serious-discussion

[solar hawk]

Long can be good long can be bad

Clearly

[tawdry pecan]

amukh discovering british people for the first time

[fresh comet]

who doesnt say epsilon naught

[visual breach]

Well anyway

[solar hawk]

EPSILON 0

NULL

[tawdry pecan]

epsilon naught

[fresh comet]

it didnt say curls, it said "looks"

[solar hawk]

NILL

[visual breach]

Ahhh

[fresh comet]

this one i can accept

[tawdry pecan]

you are naught correct

[fresh comet]

nill/null is okay

[visual breach]

“That looks like plane”

[fresh comet]

0 is not okay

[visual breach]

Now it makes sense

[fresh comet]

im not british??

[tawdry pecan]

you are now

sorry

[fresh comet]

i guess canada used to be a british colony

[solar hawk]

Wait

[fresh comet]

so close enough

[solar hawk]

Americans say

epsilon “not”

Right

[fresh comet]

that is how you pronounce naught yes

[tawdry pecan]

yeas we dont say epsilon nut

[solar hawk]

LOL

[fresh comet]

ok i'll stop sending my terrible handwriting here

i don't think i need to convince the world more about my doctor handwriting

[tawdry pecan]

i am well and thoroughly convinced

[solar hawk]

LOL

[sturdy gulch]

i just came back to look at this
i feel bad for whoever needs to read this like its literally hieroglyphics

honestly they should put this on the captcha

[fresh comet]

so true

i think only an AI could read my writing

if you fail to read my handwriting, you are 100% a human

[velvet dagger]

Acetaminophen?

[solar hawk]

🐸🐸🐸😭😎

16 stages of frog

[fresh comet]

Is your pfp supposed to be you in a frog suit?

[tender tulip]

Cochain complexes are weird

[sturdy gulch]

what am i looking at

[tawdry pecan]

computer screen

[ripe needle]

a frog

[tawdry pecan]

🐸

[neat lintel]

Epsilon Nut

[tawdry pecan]

thats my least favorite beverage

[alpine valley]

yum

[solar hawk]

Yes

[burnt ledge]

Bruh u gotta at least separate the dot and the stem of the i

[hidden isle]

whats up discussy

[iron osprey]

man i hate this

[neat lintel]

this looks a lot like mine

i cant read my own stuff sometimes

[sly flint]

Very similar to my actual handwriting now:

[fresh comet]

please teach me how to write like this

[burnt ledge]

Join no letters

then bring it back afterwards

[neat lintel]

thats painful shit

[violet urchin]

The dual of a chain complex

[opal quail]

could someone explain me what this https://imgur.com/pTyRy63 stands for

[sly flint]

didn't see your message lul
but basically you practice doing individual letters and eventually it clicks

[burnt ledge]

every chnage takes work

you can bring back joining after you practice forming letters individually tho

you can see rage joined their "der" in "Under"

but each letter is still well formed because they can form them unjoined, as in "down" and "pressure"

[fair mural]

wow this is good

[sly flint]

thanks!

[old nest]

Anyone know where I can find a reputable time series dataset

like government type etc

[sonic sentinel]

how is 6 months of runway considered financially secure if a typical job search is 5 months (source: googled "typical job search length")??

[solid spear]

anyone else here prefer node to node distances instead of nodes for distances
or travelling

[fervent flame]

why do you not think its the case?

[peak tide]

i don't think anyone claims 6 months is "secure", but it's the bare minimum recommendation for an emergency fund

[sonic sentinel]

surely if 5 months is average then 6 months is not very unlikely?

[fervent flame]

why only have 6 months of runway then? what about 7? 8? 9? 10?...

[sonic sentinel]

ah ok

[fervent flame]

its just a general guideline

[sonic sentinel]

yeah but it sounds like a bad guideline

[fervent flame]

what would you suggest?

[peak tide]

obviously you should have as much as you can
i've known people who went a year or two looking for work

[sonic sentinel]

do your own math

[fervent flame]

great. now when people look up "about how much runway should i have", they get told to "do your own math"

[sonic sentinel]

not a very helpful rule either, i would guess that most people have stuff they want to spend money on

[fervent flame]

how helpful is that as a general guideline?

[peak tide]

there is no "rule" that's gonna be 100% safe, i don't know what you're looking for

my point being, you don't stop saving just because you reach 6 months of savings

[fervent flame]

the point of general guidelines is that the are general guidelines. this applies to literally everythjng ever

[peak tide]

yea, and as you discovered, 6 months as a general guideline isn't 100% failsafe

[sonic sentinel]

or what about a calculator :)

[fervent flame]

what is your formula?

[peak tide]

but i don't think anyone ever claimed it is, 6 months is the minimum to even consider yourself not in crisis mode

[sonic sentinel]

how failsafe is it? like two thirds chance of succeeding?

[sonic sentinel]

bet

https://80000hours.org/2015/11/why-everyone-even-our-readers-should-save-enough-to-live-for-6-24-months/

[peak tide]

it depends on many factors, like the job market you're in, the type of job, how old you are, what your monthly expenses are, etc

[river moon]

surely you can easily count your spending and what you can/can't cut from it and roughly get an idea how risky it is or how long you can last

nobody else knows what your spending is like

[sonic sentinel]

save more if (Expected loss (factoring probability of occurence) from running out of money)>(Loss of saving more money)

[peak tide]

also on what kind of flexibility you have in your life
are you a month to month renter or do you have a huge mortgage, things like that

if you are in a position to dial back spending to nearly zero (like move in with parents or some such) if the shit hits the fan, then you might not need a big cash cushion
if you yourself are a parent with a house and mortgage and bills to pay, you'd better have a substantial one

[sonic sentinel]

here is my attempt at something more useful:
let's suppose that there is a 50% you get a job every 7 months and this probability is independent

let current runway=x

chance of running out: 0.5^(x/7)=p

suppose the negative value of running out of money is 50 months of runway, then p(-50) would be the expected value of losing your job right now, then you could find the derivative of p(-50), call it u

the point at which u(x)=1 would be your max. runway, since anything after that would mean the expected value of putting more money into runway would be less than the actual value of that money. in our case x=16.16

if you give a very conservative (i think) number that the negative value of running out of money is 20 years of runway, then the x would be almost 32

[queen latch]

is their a way too look at a factorial and know what it will be without having too do all the multiplying so like know 6! is 720 without doing the 1x2x3x4x5x6?

[glass peak]

Memorise them all

[sonic sentinel]

see https://en.wikipedia.org/wiki/Stirling's_approximation
https://stackoverflow.com/questions/1751334

[queen latch]

ty

[rich magnet]

I love discusion 2!

It's so cozy and camp

[sonic sentinel]

shit my math is wrong

surprisingly, my mistake wasn't catastrophic, and the values i gave still hold

rather than explain it all over again, just see: https://www.desmos.com/calculator/h9axovyllw

p(x) is the chance of running out of money if you have x months saved

L is the negative utility (in months of living cost) if you run out of all money

[sonic sentinel]

u(x) is the expected value of losing your current job if you have x months of money saved

you want to see where u'(x)=-1, meaning that the value of saving that money (for runway) is the same as not

problems with the model:
-an average of 7 months search doesn't mean "50% chance of gaining a job in 7 months"
-the probability function might increase too slowly, since finding a job by t time and t+1 time are not independent
-discounting is not considered
-pensions or any other change in future situation is not considered
-its not exactly clear how you would get the "loss value if you run out of money" anyway. you could look at different scenarios and likelihoods (e.g. living with parents/siblings, homelessness, idk) but you would likely still have a lot of error with the likelihoods AND the estimation of how bad each thing is.

[old nest]

PLEASE help me it's been 4 hours

[neat lintel]

still need help?

[tawdry pecan]

why

[solar hawk]

because it told me to

it told me to re install when i tried to load it up

XD

[tawdry pecan]

understandable

[solar hawk]

i was already playing all along

tbh some roblox games r good

sad there are some bad ppl on soem of the others tho

[tawdry pecan]

ive never tried any roblox games

yeah

[solar hawk]

there aer some good ones

i mean like

some of the developers know what they r doing

some are original completely, something i cant get off of roblox

some are just games i cant run outside of robglox

[tawdry pecan]

yeah

[hidden isle]

@burnt ledge I have a question regarding chemistry, do u have time?

(Legit one)

[gusty socket]

@burnt ledge i have a question regarding… chemistry…

[fresh comet]

can @burnt ledge recommend me a book in organic chem

[sick kite]

@burnt ledge do you like chemistry

[next schooner]

@burnt ledge so I'm currently working on a project to do with chemistry and I hear you're somewhat of an expert

[burnt ledge]

Yes i do now

[burnt ledge]

Ask away

[burnt ledge]

Clayden Organic Chem

[hidden isle]

what the hell i didnt even check this channel and i just see all of this

lmfaooo

😭

[burnt ledge]

Yea kinda. not so much as i use to

[burnt ledge]

Could be epic. Ask away

[hidden isle]

ok i have a question

[burnt ledge]

@burnt ledge Do you know much about chemistry? I hear you're the expert

[hidden isle]

you know magnesium ribbons?

[burnt ledge]

Yeag hes my buddy

[hidden isle]

is it safe to run an electric current through them

all i know is that theyre flammable

[burnt ledge]

if theres any chance the current will get high, then no (because high current -> high temp -> ignite the magnesium)

[hidden isle]

what about like 9 volts

[burnt ledge]

add resistor maybe

[hidden isle]

hm

ok maybe ill just use aluminium foil because its safer

[hidden isle]

i think it would be too complicated to add for a simple diy commutator ring dX

[hidden isle]

but thanks you just saved a potential arson

[burnt ledge]

yeag flammable metals are a pain

Cant even extinguish them

[short fiber]

are you a magnesium ribbon? bc ur always so fire

[onyx reef]

are you anhydrous calcium chloride? becuase you make every woman around you dry

[short fiber]

jokes on you buddy im a woman

[onyx reef]

Don care

[short fiber]

it was international womens day yesterday

[bright hill]

trying to think of all the possible impolications this response holds

[short fiber]

wh

im not

lying

[neat lintel]

ok trippie redd

[deep mango]

<@&268886789983436800> spam

[fresh comet]

lmao, I actually asked in #book-recommendations for an organic chem book which was not Clayden

[burnt ledge]

why would you do that

[fresh comet]

my friend is looking for orgo books, and they are considering clayden, but want to know if there are other alternatives

I am not studying ochem

[burnt ledge]

chemical structure and reactivity by keeler and wothers is a good one for the fundamentals too

goes into detail about organic but doesnt focus only on organic (and spends a while talking about bonding and spectroscopy

[fresh comet]

Ty!

[burnt ledge]

thats how i learnt it personally, CSR into clayden

[grizzled arch]

hi everyone

I'd love to learn from you

[bright hill]

I'm not questioning you lmfaoo

I just meant that, what you said must imply that woman don't make women dry

does that mean all women are homosexual?

guess not hmm

maybe the opposite?

I dunno, your response makes no sense to me

[acoustic yarrow]

https://youtu.be/R6grQAtAb4o?si=5Rniw-qIG4IeQQpc

[neat lintel]

you poor poor thing

[calm vessel]

:C

[ocean harbor]

https://tenor.com/view/doug-maclean-nhl-hockey-stats-statistics-gif-13408391465163304912

[grizzled arch]

same here

[ocean harbor]

[grizzled arch]

can you chat in English?

[ocean harbor]

ye

you can talk non-English in help channels though

[grizzled arch]

are you good at mathematics?

[ocean harbor]

no

[grizzled arch]

how about direct chat?

[ocean harbor]

ye

hi david

[tame egret]

Again, it is impossible to be 'good' at math

Hi Akira

[grizzled arch]

agree with you

[ocean harbor]

https://cdn.discordapp.com/emojis/1083562289371824228.gif?size=160&quality=lossless

[tame egret]

How's Java

[ocean harbor]

I finished it a long time ago

[tame egret]

Everyone does!

[tame egret]

[grizzled arch]

what about JavaScript?

[ocean harbor]

i use bing ai for that

[tame egret]

way better than java

[ocean harbor]

so pretty much not good at it lol

[ocean harbor]

true true

I use js, react, html and css for creating a website or smth

https://cdn.discordapp.com/emojis/1048660781123780749.gif?v=1&size=48&quality=lossless

[tame egret]

I saw an 'if dora had african parents vid'

it was brutal

Good bye Akira!

[ocean harbor]

bai

studying for da canadian citizenship test 🙏

[neat lintel]

good luck

[tame egret]

Minato don't randomly send messages to people!

[neat lintel]

Hello people

[mystic ivy]

hi myanus

[burnt ledge]

you should italicise the quote marks when italicising quoted text

‘good’ rather than 'good'

[fresh comet]

@neat lintel what were you going to say after this
#math-discussion message

[neat lintel]

hi

okay so

i'll ask you to take some (hopefully believable) things on faith there

mainly about how sequences and convergence work in R^2

[fresh comet]

dw I already do this in class

I usually have to convince myself of stuff after the fact

[neat lintel]

that's how i've been doing it since i was in 157/247

alright so

let's say we have a continuous function f: R -> R

we are interested in saying something about the graph of f

[fresh comet]

okay..

[neat lintel]

sorry hold on i'm also sorting out some work stuff at the same time

[fresh comet]

no worries

[neat lintel]

my job training got approved, i can start making money now

[fresh comet]

do your job first lmao

[neat lintel]

it's the weekend so it's not really doing my job lol. just sorting a few personal things out (payment accounts n tax shit)

US people have crazy ass tax forms

[fresh comet]

tax forms seem very annoying

I had to print out my first forms 2 weeks ago

[neat lintel]

i need to sign a form that basically tells the IRS not to tax me because i'm not a US citizen

okay so, what do we know about f? if x_n -> x, then f(x_n) -> f(x). so this implies (and this is where you'll have to start believing) that (x_n, f(x_n)) converges to (x, f(x))

[fresh comet]

okay

[neat lintel]

this (x_n, f(x_n)) is a sequence contained in the graph of f

what the condition "x_n -> x, then f(x_n) -> f(x)" is saying is that, if a sequence in the graph of f converges, then it must converge to something in the graph of f

if (x_n, f(x_n)) converges to something in R^2, say, (x, y), then (believe me!) x_n -> x and f(x_n) -> y. by continuity we know that f(x_n) -> f(x) as well, so (x, y) = (x, f(x))

[fresh comet]

hmm

I don't really have a good mental picture of what's going on lol

[neat lintel]

picture the graph of f and a convergent sequence inside of it

(do you have a good idea of what a convergent sequence in R^2 would look like?)

(the points get closer and closer to something)

[fresh comet]

I think so

[neat lintel]

cool

we won't worry about the definition; definitions are for mathematicians and we're physicists

[fresh comet]

[neat lintel]

by what i said above, the continuity condition on f is implying that a convergent sequence contained in the graph of f must actually converge to something in the graph of f

the limit of the sequence cannot lie outside the graph; it must be inside

let me illustrate with a non-example, actually

let's say f is zero everywhere, except for 0 where it equals 1

in the graph of f, let's consider the sequence (1/n, f(1/n)) = (1/n, 0)

what does this converge to?

[fresh comet]

uhh

I would think that it approaches 0?

[neat lintel]

1/n does, but what about the tuple (1/n, 0)?

(don't overthink it)

[fresh comet]

okay let me clear something up

[neat lintel]

sure

[fresh comet]

how am I supposed to think about this graph

is it in 3D?

or something else

[neat lintel]

it's sitting inside R^2

[fresh comet]

so on a sheet of paper

?

[neat lintel]

sure

[fresh comet]

(0,0)?

[neat lintel]

yup

is (0, 0) in the graph of our function f?

[fresh comet]

no

[neat lintel]

indeed

[fresh comet]

?

[neat lintel]

f is discontinuous, and (0, 0) isn't in the graph of f

so despite this convergent sequence being in the graph of f, its limit ended up outside because f was discontinuous

[fresh comet]

right

[neat lintel]

(maybe i should say it the other way around, that f is discontinuous because this limit is outside the graph, since i've only been talking about the "f continuous implies graph sequence etc." direction)

[fresh comet]

(is a contour the best way to think about graphs in R^2??)

that's the mental image I'm using

[neat lintel]

as long as the contour is actually the graph of a function (vertical line test), sure

so this property - that a convergent sequence sitting inside the set actually converges to something in the set - is called "closedness"

[fresh comet]

hm, okay

[neat lintel]

so we've established (up to taking how sequences work in R^2 on faith) that, if f: R -> R is continuous, then the graph of f (a subset of R^2) is "closed"

[fresh comet]

right

[neat lintel]

as for the other direction...

this is where things get quite unfortunate

let's try to follow our noses and see what we can come up with

we assume that the graph is closed, a condition on convergent sequences contained in it. we want to take a convergent sequence x_n -> x in R and show that f(x_n) -> f(x)

well, we know something about sequences in the graph, so the natural thing to consider is (x_n, f(x_n))

but we can't apply the graph closed hypothesis!!!!! this might not converge!!!!!!!!

woe is us

[fresh comet]

so then what?

[neat lintel]

we cry

our classification broke

we need to impose an extra condition on the codomain of f for this to hold

have you learned about the bolzano-weierstrass theorem yet?

[fresh comet]

yes, this was in our first month actually (september)

[neat lintel]

cool

i wish we had learned it that early

god, i just fucking LOVE dedekind cuts!

[fresh comet]

we did dedekind cuts in our first month too

[neat lintel]

i'm still mad about 157

[fresh comet]

(I died)

[neat lintel]

so

what i will assume about the codomain of f is that every sequence inside of it has a convergent subsequence

a condition which should look familiar

so now we're considering some weird thing like f: R -> (some subset of R with the above property like [0, 1] or [-21342131313, 100])

the meaning of continuity doesn't really change

but i figure it's good to point out

[fresh comet]

I see

[neat lintel]

so let's go back here with this new assumption in mind

is today a holiday? i think i can hear fireworks downtown

[fresh comet]

I don't live downtown

I don't even live in Toronto lmao

[neat lintel]

i'm like riiiight in the middle

[woven cape]

hi i'm new

[neat lintel]

ok let's not let me distract us

so x_n converges to x, cool. now we know that some subsequence of f(x_n) converges

let's say that that subsequence is f(x_{n_k}), and that it converges to y

x_{n_k} still converges to x

sounds good so far?

[fresh comet]

good so far.

[neat lintel]

so now we can get a convergent sequence in the graph!

(x_{n_k}, f(x_{n_k}))

wow that looks awful in plain text

$x_{n_k} \to x$ and $f(x_{n_k}) \to y$, so $$(x_{n_k}, f(x_{n_k})) \to (x, y)$$

[fathom swallow]

ТТерра

[neat lintel]

it's time for our assumption about the graph of f to shine

we have this sequence in the graph of f which converges to (x, y), so, by our assumption, (x, y) is in the graph!

what we have ultimately shown is that, if x_n -> x, then f(x_n) -> y = f(x). f is continuous!

[fresh comet]

hmm

this is something I'd do in 257?

[neat lintel]

yeah

the first bit of 257 should talk about topology in R^n

[fresh comet]

even more reason to study top over the summer lol

[fresh comet]

it's my understanding that there's a lot of moments like this in real analysis

why is that

[neat lintel]

to recap all this math discussion,

1. if f is continuous, then its graph is "closed"
2. if the graph is "closed" and sequences in the codomain of f have convergent subsequences, then f is continuous
   so "graph is 'closed'" is almost a characterization of continuous functions

[neat lintel]

analysis bad

[fresh comet]

I can't think of a major counterexample in LA now that I think about it

[neat lintel]

i'm surprised someone hasn't come in and told me that i need to assume f maps to a Hausdorff space. what's happened to this fucking server...

[fresh comet]

but I can think of maybe half a dozen in 157 analysis

[fresh comet]

maybe everyone went to sleep

what is a Hausdorff space though

[neat lintel]

distinct points can be separated by disjoint open neighbourhoods

it's what lets you say that limits of sequences are unique, for example

[neat lintel]

we needed this way back here. f(x_n) converged to y, but it also converged to f(x)

hausdorffness implies that y and f(x) are equal, but in some turbo shit space no one really cares about we may not have been able to say this

[jagged forge]

i still remember learning what convergence in the cofinite topology is like and being like "wait, wtf"

[neat lintel]

(inb4 nets)

[fresh comet]

I love the fact that analysis is always adding extra conditions just to deal with those spaces

lmao

or whatever other stupid situation nobody talks about

or cares about, rather

[fresh comet]

on an unrelated note, do you know of any examples/situations that forced extra hypotheses to be assumed in LA?

[neat lintel]

i woooooouuuld like to comment: functional analysis has a result called the "closed graph theorem" which says that a linear map between two nice whatever spaces (e.g. hilbert spaces, which i was telling you about when we discussed riesz's theorem) is continuous if and only its graph is closed

so over there life is good

[neat lintel]

so many things only hold for finite-dimensional spaces

i dunno if linear algebra really has any "key counterexamples"

it's just too nice

[fresh comet]

I like thinking about LA more than RA for that reason

it makes more sense to me

[neat lintel]

the first one that comes to mind is that an infinite-dimensional vector space is no longer isomorphic to its dual. this is disastrous

terrible!

[fresh comet]

what do we lose for it

[neat lintel]

nothing because the only time anyone cares about an infinite-dimensional vector space is when it's a hilbert space and there we only care about continuous functionals

(the "the only time anyone cares..." part is a lie, but pretend it's true so i can have answered your question)

[fresh comet]

fair enough lol

[neat lintel]

maybe a "main counterexample" would be like

0 1
is not diagonalizable```

idk

[fresh comet]

I don't know if I've mentioned this, but this matrix and

0 1
0 0

are my go to counterexamples in LA

[neat lintel]

so true

[tender tulip]

This looks AI generated

[fair mural]

idk why but this picture reminds me of that one image where everything in it looks familiar but you don’t actually recognize anything in it

[tender tulip]

Bender and the drink machine

[fair mural]

ok wait that’s totally a bear in the bottom right

[tender tulip]

Dog

[fair mural]

aren’t they both canines

[glacial panther]

I just learnt that latex actually takes time to learn

I thought it'd be like desmos where I just need to type stuff in

so dissapointed

[neat lintel]

1 1
0 1 isnt diagonalizable

[neat lintel]

Also the equivalence of symmetric bilinear forms and quadratic forms fails over fields of characteristic 2

[visual breach]

Tho it is worthy to point out that LA stuff is generally behaving well

[sly flint]

Iswtg this will give me a stroke

[neat lintel]

Peak artbreeder usage

[sonic sentinel]

i see a takeout carton, some jewellery, plastic bags, a red lid, and some ai artifacts

[worthy orbit]

just quickly;
My Coursework asked to plot a "theta versus t , and and x versus y" X and Y are parametric. But it feels unconvential to plot X on the y-axis am i being tricked

confused if versus is as significant a statement as against

or if im just meant to use common sense :|

bonkers stuff

[knotty spoke]

I don’t think this is ai generated, the background is great and I don’t see any stupid details. Specially the Coca-Cola can and stuff

Also the patterns on computers and stuff are flawless

if it was ai generated, it wouldn’t be like that

[tender tulip]

That’s the joke

It’s funny because it looks AI generated at first but it isn’t

[quartz crypt]

what is heat?

like when heat radiates into vacuum

what is actually lost

(this should be the smartest discord server im in)

[mystic flower]

[quartz crypt]

whats magnetic force, like when those double donut things radiate out of a magnet bar, whats actually travelling

[sonic sentinel]

alshfik's tips for success:

1. put zero effort, and expect the best
2. never apologize; it shows weakness
3. ruminate on lost time
4. optimistic plan + optimistic deadline = realistic action + realistic deadline
5. ruminate on lost time

[quartz crypt]

woah. i watch discord say you were typing for a long time, anticipating an answer. but this

i wonder if the moon is cooler when earth has rampant greenhouse effect

[sonic sentinel]

yeah i kept trying to think of more items but it made the joke less funny

its not even that funny in its current form

[naive hull]

uhm, its kind of a question from relativity

including length contranction and pseudo forces yk

[quartz crypt]

so ICP was right

[naive hull]

ICP?

[quartz crypt]

pseudo is just science lingo for magic

[naive hull]

pseudo is a greater concept

[naive hull]

its easy to understand but hard to comprehend

[quartz crypt]

its warps reality of magnetic materials

oh

https://theconversation.com/curious-kids-how-does-heat-travel-through-space-if-space-is-a-vacuum-111889

its for kids too

[naive hull]

ig it is like a fundamental rule of the universe

"energy always spreads out"

or maybe something like ||entropy||

[quartz crypt]

well anyway, its called "electromagnetic energy" and is possibly the "excitation in a quantum field"
but i reached the limit of my curiosity

[naive hull]

oh

[knotty spoke]

Ah lol, didn't realize it was supposed to be a joke

[unborn trellis]

Magnetism is electromagnetic energy book-keeping

When a charge distribution moves, you get current which by Ampere's law produces a new magnetic field. You can think of this being necessary because without the induced magnetic field, the electromagnetic energy contained in your configuration depends on which reference frame you're viewing the physics from

If you don't have an induced magnetic field, then moving from a frame in which a charge is still (the rest frame of the charge) to a frame where it's moving (some other frame where it looks like current), then the energy contained in the current is not the same as just the charge

[naive hull]

wait then why do some objects like iron get attracted towards magnets even if there is no current?

[unborn trellis]

Iron exhibits ferromagnetism, where the magnetic field is static

It arises from spin coupling of electrons inside the material

[naive hull]

ah MOT?

[unborn trellis]

So there is tiny currents going up and down constantly randomly inside

[unborn trellis]

Idk what MOT is

[naive hull]

Molecular Orbital Theory

[unborn trellis]

Maybe

This is more solid state physics

[naive hull]

yeah cos ferromagnetism arises from there ih

[proud olive]

What does that involve

Fear that I'm supposed to know this

[naive hull]

theory of chemical bonding

the latest one

(chemistry)

[proud olive]

Type of bonds?

Pi bonds and stuff?

[naive hull]

kind of but its not valence bond theory

there are like 5 theories on chemical bonding

[proud olive]

Is the other one called the sigma Bond?

[naive hull]

3*

[unborn trellis]

this one has quantum mechanics.....

[naive hull]

yes in VBT

[naive hull]

closely linked tho

[proud olive]

Aight ty

That's probably the thing I'm supposed to know

[naive hull]

no probs

[naive hull]

what are you into?

[proud olive]

Math

And physics ig

[naive hull]

then why are you supposed to know chem

oh-

[naive hull]

thats some deep physics tho

[sly flint]

What is solid state physics?

[naive hull]

like the properties of solids

[unborn trellis]

Physics of solids yeah

[proud olive]

It was taught in a general chemistry course. Wasn't much more advanced than that

[naive hull]

elasticity and stress

[naive hull]

oh

[sly flint]

ah, of course

[naive hull]

more than that ofc

[unborn trellis]

Those aren't usually what they care about in solid state

[naive hull]

thats some basic stuff ik about

[naive hull]

oh

[unborn trellis]

It's usually thermal and electrical properties

[proud olive]

Historese diagram and stuff

[unborn trellis]

Those are linked to the physics of the material itself pretty deeply

[sly flint]

So the study of say super conductors comes under solid state physics?

[proud olive]

Extremely boring stuff by other words

[unborn trellis]

Definitely

[proud olive]

Impressive that very able to make progress in a field so unbelievably boring holy shid

[naive hull]

super conducters aint boring

[naive hull]

ig its on ur interest tho

[unborn trellis]

if you knew statistical mechanics you wouldn't say that lol

[naive hull]

wait whats that

[alpine comet]

well, you can do it under string theory , at least string theorists would say so

[proud olive]

You got me. Idk statistical mechanics

[naive hull]

same here

[unborn trellis]

You can literally get formulas for the statistical behavior of gasses by approximating the number of lattice points in a sphere using stat mech

There's a lot of cool emergent physical properties that come from somewhat simple math

[sly flint]

string theory

[naive hull]

I only know about RMS in this stuff

[naive hull]

what does that mainly focus about?

[unborn trellis]

Lol

[fresh comet]

I see we're on the topic of physics

[unborn trellis]

Strings

[naive hull]

strings?

[alpine comet]

technically true tho. Iirc, AdS/CFT correspondence would translate CFT which describes some matter, to AdS where string theory works very well

[naive hull]

tension and stuff?

[fresh comet]

there's something I need to get cleared up lmao

[naive hull]

NLM?

[alpine comet]

but afaik, that has gone to nowhere

[fresh comet]

how do charges feel the electric force

[unborn trellis]

It's like if you did quantum field theory but your lagrangian for relativity uses surface area of "world sheets" instead of lines through spacetime

[sly flint]

I have 0 clue what those acronyms mean, hopefully by the end of this year I have some idea

[fresh comet]

I need a resolution to this this lol

[naive hull]

fundamental?

[fresh comet]

I feel like there should be a better answer

[unborn trellis]

how do they feel it...

[alpine comet]

CFT is Conformal Field theory, and AdS is Anti de-Sitter space, i.e. spaces where the cosmological constant is negative

[unborn trellis]

Photons get pinged back and forth

[naive hull]

really

[fresh comet]

real photons?

[sly flint]

yeah I-

[alpine comet]

I feel cursed already just by knowing what they mean

[naive hull]

now what causes that should be a real question then

[unborn trellis]

In fact, if you do relativistic E&M, you'll see that there's something called a domain of influence around a charge

[naive hull]

electric field?

[unborn trellis]

Basically, depending on how a charge is moving, there is a region around it corresponding to how far photons can move in a specific small chunk of delay time

It's called "retarded time" electromagnetism

[fresh comet]

are these photons observable

[unborn trellis]

Probably

[fresh comet]

[naive hull]

oh i see

[alpine comet]

valid r-word pass

[unborn trellis]

But yeah, time retarded electric fields suggest that photons have to propagate at speed c to influence a charge

[fresh comet]

then what happens if I create a new charge out of thin air

[unborn trellis]

You would violate conservation of charge

[fresh comet]

do photons immediately start getting sent everywhere in space

[unborn trellis]

[unborn trellis]

Yep

[fresh comet]

what if I create a pair of charges out of thin air

lmao

[unborn trellis]

This is what radiation is

[unborn trellis]

THIS IS A FUN QUESTION

[naive hull]

valid

[sly flint]

How do these charges produce said photons out of seemingly nothing?

[naive hull]

wouldnt that violate physics' laws?

[unborn trellis]

uh so basically if you spawn two opposite charges, this violates physics when you do the math yes

And this is suggestive of a specific flaw, which is that point charges as delta functions are unphysical

[alpine comet]

there's also the conservation of energy (i.e. mass) tho

[naive hull]

true

didnt notice that

[fresh comet]

how does pair production work then?

[alpine comet]

but if one of the particle is antimatter

then nothing stops you from doing just that. In fact, it happens all the time. That's how Hawking radiation works

[unborn trellis]

Pair production doesn't come from nowhere lol

[fresh comet]

I know

[unborn trellis]

Photons have to decay into the electrons

[fresh comet]

but it doesn't come from charges

[naive hull]

and what causes that? weak forces?

[unborn trellis]

Yes, you go from 0 net charge to 0 net charge

[unborn trellis]

Electromagnetic force

It's the fundamental interaction

[fresh comet]

yes, but this is creating charge is it not?

[naive hull]

oh

[fresh comet]

and then photons start getting sent to everyone?

[sly flint]

I have motivation to study physics now

[unborn trellis]

No, because the net charge is what must be conserved

[fresh comet]

yes, I agree

but these new electrons/positrons need to start telling everyone they exist

right?

[unborn trellis]

Im saying a charge configuration of two electrons of equal and opposite charge getting sent toward each other as "equivalent to no charge at all" is unphysical

You're talking about a photon decaying into two electrons which will scatter in literally opposite directions

[fresh comet]

mhm

but that wasn't the point I was trying to make

I was asking about how that newly formed electron/positron pair starts sending photons everywhere

what causes that to just start happening

[unborn trellis]

Anything that interacts with the electromagnetic force emits photons constantly

It's just the particles spitting out energy essentially

[fresh comet]

how do they not lose energy then?

[unborn trellis]

They do, which is why high energy particles fizzle out of existence

[proud olive]

Which is why the electron is spiraling down into the nucleus

Currently

[unborn trellis]

They decay immediately into lower energy things

[unborn trellis]

Nope, this is just the bohr model

In fact this is why they developed quantum mechanics

[fresh comet]

why don't lower energy things keep losing energy then

[unborn trellis]

They do! But they can exist longer because they're more stable

[proud olive]

Don't tell me that electrons act like clouds around the nucleus that's just nonsense

[fresh comet]

hmm

[proud olive]

(I was too slow)

[fresh comet]

can we measure the rate at which things emit photons

[jagged forge]

is this virtual particles

[fresh comet]

idk?

I can't tell if these photons are real or not

[unborn trellis]

Yep, this is a thing they measure

[fresh comet]

I see

is that rate supposed to be high?

[unborn trellis]

Virtual particles are any particles that spawn in and out of existence immediately for facilitating an interaction

[fresh comet]

why doesn't everything look insanely bright then

[unborn trellis]

It can be high

It's called blackbody radiation

[fresh comet]

I see

[unborn trellis]

Most things do not have high "emissivity"

Glad to know studying physics has been useful for something lol

[proud olive]

Except for my car brakes

[fresh comet]

what are you in?

as in, what field of physics do you study

[unborn trellis]

I'm an undergrad in math and physics

Next year I'll be starting my PhD in math but I'll be studying mathematical physics

I do all sorts of stuff

QM is my niche I guess

[jagged forge]

i was just wondering if it was related when you said spawning pairs of opposite particles violates physics when you do the math, it sounded vaguely like virtual particles

[unborn trellis]

I see, my point is that with virtual particles it's just a different physical scenario

[jagged forge]

ah

[fresh comet]

math phys is cool as hell

good luck with your studies

[proud olive]

Made up concepts in order for the math to work out

But sometimes that doesn't always work either so then we use a special tool called "renormalization" so that everything works out even when the math doesn't

Anyway, shoutout to Fubini for inventing Feynman's trick

[dire glen]

i'm planing to take this course once i finish the prerequisites.
https://ocw.mit.edu/courses/18-085-computational-science-and-engineering-i-fall-2008/pages/syllabus/
but in this case the course on the website is a series of videos , a textbook and exercises.
it's not really structured as others courses, with videos, exercises, examples...
Anyone took this course or similar? suggestions? comments?

[proud olive]

Wow you'll be learning about finite difference and finite element

Weird that they lump it together with LU and qr decomp since these topics feel much more vast in comparison

It's a good and highly relevant course if you're not familiar with this stuff from before

If you don't take a whole lot of math courses then yeah, that could very much be the most important math course you'll ever take

[tame egret]

Oh ok 'thanks!' 👍

[burnt ledge]

no prob 😁👍

[dire glen]

@proud olive thanks for the encouragement

from what i see it's basically the book and some videos.

[proud olive]

I'm unbelievably jelly. The professor in those videos is a legend

[dire glen]

i'm worreid that it might be too complex and i get stuck somewhere

[proud olive]

Seen him many times before for when I needed to learn about these stuff

It does indeed seem like the curriculum is pretty massive for a course like that

You'd be right in being worried, but man I wish I could take a course from MIT tho

[dire glen]

if you see this course for example, is structured differently. I mean it's all on the website

https://ocw.mit.edu/courses/18-01sc-single-variable-calculus-fall-2010/

i guess if i get the book it would be the same... but i need to figure out when to look for the videos

[proud olive]

Yeah maybe but it's just not the same as actually being there seeing those professors irl that constantly appear in your yt feed

[dire glen]

yea but i can't be there so i'm trying the best option haha

[proud olive]

Not completely sure what I should compare between these two courses in terms of structure

They seem pretty similar to me

But if you haven't had single variable calculus then you should start with that

I'd imagine it's an easier course

[dire glen]

i mean how the course is presented. in the latter you have the menu on the left with all chapters and subchapters. and in each page you have clips, pdf lectures, exercises, recitations....

the previous link it's not like that

it's like,get the book, here are the recordings, here the exercises

up to you figure out what to do when

good luck

[proud olive]

These styles highly depend on the professors lecturing them and how long the course has existed and how many students that are taking the course

I'd imagine more student take the latter course you mentioned which also leads to the professor getting more feedback on the site and other resources

While this is a course fewer but more experienced students would take who might not require as much assistance as the more freshman like student would need

As I see it, it is a course for the more mature engineering student

[dire glen]

gotcha

[proud olive]

A 2 year student maybe

[random rover]

is there anyone alive here

[tame egret]

no'

[remote oxide]

yes

[tame egret]

no

[remote oxide]

yes

[tame egret]

no

[random rover]

OK guys eat well and sleep well OK

[tame egret]

no

[random rover]

dare to say that again and u well be eaten by a hellokitty monster

[lilac folio]

1 grillion dollars to the first person to give me 100 dollars

[remote oxide]

https://youtu.be/QlKl3FR7jWE?si=QDh5BU1544NqUn3O

[clear fox]

What are the differences between differential, point set, and algebraic topology?

[deep mango]

Point set topology just studies topological spaces on their own (stuff like open and closed sets, compactness, connectedness, continuous functions, and homeomorphisms)

Differential topology studies smooth manifolds, which are a certain kind of topological space. And it studies smooth functions between them

Topics in differential topology include embeddings, intersection theory, and differential forms

And like genus n surfaces and stuff

Algebraic topology studies how abstract algebra can be used to understand topological spaces, mainly via homotopy (the fundamental group) and homology (the homology groups).

[lapis jungle]

wtf are these nerd reactions

[stray epoch]

how would I calculate a 45% chance of something happening and that thing happening 7 times in a row

[magic meteor]

isn't that (45%)^7

[deep mango]

This server is full of idiots

[compact magnet]

I was in discussion with someone in help but I think they went off, anyone got a spare minute to answer a quick question?

It’s about simple trigonometry

I don’t need solutions I already have the answer, I just want to ask if my working out method is viable is all

Just to clarify if I have 1.1 = 15/x, I can either divide by 15 on both sides to get x on its own, or I can multiply both sides by x which gives me 1.1x = 15 then divide by 1.1 on both sides to get x on its own, I’m just wanting to make sure that 1.1x divided by 1.1 is x that’s all

[wild lantern]

Yes, if you have 1.1=15/x you can do either of those things. Either way you'll eventually want to multiply both sides by x to get it out of the denominator.

Also, yes if you have 1.1x=15 you can divide both sides by 1.1 to isolate the x.

[compact magnet]

Ty

[jade ocean]

I will give you the 100 dollars if you first pay me 10 dollars

[dire glen]

a parametrization of a line is a way of listing all the points on the line.
how is this different from an equation of a line?

in y(x), can't i interpret x as a parameter?

maybe the parametrization is an "explicit" form of setting the coordinates?

[river moon]

they are two ways to represent the same thing

[plain owl]

"equation of a line" sounds like an unconventional name for parametrization

[dire glen]

but like

y = 2x +5

is the one is normally teached right?

it's an equation

i'm asking because of this
https://youtu.be/rtEaK_Jp7zU?t=146

it starts at the right time

[river moon]

in the school, yes

there are many ways to describe a line which are taught in the university

the set of points of the form (t, 2t+5) for all real t is the same line as the one described by y = 2x+5

[ocean harbor]

<@&268886789983436800>

[leaden torrent]

@neat lintel dont post unsolicited ads

[neat lintel]

2

[neat lintel]

don't say that

[alpine comet]

!da2a

[quasi jetty]

No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/

[prime lily]

is there any fast algorithm to compute square of a 4x4 matrix by hand? Or the definition is the only way

[neat lintel]

compute the jordan normal form, then squaring is easier

[alpine comet]

he said fast

[fresh comet]

this is damn slow lol

[alpine comet]

You can also do Jordan-Chevalley decomposition

[sudden surge]

Is there a graphing calculator that can handle multiple functions besides Desmos?

[sly flint]

geogebra

[sudden surge]

Okay. Great. I think I was having trouble using Desmos to graph equations with multiple functions.

[neat lintel]

@shrewd loom lets talk here

[sly flint]

im gonna join in

[neat lintel]

i code python a lot

[fresh comet]

discussy exploding today fr

[neat lintel]

on my school chromebook

[fresh comet]

wth

[sly flint]

IKR

literal madness

[neat lintel]

i used to use online-python.com

[sly flint]

and nami with his semantic arguments like the fuck dude

[neat lintel]

yeah #discussion is crazy

use vscode.dev

[sly flint]

welcome to the gang

[neat lintel]

for running code i have a program called WRECKED (working runtime environment creation kit enabling debugging) which is written in js

which graphics library are u using

i personally use html and the dom bc school chromebook

ah

oh ok

oh ok

yeah i’m very advanced

today i coded a program to simplify arbitrary boolean functions

for my redstone computer

good thing amukh isnt here rn he would be so angry at me

[sly flint]

oh how does it work

I'm planning to make an outfit chooser thing based on colour theory and AI, lets see how that goes

[neat lintel]

modified quine mcchusley that i figured out myself, basically finds canonical sop, merges terms iteratively through absorbtion and AB’ + AB = A, and then brute forces set cover problem/various polynomial time approximations i invented/normal O(n) algorithm

[sly flint]

since I only got like 4 pants and 12 tshirts

[neat lintel]

solves a 5x7 truth table in a negligable amount of time

[sly flint]

https://tenor.com/view/opossum-meh-cute-animal-gif-17580771

[neat lintel]

brb guys be back in 10ish mins

go look at the wiki page for “karnaugh maps” and outlinks to understand lingo

designed based on 32x8.com

[sly flint]

oh we were actually supposed to have kmaps this year in AI but they deleted it for some reason

[neat lintel]

yeah

fun fact i have no formal cs education

anyway be back soon

[sly flint]

I've took it as an HS elective but it doesn't go too deep

duck, what field do you want to go into?

[fresh comet]

TCS!

[sly flint]

Yes, 100%

[fresh comet]

theoretical computer science

[sly flint]

pre prepared for copious math though v

fr fr

[fresh comet]

waste of effort, you should figure out how to make fusion power efficient instead

then maybe the colleges will accept you

[sly flint]

But don't forget to establish world peace first, college likes diversity

[fresh comet]

you need to cure cancer before even being considered for a nobel

[sly flint]

^^

[neat lintel]

back who wants to talk about cs

[ocean harbor]

lets talk about how cringe java is

[neat lintel]

sure

[ocean harbor]

lmao what

[neat lintel]

SO MANY WORDS AND SO SLOW

[ocean harbor]

I saw what you deleted

no you

but duck

https://cdn.discordapp.com/emojis/1048660781123780749.gif?v=1&size=48&quality=lossless

[neat lintel]

oh that

[sly flint]

discussy is political again

[neat lintel]

^

ye

[sly flint]

speed what's a hash map

[fathom swallow]

Gave you the studying! selfrole.

[ocean harbor]

the green politics

[neat lintel]

table of hashes of objects and the actual objects has O(n) something which is faster than arrays

[ocean harbor]

smh you leave when im here

[sly flint]

so from where did you learn all of this?

[neat lintel]

wikipedia, other websites

experience

[sly flint]

wikipedia 💀
I think it's more of a reference than anything

yes but how did you get that experience

[neat lintel]

used linux, first touched windows at 8, started scratch at 7 and python at 8

[sly flint]

ah, i see

[neat lintel]

dad’s good at coding

also i do schoolwork fast (100 wpm + bad handwriting = teachers let you type assignments also smart)

so can code at school

[sly flint]

wait what, that's so based
our school doesn't even have the provision for laptops at school

can't even bring phones

[neat lintel]

we got chromebooks

4 gb ram

[sly flint]

we got uhh- paper and pens

[neat lintel]

oh ok

tho coding python on a school chromebook without knowing anything about js/html is hard

ofc now i know js/html

[sly flint]

decent for general use ngl, I had been on 4 gigs for 5 years before I got an upgrade

[neat lintel]

yeah i always push the limits

my 3rd question to gpt4 broke it

also i like running large brute-force np-hard problems

[sly flint]

I pushed the limits too hard and my laptop started melting so 💀

[sly flint]

i see

[neat lintel]

lol

anyway time for daily minecraft session

also one time i accidentally had my computer running for 5 hours computing steiner systems

[sly flint]

what for?

[neat lintel]

hamming distance

oh no amukhs on hopefully he dosent see this

[sly flint]

lul

[solar hawk]

I don’t get it

[neat lintel]

last time i talked about coding u said u were gonna block me

[solar hawk]

Yeah

Cuz u were being a freaking crank

[tawdry pecan]

lmao

[neat lintel]

scroll up

[solar hawk]

LOL

[tawdry pecan]

Are steiner systems related to topology at all? They give off that vibe

[solar hawk]

Topology is good

[tawdry pecan]

I dont know too much about topology, but what i do know is fun

[sly flint]

https://tenor.com/view/topology-cup-mug-donut-gif-17014077

[solar hawk]

So good

[neat lintel]

no its like "whats the best lottery ticket" or whats the combination of bitstrings with highest hamming distance (what i was trying to do)

[tawdry pecan]

yeah but something about the way that its groups of digits that share a certain number seems like topology on sets

[sly flint]

under what field of study do steiner systems come?

[neat lintel]

idk

[tawdry pecan]

uhhh error correction

idk the math field

[neat lintel]

lottery gaming

[tawdry pecan]

true

[neat lintel]

how i learned about them

and then i realized why my hamming distance calculations took so long

[tawdry pecan]

i wathced that one video on them

ill try to find it

[solar hawk]

What happened you your state of the art adder design speedy

[tawdry pecan]

https://www.youtube.com/watch?v=4xnRZqD7rAo&t=840s&pp=ygUPc3RlaW5lciBzeXN0ZW1z

this one

[sly flint]

hmm, tbh, i've lost motivation to study further cs

[solar hawk]

:(

[tawdry pecan]

lol

[solar hawk]

What the fuck have you done speedy

[neat lintel]

scroll up

kmaps were mentioned earlier

[solar hawk]

This is WHY CS CRANKS ARENT ALLOWED

[tawdry pecan]

what are you gonna study next?

[neat lintel]

was working on it all day

im not a crank

[sly flint]

well physics is my main focus

[tawdry pecan]

ah nice

i am really bad at physics, i have 0 intuition lmfao

[neat lintel]

also its not state of the art design

its for 4-bit redstone computers in minecraft

[solar hawk]

State of the ORE

design

[neat lintel]

wait whats ore

[solar hawk]

Bruh

I’m blocking you

[neat lintel]

no actually

tell me

oh wait

[sly flint]

Early physics is pretty intuitive ngl cause we experience most of what is taught

[neat lintel]

forgot about google

[solar hawk]

Open redstone winger it’s

Einteiler

ENGINEERS

FUCK

ok

[neat lintel]

oh those guys

not part of that

[solar hawk]

Why

Ore is good

[tawdry pecan]

yeah, part of the problem is I just havent put time in to learn it, but also like, its a lot of work to program anything physics related 😭

[neat lintel]

i will when i finish my 4 bit computer

[solar hawk]

U will what

Go on ORE?

[neat lintel]

ig

[tawdry pecan]

ive tried to program a double pendulum a couple times, and it just ends with me randomly changing values praying it works lmao

[neat lintel]

oh gl

[tawdry pecan]

too much trig

and too many ways to simulate physics too lmao

[sly flint]

Just use a physics engine, most make it really simple to do something like this

[tawdry pecan]

I mean yeah i could, but then you dont learn as much

[sly flint]

You don't need to start from scratch every time, there are tools and you use them to accomplish what you want to simulate
but if you want to practice, it's good practice, however doing both at the same time is just a waste of time

[tawdry pecan]

yeah

[neat lintel]

one of my rules is ALWAYS start from scratch

[tawdry pecan]

its mostly for fun anyways, but if I ever become super desparate ill use a library(god forbid)

[sly flint]

@solar hawk

[neat lintel]

and then when u figure out you cant/it'll take too long give up and use a library

[sly flint]

oh

[neat lintel]

(generally happens within an hour for me)

[tawdry pecan]

i think out of everything ive made, ive only used a library once or twice, i just like the feeling of doing it all, ik im screwing myself over tho

[sly flint]

another thing with physics is that there's an abscence of clarity in what your next steps should be, I find math to be just more "well organised"

[tawdry pecan]

most the stuff i make is pretty short anyways

[neat lintel]

i use libraries like pyodide, numpy (sometimes), graphics libraries

and ai libraries

[tawdry pecan]

i use javascript so i dont use them lmfao

[sly flint]

teach me tensorflow

[tawdry pecan]

obviously when im doing a school project or smth i use libraries (and a better language)

[neat lintel]

i use keras lol

im not doing all that matrix algebra

[sly flint]

it's a part of tensorflow

[neat lintel]

keras.io

also tutorial in book i think its called "ai with python" or one of those generic names

show pic of cover

and i will verify

[sly flint]

wdym

[neat lintel]

kw later i can show pic of the cover of the book i used to learn keras

[sly flint]

ah

[neat lintel]

discussy's somehow still political

nvm

[solar hawk]

• uses python

[solar hawk]

😭

[solar hawk]

what does the letters means

[neat lintel]

*and then give up starting from scratch a few mins later

[solar hawk]

lol

[neat lintel]

the one and only way i am not a crank

[solar hawk]

😭

[neat lintel]

at least according to u

imo i am not a crank i am just a self-taught coder

[fresh comet]

@solar hawk from FIS

[solar hawk]

whats Fis?

abs alg?

ngl idk what these words iz

[fresh comet]

Friedberg, Insel, Spence

my LA textbook

[solar hawk]

damn

what chapter is this

[fresh comet]

6.8

[solar hawk]

i mean the topic

[fresh comet]

pg 430

[solar hawk]

did do fish iso yet

[fresh comet]

the chapter's name?

[solar hawk]

ye

[fresh comet]

"Inner product spaces"

[solar hawk]

ohh

thanks

[fresh comet]

I don't think we're gonna cover FIT

[solar hawk]

why?

[fresh comet]

I'll probably look into it in my own time

[solar hawk]

its my favroite

[fresh comet]

we should be past that point by now in the course

back when we did R-N last semester, we shoulda done it lmao

but we didn't so

here we are

[solar hawk]

you would do it when you do quotients

[fresh comet]

we aren't really touching quotient spaces afaik

[solar hawk]

:(

[fresh comet]

I could be wrong

[tender tulip]

Amukh knows group quotients? Real

[fresh comet]

we have some extra topics at the end of the course

maybe then

[solar hawk]

vector space quptients

[solar hawk]

they r just as good

no worry bt normal subgroup

[unreal basin]

Hi, Is anyone aware of any tools that would integrate free hand drawing on a tablet with something like wolfram alpha? Optimally I'd like to free-hand write an equation and if i need help send that off to wolfram alpha? I tried searching online, there seems to be microsoft math assistant or one note, but doesn't seem to allow for advanced stuff

[neat lintel]

did u remove 2 or what happened i got a notif

[main void]

Paraboloid

[neat lintel]

why would you do that tho

[unreal basin]

I like solving stuff with handwriting, but would also want to quickly transform them into something machine readable (for step by step solving/plotting etc)

[sudden surge]

Is this true:

Difference between Δ, 𝑑, 𝛿 and ∂
Δ - finite variation of a quantity (not infinitesimal)
𝑑 - infinitesimal variation of a quantity or differential operator
𝛿 - infinitesimal variation of a quantity or variation of a functional

[solid snow]

infinitesimal

[neat lintel]

I've probably said this a million times but it's really humbling knowing that math goes so much deeper than calculus. As a sophomore I thought I was a genius, and when I stumble upon other parts of math I feel increasingly ignorant.

[visual breach]

Same.
tho in my case it could be that I am literally becoming dumber

[neat lintel]

probably not - but why do you think that?

[visual breach]

Well, it seems so when e.g. peers are going much ahead, and I seem to achieve nothing

Some part of it is my laziness, but still..

[neat lintel]

it might just be different pathways in learning.

what are you studying?

[visual breach]

I am searching around various subjects rn

Taking algebraic geometry, differential topology and basic arithmetic number theory classes.

[neat lintel]

are you having success in those classes?

[visual breach]

I don’t know, the grades are generally generous and I am understanding some

But I am not able to go beyond just understanding, it seems.

It’s even worse when some parts just seem like definition bashing

[neat lintel]

would you mind explaining what you mean by "beyond"? Like are you talking about mathematic intuition?

[visual breach]

Yep, intuitions and stuffs like

I am supposed to understand what people are saying when they state some mathematical stuff

[neat lintel]

Granted, it would be hard for me to understand given that I'm not in your boat. I think that when you are looking at math(or any topic) from an extensively broad standpoint, the nuances of certain problems can result in challenges in understanding and applying a practice. Error and fatigue is inevitable, but time helps to alleviate those problems.