serious-discussion

[cyan goblet]

i forgot to include that R 🤓 is a commutative ring 🤓 with identity

[arctic grove]

anamono, i have forgotten

are u also in hs?

[cyan goblet]

im a freshman in college now

:)

[bright hill]

neamesis, do you know what matrices are?

[errant ridge]

yea

[arctic grove]

damn

nice!

[cyan goblet]

non-traditional student, im actually 80 years old

[bright hill]

wait, what

[arctic grove]

wut

[cyan goblet]

i jk

well back in my day

[errant ridge]

quaternions

[cyan goblet]

non-traditional student, i am actually 12

[arctic grove]

i wanna hear_ u tell a joke when no ones, laughing in the background_

[errant ridge]

I'm actually 4 + 2i

[arctic grove]

Ohh moddddddssssssssssssssssssssss!

gonna save this one

[errant ridge]

[arctic grove]

but seriously

dont joke about this

mirza lost her account once coz someone reported her

for the same joke

yohan i am 18

wtf

[cyan goblet]

dear discord

[errant ridge]

yikes

[cyan goblet]

if u are reading this chat log

[bright hill]

lies

[cyan goblet]

i am of legal age to use your platform

[arctic grove]

i am not a middle schooler!

[errant ridge]

you're now old enough to be arrested

[bright hill]

lies

[arctic grove]

wha-

i was a pop sci fan in 2016!

[arctic grove]

wow

maybe i am a genius

[errant ridge]

,w 2016!

[fathom swallow]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by Neamesis#6134

[errant ridge]

damn shyshu's from the far future

[bright hill]

you could read pop sci at 7???

[arctic grove]

what the hell

[cyan goblet]

is the pop sci magazine not intended for younger population?

[arctic grove]

technically yes

[errant ridge]

actually he was reading TQFT research papers when he was 7

[cyan goblet]

i feel like im thinking about a diff pop sci

wait no yeah

[bright hill]

you knew english at 7?

I'm fr this time lol

[arctic grove]

i understood the many worlds interpretation at 4

without the QM part

[dense belfry]

Do you understand kripke semantics shyshu

[errant ridge]

hog riderrrrr

[arctic grove]

considering the only kripke i only is from big bang theory, no

[bright hill]

why do you think I'm learning japanese?

[dense belfry]

That kripke is named after the kripke I'm talking about

Lol

[arctic grove]

Ooo

[errant ridge]

[arctic grove]

idk what that is still

[arctic grove]

wow

[dense belfry]

It's quantifying over accessible worlds

[arctic grove]

[dense belfry]

You have a set of world and to each world you have a set of accessible worlds

[arctic grove]

Ooo

[errant ridge]

[dense belfry]

And you say something is necessarily true in a world if it is true in all accessible worlds

[arctic grove]

interesting

[dense belfry]

And possibly true if it is true in some Accessible world

[arctic grove]

this stuff seems like it can be related to many worlds to some extent

[dense belfry]

Yes

[errant ridge]

what is this about?

[dense belfry]

This is modal logic

[arctic grove]

coz many world says every choice gives of a new world

[errant ridge]

okay someone who's doing model logic, do you think math is invented or discovered?

[arctic grove]

and if something is true in that new world, it has to be true in every world that comes from every choice that was made in the universe that it stemmed from

[dense belfry]

I think math is nothing but a fragment of human intuition

[errant ridge]

[arctic grove]

i cant say i missed blushysully

brb

[dense belfry]

Brouwer memes for intuitionistic teens

[errant ridge]

blushysully creeps me out

[dense belfry]

https://open.spotify.com/track/5ZDfLQU9SdH67cHxbgQXlw?si=QqUyZc-7T8W0Bd01ofxvJg&utm_source=copy-link

This song is so good

Sure yohan

[full isle]

what this mean?

[sleek wing]

Means what it says innit

[bright hill]

I was wondering about that actually

[storm sage]

what is Not very ppl

[severe swallow]

it sounds like a status you have when you don't like interacting with other individuals

[bright hill]

What is the point of pursuing math if it's just mindlessly reasoning about abstract nonsense

[ancient flame]

wondering*

also rip active darq

[storm sage]

darq still has very active

[bright hill]

But that's exactly what cat theorists do isn't it?

[fading tusk]

is active based on quality of comments?

[storm sage]

abstract nonsense is fun

[bright hill]

Duck, I keep making that typo

[ancient flame]

oh he's just Not Very Ppl

[bright hill]

Yee

[ancient flame]

how did u get that

[bright hill]

Paypalled mniip

[ancient flame]

LOL

[bright hill]

There's no other way

[ancient flame]

did u sign an NDA

[storm sage]

abstract nonsense is just an affectionate term anyways

it's not actually nonsense obviously

[bright hill]

But like

[storm sage]

I think mathematics, like a lot of human activities, is just curiosity that grows into passion

it's like if you're into it then do it; if not then try something else and see if you like it

[bright hill]

I feel like things are just gonna get more and more abstract as you go higher and higher until they practically make no sense at all

[deep mango]

darq asked for it in modmail so i guess he was trying to self-own?

[deep mango]

that's not what most math is!

[ancient flame]

oh

[bright hill]

And I don't want that

[ancient flame]

wait so ryc

if I just

ask modmail

then

!!!

[deep mango]

do you want not very ppl?

[ancient flame]

yes

actuslly

no

[deep mango]

[ancient flame]

bc I like blue name

[deep mango]

see?

[ancient flame]

I don't wanna look like a non

[bright hill]

Maybe not all area of math

[ancient flame]

what's the purpose of the role

[deep mango]

you don't want to look like a roblox guest?

[ancient flame]

no

[bright hill]

But things like category theory and model theory

[storm sage]

you already know enough math where all of it is abstract nonsense to the average person

[ancient flame]

can I get another role instead

[storm sage]

it's a matter of perspective

[deep mango]

those are like the only two areas of math that are like this

[deep mango]

no

[ancient flame]

-_-

there are many inactive roles

[storm sage]

idt model theory is abstract nonsense

[deep mango]

and they do have a lot of relevant meaning and concrete interpretation if you learn the language

[storm sage]

it answers a lot of questions people have about the nature of mathematics

and asks a lot of new questions

[deep mango]

i don't think the abstract category theory stuff is either, usually

again, it looks like it if you don't know the language

[storm sage]

yeah abstract nonsense is just what category theorists call it to fend off competition /s

[deep mango]

but good expositors (which we have here) can tell you why that's not the case

[storm sage]

I think category theory is the art of revealing deep similarities between wide reaching areas of math

and that's why people like it

even if it becomes abstract very quickly

[deep mango]

yes, i would also say that, but it's also a very useful toolkit for studying things that are more concrete

[bright hill]

I also don't want to stop visualizing stuff

[deep mango]

which is the way most people use it

[severe swallow]

everyone talks about this as motivation, but in the end I kind of feel like no one who does category actually cares about its motivations lol

[bright hill]

but I feel like if you pursue topology or smth you're gonna have to do that sooner or later

[deep mango]

again, in fields like geometry or analysis or dynamics, you're visualizing stuff constantly no matter how modern your work is (except maybe in modern algebraic geometry)

or in, say, algebraic topology

[severe swallow]

plz draw me a pic of a scheme, I need intuition

[storm sage]

category theory is also visual af

[deep mango]

just because you have to do algebraic things mostly doesn't mean you aren't constantly drawing pictures of what you're doing to help you

[deep mango]

hence why i said modern algebraic geometry is an exception

[severe swallow]

category theory showed me visual not always good

[storm sage]

bah

do it without diagrams then

[bright hill]

then why are people so interested AT?

[storm sage]

it's massively useful

[severe swallow]

yeah I totally wanna do this when I'm better at math

[storm sage]

for one

[storm sage]

yeah!

[bright hill]

I get the impression that pure mathematicians don't care about being useful lmfao

[storm sage]

also in some ways math is just the art of trying to find the right intuition

[storm sage]

okay how about it beautifully combines two different fields

also idt there's as big a distinction between pure and applied mathematics as people make out

the boundary is extremely wishy washy

number theory is pure.. until it becomes applied

statistics is applied.. unless you do like theoretical work in statistics?

[bright hill]

does it tho?

if you're not visualizing shit, isn't it just algebra at that point?

[storm sage]

how is it not topology

I mean.. try visualizing half the stuff they talk about in topology

[bright hill]

for the record, I know basically no algebraic topology

[storm sage]

the visualization skill just comes with time

[bright hill]

it's possible

[storm sage]

and in some ways, learning math is the art of trying to get rid of bad intuition and hone good intuition in any field

I think that once you learn stuff, it feels a lot more tangible than you realize

[bright hill]

[severe swallow]

you know what really would've gotten me hooked. there was one section in a differential topology script where the prof (rest in peace) starts talking about how the proof of insert theorem I can't remember doesn't involve anything of topological substance, but is more category theoretical and then he starts talking about how category theory can be used to prove multiple results we know about seemingly unrelated fields at the same time. I always found that paragraph an amazing advertisement for category theory.... but yeah so far I have yet to witness it, my experiences with cat theory afterwards have been rather underwhelming

and I feel like it's a shame

[bright hill]

I love when math takes intuitive things and makes them rigorous

[wide river]

HELLO GAMERS

[bright hill]

what's the point if I'm actively trying to make rigorous things intuitive?

I don't wanna do that

that feels pointless

[storm sage]

rigor really isn't everything isn't mathematics, the point of mathematics is that you want to understand ideas correctly, and rigor is a stepping stone to do that, but if you rely too much on it, it also becomes sort of a crutch that prevents you from making big leaps

the point of doing things rigorously is that you develop good intuition for what will work and what won't and then once you make that conjecture, you already have a good idea of what it takes to prove it rigorously

after the fact once you decide something is probably correct then you can start formalizing it, but you only do that if your intuition tells you it will be useful in some way

[odd narwhal]

You can't visualize 99% of spaces

[bright hill]

I get that intuition can only take you so far so you need rigor to guide your intuition

but, like

it bothers me that, for example, continuty depends on the topology you choose

and in the discrete topology all functions are continuous

[bronze pelican]

Intuition can be false, and so can proofs. Concrete computations are the only truth in this world.

[bright hill]

that doesn't make sense to me

it also bothers me that we can view R as a vector space over Q (assuming axioms of choice)

maybe these examples are just extremes

but it's not like I'm very far into pure mathematics and I know about them

[fading tusk]

euler would work at faang if he was still with us

[bright hill]

and I'm afraid it's just gonna keep getting worse the further you go

@storm sage

[fading tusk]

if you don't like math in like second year of undergrad then it's doomed

stuff gets way worse

[sick burrow]

I think this is just a case of not having your intuition developed enough

As Eric Tao said, one of the main benefits of rigor is it helps to build intuition

[winged token]

just a bunch of symbols at that point

how do you look at this and say "yea this make sense"

fake math

[sick burrow]

The fact that continuity depends on the topology you use is super intuitive to me

[deep mango]

but you just visualize that as a bunch of disconnected points, so it's fine right?

a set is just a bunch of things with nothing like, gluing them together in one way or another

[sick burrow]

Because the topology is what makes a space a space. Without it you only have a cardinality

[deep mango]

the topology tells you what's glued to what and where

exactly

so idk what wouldn't be intuitive about a discrete space having functions out of it be continuous. it's discrete

[sick burrow]

Thinking of it as, for example, "putting a different topology oh R" is helpful insofsar as you might be using the order of R to help define that topology but really you're just putting a topology on $\beth_1$

[fathom swallow]

Poppy Lascelles

[sick burrow]

This is also super intuitive imo

Once your intuition is developed enough

Like this was weird the first time I heard it but it makes perfect sense to me now

[bright hill]

ok, that actually makes a lot of sense

lol

[sick burrow]

So like, you won't stop seeing things that feel weird, but the thing is, it's generally only the boundary of your knowledge that things feel weird at

[bright hill]

it makes sense ig, I don't know about intuitive

[sick burrow]

Because once you work with an initially weird thing enough you start to develop an intuition under which it makes sense

[sick burrow]

It feels intuitive to me

Just think of it in terms of field extensions

[tall badge]

to simply view this as a space, aoc isnt needed

[hushed turret]

you only need aoc for a basis

[sick burrow]

It's not really R that's a vector space too. You're losing the order which is what arguably makes R R

[tall badge]

aoc is for picking a basis

[sick burrow]

It's just Q[a basis for R\Q] where Q is viewed as unordered field

Remember: once you've forgotten the order there's no way to tell two transcendental numbers apart

They're just symbols really

This definitely tripped me up when I was first learning it but it feels super intuitive now

[full isle]

i dont see what this means

[sick burrow]

Hm maybe I'm thinking of this wrong myself

[bright hill]

wtf, that also makes sense now

[full isle]

so like Q as vectorspace over R

wait that doesnt make sense

[sick burrow]

I mean like if a and b are two linearly independent transcendental numbers then Q[a] Q[b] and Q[x] are basically all the same thing

[sick burrow]

R over Q

[hollow sundial]

https://giphy.com/gifs/news-twitch-aoc-alexandria-ocasio-cortez-1fraZz7YFDKuUz7Qoo

[full isle]

oh yeah

thats true

but this is because they are defined as having no solution to any polynomial equation

[sick burrow]

So just think of R as a vector space as Q[uncountably many symbols]

[full isle]

oh yeah thats a question ig

[sick burrow]

Where the uncountably many symbols are a basis for the irrational numbers

[full isle]

how many more useful transcendentals do you think will be discovered during our lifetime

im saying none

because i have no imagination

[sick burrow]

This of course has the issue that it assumes you have a basis but it's how I like to think about it intuitively

[sick burrow]

Would proving Gamma is transcendental count

[full isle]

what is gamma

euler maschinito constant?

no right

[sick burrow]

Yeah

Well you spelled it wrong

[full isle]

i cant spell

[sick burrow]

But that

Euler maceroni 🍝

[full isle]

also

i mean discovering one that isnt suspected to be one

if that makes sense

[sick burrow]

euler mascheroni is how you actually spell it

[full isle]

an unknown one

[sick burrow]

According to google

How many useful transcendental numbers have we even discovered

pi e what else

[full isle]

i know others

but dont know their uses

chaitin constant

and liouville constant

something with halting problem for first one

idk what liouville used for

[fading tusk]

https://en.wikipedia.org/wiki/Lindemann–Weierstrass_theorem

[neat lintel]

there are some in analytic number theory, e.g. some values of the \Gamma function. also some constants there are conjectured to be transcendental (euler-mascheroni constant \gamma, some values of the riemann zeta function)

[full isle]

oh

dont we only know a countable number of transcendentals?

so how can there be uncountable real numbers

[fading tusk]

yes

[bright hill]

do we?

[neat lintel]

the number of transcendental numbers is uncountably infinite

[full isle]

but we only know a countable number of them

checkmate realists

[neat lintel]

[full isle]

honestly im having a big brain moment

everything in our universe is apparently discrete it seems

[bright hill]

it is

[fading tusk]

how many irrational numbers do we know mr jass

[full isle]

is there anything that can be uncountable irl

[bright hill]

are at least, theorized to be

[full isle]

or are limits just a tool for calculations

[bright hill]

coz QM

[fading tusk]

mr jass is so smart and ez to talk too 🙂

[full isle]

we know countably infinite number

meaning we can construct a countably infinite number

[fading tusk]

we can construct the reals

[full isle]

we know uncountable number of irrationals exist because the reals are uncountable by a diagonalization argument and reals-rationals is uncountable

we can construct the set of reals via equivalence classes

but any random real number exists but is most likely hard for us to construct

and we cant tell if its transcendental or not easily

we dont have a closed form construction for most transcendentals is the truth

[full isle]

i never claimed otherwise

[fading tusk]

you asked if there is anything that can be uncountable irl

[full isle]

yes

does the continuum exist irl

[fading tusk]

idk ur the expert

[full isle]

no?

[fading tusk]

😦

[full isle]

the real numbers are really unintuitive

in a lot of ways

[fading tusk]

there is an uncountable number of ways to say "hello world"

with human voice ?

or no sir

[full isle]

probably not

but maybe

if we are saying ways to say as different sound frequencies

[fading tusk]

how many different weights can a banana be ?

uncountable?

[full isle]

and we know sound is vibrations propogating through air

[full isle]

this is probably a discrete value

countable

because atoms are finite and fixed mass

[fading tusk]

space is discrete ?

they can't be positioned in continuous way?

[full isle]

no one knows

but its honestly likely

[fading tusk]

not even u?

[full isle]

you know energy levels right?

those are discrete

[fading tusk]

they are an abstraction ?

[full isle]

what?

[fading tusk]

ok energy levels are discrete

they are a concept

[full isle]

yes this is true

what about it

[fading tusk]

idk

so what are we going to say about energy levels now ?

[full isle]

my point in saying they are discrete is to say a lot of things are intuitive irl

so maybe the world can be described in a countable set

[fading tusk]

oh ok

but then you would stop using the reals?

just do everything in Q ?

and not get closed formulas for solutions to equations?

or you can use A I guess

[full isle]

i previously said maybe the reals are only used a helpful tool for computing

[fading tusk]

Wildberger has a video on rational trigonometry

[full isle]

similar to how the idea of randomness is

[fading tusk]

but are the reals used for computing?

it's like floating point or symbolic stuff

[odd narwhal]

wildberger

[full isle]

yes

reals are used for computing often

limiting processes showing things are equivalent

[storm sage]

all human perception is discrete, if you believe perception is done solely through neurons

[full isle]

i dont want to believe this

a computer being able to digitalize my perception would be crazy

[fading tusk]

wouldn't it depend on where the neurons are positioned?

[full isle]

wdym?

[bright hill]

QM says no, but GR assumes we do

and GR works pretty well

[full isle]

GR?

[bright hill]

yeah, lol

[fading tusk]

does the distance between neuron a and neuron b affect ur perception?

[full isle]

maybe lol

[dapper badge]

i bet that's why my reaction time is so slow

[storm sage]

well only countably many are (the computable reals)

[sleek wing]

Not sure about that, electrical impulses tend to be continuous things

[full isle]

yeah

honestly

[sleek wing]

It’s not a binary on/off signal

[full isle]

ultrafinitist arent crazy

[storm sage]

we only really care if the electrical impulse is above or below a certain threshold though

[fading tusk]

why do you say space discrete in QM ?

[full isle]

quantum

quantization

process of making cts things discrete

[sleek wing]

Speak for yourself

[storm sage]

Lol

[bright hill]

coz plank length

did I spell that correctly?

[storm sage]

the planck length doesn't really say stuff is discrete

[full isle]

it doesnt

[storm sage]

but there is a limit to stuff we can measure

[full isle]

its more than qm quantizes often

[storm sage]

which might say that measurable space is discrete

[full isle]

that*

[compact tartan]

it's very far from discrete in fact

[full isle]

lol what

far from discrete

its either discrete or not

[bronze wedge]

you might even say its a continuum

[storm sage]

it could be a continuum, but there's nothing that says it has to be

[bronze wedge]

i was just saying that the negation of discrete means continuum

[storm sage]

below a certain length is unmeasurable so it's only guessing

[full isle]

thank god i have a continuum of brain cells

[fading tusk]

would it be cool if irl was Mein Craft?

[storm sage]

ah okay

[full isle]

ngl doesnt matter

i dont think so atleast

[fading tusk]

the negation of discrete is inconspicuous

[storm sage]

yeah it's independent of what we can test

[full isle]

im gonna bet that the world is continuous

because time feels that way

even though it might not be

[storm sage]

actually I'm not sure it even means anything to say that the world is continuous

[fading tusk]

why not?

[storm sage]

imo for a scientific statement to mean something it has to be testable

in some way

[full isle]

yeah

idk how to test for that

[fading tusk]

who said anything about scientific

[storm sage]

I did

[full isle]

well we are having a discussion about truth

[fading tusk]

you did it after the fact

[full isle]

so science only makes sense

[bronze wedge]

either way, continuity is "close enough" to discreteness for the vast majority of applications

[storm sage]

we're literally talking about physics lol

[fading tusk]

that was an accident

[storm sage]

huh

[full isle]

but discreteness is never close enough to continuity

biased much

[hollow sundial]

i'm sure physicists have modeled the world using plank length scale discretization

[fading tusk]

I wanted the conversation to go another way

[storm sage]

bruh

say what you want to say then

[full isle]

you know how time travel is a concept

[fading tusk]

actually nvm ur right

[full isle]

is there a way to test for it?

[fading tusk]

yes

if time travel exists I will go back in time to 2025 and tell myself

[full isle]

but it doesnt work like that

[fading tusk]

I'll let u know

[full isle]

because you wouldve done it already

[fading tusk]

but it isn't 2025 yet

[full isle]

if some future instance of you time traveled to 2025

then you wouldve traveled there already

unless you are saying future you isnt you

[storm sage]

always wondered what the fundamental difference between how we experience time and how we experience space is

[full isle]

smoke weed lol

[fading tusk]

I experience both at the same time

[storm sage]

it seems weird that it's not like, symmetric

[full isle]

wdym symmetric

[fading tusk]

like one is not like the other

like, why is being tall attractive but fat unnatractive

it makes no sense

they're basically the same thing

[storm sage]

okay that is a bad analogy

[storm sage]

like how you can travel through space but it's very different from how you travel through time

[full isle]

yeah its like we have no control over either

but more control over space

[dapper badge]

I go back to uni tomorrow

Can't wait to figure out my first meal

[sleek wing]

Nugs

And chips

[dapper badge]

hmm

perhaps

was thinking waffles

[odd narwhal]

Waffles are good

But

Not frozen

Either make or buy from a respected establishment

[dapper badge]

hmm

we have waffle house

[burnt dune]

aaaaa

we are taking galois fields in my crypto class finally

finally math

now its my time to shine

jjkjk

[wooden flax]

waffle house owo

[deep mango]

I was so disappointed when I found out waffle house didnt have chicken and waffles

Their waffles were definitely good though

[dapper badge]

yeah I don't think they have fryers, only grill

but nothing quite hits the spot like 2 am waffles after failing my cs exams 🙃

[wooden flax]

coding sucks

[dapper badge]

Idk I like it, I'm just not all that great at it

And it's fun making personal projects

[open aspen]

programming is fun as like a casual thing

when there's expectations is when I nope out lol

[dapper badge]

In my high school CS class I made a program that takes an image and lowers the resolution

That was fun

[wooden flax]

i tried making an app first

but then i got bored and quit

algs/tcs is kinda cool tho ngl

idk if that counts as cs or math though

[ancient flame]

lmao amazing

[full isle]

you know

no one here is competent to debate an actual flat earther

[open aspen]

?

[full isle]

have you met any?

[open aspen]

wdym no one here is competent lol

[full isle]

i heard from some friends that are astrophysics phds is that they larp as flat earthers

and its not uncommon for people to do this online

actual trolls

[open aspen]

seems to me then thaat they are not an "actual" flat earther

[full isle]

maybe not by typical definition but they can make strong arguments for a flat earth

[bronze wedge]

If the earth isnt flat, how does Australia exist 🤔🤔🤔

[full isle]

if you are an expert in some topics you have the ability to do this

evolutionary biologist are best at this

the scientific narratives are so complicated sometimes that people can argue for conspiracy positions amazingly well

also for some theories its not necessarily that what they are saying is consistent with any science

but the theory they posit is very hard to refute

in that they make their own consistent theories counter to what is generally accepted

[dapper badge]

thanks, other notable programs include a game that measures how quickly you can type the alphabet and a camera app that spams my friend edward with emails every time it detects his face

[bronze wedge]

Define spams

[dapper badge]

i set it to run detection twice per second to make the frame rate decent, every time it detects it sends 20 emails

[bronze wedge]

20 lmao

[dapper badge]

i mean ig i could've done more but I'm confident in my own limits

[wooden flax]

woah thats crazy

nice!

[dapper badge]

it helps that he didn't check his email until like an hour after I showed him. he just liked that the camera put a green box around his face so he would stare at it lmao

[wooden flax]

what language were thse in?

[dapper badge]

lowresifier was java, alphabet game was C, camera was python (my first time working with openCV)

[fading zealot]

Do you guys use “unreproduceable”, “irreproduceable”, “non-reproduceable” or simply “not reproduceable”?

[storm sage]

that's a good question

I think not reproducible is the safest

irreproducible is logical though

[velvet dagger]

Unreproduceable sounds right when I think about it but then non-reproducible/not reproducible sound more right when I think about them

[errant ridge]

"unable to be reproduced"

[storm sage]

CNR

[storm sage]

yeah unreproducible sounds right until I start thinking about it for more than a second

[velvet dagger]

Reproduciblen't

[storm sage]

and then it sounds really uncomfortable

tbh

if you just say something enough

and convince other people to say it

[velvet dagger]

Yeah it's like the feeling of your tongue not fitting correctly in your mouth

[storm sage]

it's a word

irreproducible = irrep?

[velvet dagger]

Also you're welcome Eric for making you think about that now

[errant ridge]

[ancient flame]

the MIT quantum physics prof denotes the real part of a complex number as $\bR$e$(z)$

[fathom swallow]

gmod

[zealous garden]

ew

[arctic grove]

wait so like

he didnt \b{Re}
just R?

😵‍💫

[neon silo]

Yet another sin committed by the physicists

[terse flax]

What's wrong with Re(z)

Everyone uses it

[arctic grove]

lemme explain

$\mathbb{R}\mathbb{e}$ vs $\mathbb{R}e$

[fathom swallow]

Shyshu of the Golden Storm✓

[arctic grove]

what the hell

anyways

[neon silo]

Nothing wrong with Re(z), but the bold R is strange

[arctic grove]

yeah

if u wanna use crazy letters, use $\mathfrak{R}$

[fathom swallow]

Shyshu of the Golden Storm✓

[bronze wedge]

ive never seen mathbb used for that purpose

always mathfrak

[arctic grove]

i have seen mathbb sometimes

[hollow sundial]

$\mbb{Shyshu}$

[fathom swallow]

riemann

[hollow sundial]

[errant ridge]

yikes

[arctic grove]

huh

[errant ridge]

\mbb{R}

[hollow sundial]

\mbb is the default shortcut for \mathbb built into your preamble

[errant ridge]

yes which is nice

[light needle]

yo guys so I am doing some publicity on my TeX group, the TeXromancers

check out https://www.reddit.com/r/math/comments/wrbov3/the_texromancers_a_tex_group

and also remember to upvote, more publicity means we get more people learning about the books :))

[frail lagoon]

Awesome

[sacred forge]

so when evaluating the geometric multiplicity, of an eigenvalue, you dont count the 0 vector right?

because its not linearly independent when there is an eigenvector

[frozen merlin]

the 0 vector is not an eigenvector

[arctic grove]

potato is honorable!

congrats!

[neat frost]

Damn

Potats

[neat lintel]

#computing-software

[cyan goblet]

hi slurp

congrats potato

[toxic gale]

Aye grats on honorable potato! Thanks for the analysis help.

[arctic grove]

why did this get hmmed @deep mango

[cyan goblet]

ricey sullied me

i think he just in a bullying mood today

[deep mango]

no i am not

[cyan goblet]

yes u r

it's ok

if u are going through something i am here for u

[deep mango]

something about it was hollow...

[arctic grove]

what

how was it hollow?

[neat frost]

Hola anemone

[cyan goblet]

wow

spanish

[ancient flame]

3 days!!!

[arctic grove]

yay!

go get them gmod!

become a math major!

[ancient flame]

FUCK YOU

[bright hill]

don't listen to him, gmod

you can be cog in the wheels of capitalism

[arctic grove]

u know u want to

[ancient flame]

lol

[bright hill]

no judgement

promise

:)

[arctic grove]

i wont let him!

[ancient flame]

yay

<3

[arctic grove]

my friends have to be respectable

[arctic grove]

darq remove this role

😭

u are very ppl

[bright hill]

I can't

[bright hill]

not atm

[arctic grove]

ask modmail

[arctic grove]

aww

why

[bright hill]

shit

I didn't think you'd take that literally

uh

I don't know

[arctic grove]

dont try to predict what i do

im what true randomness is like

[bright hill]

lol

[bright hill]

I don't feel like I truly enjoy anything atm

I guess that's right

maybe it's just depression

[arctic grove]

relatable

it feels like u have derealized from the world

a sort of numbness

[neat frost]

Capitalism is cool tho

Mooleh mooleh

You’re just jealy-welly that moddy’s gonna be the next Jeff bezos (but with hair and a good personality)

[bright hill]

capitalism isn't cool

it's just the best we have

and it's not even close to being good

I would take scavenging for food each day, wandering the lands all year round, painting on cave walls for no reason instead of capitalism any time of the day

fighting bears for fun, killing mammoths with the boys, domesticating literal wolves etc etc

[arctic grove]

u would hate this after 2 days of actually having to do it

[storm sage]

it sounds like you're gonna die immediately

[deep mango]

I'm with darq

I want to live off the grid

[fading tusk]

what do you mean off the grid?

like off the grid or off-grid

[deep mango]

Idk what the difference between those is

[fading tusk]

sorry

off-the-grid

or off the grid

[deep mango]

Also I'm not sacrificing discord of Big Brother live feed updates

so

[fading tusk]

like living off of wellfare

[deep mango]

i think i just don't want to live off the grid after all

[fading tusk]

do you catch my drift ?

[deep mango]

i mean like

living in a secluded place and not utilizing public goods or buying things

[cyan goblet]

we off the grid grid grid

this for my kid kid kid

[fading tusk]

is that kendrick lammar ?

[cyan goblet]

for when my kid kid kids have kids

nah kanye

[fading tusk]

oh

it's donda ?

[cyan goblet]

https://open.spotify.com/track/6LNoArVBBVZzUTUiAX2aKO?si=b4e60dd1819c44c4

ye

[fading tusk]

I heard he is getting back together with Kim

[cyan goblet]

frankly, i dont know nor do i really pay attention to kanye kim pete shit

it is a mess

[neat frost]

No you wouldn’t

Anyway capitalism is GREAT!!! MOOLEH MOOLEH

[sleek wing]

I love capitalism I get to steal people's money by giving them things

[bright hill]

https://tenor.com/view/thanos-marvel-small-price-pay-for-salvation-gif-14748250

[bright hill]

You're just projecting

I'm built different

I'm literally a cave man with glasses

[bright hill]

[bright hill]

Maybe

But also, maybe not

[arctic grove]

im fairly certain u will

[bright hill]

.

[arctic grove]

you are not built different

as much as you think

[deep mango]

some of us are made for this kind of lifestyle

[ancient flame]

hi ryc

[deep mango]

i'm not overly fit or anything but i'm good at rigging things up and quick problem solving with limited resources

hello gmod

[errant ridge]

really? go do it then

[errant ridge]

shyshu is a stochastic function

[arctic grove]

😌

[deep mango]

it would be lonely to do it alone. we need to put together a crew

[errant ridge]

Yes, the entirety of the math server

[zealous garden]

I refuse

[deep mango]

That would be a disaster

[errant ridge]

to rival all other disasters

[neat frost]

You have glasses????

[bright hill]

oh, lol

you guys don't know that lmfao

yeah

[neat frost]

Now I know everything about you

Send selfie

[bright hill]

uh

sure

[arctic grove]

u never sent us a selfie

even tho u have seen my face

[neat frost]

Yay

[bright hill]

I did not D:

[arctic grove]

whaaa

[neat frost]

I have seen shyshus face

But shyshu will never see mine

[arctic grove]

i dont mind

coz u look like shit

[neat frost]

Ouchie wouchie

I’m actually super hot

Easily a 10

[arctic grove]

send proof

i wanna verify

pwease

[neat frost]

I would send you a picture of me giving you the middle finger but one time I did that and someone made fun of my fingers

[bright hill]

one sec

[arctic grove]

i wont do that

coz i have funny fingers

myself

[neat frost]

Tbh all fingers look weird

[arctic grove]

yeah!

[neat frost]

Do you have a callus from using pens and stuff?

[arctic grove]

callus as in?

ink on hand?

[bright hill]

[neat frost]

Like thicker skin

Uh

[arctic grove]

my skin is already thick

so i cant tell

[neat frost]

No but like

Do you have a bump on your skin from where you rest your pens/pencils?

[arctic grove]

me too!

oh yeah i do

[neat frost]

Ayyy

[arctic grove]

lol

my fingers are really weird

[bright hill]

sure lol

[bright hill]

@neat frost just called me hot

I don't know how to feel about this

[neat frost]

Happy

[arctic grove]

coz u are

smh

[odd narwhal]

are you hot dark cue

[bright hill]

I dunno

I guess?

[neat lintel]

Hi, am I too late getting hungry for math at my senior year of undergrad?

Like so far I've just did what I was requested in order to pass exams

But now I really want to do it all the time

[peak tide]

too late for what?

grad school for example?

[neat lintel]

Well I just think I should have started getting hungry earlier

[peak tide]

quite possibly it wasn't until now that you started covering material that you find interesting

that's probably not that unusual

[neat lintel]

Exactly

[peak tide]

lower level stuff can be quite boring

[neat lintel]

I found only real analysis and set theory fun in the lower level stuff, but everything else was meh so I didn't spend a lot of time on that

Now that I've done FA and topology I started to like everything (LA which I hated for example)

[peak tide]

the instructor and textbook can make a huge difference between a blah experience and a great one

as well as your own mindset of course

[velvet dagger]

Dude I swear if I taught a linear algebra class

It would be the most popular class at a school

[wooden flax]

How would you structure it

[velvet dagger]

So let's say year long linear algebra class

I guess it depends on some other parameters. Is this intro to proofs as well, etc

But basically there's so much cool stuff in the subject and a lot of different angles

And my shtick would be to include as many of the angles as possible

[zealous garden]

but what is your focus

[velvet dagger]

So I'll try to throw in some finite fields, combo applications

As well as the analysis side

[zealous garden]

systems of equations? linear maps? vectors? vector spaces?

I'd hope to see all of them

[wooden flax]

If I was teaching a semester linear class to people interested in math and have done like an intro proofs class@

[velvet dagger]

The goal is to make people as conversant as possible in jumping between all those perspectives

[zealous garden]

but which is your object of focus

you want to try to be agnostic?

interesting

[wooden flax]

I would spend lecture one and two on Treil first two chapters respectively

[velvet dagger]

So maybe I might in class give one proof of something

[wooden flax]

And then I would do 2 lectures per chapter, one lecture would be what is in the book chapter like the theorems proofs etc and then the second lecture would be some kind of more advanced application of that concept

So maybe something in rep theory, analysis, etc

Would probably skip the proofs of stuff that’s not enlightening/difficult

[velvet dagger]

Sorry trailed off, but yeah if I think that both the "linear maps" proof and the "matrix" proof of something are enlightening

Then I'd give one proof in class and one as a homework problem

[wooden flax]

Yeah but only the first time you see that kind of thing

[velvet dagger]

Whichever works better for each

[zealous garden]

I don't know if I could teach a linear algebra class

I'd make it about geometric algebra compulsively

[velvet dagger]

You have very specific interests

Non-standard analysis, geometric algebra

[neat lintel]

What's geometric algebra?

[storm sage]

I support

[velvet dagger]

Lol yeah Eric and I both get it.

Also Eric I should teach you some of the analysis-y stuff, combo

Like the raw theory is cute but really

[neat lintel]

It's a difficult task to teach LA

[velvet dagger]

What you can do with the stuff blows it up tenfold

[neat lintel]

My professor added for some reason interpolation in his linear algebra book....

[pure sun]

Why not? It’s a nice application of the ideas of linear algebra

[velvet dagger]

Eric have you seen Lagrange multipliers?

[neat lintel]

Well he didn't cover it in class, it was covid time so we had no class

tldr I was trying to remember the formula just out of the book without any intuition for it

[velvet dagger]

There's a very nice proof of the spectral theorem via Lagrange multipliers

[wooden flax]

what is it 👀

[pure sun]

Hahaha thats funny

When i taught LA i did find that topic to be a difficult one for students

[wooden flax]

i think i know the proof via induction

[velvet dagger]

Not allowed to practice on??

But yeah the proofs are all inductive

[storm sage]

Yeah

[storm sage]

Oh??? 👀

[velvet dagger]

The idea is that for a symmetric matrix, the orthogonal complement of an invariant subspace is invariant

So your task is to produce an eigenvector

One way is to say, oh eigenvalues of a symmetric matrix have to be real, FTA gives us one, and we have rank insensitivity to field extensions

There's also Rayleigh quotient business

[storm sage]

Rayleigh quotients scare me

I saw the formula

For the Sturm-Liouville equations in 3D

[velvet dagger]

But one slick thing is to say is

[storm sage]

Pain

But now I get to inflict that pain on others since I am TAing PDEs

[velvet dagger]

Maximize the quadratic form Q(x) = <Ax,x> over the unit sphere

[storm sage]

wait the RQ definition is so simple in linear algebra??

wtf

it looked so convoluted in my pde textbook

[storm sage]

oh that's a neat idea

also just wondering, are there any spectral-like theorems for vector spaces that aren't inner product spaces

[wooden flax]

super cool dami

[velvet dagger]

Hmm

So my instinct is this

If you think about the standard proof

Using LM

It feels like a big part is compactness of the unit ball and the fact that orthogonal complements of invariant subspace are invariants

[storm sage]

yeah I was thinking it'd be hard to translate anything over

also wow I need to learn more about rayleigh quotients

I didn't know they were a thing in linear algebra

[wooden flax]

what does LM stand for

oh nvm lagrange maltipliers

[storm sage]

man if I ever ta linear algebra, I need to spam my kids with these

[velvet dagger]

@storm sage do you see how the LM proof goes?

And Invictus

I can elaborate more

[storm sage]

I'll think about it in a sec, I'm a little busy rn

I see how there would be a connection though

I remember maximizing the Laplacian using eigenvectors for some graph theory application :))

[wooden flax]

i think your general idea makes sense

but how do you do it with rayleigh quotients?

[storm sage]

<x, Ax> is maximized when the rayleigh quotient is (assuming <x,x> = 1)

[wooden flax]

ahh

ok

[velvet dagger]

The quick version is that you compute lim_{t->0} (Q(x+tv) - Q(x))/t = 2 <Ax,v>

So the gradient of Q is 2Ax

While the sphere is defined by <x,x>-1=0 which has gradient 2x

So max of Q must be an eigenvector of A by LM

But obv the max exists by compactness

I don't remember Rayleigh stuff offhand super well but I could prob figure it out?

[storm sage]

yeee this makes sense

:))

I love it

[velvet dagger]

Here's something in combo

Let's say you have a town with 32 people

They love forming clubs

Like they just want to register clubs for no reason, including having many with the same members

Paperwork is getting out of control

So we put some rules

[odd narwhal]

♣️

[velvet dagger]

Every club must have an even number of people

Every pair of clubs must have an even number of people in the intersection

No duplicates

Have we solved the problem?

I guess I'll go ahead and say, the answer is no

We marry the 32 people into 16 couples

Every subset forms of a club

So 2^{16} clubs at least

[wooden flax]

wait i think ive seen this lol

or something similar

but i think for a town with odd people

[tough scaffold]

[velvet dagger]

Yeah so

If we now say every club must have an odd number of people

Well now we know there can't be duplicates

And in fact

Exercise

There can be at most 32 clubs

[hushed turret]

and every two clubs have an odd number of people in the intersection?

or an even number?

[storm sage]

oh boy time to learn about this, I skipped it the first time around

[neat lintel]

👀

But, is it?

[storm sage]

Lol

[unborn trellis]

You're about to become woke

you only need to see tensor algebras quotiented by relations once to get the point

[open aspen]

when i teach my first proof based undergrad course imma ask them to prove that any even integer other than 2 can be written as the sum of two primes

just in case you know

[neat lintel]

2 = 1 + 1

[open aspen]

i edited it first u cant do that

[zealous garden]

just let 1 be a prime number

easy

[neat lintel]

i had it typed before you edited so get fucked lol

[chilly hull]

wait what was that called again

i think i saw it in hammack

[open aspen]

goldbach conjecture

[chilly hull]

ah yeah

i saw it in 2.1

[bright hill]

it's still a conjecture?

[open aspen]

yes

[bright hill]

bruh, I almost wasted time on this

[open aspen]

we suck at number theory

[bright hill]

[open aspen]

attempting a hard problem is never a waste

[storm sage]

okay wiles

[bright hill]

[neat lintel]

okay CV

[bright hill]

lmfao

[open aspen]

whats cv

contravariant?

[neat lintel]

complexvariable

collatz crank who was on this server

got banned

[open aspen]

I remember that!

[bright hill]

wait, he got banned???

[deep mango]

What a drastic simplification of the CV narrative

[bright hill]

whyyy

[neat lintel]

i WAS going to go into detail, ryc, but now i don't want to

[open aspen]

one day CV is gonna prove collatz and the mods will rue the day

[storm sage]

lol I wanna hear this story now

[deep mango]

Broke server rules pretty severely

This is not up for discussion

Lol

[open aspen]

in the acknowledgements: "ryc doubted me, and I want the world to know"

[neat lintel]

what CV did to get banned is not for discussion, but what CV did to earn mine and many others' ridicule is

[bright hill]

I don't wanna discuss it, I just wanna no what the reason is

[storm sage]

isn't that the definition of discuss

[open aspen]

he helped me with an analysis problem once I think

[deep mango]

Yes thats fine

[neat lintel]

darq just pretend they got banned for being a collatz crank okay

[bright hill]

ok

[open aspen]

yeah so dont claim you can prove collatz

or you get the axe

[storm sage]

that sounds so shady I don't even wanna think about what they did

time to think about multilinear maps instead

[chilly hull]

wait

was it that person who was in help chat for an hour

[deep mango]

It was some nsfw stuff in the discussion channels that was far over the line, but im not talking about the content of it.

[open aspen]

thats when the a goes in and out, you can thank me later

[storm sage]

no

[chilly hull]

oh

[storm sage]

if you're talking about the one I was talking to

[chilly hull]

yes i was

[bright hill]

oh, I saw that lmfao

[deep mango]

I figured

[open aspen]

remember when we all argued about if .99999... = 1 with that one guy for like hours

that was a good time

[bright hill]

I stopped reading CV's messages that exceeded 3 lines so I only noticed waht he was writing until mniip was like "bruh, too far"

[deep mango]

Lol

[zealous garden]

yes it is

[deep mango]

"I stopped readinf cvs messages that exceeded 3 lines" is a good tagline for this memoir

[chilly hull]

.999...=.999...
10(.999...)=10(.999...)
9.999=10(.999...)
9=9(.999...)
.999...=1

[storm sage]

lol

[open aspen]

i get so lost in the sauce when people change their pfp. ong I didn't know who ryc is for days after he changed his pfp

[zealous garden]

0.999... is indisputably in the monad of 1

this means, if we take it to refer to a Real number, it can only be 1

[tiny forge]

It's worse when someone changes their name and profile pic and you never know who they are again

[storm sage]

mom I'm a real number now!

[zealous garden]

that's not what transfinite means

[tiny forge]

There was someone a few months ago with the name "something CAT" all in caps and they were nice but I've no idea who they are now

[deep mango]

Im glad I committed to the change tbh

The meme bird was a brand

[open aspen]

yeah this one is better

[deep mango]

This is more authentic

Even though a robot made it

[open aspen]

oh did that new AI make it?

[deep mango]

Dall-e made this

Like the full proper dall-e

[open aspen]

neat!

[bright hill]

oh

huh

that's super good

[open aspen]

darq werent you blue at some point