serious-discussion

[crystal stone]

I don't think anyone is implying this

I think the honors pure math courses are just designed for a challenge for those who are up to it

It's geared towards making you into a pure mathematician

[atomic cypress]

I don't think anyone is implying this

I'm implying it

[swift steeple]

imma take em

i've never seen a single proof in school

and i wanna see rigor and abstractness

[crystal stone]

Cool

[velvet dagger]

@atomic cypress I mean let's put it this way

I'm happy to have theory LA and practical LA

And both split as regular + honors

Honors will cover more in each case but the emphasis is different

Maybe practical honors emphasizes more advanced matrix factorizations, coding, numerical stuff, algorithm analysis

Theory honors will do stuff like modules, determinant as a multilinear form, etc

So that's my point when I say practical vs theory in my mind should be orthogonal to the question of regular vs honors

Because there are classes which will be, perhaps on the upper level of "reasonable intensity" for normal students

And which will be boring for others

But having an available honors class allows you to push the more advanced students to something closer to their potential

[atomic cypress]

Right, I don't care about honors classes, I mean creating a select group of students called honors students is irksome. Elitism is a pest, unless it's me, in which case it's cool.

[velvet dagger]

Lol. Idk what I think of elitism

I guess like

It has too much potential that "the elite" at X extrapolate from being skilled at X to simply "being better™️"

[crystal stone]

I didn't see in math ppl saying they're elite for taking honors courses

Instead I saw "Yeah I dunno why I chose this"

[pale orchid]

what are honors courses?

[crystal stone]

It varies from school to school

But in general honors math course means in someway it will challenge you

e.g. in honors real analysis at UCLA we used Rudin's principles and had harder exams and problem sets

Honors Linear Algebra covered significantly more material

[pale orchid]

i see

honors is a weird name for it

[atomic cypress]

I think they're a waste of time frankly, just skip calculus and do real analysis.

Or alternatively do calculus like the rest of us plebs.

There's no point doing shitty real analysis instead of calculus.

That way you get neither the computational training of calculus nor the rigor training of real analysis.

[crystal stone]

well what if I took an honors calculus sequence that gave me both

Through spivak's calculus, you get good at computation

and you get rigor

[rich bay]

Isn’t Spivak like the calcbook that teaches u proof

[somber aspen]

you see that's why you play both sides

so you always end up on top

[atomic cypress]

Through spivak's calculus, you get good at computation
and you get rigor

Unless you felt that Spivak let you skip Rudin Principles for Real and Complex, I'm not sure one gets rigor from Spivak.

Or sufficient practice in rigor, at least.

[neat lintel]

Hello All. Where can I find information on the financial viability of doing a Masters Degree on Pure Maths? Thanks in advance.

[vast surge]

#❓how-to-get-help

[neat lintel]

ty

[devout nacelle]

Ummmm

I thought the question was more of a general one

[leaden skiff]

also #❓how-to-get-help is for hw problems mostly no?

[stable oar]

yeah, this question feels reasonable for discussions

[devout nacelle]

@neat lintel This channel should be fine. It would help if you explain your background with respect to education, why you'd like to pursue a math degree, and your particular interests (if any) within maths.

[velvet dagger]

@atomic cypress you could jump to Royden from Spivak

Maybe not big Rudin

Because big Rudin wants you to know metric spaces

Spivak is basically like

How to put it

Let's say you haven't seen computational calculus or any sort of proof-based math before

Unless you're really clever, you do not want Rudin to simultaneously be your intro to calculus and your intro to proofs

Spivak can function as such

And then you do smth like Royden to get metric spaces, measure theory, and baby functional

[neat lintel]

Thanks @devout nacelle I'm an Industrial Engineer. I have completed online courses in Abstract Algebra, Number Theory, Topology, Probability Theory, Real & Complex Analysis, and Differential Equations. My particular interest is Analysis and Topology. However, I seem to have learned all these subjects for practically free, buying the reccommended books on the areas (Rudin, Jacobson, Willard, Hoffman and Kunze, Rosen, Dummit and Foote, etc.) and searching online whenever I get stuck. My question is how to make Maths my daily job without having to pay for $50k+ Degrees.

[velvet dagger]

Or if you've seen calc a la Stewart

You do Rudin -> Big Rudin

[atomic cypress]

Yeah this is kind of what I mean. You can read Spivak -> Abbot/Royden/whatever -> Big Rudin or Any Calculus Textbook -> Baby Rudin -> Daddy Rudin

You end up learning the proofs anyways but at least on the latter path you have more calc practice

[velvet dagger]

Not quite

Royden is basically half of big Rudin lol

Plus some metric spaces

Abbott is basically Spivak + epsilon

So I'm saying you either do Spivak -> Royden + complex analysis

Or Stewart -> Rudin -> Big Rudin

[devout nacelle]

Have you looked into masters programs that are willing to take in students who did not major in math? I don't think a masters in math should cost as much, although I don't know much about the specifics of the place you're at.

[neat lintel]

Will do, @devout nacelle Thanks for the help.

[eager crescent]

Some applied maths masters may be recruiting non maths majors, if your major had sufficient maths. As an industrial engineer it shouldn't be a problem

Might be trickier with pure maths but you can still try

[neat lintel]

Thanks @eager crescent . Boy do I love pure Maths 🤓

hi

hi

how are you

i also like pure maths

but cant understand

any part of it

like really

[primal crater]

[velvet dagger]

That's how people start

[neat lintel]

@neat lintel . Do you know how to do proofs?

well there is the difference of not being able to learn well and overthinking too much and getting burned out too much and die and respawn

[bronze pelican]

i remember when every math wikipedia page was absolute gibberish

[neat lintel]

well i know types of proofs but not every

[bronze pelican]

then slowly over the course of undergrad, i was like, hey this is actually readable

[neat lintel]

well when did you start your undergrad

[bronze pelican]

4 yrs ago?

[neat lintel]

and do you want to become the greatest mathematician of all time

[bronze pelican]

no

[neat lintel]

i am sorry but your age

[neat lintel]

good

there is no such thing as that

[leaden skiff]

how old are you

[bronze pelican]

i started undergrad at like 18 ?

idk

[neat lintel]

ohh

very early

[leaden skiff]

isn't undergrad first year of college?

[bronze pelican]

yes

[neat lintel]

i am 15 just 3 yrs behind joining in an undergrad

[velvet dagger]

Most people don't want to be the best

And if they do it gets beaten out of them fast

[neat lintel]

then they started with motivation and not curiosity

[bronze pelican]

im almost 22

[neat lintel]

what

then why arent yo still in your doctorate program

how many years will it take to complete undergrad

[bronze pelican]

i finished this year

[neat lintel]

ohh good

then when will you get your phd

[bronze pelican]

5 years from now?

[neat lintel]

what

you will be 30 by them

then

where do you study

[bronze pelican]

yes 22 +5 = 30

[neat lintel]

no no

i was rounding off

dont worry

[limber perch]

Big Rudin -> Baby Rudin
???

surely you just switched them

[velvet dagger]

Put a parenthesis between Big Rudin and (or any calculus...)

[crystal stone]

I dunno, I feel like papa rudin is hard to learn from without guidance

Like there's a part where he just states that every open set can be written as a countable union of rectangles

[velvet dagger]

Probably, he meant more the level than the book

[atomic cypress]

surely you just switched them

Actually one should start with Stein's monograph on singular integrals before even attempting Principles of Analysis

[delicate knoll]

There is a definition of "continnuos function" with predicate logic?

Good,pal...good...

[neat lintel]

what is a simple region?

[deep mango]

usually means something like connected and simply connected?

so

every loop contracts to a point inside the region, there are no holes

[vivid halo]

if this is in the context of vector calculus it usually means contractable as well

since you don't want higher dimensional holes either

[patent wind]

Idk why everyone here simps over Rudin

It's like the McDonald's of analysis books

[leaden torrent]

???

[cold needle]

lmao

[visual hearth]

Has anyone studied Optimisation here?

[deep mango]

rudin is garbie

terrible

pugh is the five guys of analysis books, messy but delicious

[cold needle]

tterra moment

proof by picture

[light needle]

tao is the chick-fil-A of analysis books.

I dont like anyone who goes to tao

[cold needle]

tao is homophobic, even.

[deep mango]

rudin is actually more like in n out tbh

like

fine, and good value, but not actually very good if you look at it in a human way instead of as an accountant

[velvet dagger]

Pugh chapter 2 is not good is the problem

I haven't read 3 and 4 but heard they're solid

But 2 is just

[deep mango]

2 is fine

oh my god

what is wrong with 2

[velvet dagger]

Worst treatment on metric topology

[deep mango]

[velvet dagger]

Problem is it doesn't really have a clear delineation about what's going on with sequences vs open sets vs continuous functions

It just kinda does everything at the same time

No real organization

[limber perch]

spivak is the burger king

i’ve never had it

[devout nacelle]

[leaden skiff]

do you need to study more than any one analysis text?

im using abbot, is that enough?

or should i like, read rudin after?

[crystal stone]

in general it depends on what you wanna do

If you want to learn more analysis then yes

If you get a taste from abott

And you don't like it

Just learn abbott and put it away

[devout nacelle]

(I personally feel revisiting the same subject again with different texts after an interval of time helps me understand stuff better)

[crystal stone]

The key thing being after an interval of time

A non-trivial one

At least a few months

[devout nacelle]

Right

Too much at the same time can be overwhelming and simply boring

[leaden skiff]

I mostly just kinda wanna get to the good stuff. like complex analysis. and differential forms

[fringe needle]

For complex analysis you need a complex analysis textbook, and differential forms it seems tend to be treated in a rush at the end of intro analysis textbooks

I say it seems because I don’t have much experience with differential forms

[vast surge]

So I decided to sit down and finally listen to an album by the Clash, having only previously heard a bunch of their songs. I guess I was expected a bit less reggae, honestly.

[bronze pelican]

Who talks like this

Sheesh

[toxic schooner]

light mode 🤢

[vast surge]

@light needle does

But also honestly comparing something to chick-fil-A is actually a genuinely good insult and one that I will add to my repertoire.

[deep mango]

what is the point of chic fil a now that so many other quality fast food chicken sandwiches exist

do they need to exist anymore

[thorn brook]

Why do I constantly want to drink coffee?

[ashen river]

I do as well

It calms my nerves

[thorn brook]

Coffee just tastes so good

[ashen river]

As long as I don't overdo it

[thorn brook]

Ye it just doesn’t feel right to drink like more than 4 cups a day

Imma just make some tea instead

But then I fall asleep

[ashen river]

For a while i had a medical reason that i couldn't drink coffee

It was horrible

Never again pls God

[thorn brook]

Ouuf that sounds harsh

[pale orchid]

coffee and calm nerves should only go together with a negation in between

[ashen river]

Nah it's kind of like how cigarettes calm ppls nerves. I dont smoke but i see it in my friends faces after they do

[pale orchid]

i'm just talking physiologically

[ashen river]

Also the taste and the "roundness" of the coffee are so calming, i can't describe it

[pale orchid]

coffee is a stimulant and is linked to increased anxiety

[ashen river]

Oh physiologically your 100% correct

😂😂

[thorn brook]

I honestly might get some caffeine free coffee

[pale orchid]

once you drink it often enough that it doesn't tickle you anymore, then sure

[thorn brook]

And just drink that all day

[pale orchid]

just enjoy the taste 😛

[ashen river]

Without caffeine it's not as addictive :-( you stop making the mental association

[thorn brook]

But I’m like drinking coffee for the taste anyway it feels like

When I’m reading I just want to sip on something

And that something is always coffee

[neat lintel]

I don't drink coffee I drink tea my dear

[ashen river]

I've switched to instant coffee

It doesn't taste good

[thorn brook]

Tea is way too hot tho

[ashen river]

But it staves off the headaches I'd get if i drank <5 cups a day

[thorn brook]

You have to wait like 4 years before you can finally drink it in peace

[neat lintel]

It's a song

[ashen river]

@deep mango do you drink coffee

[deep mango]

not really

[ashen river]

And are you snobbish about it at all?

[deep mango]

i like tea better

[ashen river]

Aww damn

[deep mango]

i like coffee but

it makes be feel really bad

usually

[ashen river]

There's a really good place close to campus

Organic coffee

[neat lintel]

I used to drink coffee and now I drink water
And sometimes tea, with milk

[ashen river]

It's expensive tho

[deep mango]

i see

matto looked really good

and cheap

matto has mochas for 2.50

[crystal dagger]

can a cool mod change my name to C*-algebra

uwu

[deep mango]

[thorn brook]

Ahhh I was about to send that

[frail lagoon]

owo

[toxic schooner]

OwO

[warm estuary]

Hey i need friends. pls add me

[neat lintel]

Hmm. No

[warm estuary]

Hey i need friends. pls add me

[neat lintel]

moniker plsss add him

[spring crypt]

Just dropped by to say I'm writing about what I've learnt this week for my master's thesis and I love it! I haven't felt so motivated since... well, forever!

also I love summing diagrams lol

[vast surge]

I just realized, despite the ongoing global pandemic and the lockdown, I know more people who died in (totally unrelated) car crashes since the pandemic began than people who have died of covid.

[pale orchid]

seatbelts don't work confirmed

[eager crescent]

[halcyon basin]

so many questions

like what does a square root do to a number and why

and why do we need it

why do exponents multiply a number by itslf

https://tenor.com/view/math-thinking-zach-galifianakis-formulas-numbers-gif-7715569

[wild jay]

yeah man

[chrome vault]

yeah man

[fathom cedar]

nah man

[crystal dagger]

Whats it about? Roughly

[spring crypt]

Thanks for asking! Here goes 😛

So firstly I don't know yet where we're going to end up with this but the starting point is a paper where the aim is to construct a topological quantum field theory (which to my understanding is a topological invariant like homology but the properties are a bit different) for a class of surfaces, and said TQFT is constructed with the help of a coxeter group and its associated hecke algebra (so more or less like you fix a base abelian group for homology)

oh and by triangulating the surfaces and that's how those squares come about, the invariant is preserved by swapping diagonals on the triangulation and that's what that expression proves 😄

[crystal dagger]

Ooh

Sounds pog

[alpine adder]

can you please walk me through W=x+xyz for z?

[spring crypt]

extremely! oh and in the paper there's also some interpretation of those algebras that allow the authors to compute stuff with drawings and it's so nice lmao

I don't know much yet tho, haven't really reached that yet

but it's like performing some operations on the drawings is equivalent to performing operations on the algebra and it's apparently easier

like how can I not like this right away? it's just like undoing knots or something (like the 2nd one)

it's so neat 😂

[untold sapphire]

yeah string diagrams are weird as shit

[meager sonnet]

string diagrams

I want to learn them but like

it's hard to do examples when it's more drawing

[vast surge]

Oh god I forgot what it's like to struggle to learn a new computer algebra system. I'm trying to pick up Macaulay2 for my commalg class right now and I'm half inclined to just compute these Groebner bases by hand.

Maybe it'll be easier tomorrow when I'm less tired.

[devout cypress]

Help in #help-4

[leaden torrent]

when you posted this in #discussion , you were met with the following message:

[quasi jetty]

From

#❓how-to-get-help

Rule 3

Stick to one channel and don't post the same question in multiple channels. Please don't ask for help in other channels if no one is responding in the one you have posted your question in.

[leaden torrent]

seems you didnt listen.

[cold needle]

[leaden torrent]

i suggest you do in the future.

[neat lintel]

(Daman)x+c

[modest steppe]

b

1+1

=2

2x2

=4

actually c

cuz it says Hint

is this a part of multi variable

I only know multi variable

dang

[last oxide]

to some extent

[dapper pivot]

is anthropology a controversial field ? i see a lot of theories on it but no strong answer

[neat lintel]

This is not math I think.

[limber thunder]

this channel is for general discussion

[limber thunder]

about as controversial as any other social science really, it's got its own methods which are validated by the community

[neat lintel]

Any topic humans are involved is controversial.

[limber thunder]

that's to say, not controversial at all except for like hardline scientists who like to give social science a hard time lol

[dapper pivot]

i read into anthropology a bit more and i think i can draw a conclusion that humans are vastly different in everything

bruh and it says we are closely related to apes and stuff but how come all most apes look a like but we don’t

[leaden torrent]

do apes not look alike? or are you more sensitive to the differences because you are a human?

that said, we do have a fair amount of differences because humans diverged from apes longer ago than apes themselves did

human ancestors branch off from, say, chimps and other primates with the Australopithecine subtribe

the rest of this subtribe is entirely extinct

plenty of members of it in the fossil record are fairly human-like

but it seems humans outcompeted with them all (or in some cases, like neanderthals, interbred)

its unclear why humans outcompeted other lines so well.

the old hypothesis was simply that we were smarter and more energy-efficient (required less food, could hunt longer)

and cooking food let us optimize even more energy

but AFAIK most anthropologists think this theory is a bit limited (our pre-human ancestors left behind evidence of tool and fire use, after all)

its not particularly uncommon for an entire evolutionary branch except one member to go extinct, though

humans are special but not THAT special

[dapper pivot]

will we ever find strong evidence on why?

or is it too hard

[neat lintel]

hey bitches

please well behave

if you want joking, please go to #chill

[leaden skiff]

probably eventually.

[bold carbon]

Do you want to do mathematics research? Or are you just looking for quantitative finance? Or are you looking for statistics?

[neat lintel]

Umm... wdym fractals

You can study self-similar sets

And it's not as easy as it seems

Why would I want to motivate you to pursue math research?

[bold carbon]

@neat lintel
assuming you already done calculus and linear algebra, but if you haven't that's definitely part of the math curriculum

well, there's group theory which leads to representation theory, which is something you might want to look into
and there's metric spaces and topological spaces
and there's differential equations, ordinary and partial

beyond that there's set theory where they cover ZFC rigourously and ordinals

and more...
combinatorics
number theory but not just modular arithmetic
number fields
numerical analysis

and there's two main routes afterwards, algebraists and analysts, algebraists typically focuses on structure to prove stuff and analysts are more of bounding and inequalities to prove stuff

[wheat crater]

group theory leads to a lot of things, representation theory is only one of them and by no means is it the best of the bunch

[neat lintel]

What do you find appealing in pursuing a math degree

[latent forge]

homelessness impending

[bold carbon]

yeah there's other stuff in group theory too but I just know representation theory

maybe stuff about homotopy and homology groups tho

[latent forge]

math degree is impressive to almost everyone

it shows that most people dont care what you learn for the most part

thats a good sign

shit is boring af

[bold carbon]

honestly, you should ask yourself that question first, does math drive you

[latent forge]

you are essentially learning arithmetic right now

[bold carbon]

don't worry if the answer is no

you might be interested in computing or physics or other related stuff that uses math

[latent forge]

if you want to learn why things work the way to do and being able to show that then math is for you

[bold carbon]

see the numbers? well some math has almost no numbers

[neat lintel]

Oh, sad, calculus is what interested me into math

[bold carbon]

then, maybe it's philosophy you might be into

[latent forge]

you should try and learn about proofs too

[bold carbon]

then maybe topology might pique your interest

[latent forge]

or number theory?

nothing feels intuitive in number theory to me

[bold carbon]

not your standard coffee cup stuff, no, we have topological spaces and open sets here

[latent forge]

if you like counter intuitive results topology is probably best bet

[neat lintel]

Topology and analysis?

[latent forge]

oh yea true

cantor sets are pretty counter intuitive

abstract algebra is another branch of math

where you talk about algebraic structure of sets of objects including numbers

its pretty much everything youve done until now and more

but you formalize which rules are allowed

it gets more interesting the more math you learn

[neat lintel]

I loved abstract algebra when I first learned the basics of it

If you want to have more fun with calculus you can try to learn symbolic integration

Algorithms for calculating indefinite integrals and stuff

It has a lot of abstract algebra in it

[river linden]

@neat lintel calculus is fun when you find different paths to the same answer

optimization and approximation are also fun, newtons method & gradient descent are nifty

like try approximating n! by approxomating ln(n!) with an integral (since it is a series)

[strlings formula basically]

[neat lintel]

sitrling's formula

[river linden]

sush tterra I'm still amazed by baby math

[latent forge]

what are prereqs for AG mr ttera

dont wanna invest time into reading over my head if that makes sense

[neat lintel]

i don't know because i don't know AG

commutative algebra?

[latent forge]

i thought u were geometry guy

[neat lintel]

differential geometry, yes

[latent forge]

oh thats still good for mee

[neat lintel]

even if it's been a while since i've done any classes in it

[latent forge]

what ur classes now innit

[neat lintel]

measure theory, analytic nt, and control theory

last one might do some subriemannian geometry (DG) at the end

[latent forge]

oh cool

im scared of middle class

sounds spooky

idk what control theory is

[neat lintel]

i kind of spaced out during the lecture explaining what it is

seems like optimization on crack

[river linden]

control theory is based

rocket control software go brrr

[neat lintel]

analytic number theory so far just feels like proving a bunch of random identities and estimates

without really any focus

that should change soon

[latent forge]

hmm

online says i should be ok to learn AG

but I would benefit from learning comm algebra

[neat lintel]

ask like

shamrock or chmonkey or someone

they can probably tell you what you need to start ag

[latent forge]

should i ping?

wait

@shell roost @jovial ember @crystal atlas

[jovial ember]

What do you want to learn

[neat lintel]

look you're the AG guys in my mind

[jovial ember]

@ someone

My recommendation is that being fluent in commutative algebra before starting is incredibly helpful if you can stomach just learning commutative algebra without knowing why you’re learning it

[latent forge]

i probably cant

[jovial ember]

I wasn’t able to really like commutative algebra until I saw how you use it in AG

But it was incredibly painful to do AG without it

[latent forge]

so rn im taking a grad algebra sequence

when will i learn com alg

i think second sem maybe?

[jovial ember]

I don’t know lol

It depends on ur syllabus

[latent forge]

yea

[jovial ember]

Does it state what you learn in each semester somewhere

[latent forge]

im learning it in second sen

[jovial ember]

Ah

[latent forge]

nesr beginning

maybe i should wait

[jovial ember]

Do you have a copy of the description

[latent forge]

and learn something else in meantime that relates to what im learning rn

[jovial ember]

The thing is there’s ways to learn AG that aren’t comm alg heavy

It’s just like… you can’t really do everything

[latent forge]

last topic is algebraic geom

looks like a lotta shit ngl

[jovial ember]

Hmmm

What school is this or if u don’t wanna dox is ur school good

Lol

Because if you’re at a decent school the comm alg you learn will probably be sufficient for a while

But if not it could be a crapshoot

[latent forge]

nothing spectacular

[warm estuary]

hi i need friends. pls add me

[odd narwhal]

Well it's a topics course so it's not gonna be super in depth

[bold carbon]

https://www.bu.edu/academics/grs/courses/grs-ma-742/

found it lol

[ashen river]

This is just a bit too advanced to put in questions, but far too stupid to put in any advanced channel.
How do you find upper and lower bounds for $T(0) = O(1), T(n) = T(n / 3) + T(n / 2) + O(n)$ ?

[fathom swallow]

jcob_the_student

[ashen river]

my classmate swears that its bound above and below by a linear function O(n)

not swears

but thinks

I don't know...

[tawny spoke]

thoughts on making a discord server for a math class? i'm debating whether or not it'll be worth it to run one this quarter

[crystal stone]

For a single class it's usually not that useful

If it's a discord for a cohort of students at the school where there are specific channels for different classes

That's more useful

Oh anyone know a topic that would be good for analysis noobs to explore PDEs?

I'm writing some proposal for a mini-REU, but the math background of students is lack-luster

[untold sapphire]

this is so much easier said than done loool

idk i think i just have really low tolerance for this stuff.

[jovial ember]

That’s why I said

“If you can stomach it”

And immediately qualified it by saying I was not

[untold sapphire]

Yeah, yeah, i get it. i'm just groaning

[jovial ember]

Yeah

[untold sapphire]

as soon as I see shit i don't understand i basically close the book

i mean the purpose

[blazing pawn]

woke approach is to read szamuely which has no details and then read comm alg to understand all the details

[jovial ember]

Ummmmm how about no hun

💅

[untold sapphire]

this is something of an exaggeration, i just have a really low tolerance for wading through derivations i don't understand the point of.

[jovial ember]

Yeah I don’t really mind them

[untold sapphire]

i've been trying to read this chapter on derived categories for like 2 weeks and made zero progress

[jovial ember]

I just didn’t get comm alg until I saw it in use a bit

[untold sapphire]

because i keep just going "but why"

[jovial ember]

It helps that I like algebra a lot so I now enjoy learning CA for its own sake

[untold sapphire]

well

what do you like about algebra

or like

[jovial ember]

Idk I just like it

[untold sapphire]

what have you studied that most gave you a taste for it

[jovial ember]

I like learning more

Idk lol I liked it from the start sorta

[blazing pawn]

Chmonkey has no motivation but unending masochism

[jovial ember]

True

[untold sapphire]

i'm actually extremely sympathetic to this pov

i too enjoy self mutilation

[jovial ember]

I basically did AG because I liked algebra

And this was the first algebraic ___

I did

And I was like “ok I do this now”

To an extent

[untold sapphire]

if anyone wants to discuss Spanier's Algebraic Topology with me, i'd be down lol

hahaha. gotcha

yeah grad school kinda blew my doors off in terms of exposure to new ideas, i thought i was just going to study computability and model theory and shit

together with like, more philosophical questions in logic

What i've liked most in commutative algebra is like, the chain of results that culminates in Hilbert's Nullstellensatz. and here i'll include as part of that chain the krull-cohen-seidenberg 'goingup' stuff

those chapters in altman-kleiman were most interesting to me.

i feel like i've asked this before, but idk if i've asked you

if i have no intuition for DVRs and know zero number theory

what is the best way to gain intuition for them

also is there any motivation for regular local rings other than smoothness?

or do we exclusively study them because they code smoothness

are they of any a priori interest from a purely CA POV

this is probably a lot of questions lol

[deep mango]

its based i would never support piracy in accordance with the discord TOS and server guidelines®

[surreal sapphire]

the quality varies

there is some science on the effect of technology on learning and it seems to have a negative effect (if its not a purely work computer)

[blazing pawn]

okay unironically a neat one is that if you fix a field k and an extension K of k with transcendence degree 1 then the set of DVRs of containing k with field of fractions K forms a 1 dim scheme, say X

and if you pick some f in K transcendental over k then normalizing k[f] and k[f^{-1}] in K (meaning take the curve coming from the integral closure of each in K) gives you two affine dim 1 schemes say X^+ and X^- covering X, with X - X^+ containing exactly the points of X coming from prime ideals above (f^{-1})

this happens because every ideal will contain either f or f^{-1}

This is my intuition for them anyway and i think historically how they came about, its a kind of abstract projective analogue

oh over C this will look pretty much like gluing together noncompact riemann surfaces to get a compact one

like let k be a field, K = k(t), then normalizing k[t] and k[t^{-1}] will get you two copies of the affine line C and they are glued together in exactly the same way we glue together riemann surfaces C to get the riemann sphere

[untold sapphire]

are you saying that if you take all these DVR's there's some canonical way to glue them together into a scheme, based on like, the prime ideals in their common intersection or something

i'm not sure I get how this construction would work. a superficial sketch is fine

[blazing pawn]

oh its not too hard

so let X be the set of DVRs

[untold sapphire]

wait, is the rest of your message sketching the construction

[blazing pawn]

Uh not really

[untold sapphire]

ok.

[blazing pawn]

kind of but i can do it explicitly

the topology on X has closed sets be finite ones not containing K itself

the local ring at a DVR R is R itself

so the sheaf is given by taking intersections

like the sheaf on U is the intersection of all DVRs R in U

[untold sapphire]

this is truly weird. i assume this identification of rings with points works somewhat because the dvr only has one nonzero prime so it's fine to think of it as a point?

[blazing pawn]

Yes

this gets incredibly pathological in higher dimension

[untold sapphire]

Hahaha.

[blazing pawn]

this is called a zariski riemann space and its like

in dim 2 theyre all trivial

in dim 3 theyre not

shit like that

and for dim higher than 1 theyre not even schemes

But for dim 1 they are!

if its any help like if X is an integral affine normal curve over k with function field K(X) and coord ring O(X)

then the local rings of X are exactly the DVRs with field of fractions K(X) containing O(X)

so this is sort of expanding the net a bit and making the local rings all the ones containing the base field k

[blazing pawn]

in dim 1 theyre all going to contain either k[x] or k[x^{-1}] for some x transcendental which is what i talked about here

[untold sapphire]

wait, if K is transcendental over k, is it necessarily infinite

Sorry, nvm, i misread "subsets of (DVRS in) K" as "subsets of K" for a minute. the question is irrelevant.

[blazing pawn]

Ah

Over C these are equivalent to riemann surfaces so this is a nice lower tech way to start working with etale things

[untold sapphire]

Yeah. I'm still digesting this but certainly Riemann surfaces were the example I was working out.

i'm stuck on something basic, maybe somebody can help me out. Say I have a point x in a Riemann surface, X. The stalk of the sheaf of holomorphic functions at x should be a DVR. And I think that the big field K we are supposed to be thinking of is the field of meromorphic functions on X. But I am thinking that a locally defined holomorphic function does not extend, necessarily, to a global holomorphic function. For example if X is the punctured complex plane, and x is, say, 1, I can take the germ of a branch of the natural logarithm. This should not extend to any global meromorphic function. So the DVR associated to x is not a subring of the field of functions.

I suppose in the Zariski topology, since every open subset is cofinite, this issue does not occur. So it is more a hangup of being overly literal about the classical interpretation.

[blazing pawn]

Fwiw it should correspond to compact riemann surfaces

idk enough complex geometry to answer if this problem still occurs in that case

[untold sapphire]

Hmm, I see. That is helpful. The issue I am describing seems to arise more from a nontrivial fundamental group than compactness. I could be wrong about this. I don't know of any good examples wrt an elliptic curve structure on the torus off the top of my head.

I suppose this question is something like: is the sheaf of meromorphic functions on a compact Riemann surface flasque?

[slim meadow]

No?

The meromorphic functions on the riemann sphere is only rational functions, but there are a lot more meromorphic functions on the complex plane

[blazing pawn]

im not actually sure that the sheaf of holomorphic functions should be equivalent to the sheaf on the zariski riemann space though it... sounds like it should

or like

to be clear the closed points will form a compact riemann surface

[untold sapphire]

Ok, thank you, good counterexample.

[blazing pawn]

But anyway i hope thats neat enough motivation for DVRs

[untold sapphire]

I think probably it will be once I finish parsing it. I'll let you know

It definitely seems interesting. Thank you

[untold sapphire]

Over an integral variety, one can define a sheaf of fields of rational functions. But actually all the restriction maps would be isomorphisms, right? As a consequence of the space being irreducible. I am not sure if the same thing is true if the variety is not irreducible, but that's fine, I don't mind that assumption.

So there's a slight obstacle with me trying to think of the field of rational functions over a variety as being too much like meromorphic functions.

Every inclusion of an open subset is a birational equivalence.

And something analogous isn't true for meromorphic functions.

[neat lintel]

If you stay in category of projective things analogy is almost perfect though.

If variety is not irreducible than it's not true, think about variety=two points, say. I know that you emphasized that you are not interesting in this case, just side remark

[untold sapphire]

Ok, I think I understand the basic idea. That's cool.

[untold sapphire]

I'm not your Guy, pal.

[bronze pelican]

So well said

[untold sapphire]

Ok. I remember from the first chapter of hartshorne that one can associate to every finitely generated field K/k a variety which has K as its field of functions, and we can take this variety to be affine, because every variety is birationally equivalent to an affine one.

So this construction is something similar, but it's more fine grained and doesn't involve arbitrary choices.

And it won't be affine in general.

[neat lintel]

which construction?

[untold sapphire]

The construction that Moth sketched above. It associates to a field K of transcendence degree 1 a scheme whose points are exactly the DVRS in K whose field of fractions is K, and the field of functions on this scheme is K.

[neat lintel]

ok I see

[rare pond]

Where is this from?

[sick burrow]

I have thought of a very dumb joke

Why are set theorists bad at mtg draft

[deep mango]

[sick burrow]

Because...

Because they're always forcing

Eh..?

It barely even works tbh

[deep mango]

i am going to use this on jesse and ultra to make them mad

[sick burrow]

Than you ryc

[vivid halo]

Why do set theorists keep buying up land owned by the Catholic Church?

They’re interested in large cardinal properties

[limber thunder]

[dawn orchid]

I'm studying analysis

using Marsden elementary classical analysis

does anyone prefer a different textbook/suggestions?

[vivid halo]

Not Rudin

[deep mango]

a lot of people like abbot's understanding analysis

i like pugh's analysis but it's a bit goofy

[dawn orchid]

oh I didn't know about that one thanks

I mostly heard about marsden and tao

[bronze pelican]

100 years of Frobenius Uniqueness Conjecture by Aigner

Not enough people know about Markov's theorem

[light needle]

Pi_1 is a functor from Top* to Grp that preserves products, so it maps group objects in Top* to group objects in Grp. So fundemental groups of topological groups are abelian

so cursed lol

[neat lintel]

it's eckman hilton in an essence

but also like this argument

[bronze pelican]

that's fkin cursed

[light needle]

Ikr lol.

[warm estuary]

Hey i need friends. pls add me

[neat lintel]

Hey i need cup of twinings tea. pls do not add sugar to it

[buoyant grove]

hey i need a back massage

[neat lintel]

i need a bear

[devout nacelle]

[shut sapphire]

anyone know where to practice like good derivative questions (that use like chain, product, quotient, power, trig functions type of stuff)

[neat lintel]

obligatory khan academy recommendation

you could also just come up with your own functions to differentiate

you can check answers on wolframalpha

[shut sapphire]

They don’t seem that difficult

[shut sapphire]

Not a bad idea thanks

[toxic schooner]

pauls online notes have many if need

[neat lintel]

Hello there

[thorn brook]

yo what is the difference between the direct sum and the direct product?

they seem identical to me

[toxic schooner]

one is a product, one is a sum

[deep mango]

The difference is when you have an infinite collection of stuff

The direct sum says "all but finitely many of the terms should be 0/e/1, whatever the identity is"

The direct product says the terms can be anything at all

So you should think of direct sums like finite sequences (of any length), and direct products like infinite sequences.

E.g. the direct sum of infinitely many copies of Z is all the sequences like (a_1, a_2, ..., a_n, 0, 0, 0, ...) while the direct product of infinitely many copies of Z is just all sequences of integers

[thorn brook]

yeee okay I see I see

[deep mango]

The point is that direct sums are algebraically a lot easier to work with (cause algebraic operations are finitary)

But once you have a topology and can take limits, suddenly direct products are a lot easier to work with (because I want to be able to say that the limit of the sequence of sequences with n 1's and then 0's is the sequence of all 1's)

[thorn brook]

yee okay now I get it. Thank you so much!

Kind of reminds me of like the box and product topology

[deep mango]

Yeah it's exactly that

Well

Yeah

[thorn brook]

[candid cosmos]

@dusk relic

[dusk relic]

mmmm

[neat lintel]

Where can I study "graph collisions"?

Or "stream interaction"?

I need to study other subjects really bad but I just can't get this collision idéa out of my head

[bronze pelican]

@slim meadow are you submitting an abstract to JMM?

[fringe needle]

ive determined my lin alg teacher uses pruposefully weird notation

[dapper pivot]

had string theory been proven yet

has

[untold sapphire]

yeah i looked at this recently and it's pretty casual

very informal, i can see it being a bit rough for the student who is new to this stuff. it flies through the initial stuff pretty fast.

[whole copper]

No such thing as a

[deep mango]

a...?

[whole copper]

Proof

[neat lintel]

What does that symbol even mean?

[sick burrow]

[latent forge]

Nyone have time

Explaining taking integrals on manifolds

I poorly understand partition of unity

but that seems like its essential

[slim meadow]

i can try

[latent forge]

ok

[slim meadow]

what exactly are you confused about

[latent forge]

tbh the entire construction of part of unity

So like

[slim meadow]

are you reading Lee?

[latent forge]

I should be

but ive been going off lecture mostly

we are just starting chapter 3

but went through 2 very quickly

three is tangent spaces

on manifolds

and I followed the entire construction in class

partition of unity sort of alludes me

[slim meadow]

tbh, I've never used the construction of partiton of unity. You really only use its properties once you construct it

[latent forge]

why do we want functions from the manifold to 0,1

and what does compact support mean

[slim meadow]

Well, you can think of the functions as being to R, but the image is contained in [0,1]

[latent forge]

locally finite means every neighborhood instersects finitely open sets iirc

[slim meadow]

Compact support means the support is compact lmao

[latent forge]

support of f is all the inputs not sent to 0

and you want that to be a compact set for some reason?

not sure what this corresponds to

[slim meadow]

You want each function to be bounded is how I think about it

[latent forge]

oh wait wtf

[slim meadow]

and by bounded, I mean like, outside of some closed set, its 0

[latent forge]

So we cant havr support being bounded since support contains points on manifold

So the only form of boundedness we can get is having it being compact

Finiteness*

[slim meadow]

yeah exactly

[latent forge]

why do we care about the support though

[slim meadow]

I mean, in some sense the function will tell us things about the set its supported on

and be 0 outside of its support

Like, if we have a function f on the manifold

and we multiply it by the function with compact support, this new function tells us about f on the support

and you can replace function with vector field or anything on your manifold really

[latent forge]

So if we have f:M->M and compactly supported q:M->[0,1] ?

when you mean function on manifold

you mean from manifold to reals?

[slim meadow]

yes

function on a manifold always means M -> R

[latent forge]

like charts?

oh

more than just charts ok

oh wait

[slim meadow]

not like chart

[latent forge]

you mean M->R

not Rn

[slim meadow]

yes

[latent forge]

ig

why do we care about support and not when it is 0

[slim meadow]

I mean

the 0 function is pretty boring

[latent forge]

oh wait

im piecing it together

slowly though

Hmm

So like

say we have a function on manifold f

[slim meadow]

no its good you're asking good questions

[latent forge]

We have our partition of unity being a collection of continuous compactly supported functions f_alpha(x) with the sum of f_alpha(x) equal to 1

oh rip lol

[slim meadow]

Yep

[latent forge]

but pretty much

bad choices wtf

multiplying each f_i by f

is a way to talk about the values of f we care about at small sections

[slim meadow]

Yeah thats right

[latent forge]

and if you sum f*f_i you sort of get the values you should care about for f

[slim meadow]

Well if you sum f*f_i you just get back f

cause the f_i sum to 1

[latent forge]

so you arent trying to sum ff_i but talk about individual f_if

how exactly is partition of unity used from here

i sort of understand why we want compactly supported instead of having f_i have compact preimages

[slim meadow]

so one of the important things is that you can actually choose your partitions of unities with respect to some covering of your manifold

So if you choose some covering of your manifold by charts

[latent forge]

yea

[slim meadow]

It's usually called choosing a partition of unity subordinate to this covering

[latent forge]

ive heard that phrasing

[slim meadow]

right

And so one application of this is how you define integrals on a manifold

[latent forge]

and paraconpact

[slim meadow]

You first define the integral on a coordinate chart

And that's easy because you just pull back the function so its a function on R^n and just take the usual integral

Then, partition of unities allow you to extend this definition to functions on any open set

[latent forge]

pull back like with category theory pullbacks?

[slim meadow]

no

[latent forge]

or do you just mean the coordinate function

[slim meadow]

pullback is like a functor in this sense

[latent forge]

from Rn to M

[slim meadow]

what I mean is that

[latent forge]

wait wtf

its a formal thing?

[slim meadow]

if you have some chart from U \subseteq R^n to some open set V on your manifold M

and you have a function from V to R

then you can precompose with your chart to get a function from U to R

[latent forge]

precompose just means left compose?

[slim meadow]

This is the hom functor or something

yeah

[latent forge]

wait isnt the chart from V->Rn?

you said a chart from U in Rn to V in M

[slim meadow]

sure, I'm letting the image of that be U

I mean you can let charts go in either direction

since charts are diffeomorphisms

[latent forge]

ok lol can i clear something up really quick

So one book i read said charts/coordinate maps/coordinate functions are diffeomorphisms from U to Rn where U is a neighborhood of a point x in M. It gave a name to the inverse chart and called it coordinate somethings

is there a name for the inverse of a chart?

[slim meadow]

Coordinate functions?

[latent forge]

so many names to keep track of

oh ok

im not sure tbh

[slim meadow]

Because you have a function from some open subset of R^n to U

[latent forge]

yeah

[slim meadow]

and you can think of it like laying coordinates onto U

[latent forge]

the convention for whatever god forsaken reason is x^i

i still see no reason for it

[slim meadow]

cause of Einstein summation conventions mostly

[latent forge]

i definitely need to review that

it was used when we differential I think

or derivative

can’t remember which one anymore

[slim meadow]

i have no clue how it works either tbh

[latent forge]

tysm

i feel like intuition is super important for this topic atleast right now

also im a little weird on the entire smooth mappings/atlas/smooth structures on manifolds idea

so like

every topological manifold I can think of

[slim meadow]

yeah its important to understand that stuff well first

[latent forge]

has a smooth structure

i was given examples in my class

about people who won fields medals for proofs about which dimensions had topological manifolds with no smooth structures

[slim meadow]

yeah

i have 0 intuition for any of these things either

[latent forge]

i dont even think there is intuition to be had

like apparently R4 or R5 have no smooth structure

[slim meadow]

haha, I don't think mathematicians can do math without any intuition

Uh

[latent forge]

or wait

[slim meadow]

R4 and R5 definitely have smooth structures

[latent forge]

open sets

open subsets of them i think

[slim meadow]

yeah I believe that

[latent forge]

oh wait

nvm

it was that R4 has infinitely many inequivalent smooth structures

[slim meadow]

Right that

[latent forge]

this sorta sucks thoug

[slim meadow]

yea i have 0 intuition for this too

[latent forge]

because I can’t visualize past 3

i dont think anyone can lol

i also can barely visualize 3

So i sorta have no quick and easy pathological examples

and nothing worth computing ig

Also when you need to show a function on a manifold is smooth

you need to show psi o f o phi-1 smooth for different charts phi and psi?

but isnt f:M->R and psi M toRn?

[slim meadow]

So what that formula is for

[latent forge]

no

[slim meadow]

is when you have a function between manifolds

[latent forge]

ok

[slim meadow]

when f : M -> N

[latent forge]

that makes more sense yea

[slim meadow]

and psi is a chart on M

and phi is a chart on N

[latent forge]

you need to only check f o psi^-1 is smooth

[slim meadow]

Technically when f is from M -> R you can still do this, but charts on R are trivial

[latent forge]

so ig this is where i get tripped up

i have an easier time telling for good examples when a function isnt smooth

how do I in general show a function is smooth, differentiate and then induction or something lol?

[slim meadow]

Uh I'm not sure what you're really asking

Almost all the time, you just check the definition

Choose charts for your manifold, compute the composition of f with the charts, check that this is smooth

[latent forge]

yes

the last part

how do you check every partial is infinitely differentiable

do you just write them out?

but if its smooth you shouldnt run out

[slim meadow]

uhhhhhhhhhhhhhhhhhh

generally you just show things like

[latent forge]

ig this is a problem carried over from analysis

[slim meadow]

polynomials are smooth

sums/products/quotients (avoiding poles) are smooth

[latent forge]

yea

but cant this get really hard

because there are a lot of functions

[slim meadow]

ig, but none of these really come up in practice

[latent forge]

ic ic

[slim meadow]

I mean

maybe sometimes you use the fact that analytic implies smooth too

[latent forge]

in learning they shouldnt come up often

[slim meadow]

so this implies that like, e^x is smooth and stuff idk

[latent forge]

what topics are usually after defining a derivative on manifolds

integral*

in a first sem diftop

[slim meadow]

the whole like, differential form/de rham cohomology story probably

thats what Lee does ig

[latent forge]

o

im really excited tbh

[neat lintel]

you could also go onto riemannian geometry from there (not dt though)

[latent forge]

diff top and algebra are most exciting classes for me rn

RG?

regular guy

[slim meadow]

riemannian geo

I find diff top really interesting and hate riemannian geo im not gonna lie

[latent forge]

i want to learn geometry eventually

[neat lintel]

no you don't

[latent forge]

you are def right

[slim meadow]

LMAo

things get worse the more geometric u get

[latent forge]

I want to atleast touch algebrsic geometry

[neat lintel]

god i love riemannian geometry so much

[slim meadow]

[latent forge]

but the current prof is literally in shambles

and i want to avoid at all costs

[slim meadow]

I just don't get riemannian geo

[latent forge]

lol

[slim meadow]

idk, everything in diff top is relatively nice and neat

[latent forge]

actually you know that scuffed wojak meme

[slim meadow]

and then riemannian geo gets so messy

[latent forge]

he is embodiment

[neat lintel]

what's wrong with messy things

[latent forge]

geometers be like

[slim meadow]

i mean maybe if ur a messy person

[neat lintel]

i am

[slim meadow]

makes sense

[latent forge]

are you saying messy because notation looks crank

[slim meadow]

not really, Einstein notation is actually really helpful

christoffel symbols are terrible though

its just more than idk

[latent forge]

woah

[slim meadow]

So riemannian geometry allows you to add a metric onto your manifold

[latent forge]

sounds like a cool concept

wait wtf

not all geometry can do this?

[slim meadow]

and with that metric, things get a lot more analysisy imo

you get a lot more arguments with approximations and stuff like analysis

so imo it gets a lot messier

I'm not sure what you mean by that

the spaces in algebraic geometry aren't usually hausdorff so you definitely can't put a metric on them lmao

[latent forge]

i guess its just that im not sure what key objects in geometry are

my guess is topologies

[slim meadow]

i dont think anyone knows lmao

[latent forge]

is there a study of geometry on things that arent topologies?

[cerulean kernel]

i just learned about k vectors 5 minutes ago

[neat lintel]

the key objects in geometry are geometries just as the key objects in topology are topologies

[cerulean kernel]

or that they are a thing

[leaden torrent]

graph theory

[slim meadow]

No everything in geometry is a topology at least I think

but a topology is way way way too general to do anything close to geometry I think

[leaden torrent]

what is a k vector

[neat lintel]

dnt sully me

[latent forge]

i wish a geometry was an object

[slim meadow]

a line of ket nami

[latent forge]

id probably get excited

[cerulean kernel]

vectors have a magnitude and direction, a bivector has area and orientation, then there is trivectors etc. There is different products with them too, the video I am watching is related to Clifford Algebra

[latent forge]

woa

send pop math video

it better not be veritasoyum

[neat lintel]

what can you do with k vectors

[cerulean kernel]

https://www.youtube.com/watch?v=60z_hpEAtD8 no kinda a quirky vid i thought it was a meme or fake at first XD

[slim meadow]

is there a mathematical explanation of k vectors tbh

i still dont know what physicists mean when they say these things

[latent forge]

how much of physics is unfounded pseudoscience?

0% cant be true

[neat lintel]

100%.

[leaden torrent]

oh so they just mean k as a variable

[cerulean kernel]

physics is based on falsificationism i believe

[leaden torrent]

here

[latent forge]

like math is probably 10% unfounded bullshit somewhere

[leaden torrent]

damn i got excited

K is my favourite letter

but here its just being a dumb variable

[latent forge]

what is vid nami

quick explanation

[leaden torrent]

i havent watched it but so many people have asked about it that i get the gist

geometric algebra is a weird thing used by physicists thats arguably a bit more convenient than vector calculus

mathematicians dont really use it much at all

[cerulean kernel]

i am interested in physics too so i was watching it 😛

[latent forge]

hmm

[leaden torrent]

i dont know the exact details but apparently physicists find it handy for multivar

so i cant judge

multivar is kind of dumb anyway so anything that makes it easier im cool with

[latent forge]

i heard from some excited undergrad last yesr that tensors are important when describing quantum entanglement

[cerulean kernel]

yeah im in multivar calc rn

[latent forge]

how?

[leaden torrent]

tensors are important in all of physics

[latent forge]

);

and i still havent touched em

[leaden torrent]

to the point where "important when describing quantum entanglement" is really vague

[latent forge]

where is first place you encounter them

if you are physician

physisicst

[leaden torrent]

idk im not a physicist lmao

[latent forge]

physiciast student

[leaden torrent]

i think theyre usually first introduced informally in a QM course

[latent forge]

o

[leaden torrent]

or maybe relativity

[latent forge]

reference frames lol

[toxic schooner]

in one of those 2 yeah

[latent forge]

sounds like pseudoscience

[toxic schooner]

or if u take a grad level course on CM

[latent forge]

Celestial mechanics?

[toxic schooner]

then u will see tensors like moment of inertia pop up

Classical mechanics

[leaden torrent]

how tf does reference frame sound like pseudoscience

you learn about them in high school physics

[cerulean kernel]

lol

[latent forge]

i get the concept

[leaden torrent]

"if youre in a bus moving forward, and you throw a baseball backwards, what happens?"

[vivid halo]

as soon as you study GR tensors come up in a completely unavoidable way

they do come up in QM and QFT as well

maybe less so in early QM

[latent forge]

if the earth is rotating why we no fly off

i get the concept

but ive always felt like its one hypothesis of many if that makes sense

[vivid halo]

if the sun is traveling quickly with respect to the galactic center why don't the planets fly off?

[latent forge]

boom

im not sure what my doubt is similar to

[cerulean kernel]

thing is, the planets formed around the sun

[latent forge]

but its not completely irrational

[cerulean kernel]

it was already going fast

[latent forge]

like there is always the question in science, what if more reasons?

[leaden torrent]

i dont follow

[toxic schooner]

[leaden torrent]

are you implying the universe ought to have a canonical reference frame

if so, how fast am i moving in it

[latent forge]

i think you mean like every object in the universe has its own properties independent of which situation its in if that makes sense

[sick burrow]

Ooh do we have some relativity crankery

[latent forge]

and maybe thats possible idk

im not a crank

im just uneducated

[leaden torrent]

i mean sure, one of those properties is mass

[latent forge]

is it not normal to have doubts

[vivid halo]

yea so I mean the solution to this is to consider reference frames

[latent forge]

pfft

[leaden torrent]

but yes plenty of things change depending on situation

thats why we have ways of modelling situations

[latent forge]

i agree they are useful but why I called it pseudoscience was partially meme

[cerulean kernel]

maybe at one point in the universe there was only 1 reference frame, like big bang or something