’s true but i’m not sure

[leaden torrent]

the complex numbers cannot be well-ordered

[sick kite]

nami but the well ordering principle

[leaden torrent]

but you can give them pseudo-orders

[neat lintel]

ik, I once tried to give them an order

but it didnt work out

which is very bad for inequalities which use complex numbers

[sick burrow]

Just well-order the Guassian integers via a spiral and then extend apply analytic continuation or extend by linearity or someshit.

[neat lintel]

sounds interesting

but it might be a different order than size

but that is actually a great thought

I never thought of that

[deep mango]

[neat lintel]

I knew you put that

[deep mango]

That order wont be compatible with the field structure

[neat lintel]

somehow I have a sense

I need to be told where to be or where to go

[sick burrow]

In case it was unclear that was a shitpost

[neat lintel]

ic, thx

but while we are talking about ordering numbers

Lol

[sick burrow]

I wanted to give eryc something obviously stupid to sully to throw him a bone

[neat lintel]

Me when Landau-Ginsberg theory

[sick burrow]

Get his record back on track

[neat lintel]

I think I can help with that

I have an idea

[sick burrow]

[neat lintel]

although it is not much of an idea

if he knows the context

so Imma do it in 2days

ofc, if it is ok with you

[deep mango]

I refuse to take the bait.

I never sullied a thing.

[ancient flame]

real numbers are imaginary

[sick burrow]

Based

Based and finitistpilled

[sick burrow]

Can we ban eryc

[neat lintel]

0 is imaginary because it can be written in the form 0+0i. It is also a real number. Edit: all real numbers can be written in the form n+0i which makes them all imaginary

[ancient flame]

I know

[fair mural]

0 is a sedenion

[ancient flame]

lol

[jovial ember]

Fuck you

[ancient flame]

when?

[jovial ember]

Idk whenever quantum wants 😉

[ancient flame]

fuck me pls

daddy

[jovial ember]

No

[fair mural]

i guess you don’t like 2^n-ons

[jovial ember]

[fair mural]

please stop

[ancient flame]

oh

[jovial ember]

Only with quantum

😉

[ancient flame]

damn

sexy

[jovial ember]

(Get the hint already)

😉

[fair mural]

chmonkey i don’t like you in that way sorry

[ancient flame]

damnnnnn

[jovial ember]

😧

[ancient flame]

rejected

[fair mural]

let’s just stay friends

[jovial ember]

😧

🤬

You led me on!

https://youtu.be/h3EJICKwITw

[fair mural]

good song

[jovial ember]

No talk me

[fair mural]

,w sedenion

[fathom swallow]

Wolfram Alpha doesn't understand your query!
Perhaps try rephrasing your question?
Click here to refine your query online

Requested by quantum#6320

[fair mural]

even wolfram alpha doesn’t know it

[jovial ember]

Haha

[fair mural]

amazing

[meager sonnet]

Chmonkey do you really wanna be pulling this shit

half of the users here are HS

[fair mural]

chmonkey is quite an odd fellow

[meager sonnet]

we're all mad here

[wild lantern]

Not me just ya'll

[meager sonnet]

nope

[wild lantern]

Dang it, you are right!

[sick burrow]

[sonic ether]

it's when it does the sedon

,w sedenion

[fathom swallow]

Wolfram Alpha doesn't understand your query!
Perhaps try rephrasing your question?
Click here to refine your query online

Requested by Chad#8741

[fair mural]

it’s like octonions but it’s 16

i think

[cold needle]

it didn't associate what you said to the definition

ahaha im funny

ok i sleep

[fair mural]

good night funny person

[cold needle]

Good morning

i already slept and woke up.

[neat lintel]

noooo

[fair mural]

hi carla

[neat lintel]

quantum

hi quantum

i have become kernel, the inverse image of 0.

[fair mural]

what is that carla

i don’t know category theory or whatever this is

[wide drift]

how do you become a helper

[fair mural]

dm modmail i think

[cold needle]

this just algebra quantum

the fiber over 0

or preimage

whatever

inverse image

so many words

[fair mural]

you say that like it’s obvious lol

[cold needle]

basically whatever gets sent to zero by a homomorphism

wait do u know nay group theury

any*

[fair mural]

no

[cold needle]

o oop

okay hmmcat

[fair mural]

lol

[cold needle]

any linear algebra

[fair mural]

nope

[cold needle]

oogissimo thats ok

let me see how to make this work

[last oxide]

[neat lintel]

[cold needle]

[fair mural]

see what you’ve done carla

[cold needle]

is fiber not the right word

[neat lintel]

*fibre

[cold needle]

True

[last oxide]

faibur

[compact tartan]

"fiber" is a little too fancy if you don't have a topological context

[last oxide]

speaking of fiber
I was messing around with tangent and cotangent bundles
and then I realized
they dont use the disjoint union topology
and I lost 20 minutes of my life

[compact tartan]

ofc not

[last oxide]

please

[compact tartan]

the whole point is that you glue the tangent spaces together in a coherent way

so that you can move between them

[iron copper]

How do I get the role?

[last oxide]

right but
how does that tell you it wouldnt be the disjoint union topology

[neat lintel]

🍞 🍴

can someone tell me good night please

[fair mural]

good night carla

[last oxide]

boa noite

[neat lintel]

🥦

[compact tartan]

disjoint union topology is disconnected

[last oxide]

true

[ancient flame]

imagine dealing with this

$\sum_{\Sigma} f_{\Sigma}(x)$

[fathom swallow]

gmod

[ancient flame]

pain

[toxic schooner]

[wild lantern]

Dang ol' latex tell u h'what.

[neat lintel]

yea weird right

its the construction thats made with disjoint union of tangent spaces

but topology is made with compatibility of transistion maps and their respective charts iirc

or you can think of it as open in the (co)tangent bundle if the set if inverse of some chart of an atlas on manifold

open in TM if pi^-1:M->TM f(U) cong U x R^n

[compact tartan]

maybe not a good way to look at them at all

you have an atlas on the manifold, and for every chart on U you can define a piece of the bundle TU

you can then show how to upgrade coherence maps between charts to coherence maps between bundles

and just glue

like a "local frame" type of approach

if U is homeo to R^n then TU is going to be what you think it is, and there's no confusion

[obtuse fjord]

Hey does anyone know roughly which field of math shuffle algebras are from? I’d like to read up on them for some stochastic analysis stuff and don’t have an excellent algebra background

[neat lintel]

Hello.

I want to start a discussion.

Do you people believe in the existence of a soul?

And if you do, or not, why?

[snow lintel]

#discussion

[neat lintel]

@snow lintel there’s already people talking.

Wouldn’t want to intrude.

[river linden]

no, because all current evidence points towards life just being complex matter obeying the laws of physics

[neat lintel]

Ok.

@river linden

I’m trying to remember what I was gonna say.

[bronze pelican]

I feel like Aleph 0's videos are getting worse

[toxic schooner]

The latest video was nice tho imo

[bronze pelican]

i have issues with it

[neat lintel]

aleph 0

is that

[bronze pelican]

Maybe because I really like Galois theory and I dont like how he's advertising it

[neat lintel]

yea it was rly weak that one imo

too little details

[bronze pelican]

I don't even think it's an issue with the details. I think the message is wrong

[neat lintel]

i dont remember the message

so long ago since i watched

[bronze pelican]

the video im taking about is less than a day old

[neat lintel]

what

he had one before tho

[bronze pelican]

yeah

i dont remember that one

The one Aleph 0 video I really like is the "The derivative isnt what you think it is"

[neat lintel]

yea in that one

i dont get what he means by

a loop dividing something in 2 regions

but has pretty drawings

[neat lintel]

what message would you give bout galois thry

[bronze pelican]

let me think about what to say

Galois theory is fundamentally about studying symmetries of polynomial equations

idk it's as simple as that

[toxic schooner]

[neat lintel]

infinite Galois theory:

[toxic schooner]

ah

i havent studied group theory, let alone galois theory so i had no issue with it

[scenic narwhal]

That is really good but disliked because the title insulted me

[bronze pelican]

You can push Galois theory really far. I'm only trying to describe finite Galois theory, that which you'd learn in a 2nd course in abstract algebra say

[neat lintel]

i had very basic Galois theory in undergraduate algebra II class, but we did very little

so idk much what to do with it

[bronze pelican]

study algebraic number theory

[neat lintel]

im scared of number theory

[bronze pelican]

its the reason Galois theory exists

Even if you arnt interested in Number theory for its own sake, studying Alg NT, particularly Number fields, is a good way to solidify your Galois theory understanding

[neat lintel]

any book recommendations?

[bronze pelican]

Number Fields by Marcus

Maybe A Conversational Introduction to Algebraic Number Theory: Arithmetic Beyond Z by Paul Pollack

I havn't read this one but it seems good

[neat lintel]

it is symmetries but whenever i hear it that way it always throws me off

[bronze pelican]

wdym

[neat lintel]

the part that sticks out to me the most is the galois correspondence thing

idk why but it sort of blew my mind at first

[bronze pelican]

Galois correspondence is pretty damn powerful

[neat lintel]

tbh this type of math scares me

the only other thing that scared me like this was intro to homology

i really wish i knew full buildup of the topic too. it is not as if their ideas came out of thin air

its a contravariant functor

[neat lintel]

aleph 0

[neat lintel]

what about it

i've taken classes with that guy

🙅

🤨

[toxic schooner]

[neat lintel]

he was in my algebra and complex analysis classes

was all online but i recognized the voice

[meager sonnet]

homology as a functor is technically correct but if you're looking at a basic homology theory it's not a very good way of thinking about it

[neat lintel]

oh i was talking about galois correspondence

[meager sonnet]

oh

carry on

[tribal dove]

couldn't |x| also mean sqrt(x^2)

[vivid halo]

Yup

[tribal dove]

is there a way to get the inverse of y = |x| so that y is isolated?

[fair mural]

did you mean so that x is isolated

[tribal dove]

instead of just x = |y|

[leaden torrent]

no, the function x ↦ |x| is not invertible

you can invert it on a subset of its domain

e.g. y = |x| behaves like y = x for x in [0, infty)

but thats not very interesting

[tribal dove]

yeah

i tried doing x = sqrt(y^2) and isolating y but it diedn't work

[leaden torrent]

again, its not invertible

so you wont have a proper inverse

but you can have a pseudoinverse of sorts

y = |x| implies y = ±x implies x = ∓y

this isnt a function though

so like

its not really useful

[neat lintel]

pseudo pseudo

[neat lintel]

the construction is amazing

ive always been super impressed by learning new math like that

also it existence of these types of topics makes math feel like a story if that makes sense

[neat lintel]

you are amazing too

[bronze pelican]

#totally-fkin-wrecked

Lmao I'm being really petty

[mild nebula]

Is that yours?

Are we making fun of it?

What emotion am I allowed to feel right now?

[bronze pelican]

Lmao

That me just saying the main message of this YouTube video is wrong

[light needle]

lol nice, I mean ur comment is accurate so its ok

[mild nebula]

Note that any equation that contains members of Q, √2, and -√2, is still valid when you swap √2 and -√2

Because the other members of Q can't "see the difference" in a sense

It's trivially true for something like √2, but much less so for something like ³√2

[light needle]

I like to interpret this model theoritically as im learning it rn

like basically in the language of Q-field extensions, we cannot null define sqrt(2) in any model, as it can always be sent to -sqrt(2) by some automorphism. like you can at best define roots of x^2-2 where these are indistinguishable.

I guess the way this is worked around is by working in the langauge of Q-field extensions which respects the order on Q

because then you can distinguish sqrt(2) and -sqrt(2) and same for other real alg numbers

[dense belfry]

Does the language of F-field extensions include a constant for each element of the field?

[light needle]

yeah it should i think

[mild nebula]

You can't distinguish if they are defined as algebraic elements from Q. That is, √2 is the element where √2² = 2

But -√2 is the exact same

But yeah, once you throw some extra construction that way, they become separate

[light needle]

like, F union (1,0,+,*,(-)^-1) and then like the axioms should require the elements of F are distinct

i think

[mild nebula]

Do I know anything about that "extra construction"? No!

[light needle]

and also the axioms should encode how all of F multiply add etc

[dense belfry]

You can define positivity and negativity if you are just looking at sqrt(2)

So if you are looking at Q(sqrt(2)) you should be able to distinguish sqrt(2) and -sqrt(2)

[light needle]

oh hmm

[mild nebula]

You gotta start seeing them as real numbers in that case, I think

[dense belfry]

Idk actually, is there an automorphism that switches sqrt(2) and -sqrt(2)? That's the easiest way to show that they are indistinguishable

I don't think that's true though

[mild nebula]

As the field axioms don't gaf if one is negative or not

[light needle]

yeah like literally just sqrt(2)-> sqrt(-2) and Q fixed

I think that should work hmm

[bronze pelican]

Typo

[light needle]

maybe my language is wrong

maybe i should interpret the F as 1-ary functions

no this is fine

[dense belfry]

I think constant symbols are good enough

Since they are a subset

You need to interpret them as 1-ary functions for vector spaces

Yeah I guess that automorphism works

[mild nebula]

I feel like this is the same as saying "Call one George and one Henry, and now they're distinguished"

[dense belfry]

Lol I get paranoid about things being automorphisms even though I know they are

[mild nebula]

Field axioms be like "what is a negative? Can I eat that?"

[light needle]

oh yeah so kaynex do you know like, first order logic

[mild nebula]

Not very well kekw

I should get around to reading a bit of it

[light needle]

let me give you like, cliffnotes of what we were trying to say

like ok first you have a "language" you work in, they have constant symbols to be interpreted as constants, functions symbols to be interpeted as functions and relation symbols to be interpreted as relations.

Im defining the language of Q-extensions to be like

Q cup {+,*} where + and * are 2-ary function symbols

[neat lintel]

there's no such thing as negative element of a field

[light needle]

and then i add a bunch of sentences in FOL that basically tell you how each of the elements of Q interact and the field axioms

[mild nebula]

I think I misread. I thought you were trying to say that "√2 > -√2 so they're distinguishable"

But you're actually telling the automorphism

[neat lintel]

what does > mean

[light needle]

and models of this theory are exactly Q field extensions. Now in a structure A we say a subset S<A is null-definable if there is some formula phi such that S is defined as the elements that satisfy phi

in this sense {sqrt(2)} is not definable in these

[dense belfry]

Do people use null-definable?

[light needle]

since automorphisms preserve the validity of formulas, they must preserve null definable sets, which isnt the case

[dense belfry]

I've just seen definable

[light needle]

like the term? idk i saw it on some notes

[neat lintel]

maybe means definable without using elements from model?

[light needle]

like ig it was talking about the more general S-definable

where ur allowed to use elements of S to define a subset

and null definable is the specail case where you cannot use any parameters

[light needle]

self studying math is why i am dead inside

well i think the first thing is to find some way to enjoy this again

rather than efficiency

which itself is pretty challenging

i dont have an advice for how to do that except talk to a therapist who can help you personalize a plan idk

I had a similar dillema

I used to legitamately think that mental issues like, decreased my cognition or w/e

but ig i realized that this thought itself baised my assessment of myself

like instead of "im rusty lets get better" id go to "damn i really lost my IQ"

and id be extra harsh when i was slow, even though old me would probably also not do this fast

etc

so yeah work on the therapy but also be patient with urself

[wet forge]

is centre and radius of curvature the same

[snow lintel]

do you think it is?

[sly thistle]

John imma be honest that’s really funny. Ik that’s like a whole thing ya been talking about with regards to mental health and I sympathise cause I’ve had similar thoughts but ya put it in such a humourous way

[snow lintel]

well to be fair, it happens to me too

if it matters

[wet forge]

yea

[neat lintel]

Good morning

How are you today?

[quiet heart]

Hello

[grizzled fjord]

It isn't the same.

The center of curvature is the center of the sphere of which the mirror is a part ( You have to cut a sphere and silver a side of the glass to get a curved mirror). It is that point relative to the mirror that would have been the center if the mirror was a full sphere.

WHILE

The radius of curvature is the distance from the center of curvature to the pole of the curved mirror.

[wet forge]

thanks man 👍🏿

[bronze pelican]

Why is this a question you're asking Michael Penn?

[light needle]

i mean this seems like a fun q

probably not right

[neat lintel]

no way it converges

[leaden skiff]

it does

[dense belfry]

How frequent are palindromes? (Asymptomatically)

[mint patio]

Is there a difference between holomorphic and smooth except for holomorphic -> infinitely differentiable whereas smooth -> differentiable up to some order (which can potentially be infinite)

[dense belfry]

Holomorphic implies analytic

[mortal igloo]

Holomorphic is a lot stronger. It preserves angles. Something simple like stretching the real axis by a factor of 2 and leaving the imaginary axis alone is smooth but not holomorphic

[light needle]

smooth means infinitely differentiable, but analytic means that on top of that you can write it as a power series

holomorphic is indeed very strong, its basically power series in z

when you restrict to holomorphic functions on things like compact surfaces, well these are practically polynomials and algebraic functions etc

which is a very restrictive class of functions right

[mint patio]

It preserves angles
Angles are important because complex numbers can be represented in polar?

[mint patio]

So smooth functions may not have a power series representation (around some point)

[light needle]

actually I should say that holomorphic functions always locally look like a polynomial

yeah

i think classic example is like

[mortal igloo]

Locally look like a polynomial?

[light needle]

x e^(-1/x) or smth

and 0 at origin

[mint patio]

Oh! Is this because holomorphic -> analytic -> equals power series (a polynomial) about that point?

[mint patio]

how'd you come up with this so fast :o

Oh wait classic example

lulw

[light needle]

kinda, its a bit tedious to proof iirc. like basically it means there is a biholomorphisms p such that locally pfp^{-1} = z^k for some k (called the ramification index)

I have mainly seen this used in studies of compact riemann surfaces

where you replace p with appropriate charts

it sounds nicer there, that you can pick coordinates that makes your function locally look like z^k

[mint patio]

pfp^{-1} means composition of p and p inverse?

[mortal igloo]

Angles are important because... multiplication by a complex number preserves angles, and the Jacobian of any holomorphic function at every point needs to be multiplication by a complex number

[light needle]

yeah should emphasize i say locally meaning this is only true in some neighborhood of any given points

not the entire plane or surface or w/e

like for each point a, there is a neighborhood U containing it and some type of biholomorphism p such that pfp^{-1} restricted to p(U) or w/e is z^k

[mortal igloo]

From a certain point of view, angles come into the picture because of the accidental isomorphism $\bC^\times\cong GO^+(2)$

[fathom swallow]

Icy001

[light needle]

whats GO+

[mortal igloo]

Orientation-preserving orthogonal similitude group of $\bR^2$

[fathom swallow]

Icy001

[mint patio]

How is this related to power series? I sense it has to do with z^k but z^k is just one complex number, not a series. Ssorry if I'm misunderstanding a lot

[mint patio]

I haven't taken AA I have no clue what this means

[mortal igloo]

O^+(2) is the group of orientation-preserving rotations, which is the same as the complex unit circle. GO^+(2) is just O^+(2) allowing for dilations

[maiden bear]

[light needle]

right z^k isnt just for a point, its for some neighborhood of that point. Like ig im trying to communicate that while for the entire plane or surface your function is a power series ("infinite polynomial"), if you restrict to looking locally its just outright a polynomial

which is an useful result

like for instance things like the open mapping theorem and louvilles theorem follow immediately from this

[sleek iron]

[mortal igloo]

[mint patio]

I'm sorry, I think I'm misunderstanding something about z^k? Isn't that just a polynomial with one term? So from my understanding, around a point (in some neighborhood about it), f(z) looks like z^k. Is that right?

[light needle]

yeah

[mortal igloo]

Up to a biholomorphism 🙃

So e^z looks like z after inverting e^z ( )

(There are no ramification points for e^z)

there is an essential singularity at infinity though

[mint patio]

Wait didn;t John say it was composition here? So it'd be e^(log z)
I haven't actually learned about complex log yet

[light needle]

let me just send a screencap of the actual theorem lol

[mortal igloo]

Riemann surfaces 🙂 That theorem puts the picture in terms of the picture of functions from C to C. But if we're already looking at functions from C to C (which I think feather wants) then these charts will just contain the holomorphic function in question

[mint patio]

What is a chart?

[light needle]

true this is kinda putting it interms of surfaces which isnt necessaciry to what iwas saying

for now you can say charts are like, biholomorphisms from a neighborhood of a point to some other neighborhood of C

[mortal igloo]

The theorem applied to $e^z\colon\bC\to\bC$ is kind of trivial: one just sets $\psi=\id$ and $\varphi=z\mapsto e^z$, then of course $F(z)=z$ for all $z$

[fathom swallow]

Icy001

[mortal igloo]

We are still begging the question of why e^z is an appropriate chart, and the answer is because e^z is holomorphic... back to square 1

[light needle]

right i see what you are saying

right in a sense that in local coordinates you are a poly, but the fact that you can transition nicely between coordiantes is cause this is a holomorphic map

its still an useful thing to have in mind ig, that holomorphic maps can be made to look like polys

[mortal igloo]

It's surprising the theorem doesn't say k is unique. Maybe that's because the charts can be ramified

[light needle]

yeah they can

its around points where "derivative" is 0

[mortal igloo]

Ramified charts are what you need to make $\text{SL}_2(\bZ)\backslash\mathbb H$ into the Riemann sphere

[fathom swallow]

Icy001

[light needle]

yeah you have like, one around i and one around omega

i think

[mortal igloo]

yes

[light needle]

iirc the way to put charts on them involved some "straightening"

which ammounts to basically the theorem i stated

[mortal igloo]

There are only 180 degrees around i and 120 degrees around omega, so you cheat to make them both 360 degrees

Sometimes I think treating H/SL_2(Z) as an orbifold has nicer properties

Correct Euler characteristic for one

[light needle]

if you know some algebraic number theory btw this ramification is kinda the same as the one there

[mortal igloo]

I do, are you actually a second year undergrad?

[light needle]

ye

[mortal igloo]

I didn't learn algebraic number theory until 4th year

Me jealous

[light needle]

kek. but yeah like the reason is like, some things can be done to prove that compact riemann surfaces are varities. Now it turns out these varities corrospond precisely to like, dedikend domains, which is why you have the same idea of ramifications

rough reasoning i dont really know all the details for the second part

[blazing pawn]

really late but the reason is that being smooth and being normal are equivalent for curves

[vestal elbow]

bro can u help me with algebra 1

[fair mural]

#prealg-and-algebra

[blazing pawn]

so the coordinate ring is dim 1, and integrally closed (this is what it means to be normal), and noetherian hence dedekind

Hence you get unique factorization

[vestal elbow]

thanks

[blazing pawn]

@light needle

[light needle]

ah i see, i remember reading this in my skim of szamuely ch4

[blazing pawn]

What this all really rests on is the fact that holomorphisms of riemann surfaces end up being the same thing as morphisms of locally ringed spaces

Ugly ass proof

Hate szamuely

[light needle]

right that just comes from category of varities and category of k-algebras are anti equivalent i think

[blazing pawn]

Well

finitely generated reduced k-algebras

[light needle]

yeah that

[blazing pawn]

but yea

[light needle]

i read this in hartshorne

[blazing pawn]

Moment

I should keep reading kempf

[light needle]

i will use another book when i rturn to AG

is kempf good

[blazing pawn]

i mean ive read 1 chapter so far but i like it

[light needle]

ill give it a try at some point ig

[leaden torrent]

kempf is an unfortunate name for a book

[blazing pawn]

I mean

i guess its just an unfortunate name for a person

i guess other than the general theres not really anyone evil with it

[leaden torrent]

i used to know someone with last name rittenhouse

it mightve been spelled a bit different

but i'd imagine recent news cycles have sucked

[gritty valley]

quick question sir

[leaden torrent]

?

go ahead

@gritty valley

[gritty valley]

why does racism exist in america today

i was going around asking people

[leaden torrent]

thats a bit of a heavy question lmao

[cold needle]

[gritty valley]

ah

[cold needle]

Quick question

[neat lintel]

because race exists

we should just paint everyone pink

[leaden torrent]

part of it is that there ARE genuine divides between races - they arent universal, but historic factors mean that different races often live in different neighbourhoods, consume different media, speak different dialects (eg AAVE)

people notice those disparities

and it subconsciously influences their view of other races

[neat lintel]

I've noticed the racism problem is larger in the UK

[leaden torrent]

if youre uncritical of your own biases, its easy for that to transform into straight up racism

this is far from unique to the US

[gritty valley]

hm

[leaden torrent]

the US is just particularly notable for being large, having influential media, and having a lot of different races (hard to find a black dude in belarus or a cherokee in china)

but again, those countries have their own racial issues

[neat lintel]

which makes it kinda sad that racism exists to the degree that it does

[gritty valley]

yeah i was going to write an essay about it

[leaden torrent]

(european countries tend to have strong stigmas against romani and muslims, china has a lot of internal racial disputes that go back literal millenia)

[gritty valley]

but nothing clicks atm

[leaden torrent]

i also think that race is an easy thing for people to blame

like, i grew up in a town with very few black people, and even to this day, when i see a black person, the first thing i notice subconsciously is their race

you hear cliches like "i dont see colour" but

that isnt really true for most people

race might be a fiction in a sociological sense but people still pick it up

so if you see a few news reports of, say, black people doing crimes

its very possible that race is the ONLY thing you remember about the criminals

[neat lintel]

the key to solving racism is blinding yourself

and I mean this in the physical sense

[leaden torrent]

combine that with confirmation bias, systemic reasons for crimes by black people to be more popularized and punished more harshly

as well as the fact that crime rates are genuinely higher in poor communities, which do tend to be blacker than average

its easy for this to subconsciously warp your perception of black people as a whole

IMO its a duty of a citizen of civil society to reevaluate your own biases regularly and notice if your thinking is straying in unsubstantiated directions

but thats hard to do

and even smart people can convince themselves their false or exaggerated viewpoints are valid

after all, smart people tend to be good at arguing

[neat lintel]

arguing is fun

[leaden torrent]

combine that with the fact that these people tend to gravitate towards others with similar views

(look at /pol/, or better yet dont)

and you can see why these things tend to stick around

even if we as a society "should know better"

[neat lintel]

there's also the internet

[leaden torrent]

idk, its a tough issue

i have had the displeasure of interacting with a lot of racists

i grew up in rural alberta and a lot of my early internet-ing was on 4chan or 4chan-adjacent sites

(even to this day, i check 4chan on occasion, though im very selective about where i go)

and in one sense i "get it"

i see how racism perpetuates, at least in a vague sense

but i cant really "explain it"

[sick kite]

racism seems to be a cope for misery

plus

the community aspect of having various racist online forums on the internet means that people gravitate towards those because they are lonely

it's no coincidence that most of the online racist community are a bunch of losers who spend all day on some social media site in their moms basement and don't shower

like you can smell 4chan through the monitor

\pol\ at least

the same kind of phenomena happens with religion but on a smaller scale, people (especially prisoners for whatever reason) tend to join various religious groups in search of this communal aspect

[neat lintel]

you dont know what you are talking about

its just a social habit, calling it a cope is dumb as shit, top midwittery

you and everyone you know would be racist had you been born 100 years ago or more

you probably hold prejudices similar to racists.

[sick burrow]

I'm not sure what this proves

[neat lintel]

saying its a cope for misery is beyond stuoid is what it proves

its nothing that soyfilled

[sick burrow]

I think it's likely there is a correlation between racism and misery in the US

[neat lintel]

??

Im sorry

I really dont intend to be rude

but racism is rooted in control and social habits

not misery

US was big into slavery

thats why there is racism on a big scale

[sick burrow]

Or at least, I think one of the ways alt-right groups are currently radicalizing people is by finding vulnerable white men and providing them with a semblance of a community while also telling them (insert often racist scapegoat group) are the problem

[neat lintel]

social habits and justifications for control

not misery

its not rooted in misery. I will tell you that for sure

[sick burrow]

But yeah misery is definitely not the root cause of racism

[neat lintel]

thats what im saying

its not a cope for misery either

lots of happy people are racist

[sick burrow]

I'm just saying swifteeees point is largley correct, possibly sans "racism is a cope for misery"

[neat lintel]

big sans

[sick burrow]

Sans Undertale???

[neat lintel]

might as well

also i dont get it sometimes

people dont view racism as a doomed social habit; they believe it can be changed

but then no one can come to agreement what is doomed or not

its good to know if its doomed so you can manage expectations in social interactions

[sick burrow]

Hm?

Racism can be changed though?

Like not easily, sure

[neat lintel]

I dont believe on a grand scale

not solved

and will always exist

only on personal levels I believe

anti racist advertisement is weird imo too

[sick burrow]

The Left does really need to work on their messaging imo

[cold needle]

[sick burrow]

But it's also worth noting that racism as we understand it today didn't always exist

[neat lintel]

i mean its kind of awkward sometimes

[sick burrow]

Augustine was a super important historical figure but we don't know his skin color since people didn't care about it back then

[neat lintel]

its weird when people who you can’t relate with on any level try to sympathize with causes that effect you but dont try to relate to you in any way.

like they remove human aspects of what should matter

[sick burrow]

Racism is a case of tribalism though and that has (to my knowledge) always existed

But racism as in classifying and discriminating against people based on skin color definitely did not always exist.

[neat lintel]

they are similar i guess but its kind of clear what racism is

no need to change definitions around

we dont need a precise definition because everyone’s definition is subjective anyways

similar to an early discussion about defining what math is

[sick burrow]

Well the point is a Black people, White people, etc weren't even always viewed as meaningful social groups

[neat lintel]

yeah no shiiit

but that isnt what racism is

[sick burrow]

Well yeah

[neat lintel]

there is general agreement that it changes with time

it will never be a solved case );

same with lots of things

[sick burrow]

I do think it's to a certain extent human nature to group people into the Other and then demonize them

But how much and in what ways that happens can very much be changed

Like I'm not sure what your point is

[neat lintel]

imo any given racist action is motivated by history

comments made by someone racist in the past influencing you in future

[sick burrow]

You're making vague general points, but I'm not sure what the underlying argument is

[sick burrow]

Also I'm not quite sure how this ties in

[neat lintel]

this

anti racist campaigning feels very silly sometimes

depends on the people doing it

[sick burrow]

I mean it's like

[neat lintel]

efforts are appreciated but im not sure how effective they are sometimes

[sick burrow]

There are statements like "all White people have some racism in them" of whatever

Or "if you're not actively antiracist then you're racist"

[neat lintel]

everyone has the ability to be racist is a more true statement imo

[neat lintel]

ao thats why people say this

its similar to voting

if you arent vocal about antiracism you are allowing it to exist

[sick burrow]

And it's like, I see the point you're trying to get across there, and it's a very important one, but that is not the right phrasing if you want to convince people who don't already agree with you

[neat lintel]

you cant convince people who dont agree with you on a mass scale is my argument

so it isnt worth the effort

almost diminished returns

its gives those who agree more catchphrases

[sick burrow]

I think you can though?

[neat lintel]

What is an example of that lol?

[sick burrow]

Like the widespread public opinion in the US has definitely gotten less racist over time

[neat lintel]

its more subtle is the true statement

[sick burrow]

Since slavery, sure, but I think I also saw a graph on like public opinion on interracial marriage

And it was a very positive trend

[neat lintel]

people do lie which is also a thing

[sick burrow]

And this is moving outside of race, but also look at something like gay marriage

[neat lintel]

kinda outts the domain of a lot of things

because talk on sexuality is completely different

imo a lot of sexual liberation advertisement only exists for economic insentive, not because people actually care

damn I had to retype this becsuse it would be instaban without context

[cold needle]

[neat lintel]

marriage as a concept has always been sorta silly to me and im not sure why people put this crazy importantance on it

so its always weird to me when gay people want gay marriage when the institution thats allows for it is completely against them? instead of fitting in wouldnt they want to make a new institution that is more coherent?

[sick burrow]

This is a complicated issue

[neat lintel]

almost as contradictory as polygamous marriage

idk if its complicated tbh

it just seems like a harmful cope

[light needle]

i mean its really just more of an equality thing

if straight people can get married so should gay people be able to

and i mean the goal is to make marraige an institution that isnt against gay ppl

like our society kinda makes marraige like, a big thing

[neat lintel]

but what is the point of marriage if not religious was always my confusion, and why do so many secular people want marriage?

[neat lintel]

im confused why

[light needle]

it is wierd

i dont like the idea of marraige myself

[neat lintel]

its dumb and inefficient imo

[light needle]

but to a lot of people it means a lot

its suppose to be a big commitment point in relationships or some shit

but yeah from that lense its understandable like

[neat lintel]

yes and no one has been able to give me a good reason why

a lot of atheists too

[light needle]

like marraige in our culture isnt really religious, not really

[neat lintel]

which makes me confused

[light needle]

its saying that your relationship has reached the ultimate level

and many people wanna do that

[neat lintel]

yeah its not coherent but ig most normal people arent

[light needle]

its not about being "normal" lol

[neat lintel]

it definitely is

[light needle]

i mean relationships etc are emotional

[neat lintel]

its a social habit

marriage is

[light needle]

like you cant expect this to be logical

[cold needle]

are you saying that being coherent is not normal

[light needle]

the vibes i get from what u said is

"im not like other girls im logical wrt marraige!"

[neat lintel]

im saying everyone is incoherent sometimes, even for big decisions

[light needle]

so im pushing back a bit on that

[neat lintel]

lol wtf

you cant just minimize my argument like that, marriage is a pretty big decision so it makes sense to be logical about it

[light needle]

i object to you saying normal people

[neat lintel]

normal meaning majority

[light needle]

cause that implies theres people who are coherent about this stuff

[neat lintel]

in USA

yes there are a minority who are

[light needle]

and i argue no one is gonna be logical about relationship stuff

like relationships are literally about emotions lol

[neat lintel]

you can still make good decisions when it comes to big things

like planning parenthood

or big purchases/commitments to lifestyle changes

including marriage

emotions motivate decisions I agree

[light needle]

sure but wether u get married or not is ultimately an emotional decision lol

[neat lintel]

marriage should be motivated by emotions and logic.

you shouldnt marry someone who you know you cant see yourself with for long term…

even if you have good emotions for the time being

just because you have a happy week with someone doesnt mean you have kids with them

logic needs to come into big decisions

and marriage is a big decision

[neat lintel]

what im saying can also be seen in this frame too

[velvet dagger]

What about being quasicoherent?

[neat lintel]

some social habits have this much of a grip on society

there is no way racism game will be solved

[velvet dagger]

Mahael I think you might be conflating the cultural significance of marriage as a part of a relationship and the institution of marriage societally

[neat lintel]

Am I? I believe both to be in need of changes

to agree with one another at the least

[velvet dagger]

Like, given things as they are, if you look at one person and a partner, you could talk about hey how do we want to take our relationship? As far as seriousness and whatnot goes

[sick burrow]

Ok so what you have to understand is that a cultural realtiy is still a very real reality

[velvet dagger]

But for instance, when you talk about why folk of other sexualities might want marriage to be legal, you sorta say look

Marriage may have been historically sourced from religion, but nowadays society at large (perhaps due to the fact that a long time ago, religion occupied a much bigger role in society than it does now) basically places marriage as the ultimate culmination of a relationship

[sick burrow]

A cultural norm might be stupid in a purely abstract setting, but that doesn't mean that it doesn't matter or should be ignored in practice.

Or even could be ignored in practice

[velvet dagger]

You can ask whether society should have done so or not. But regardless of that question, it has, and it influences how a relationship goes. A gay couple that's married is considered more serious than one that's not, concretely you have tax benefits to worry about, etc

[neat lintel]

I believe ancient traditions should be subject to deprecation

[velvet dagger]

Perhaps, but unless you're able to will that to be the case at moment's notice, you have to confront reality as it is

[sick burrow]

Marriage is a cultural reality of our society so the choice to not marry in our culture has a very different force to it then not marrying in a marriageless society

[velvet dagger]

And it turns out that simply trashing the idea of marriage entirely is, at least in the short term, incredibly unrealistic

[sick burrow]

Exactly. Perhaps the best society is going to be one without marriage, but what matters is what we do about the society we live in right now.

[neat lintel]

I agree but why not proposing a reformed version of marriage

[velvet dagger]

Not realistic in the near future

[neat lintel]

a lot of the restrictions still exist

[cold needle]

what good is it if nobody is going to change

(at least anytime soon)

[velvet dagger]

Like I said unless you can will it out of existence

[neat lintel]

polyamoous marriges are an example

[velvet dagger]

In which case go and do it

[neat lintel]

why is that more unrealistic than gay marriage

even though its being illegalized more often

[sick burrow]

I think this is a problem a lot of people get caught up in. Getting caught up in utopian ideals vs actually working with how society currently is.

[neat lintel]

goes to my point about racism sort of

[velvet dagger]

I think part of it is that the law in many countries has provisions about equality already built in

[neat lintel]

and how antiracist advertisement is not being done correctly

[velvet dagger]

And the other is that the cultural stigma against polyamorous marriages is probably much stronger

[neat lintel]

which is weird to me

[sick burrow]

The question you have to ask isn't "would gay marriage exist in a perfect world" (to which the answer might be "marriage wouldn't exist period"), but "is the net effect of legalizing gay marriage right now positive or negative"

[neat lintel]

Utah exists and I no one has ever advertised polyamorous hate afaik

imo its net positive for economy

but at same time without clear consensus for what its supposed to be based in, it becomes a silly practice to follow