serious-discussion

[fresh comet]

it's kind of weird

[cinder zephyr]

you do it with friends?

[fresh comet]

I do!

[cinder zephyr]

that probably makes it much more bearable

[fresh comet]

mhm

it would actually be better if we did it with only one vehicle but...

I have two layovers

so it's a bit annoying

I think it's worth it though

rent is looking pretty atm with the housing market

I'm saving smth like $12k CAD a year for this

anyways, @cinder zephyr what've you been up to lately?

[cinder zephyr]

studying for quals

and working on CTF chals

[fresh comet]

quals

CTF chals?

what's that

[cinder zephyr]

oooo ok

so I help run a cybersecurity club

a big thing in cybersec are these competitions called "Capture the Flag"

where whoever is running the competition makes challenges

these challenges are security based and involve some sort of hacking

and you hack to find this string (called a flag)

these challenges can range from some sort of forensics, or breaking a server, or reverse engineering a program, hacking a website, or doing some cryptography

so I'm making some cryptography challenges right now for my university's CTF we put on every summer

[fresh comet]

I see!

[cinder zephyr]

https://2023.uiuc.tf/

this was our event site last year

[fresh comet]

that sounds really cool, and fun!

[cinder zephyr]

very cool site idk how they pulled it off

[fresh comet]

indeed

[visual breach]

Yeah but you are strong, still

[fresh comet]

[neat lintel]

[fresh comet]

[neat lintel]

[fresh comet]

who ghost pinged me?

[neat lintel]

[loud snow]

I think Ill join when im back in school

I knew about these in HS

But forgot about them in uni

[patent quartz]

Hiii

[fresh comet]

hi

[craggy parcel]

hi ||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||||​||
@fresh comet

[neat lintel]

hi

[forest vale]

hi

[neat lintel]

hi

[wanton coyote]

hi

[unborn bronze]

hi

[solid yarrow]

Hello :3

[tribal field]

Helloo

[shrewd moon]

math makes me want to quit

i always forget why i started

[brittle socket]

Hi

[rich crane]

Hi

[oblique flicker]

gender

[neat lintel]

huh

[oblique flicker]

I do not need to explain

[neat lintel]

i dont undertsand

[vast wraith]

big mood

[oblique flicker]

they get it

[vast wraith]

[icy locust]

https://arxiv.org/abs/2301.13867 AI can do math now?

their overall mathematical performance is well below the level of a graduate student. Hence, if your goal is to use ChatGPT to pass a graduate-level math exam, you would be better off copying from your average peer!
L

[old oak]

Some AI can do some math, LLM's can't do any math

[icy locust]

Which AI are you referring to? Symbolic reasoning frameworks?

Compilers are technically AI in some sense so...

[old oak]

Yes, that's more or less what I mean

[icy locust]

I mean perhaps the immediate future is augmented LLMs or something, like you plug LEAN or SMT-LIB into it

That's assuming we don't get another breakthrough in a year or so

[surreal jacinth]

im kind of relying on ai being analytically helpless for my career prospects
so i hope not

[icy locust]

bet

well

the question is

If AI reaches the level where they can replace mathematicians

they might as well replace all intellectual jobs

[vast wraith]

well

you may have an exaggerated opinion of the importance of mathematics there

[surreal jacinth]

first ai came for the social science grads and i said nothng

[icy locust]

I'm obviously handwaving here but you know the vibe

[vast wraith]

yeah and i think the vibe is silly

[icy locust]

let's say "any job that purely relies on reasoning and nothing else like art or politics or athletism or something"

Not denying the possibility of highly-specialized AI that can literally only do math but

[surreal jacinth]

although my primary source of entertainment for a week last year was starting arguments on reddit and letting people unknowingly duke it out with a Bot i had like 7-8 arguments going at once it was a riot

[surreal jacinth]

yes i agree with you if it can do math it can do everything else eg engineering programming what have you

[icy locust]

reminds me of the GPT-4chan saga

[quasi copper]

hi

[pseudo helm]

[thick yacht]

Yannic's?

[ocean harbor]

ive finished calc 1

[fresh comet]

[solar hawk]

[velvet pivot]

Hi there

[fresh comet]

hi

[velvet pivot]

I am facing some issues. Maybe I am wrong or my calculator is wrong. When I plug in ( x = 1.5 ) into the expression ( \frac{1.5 + \cos(1.5)}{\sin(1.5)} ), I get 39.6, not 1.5709 as mentioned in the video

[fathom swallow]

FANI

[static loom]

degree vs radian mode issue probably

@velvet pivot stop spamming your question across multiple channels too please

[velvet pivot]

Ok

[ionic star]

why would it be so small if you do it in degrees

[velvet pivot]

If you don't mind, could you clarify more for me? I am self-studying mathematics (especially calculus from scratch)

[static loom]

!help

[quasi jetty]

To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.

[static loom]

Please read that to make a question channel @velvet pivot

[smoky quarry]

can I ask non-homework stuff in this channel?

[static loom]

the help channels are just for any math questions

[velvet pivot]

I found a YT video to fix that problem. I successfully changed the mode from degrees to radians. Previously I assumed that 1.5 was in degrees, so I multiplied it by π/180. I feel dumb about that

[snow peak]

what is gpa out of?

[velvet pivot]

Thanks for helping

[smoky quarry]

hmm alr

[trim path]

https://tenor.com/2EBO.gif

[tulip void]

is math intuitive

[old oak]

what does your gut tell you

[glass peak]

What type of maths? To who? Before or after learning it?

[vast wraith]

hungry

[quaint coyote]

who wants to be my study buddy, can't seem to find nobody

[tough island]

Question:

I understand in a set that it can be specified that the Cartesian product of 2 sets is A x B = {(a,b) | a is a element of A and b is an element of B}

How is it defined when we are doing something like

(A x B) x C? What is (a,b) inside of?

Sorry if this is a dumb question

I just started learning set theory

[ocean harbor]

!help

[quasi jetty]

To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.

[ocean harbor]

ask your classmates

[quaint coyote]

a would be pairs from AxB and elements of b would be elements of C

so one element would be ((a1, b1), c1)

why is that

[tough island]

So:

(A x B) x C = { ((a,b), c) | (a,b) is an element of (A x B) and c is an element of C }

[quaint coyote]

yea

[tough island]

Okay cool thank you

[fair mural]

they’re not asking for homework help

it’s just a general question

[ocean harbor]

I've used to the !help thing

but gotchu

[velvet dagger]

@vast surge okay I've thought about it while swimming and I'll avoid talking about complex numbers or general metric spaces in this class

It would require opening a bunch of threads that can't really be closed, and I think there's a conceptual/pedagogical case to just not introduce higher dimensional stuff just yet

Or if I'm gonna introduce general metric/topological talk, I won't bring R^n into the picture

So the real analysis part of this class is gonna be more analytical than geometric

And year 2 does metric topology, linear algebra, and multivariable analysis

In an irl university setting it might be better to have stuff be more "modular" rather than shoehorn people into a single track, and arguably there is a case to have two parallel first year math classes, basically one for people who like physics more and one for people who like CS more

[small dust]

dami pink name

[velvet dagger]

Yee

[crude prairie]

hey guys

who lives in a pineapple under the sea??

please answer,

im lonely in life

[ocean harbor]

google it

[wooden flax]

why is bro pink again

[latent edge]

why u rickrolled me

ANGERY

[velvet dagger]

hehehehehehhee

[robust holly]

@static loom i pung u

does that just work?

[static loom]

congrats

[latent edge]

congrats

[robust holly]

okay, now give me a structure coherent isomorphism of k-rank tensors with k-vectors

:T

[jaunty ibex]

That escalated quickly

[static loom]

no way, do it yourself

[robust holly]

bruh

[static loom]

skill issue

[robust holly]

nod, nod, crie

@static loom: i'm really just asking about mere existence about some paper outlining some equivalence, iff it exists

[static loom]

you want to talk about geometric algebra message that person I forget their name off the top of my head atm

[robust holly]

i'll take the skill issue on having not read preliminaries, but i won't take it if this is untreaded grounds >:(

[robust holly]

is it not mniip?

lmao

[jaunty ibex]

u guys know each other

?

[static loom]

it's @zealous garden

[robust holly]

mniip called me agda-pilled thrice

and i took it in pride.

[jaunty ibex]

I should have guessed when you mentioned geometric algebra

[robust holly]

i never did >:(

[zealous garden]

It's me

[robust holly]

hello

yes.

[static loom]

not that I'm aware lmao

[jaunty ibex]

oh nvm I thought mero said cpli is wraithlord

[robust holly]

now give me a coherent isomorphism of sums of 1..(k-1)-vectors with rank-k tensors.

[zealous garden]

I don't want to

[robust holly]

does it merely exist though q-q

[zealous garden]

Woah nelly

[robust holly]

does hestenes just outline a definition?

i don't wanna read hestenes q-q

:(

[flat harbor]

i love my tensors

[robust holly]

i don't. i just don't have an interesting way to represent multivectors

[flat harbor]

tensors arent that boring

[robust holly]

and i don't want to teach sand to check whether something is a multivector

so my goal is to find a coherent representation of multivectors as tensor values

does it exist @zealous garden?! >:(

[static loom]

https://cdn.discordapp.com/attachments/695514882216427540/1231377074648780830/attachment.gif

[robust holly]

(please don't mistake this as my actual thought, any help is appreciated, and i hope that it's fun to interact with me, nonetheless i find this github issue hilarious) https://github.com/libratbag/piper/issues/556#issuecomment-673024952

(not because i identify with the commenter [fuck them, i hope they burn in hell] but rather, how surreal they appear demanding support)

@jagged forge you were suspended in grade 8

[jagged forge]

yes

[robust holly]

up tops

[zealous garden]

What do you mean

[zealous garden]

What do you mean

Multivectors are members of an exterior/clifford algebra.

It's pretty simple

[robust holly]

not in my ram, they aren't

[zealous garden]

Yes they are

[robust holly]

i have tensors to my disposal, at least their representation as nested arrays

[zealous garden]

Oh so not actually tensors

[robust holly]

so if i vec1 * vec2 i don't mind spitting out some mat3

[zealous garden]

You have nD arrays

[robust holly]

i have #<rank>@<lowest bound 1>@lowest bound 2>@<lowest bound ...>@<lowest bound <rank>>(<array>)

[zealous garden]

I can't read that

[robust holly]

argh, i'd take me 7 min to write a katex transpiler

want me to talk mathjax?

[zealous garden]

One thing you'll want is when the unordered sum over indices is equal to (I think smth like 4x) the ordered sum over indices

[zealous garden]

I don't know what that is

Is it a soap

[robust holly]

it's a.. do i have #2((1 2 3)(4 5 6)(7 8 9))
$$
\begin{bmatrix}
1 & 2 & 3 \
4 & 5 & 6 \
7 & 8 & 9 \
\end{bmatrix}
$$

[fathom swallow]

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

[robust holly]

cool.

[zealous garden]

I need a rule for interpreting these to know what is and isn't a multivector

Like if I'm taking the "tensor" $A^{ijk}$, and then treat it as the sum $\sum_{i,j,k}A^{ijk}e_i e_j e_k$, then that is always a multivector

[robust holly]

there are no multivectors.. there are only rank-n tensors, is there still coherent geometric geometry?

[fathom swallow]

wraithlord_kontingency

[zealous garden]

Those aren't tensors please

They are just nD arrays

CS brainrot runs as deep as C++ calling dynamic arrays "Vectors"

[robust holly]

okay, i agree that that might be stupid

[zealous garden]

Tensors are a certain kind of multilinear map, or objects that respond to coordinate transformations in a particular way, depending on whom you ask

[robust holly]

but give me a finite n-linear form that isn't representable as an nD array

[zealous garden]

That isn't the issue

The issue is going back the other way

For example in order to go from object to components I need a basis

Likewise in fact to go from components to object

[robust holly]

can't you just read the fibres of the nD array?

[zealous garden]

Except you only actually notice it when I we go from components to object

No

[robust holly]

oh

[zealous garden]

Like

What transformation is

$\begin{bmatrix}0 & -1 \ 1 & 0\end{bmatrix}$

[fathom swallow]

wraithlord_kontingency

[zealous garden]

Answer: You don't know. You have almost no idea.

[robust holly]

well.. it's skew-symm-- alright

[zealous garden]

You can say it's a 90 degree rotation iff you assume you are using an orthonormal basis

Which can be quite the huge assumption

All this really says, if we must look at it as a transformation, is that the first axis ended up where the second is, and the second where the first is but antiparallel

[robust holly]

sure, it might be huge- but is it in meaningful to consider non-orthonormal bases?

[zealous garden]

What do you mean is it meaningful

It's more sensible to ask whether it's meaningful to consider orthonormal bases

[robust holly]

i mean, asides from introducing new identities does your algebra change?

[zealous garden]

I want you to construct a physical basis for a physical space with a guarantee of uniformity and orthogonality

[robust holly]

uhhm owo "physical space"?

[zealous garden]

My point here is that you are currently using language in a way that makes it hard for me to grok what it is you're actually trying to ask

Or whether you have actually formed a question that makes sense to ask of the concepts in my head even

A list of numbers isn't a multivector because we need much more structure in place in order to understand it as one

Just like a block of numbers isn't a linear map

So the question of how to associate your lists of numbers to multivectors will depend on choices

[robust holly]

assuming an orthonormal basis of e_1..e_(n-1) is there some canonical tensor isomorphic to any (1..(n-1))-vector sum?

if that is equally illegible i'll go back to reading papers q-q

[zealous garden]

Canonical? I can't imagine so

There's a lot of ways to squeeze a map/form out of a multivector

Assuming you mean tensors as p,q-linear maps

[robust holly]

because what i'm reading is that there is some skew symmetric representation up to any n dimensional (n-1)-vector

[zealous garden]

Probably but that's a little different from canonical

[robust holly]

but i can see it demonstrated anywhere for anything higher or more general than 3

[zealous garden]

Skew symmetric reps of pseudovectors?

I don't know about that

Bivectors I believe easily

So the goal is what

What is the isomorphism in respect to

Like is the isomorphism between a, subalgebra of the tensor algebra and the clifford algebra, thus a tensor and a multivector?

Where clifford multiplication is tensor multiplication?

Or like

What

Like do you need the tensors of your multivectors in G(V,B) to be tensors in T(V)?

Or can they be tensors of some other space

[robust holly]

in T(V)...

[zealous garden]

Now that I said it like that, dumb question

[robust holly]

i have no other space

[zealous garden]

Not exactly true

[robust holly]

i mean really i'm asking for some witness of G(V, B) equiv T(V), no?

[zealous garden]

It's not equivalent

They shouldn't be and can't be equivalent

[robust holly]

sorry, HoTT-brained q-q

[zealous garden]

Dimensions don't match

I think all T(V) is linear polynomials in G(V,B), but absolutely don't quote me

[robust holly]

i won't; no worries

[zealous garden]

Have you read Lie Groups as Spin Groups

[robust holly]

there's no stakes, really these are all musings q-q

[robust holly]

no, not yet

[zealous garden]

https://tenor.com/view/im-in-this-tweet-and-i-dont-like-it-amy-dallen-thanks-i-hate-it-called-out-gif-13453570

[zealous garden]

I recommend it specifically on the question of relating (multi)linear maps and polynomials in a GA

It's got other cool stuff too

I just don't understand it all

[robust holly]

doi:10.1063/1.530050?

[robust holly]

you think mniip will ever explain (co)end calculus to anyone?

[robust holly]

okie will read

[zealous garden]

No idea what that means, maybe.

[robust holly]

https://arxiv.org/abs/1501.02503

[zealous garden]

Yes that one my bad

[robust holly]

n'worrries

III. STRUCTURE OF THE MOTHER ALGEBRA

[static loom]

you're welcome 😌

[flat harbor]

the mother algebra vs the master equation

[robust holly]

The mother algebra Rn,n is, of course, a subalgebra of the infinite dimensional algebra R∞,∞, which might be called the grandmother algebra or “Eve”. Reference 4 contends that “Eve” should be regarded as the universal geometric algebra and adopted as the arena for developing a coordinate-free formulation of manifold theory.
sure @zealous garden, doesn't this just say that you can represent any k-blade as it's involution, get a linear form and call it a day?

without referring to any bases?

(3.20) then outlines the involution with threatening notation

[zealous garden]

He goes on to show a correspondence between the multivectors of the mother algebra (m,m); and left and right multiplication maps on (p,q)

He shows that every linear map is in (m,m), and that therefore every linear map is such a polynomial in (p,q)

[robust holly]

wait @zealous garden , so eve is distinctly different from §2 in isbn:978-3-642-05692-5, isbn:978-3-662-12927-2 ?

[fresh comet]

this server doesn't permit discussion of piracy

[robust holly]

understood

[north topaz]

there are rules for partnered servers so that Discord doesn't get their ass sued out of oblivion

[old oak]

I have no idea what made me think of this image, but here we are:

And also this:

[vast wraith]

ah yes, Cardano, the furry theoretician

[north topaz]

funni

[old oak]

Very sad, actually

But what can you do but laugh

[latent edge]

Funny but sad

[burnt ledge]

If only there were an archive

[brazen mulch]

(this thing, now available for free reading, discussed vocabulary inaccessible to non-scholars)

[old oak]

Not that the point doesn't still stand

[hollow ravine]

Am I blind? I thought there was a rule against paying for help in this server but I just looked and now I can’t find one

[verbal karma]

Do not cheat on tests or exams. Do not be academically dishonest. Do not offer money for doing homework assignments, and vice versa.

in #rules

[hollow ravine]

Thank you!

[uneven tinsel]

Offering money for homework is like hiring a stunt double to take your place at a family reunion, it might seem like a clever idea, but eventually, someone's going to notice the imposter.

[fresh comet]

that is a wild comparison LOL

[vast surge]

Okay but to be fair, hiring a stunt double to take your place at a family reunion sends a strong message even if they're found out. Paying someone else to do your homework just gets you in trouble.

[ionic star]

but the family will care that there is an impostor

so it's not as bad as you make it sound

[patent quartz]

hihi!

[oblique flicker]

hello

[alpine kindle]

imposter???

[raven plaza]

And sends a strong message to the school

[neat lintel]

I will congrat chatgpt to graduate at the end of year 12🤙

[shrewd moon]

anybody reading pure mathematics

atm

[old oak]

Mine preferred the impostor

[raven plaza]

Stuffed owl

[vast wraith]

is that you or the impostor

[raven plaza]

Is this what Polish owls look like

[old oak]

https://tenor.com/view/moonkin-dance-starfall-dancing-moonkin-gif-20256106

Impostor of course, this is me^

[vast wraith]

whew, such moves

[uneven tinsel]

My teacher gave some multiplication problems and said don't use tables, does that mean I need to do it on floor?

[warm plaza]

Math.

[verbal karma]

why floor when you can do it while floating?

[warm plaza]

[uneven tinsel]

Okay cat, you do your cathematics

[viscid sandal]

i don't think he/she meant "that" table

[verbal karma]

human did not learn gymathematics? sadge

[uneven tinsel]

Seems like I've accidentally crossed paths with the cat pfp squad. Better watch my step, I heard their claws are as sharp as their wit, I better step back

[neat lintel]

r u an owl

hot

[old oak]

hoot, you mean

[neat lintel]

hoot?

[small dust]

you best not get on @native oriole’s bad side

[mental stratus]

which hyzae

[wise socket]

https://www.instagram.com/tech_looom?igsh=Mm1vdTZqanp3YXhz

[fresh comet]

don’t advertise please

[vast wraith]

why can't i have normal interests even among mathematicians i have started taking notes for an article with working title Gender, Geometry and Logic

lets see if i can write something actually interesting about this (unlikely, but i gather i need the practice)

[coral terrace]

listen to hiphop and play minecraft boom you share intrests with half the world population

[mental stratus]

thats cap

[neat lintel]

mc has 300m downloads

[vast surge]

Gender theory is quite popular amongst mathematicians. Eugenia Cheng immediately comes to mind as someone who's done work in the overlap (X+Y=Gender).

There's a lot of queer mathematicians.

[neat lintel]

hm java and bedrock combined is 425 million, chinese is 475 million

[graceful flower]

is the chinese one even affiliated with microsoft?

[neat lintel]

yeah

[graceful flower]

it is?? then why dont we get the cool stuff 😭

[neat lintel]

they licensed minecraft to NetEase to devise a censored version that had CCP sponsored stuff

[graceful flower]

ah

[neat lintel]

you can go to china and play it on someone's computer

i think you can get it in the USA smhw

it checks if you're in china but that's easily bypassable

people have tried to port over the stuff using mods

[vast wraith]

currently, the plurality of medieval conceptions of algebra; renaissance readings of the ancients and epicurean explanations of hydrostatics; late 16th and early 17th century ideas of the Orphic fable in music; social logic, authority and the role of examples in our understanding of gender

are the first things that come to my mind

[neat lintel]

also apparently you can only use realms to make servers (unless you like license it if you're a company)

BUT THEY USE SPIGOT FOR SOME REASON

AND YOU CAN DOWNLOAD PLUGINS

[vast wraith]

ooh thank you i will have to look em up

[graceful flower]

sounds like interesting stuff frfr

[vast wraith]

it is >:S

[white temple]

there's at least one queer mathematician who lacks any and all notability (me)

[white temple]

i can't imagine how gender is tied to geometry but then again i haven't looked into gender studies and i'm horrible with geometry

[vast wraith]

what led me to ask the idea is question that've occupied my mind a lot lately

[sudden agate]

[vast wraith]

first i will say it is plenty clear gender is complicated and i don't understand it, yet everyone are familiar with gendered ideas because we are surrounded by examples

also i've been reading in the history of geometry, it's a mess. we have done geometry for a long time, yet there's also been so much confusion about, whose resolution comes about in clarifications and developments in logic, such as the introduction of model theory

now in both examples, of gender and geometry, there are widely found "naive" and intuitive understandings of the subject matter

and there is a disparity between any proposed theory and any model, in the form of examples

and that's about all i have to go on atm

@white temple

like for example the 15th century rediscovery of lucretius' de rerum natura (on the nature of things) and the new attention paid to these authors, visible in the many new translations of these works during the renaissance, for example Tartaglia was the first to translate Archimedes into a living language (italian)

and typically they did not simply adopt the theories of these ancient authors, but they made their own interpretations and elaborations

[brave shell]

Nah. It was just Newton, and he was too good, so they wouldn't let any more lgbt people in.

[vast wraith]

i might add that the example of lucretius in specific his critique of religion and his charming elaboration of atomism had quite some impact on the modern age

his arguments relating to colour i find very amusing

Besides, if atoms have no hue, but are endowed instead
With variations in their shapes and forms as I have said,
And they give rise to all the different colours of the rainbow
By changing their connections and positions where they go, [760]
The motions they give or take, it's instantly easy to explain
How what seemed black just now, when we look at it once again,
Has suddenly turned white as marble; for instance, take the sight
Of the sea, when winds have churned the surface to hoary white.

from alicia stallings' translation

[chrome marsh]

@sonic dagger close, but no I did not get this
#help-3 message

[vast wraith]

😭

i'm all for detail and context-oriented methods but what the hell girl

[vivid halo]

girl math

[white temple]

why is "women logicians" grammatically funny to me it's like calling Hugh Laurie "an actor doctor" (he actually became a nephrologist irl after house md)

[shy portal]

heya im tryna get into lean but have no clue where to start all i've done is that build the natural numbers game online

i finished a course on proof-based linear algebra in the last academic year so i was thinking about trying to rebuild some of the theorems there in lean buuut i still have no clue where to start with this lol

[storm sage]

I never understood gender essentialism

Why are men abstract, general, and formal?

[vast wraith]

i have no idea

claims like this are obviously not representative of feminist theory in general

[visual breach]

Really?

I thought it was prominent because it does essentially dominate those scenes here

[wispy lava]

aa I'm addicted to Muller Corner Milk Chocolate Digestives yoghurt

[pulsar pagoda]

this is an issue Mises explored when he defined his idea of polylogism

but its not gender per se

its the idea that people with different physical traits have logics which are tied to them with their own form of "valid" reasoning

which is a thing he disagrees with (and I happen to agree with him on that one)

now that last quote in the paragraph is pure gold

"unsurprisingly woman logicians have disagreed"

[white temple]

abstract? general? i can't believe it, men have actually been general linear groups this whole time! truly a breakthrough in maffs and psyence for the history books

[blazing pawn]

there is a legitimate version of this philosophy that is not "men do logic 😠 and women do EMOTIONS 😁"

platos pharmacy is maybe a good introduction to this idea

[graceful flower]

i dont think he actually did become a nephrologist, he just talked in an interview about how he could've become one in the span of time it took him to do the show

[daring ridge]

guys

what the FUCK are groebner basis

im tired of seeing them used to solve every other cryptography challenge i face

[river moon]

just a particular algorithm to solve systems of polynomial equations with multiple variables

[daring ridge]

that was underwhelming i was expecting some magic, tysm!

[empty mirage]

gonna find this fucking take its too funny

Apparently its from the book Words of Power

[vast wraith]

oh my

[neat lintel]

Should I post it again

[tender tulip]

Yes

[neat lintel]

1. Let a=x=1 => (1)(1) = 1 => 1 is in K

Suppose a,b in K and x,y in R
and
ax = 1, by = 1

Also, yx is in R by definition.
=> (by)x = x
=> a(by)x = 1

Since yx in R, we can also say
(ab)(yx)=1
=> ab is in K, hence closed

Now additionally, let c in K and z in R
and
cz = 1

Also again by definition, xyz is in R
=> c(b(ax)y)z = 1

And c(ba)(xy)z = 1 since (ba)xy = 1
Also, (cb)ax(yz) = 1 since (cb)yz = 1
And finally, since xyz in R, we can write
(cba)(xyz) = 1
Hence K is associative

which implies K is a monoid

Btw by right cancellative you mean yx = zx => y=z right?

[tender tulip]

Yes

wait I think I swapped the defs by accident

[neat lintel]

It's alright, got it 👍

[tender tulip]

For part 3:

• ax = by = cz = 1
• yx = zy in K
• y ≠ z

I will admit it is not immediate

[neat lintel]

2. Let a,b in K and x in R

Suppose
ax = 1 and bx = 1

=> (bx)x = x
=> a(bx)x = ax = 1

But also
(ax)x = x
=> b(ax)x = bx = 1

And since K is a monoid, and x² is in R by definition
(ab)x² = (ba)x²

But also, from (1),
(ab)(yx) = 1
And (ba)(xy) = 1

And yx ≠ xy since R is assumed to be non-commutative

Hence, ab≠ba => K is not commutative

Hence, (ab)x² = (ba)x² iff ab = ba, and is only possible when a=b

Hence, ax = bx = 1 iff a=b, implying K is right cancellative

[tender tulip]

Yep

[neat lintel]

I'm having trouble with the third one

Oh wait I'm cooking 2 min

[tender tulip]

Turns out I did 3 wrong, I don’t think it’s true

Sorry fam

Nvm it’s true assuming K is finite

[neat lintel]

Hmm

I'll visit this problem again after 15 min, because I have no idea how to show yx = zy in K is true

[tender tulip]

Need not be

[neat lintel]

No like to prove K is infinite

[tender tulip]

Hint: assume it’s finite

And we already have one sided cancellativity

[neat lintel]

Alright 👍

[sonic sentinel]

how does gpt training work, would it be possible to have a game where you try to predict the next token vs. another gpt and see if you perform better than it

[neat lintel]

Yeah

[neat lintel]

I'm still not getting how "left cancellativity" is defined here

Like in (2), both a and b were assumed to be from K so it made sense to say K is right cancellative

But I'm getting stuck on this one

Also, I have edited my previous two messages and went more rigorous

[tender tulip]

There’s uh like, different conventions by different authors

[neat lintel]

Oh I see

[tender tulip]

It’s really reduces to the case that if you have a finite monoid that is left cancellative, then it’s right cancellative (actually a group lol but we don’t need to wrestle with that)

[neat lintel]

Oh wow

[tender tulip]

Use pigeonhole principle on x^n lol

[neat lintel]

Oh wait
Let a in K

If K is finite, then there exist natural p,q s.t.

a^p = a^{p+q}

But a^{p+q} = a^p a^q
So a^q = 1

Also

a^{q-1}a = a^q = aa^{q-1} = 1

Also, if b is in K s.t. ab = 1

=> ab = aa^{q-1}

By left cancellativity,
b = a^{q-1} (inverses exist)

Hence K is a group

This so cool

[jolly trout]

[neat lintel]

So since K is a group and is finite, it must be right cancellative as well

Wait but

Can we conclude from here K would not be a group implying not right cancellative if K is infinite then?

[tender tulip]

No

If K consists of bi-inverses, then it’s a group (since the respective “halves” of the inverses are now also in it) which can be infinite

it’s just that if it’s finite, it must be cancellative

[neat lintel]

I see

well, this was a great exercise thanks miz o7

[tender tulip]

You’re welcome I guess lol

[halcyon mantle]

guys i'm looking for weird problems about counterexamples in real analysis, Do you have some?

[raven plaza]

There's a differentiable function whose derivative is bounded and not Riemann integrable

[halcyon mantle]

interesting, so i'm looking for a bounded function which has a primitive but has set of discontinuity points of positive outer measure

it's weird because it has to satisfy the ivp

[raven plaza]

Indeed it be curses

[tender tulip]

Me when volterra’s function

[flat cloud]

is it normal that factorizing polynomials is so exhausting or am I doing it wrong?

I dont like searching all roots then testing the polynomial on all of them

and test for intermediate values to see if a root is repeated

I feel like there should be a more straight forward way

[fathom loom]

there is always a shortcut

[static loom]

one way to find repeated roots is look at the gcd(f,f')

[fathom loom]

check the highest power

[flat cloud]

fundamental theorem of algebra says there can only be n roots, true?

[static loom]

yeah a degree n polynomial has exactly n roots in C, so that's basically an upper bound depending on where you're factoring, in rationals or reals

[prime raven]

I’m looking for someone to study analysis or algebra with

[verbal karma]

n (not necessarily unique) root, yea.

[uneven tinsel]

Number of extrovert mathematicians is increasing

[peak tide]

extrovert mathematician = looks at your shoes when he speaks instead of at his own?

[grave vault]

Do you learn quadratic inequality and step functions and data stats in algebra one but your taking it early yes or no plz help asap just a discussion

[uneven tinsel]

[iron iris]

v ± √(v²-c)

the ultimate…….

[neat lintel]

An Introduction to Mathematical Reasoning: Numbers, Sets and Functions by Peter J. Eccles -- does anyone have this book on them -- i want pdf for this book

[verbal karma]

this server does not encourage pirating books

[tender tulip]

@raven plaza I have a funny idea

Double complex? Nah, countable complex. Countable number of exact morphism chains between countably objects

Then all the “diagonal” morphisms are essentially characterized by some finite subset of the “complex level” indexing set

And you can make a lattice in that and use it to do diagram chasing through it

[empty steppe]

if i have an independent matrix then is the null space automatically the vector 0? does anyone know

[fresh comet]

what is an independent matrix? also, this question is better suited to be asked in one of the help channels (see #❓how-to-get-help ) or #linear-algebra

[deep mango]

probably like, columns are independent

[empty steppe]

Got my answer thank you tho

[raven plaza]

I don't follow

[tender tulip]

I’ll write it out later

[vast wraith]

sitting at a cafe, taking a pause from algebraic geometry to eavesdrop on a most interesting conversation

mwahahaha

[fresh comet]

what is the conversation about

[vast wraith]

managing as a freelance musician

and as a series script writer

i think

[deep mango]

i love listening to random cafe / restaurant convos

so many odd little insights into things ppl are navigating

[eager cloud]

i wish i lived in the big city with cafes :(

[uneven tinsel]

I remember I was in a cafe and there was extremely wise man sitting next to me, that day he told very important thing to me, but the music was loud so I couldn't hear

[mental stratus]

Im in a restaurant and theyre talking about uhhh... Cricket

[old oak]

The thing he was saying: ||"Don't you think the music here is a bit loud?!"||

[eager cloud]

'buy fortnite battlepass' the man whispered from across the room

[vernal token]

You casually go to restaurants?

[deep mango]

Sure

[vernal token]

Aren't most of them pretty expensive? Or are you not talking about these 4-star or 5-star ones

[deep mango]

Im not

Im just talking about any sitdown food place

[vernal token]

Yeah, in that case, going to a cafe with a math friend or something is probably really cool

If only I had some

[dense oracle]

Solve this: Sin⁶x+cos⁶x

[ocean harbor]

!help

[quasi jetty]

To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.

[near prawn]

Answer: I find myself compelled to acknowledge the gravity of your proposition, yet, it is one that my conscience cannot, in good faith, endorse. In truth, I cannot acquiesce to your frivolous request, for it would lead us down a path fraught with shadows and sorrows. Nay, I must, my heart heavy with the inertia of inevitability, respectfully, but firmly, decline. For to yield to your trivial supplication would be to court chaos and upheaval, disrupting the delicate equilibrium of our lives. May the passage of time grant us the clarity to discern the wisdom of my decision, and as our paths inevitably diverge, let us kindly find solace in the knowledge that mine was guided by the hand of prudence and virtue.

[dense oracle]

“Criticism, like rain, may dampen the spirit; yet, such showers make the soul's garden bloom ever brighter.”

Fashion a decree that bears the emperor's imprimatur

[near prawn]

My dear fellow, my answer to your question is final.

[dense oracle]

I feel betrayed

How could you do this to your own brother?

[unborn bronze]

do not try to change his mind

its done

[dense oracle]

My fate is not sealed! I refuse to accept defeat!

I must make him answer my question

[unborn bronze]

denial it is then

[dense oracle]

I'm ready to live in denial

[tawdry pecan]

denial is better than being destroyed by unwielding truth

perhaps it is for the best

[dense oracle]

Perhaps

One day

[tawdry pecan]

one day you shall understand

[dense oracle]

Yes.

I'm helpless at the hands of fate

[dense oracle]

This further obviates the need for me to realize my truth.

[tawdry pecan]

And what a favor that is! The holy hands of time make way for you for a short while.

[dense oracle]

I have inherited a predisposition to greed. Folks from my village called me ‘Evil incarnate’.

[tawdry pecan]

how unfortunate, a being stronger in numbers fends for itself.

[dense oracle]

That's one way to put it. Hunger for power shall not be juxtaposed with the will to survive

[tawdry pecan]

but... perhaps they shall be transposed. The will of change itself leaves much room for grace.

[dense oracle]

Death brings grace to life.

One could only hope to whet their intellect

For it is the only sword to be wielded

[tawdry pecan]

Death is willful in certain circumstances however. Perhaps the greater good can be held as a weapon as well

[dense oracle]

Death indemnifies us for a life that is lost.

Every soul that's become soul less

[tawdry pecan]

Indeed, Death is an equalizing force.

The transfer that takes place is not one that identity can be part of, however

all shall meld into one in the end.

[dense oracle]

Death isn't unification. It's salvation.

It frees you from all shackles

[tawdry pecan]

are those not equivalent?

good cannot exist without evil, for example.

[dense oracle]

They both accrue into something undesirable

Death isn't an equaliser

It's a manifestation

Of what many call their ‘lifetime’

[tawdry pecan]

Perhaps the concept of equality stripped of context is poorly behaved.

[dense oracle]

Indeed. Why must we expect reality to make sense? When all we've been living is a lie!

[tawdry pecan]

Truth can be found in anything.

Separately, of course, but maybe the connection is somewhere over the horizon of life.

[dense oracle]

“He who pulleth this sword and this stone anvil, is rightwise born king of all England.”

[vernal token]

What's your last sentence supposed to mean? Why?

[tawdry pecan]

I see not how such a memorial relates to the current debate

[dense oracle]

Truth can be found anywhere.

[tawdry pecan]

Indeed

[dense oracle]

Seek, and you shall find

[south wyvern]

f:g:h g is 60 percent more than h , f is a third of g , simplify f:g:h

[topaz trout]

Is math about truth

[dire stump]

if g is 60% more than h then g = 1.6h = 8/5 h. if f is a third of g, then f = 1/3 g = 1/3 * 8/5 h = 8/15 h.

then f : g : h becomes 8/15 h : 8/5 h : h, which becomes 8/15 : 8/5 : 1, and if you wanted to get rid of the fractions, you could say that's the same as 8 : 24 : 15

[velvet dagger]

Not all truth is in the scope of math

[fresh comet]

https://tenor.com/view/aesthetic-round-spinning-dots-pattern-gif-17154839

[neat lintel]

but even if so can humans verify or undertand truth that is outside of the scope of math

[velvet dagger]

True but I'm saying "is math about truth" is underdetermined

Since there are things about truth which aren't mathematical

[clear fox]

what does it mean to have fractional degrees of freedom in statistics?

[granite hound]

Pretty!

[bitter ember]

Truth is the Escape of Reality

and Math barely opens the gate

[neat lintel]

This is lowkey fire keep yapping

[bitter ember]

Think about it

[mint patio]

@surreal bison physics bestie I have a question for u

[surreal bison]

yes?

oh btw there's this book with good info that's also written simply

Basic Vacuum Practices

[eternal mesa]

Fractals?

[eternal mesa]

Idk know but ik you can have fractional dimensions when dealing with those and a degree of freedom seems to be just another dimension you're allowed to traverse whenever I've ever heard the term

[surreal bison]

that doesn't make sense in a statistics context

the hausdorff dimension is not even a measure of degrees of freedom

it's more like a measure of growth rate

[eternal mesa]

My understanding is that at a certain point you can treat fractals like functions that you're plugging into differential equations kinda sorta maybe that's not right. I can find the quote but this book I read was talking about it like how we used to only think we could solve equations with fractions and then we discovered special irrational numbers and that was a big leap in how we were able to tackle those problems. So the idea that was conveyed is that fractals are playing a similar role with higher level mathematics.

And that's important I think because ik they are doing something with differential equations in probability. I haven't ever studied it but tell me they aren't?

[solid snow]

actual yap

[mellow spruce]

pi is rational

[neat lintel]

You clearly aren’t

[mellow spruce]

tru

[tall nest]

[jagged oriole]

tikz question: if I have a list of node positions and edges between those nodes, is there a way to turn that into a tikz graph

[ocean harbor]

ask gpt to fix it for you

[verbal karma]

gpt is surprisingly bad at tikz if what you are trying to do is weird or derivate to what people are commonly do

[jagged oriole]

I'm pretty sure I'm trying to do something very normal

[ocean harbor]

I know its bad but once you explain what exactly you want, it can help you

[verbal karma]

well... the problem is that it can't see what happens

so anything position-specific will not work

well... unless that is common

[ocean harbor]

here's something I once asked and it gave me something I want lol

[novel lagoon]

guuys i wanted to learn the math behind 3d rendering , i read some material about 3d to 2d projections , camera angles and other math surrounding it , but i still find it tough to implement
can you suggest me some video or course online which will make me understand the math behind 3d rendering

[river moon]

study linear algebra

[sudden gorge]

Hi, my friend and I are developing a new algorithm and a new number system, but we need some help and are looking for talented individuals. If you think you can assist us, please reach out to me via DM.

[woven hinge]

@tender tulip add me bro

[vocal vessel]

I like that name.

[mental stratus]

add me bro

[woven hinge]

im akira

my account is hacked

[fresh comet]

what happened

[woven hinge]

im using alts for now

[vocal vessel]

Not your name.

Lesser of two weevils.

[fresh comet]

@ocean harbor this account is hacked?

[woven hinge]

yeah

[fresh comet]

by whom

and why?

[woven hinge]

there's a fake discord staff told me to verify an email and now i cannot change my previous email if i dont have a code at least from a shit email

its over

and it says "invalid user login"

[fresh comet]

oh no

[woven hinge]

worst day ever

I got graduation also and im sad as fuck

[small dust]

[fresh comet]

[woven hinge]

does discord let you change your email?

I'm pretty sure I had a phone number added as well

[fresh comet]

idk

[verbal karma]

I think you can

[fresh comet]

now I'm growing concerned that I'll get hacked too...

vero was hacked a while ago

[woven hinge]

it tells me to get a code from the hacked me and I can't access to it

[fresh comet]

now Akira too

[woven hinge]

how im supposed to get a code

[verbal karma]

bad advice but guessing does not hurt

or if you have 2fa, you will have the backup code that can use... I'm not sure

like one time password thingy that you can burn

or something

[woven hinge]

I tried the backup code and nothing has worked

I tried to reset the password and it says that its invalid user

I recovered it gg

thanks discord

[fresh comet]

oh you got it??

@ocean harbor

let's go!!

congrats on your graduation too Akira!

good luck with your exams!

[ocean harbor]

thanks

im gonna report that bitch

fake discord staff

she even told me to pay $200 lmfao

[fresh comet]

lesson learned, I will ignore all emails

[ocean harbor]

[verbal karma]

how can we know that this is not hacker who hack 2 accounts and pretend to solve the hacking problem?

[ocean harbor]

I don't get it

but if you're talking about how this hacker got my account by verifying a random email they gave me

for my main email it didn't tell me that I added a new email

there should be a message that tells you changed the email right?

[fresh comet]

Karnacademy is saying that it's possible in principle that the hacker made/hacked into the account @woven hinge too, and has been the one talking to us the whole time

[ocean harbor]

[fresh comet]

I'm 96% certain they said it in jest though

[ocean harbor]

I see

[fresh comet]

not as a serious thing

[vast wraith]

why is the job market such a scam 😭

[ocean harbor]

https://media.discordapp.net/attachments/1182503419529941164/1226585413011902655/1218065854873341962.gif

[spring falcon]

People from USA: do they usually reoffer pell/state grants every year with the same amount?

[worldly cape]

uh

idk

but what state r u from

[spring falcon]

fl

[worldly cape]

gotcha

ma here

[vast surge]

,av oxil764

[fathom swallow]

oxil764's Avatar

Click here to view the image.

[vast surge]

Your dog is so cute

[worldly cape]

lol

[spring falcon]

It's my father's

[vast surge]

Your dad's dog is so cute

[spring falcon]

yes she is

When i was little she was bigger than me

[worldly cape]

whats ur pronouns bro

[spring falcon]

yes

[worldly cape]

lol

[spring falcon]

jk he/him

[worldly cape]

gothca

r u in college

i see

what year

[spring falcon]

2nd this fall

[worldly cape]

nice nice

imma be a junior in the fall

[spring falcon]

what do you major

[worldly cape]

math

u?

[spring falcon]

math

[worldly cape]

niceee

[spring falcon]

There is only one thing i fear in my math degree

The real analysis course

[worldly cape]

what

whats that

[spring falcon]

rigorous calculus

[worldly cape]

oh

i mean after calc 3 (multivariable calculus) , i was done w/ calculus

[spring falcon]

bruh

[worldly cape]

there is no other calc requirement for me

haha yea

[spring falcon]

But you probably do have real analysis

Every math major has to go through it

[worldly cape]

I dont think i do

oh

lol

do you have a concentration

wait

dude

like

discrete math?

[spring falcon]

Idk

[worldly cape]

proofs based math? is that what ur saying

[spring falcon]

The opposite actually

Its continuous math

But yes proof based

[worldly cape]

abstract math?

[spring falcon]

Yeah?

[worldly cape]

ok

im taking that in the fall

[spring falcon]

Its really just proof based calculus

[worldly cape]

but im studying it a bit now

[spring falcon]

But the problem do get quite hard

[worldly cape]

its a proofed based class, includes inductions, logic

[spring falcon]

Haven't taken that yet

Will probably take it in the spring

[worldly cape]

Gotcha

[spring falcon]

Or next summer or fall

[worldly cape]

It cant be that bad yk

one class

[spring falcon]

I think it depends on the professor

[worldly cape]

u go to college in state

[spring falcon]

Yeah

[worldly cape]

true

nice

do u like college

[spring falcon]

I've been forced to be online for personal reasons so hasn't been fun

[worldly cape]

Oh

I see

I mean i like school for the academic part

Not much the social

I dont think ur missing a huge amount

[spring falcon]

Yes studying math is the best part

[worldly cape]

Plus u save money

Agreed

[spring falcon]

Those Gen eds are so annoying tho

huge waste of time

[worldly cape]

They are

I finsihed all mine

[spring falcon]

I still have some left

[worldly cape]

But yeah not fun but whatever easy A

I did a lot all at once lol

Whatcha doing this summer?

Classes?

[spring falcon]

Calc 3 and self studying real analysis

[worldly cape]

nice dude

im self studying stats and intro to abstract math

didnt know other ppl self studied

during teh summer tbh

for classes imma take next sem

[spring falcon]

Which book you using for the latter?

[worldly cape]

How to Prove It: A Structured Approach, 2nd Edition 2nd Edition

Free PDF online if u google it

[spring falcon]

I used book of proof

but people like that one too

[worldly cape]

I really like this one, I find it easy to understand

This is also the textbook my class will be using

[mint raven]

why is 1 mol = (Avogadro number)^-1?

why reciprocal?

[neat lintel]

wait it is

where did you see this

[mint raven]

the Avogadro constant, N_A, is 6.02214076 × 1023 mol^−1
directly from the SI brochure

[alpine kindle]

yeah so if you multiply that by the number of moles, you get number of particles

which should be dimensionless

[old sequoia]

isnt the no of particles the avocado constant?

in a mol

[alpine kindle]

so in order for it to be dimensionless N_A has to have units mol^-1

[alpine kindle]

yes

[old sequoia]

its dimensionless?

[alpine kindle]

no

[old sequoia]

since its no

[mint raven]

Or N_A could also be dimensionless?

[alpine kindle]

think about it

N_A is a scaling factor from a quantity with dimension 1

to a quantity with dimension 0

[old sequoia]

im very confused

[alpine kindle]

number of moles to number of particles

multiplying by N_A takes you from having units mol to having no units

[mint raven]

Isn’t number * number = dimensionless?

[alpine kindle]

it's easier if we introduce a new unit P for particles

if there is 200P of a substance there are 200 particles of that substance

[old sequoia]

its not like we are measuring distances or time

[alpine kindle]

then obviously N_A has units P/mol

[old sequoia]

should be dimensionless

[alpine kindle]

it's particles per mole

that's what it's describing

[mint raven]

Why can’t both P and mol be dimensionless?

[old sequoia]

however if we let the numbers of particle as a measure then it can have «dimension» i guess

[alpine kindle]

but usually in science people use no unit to mean number of particles

[old sequoia]

that makes sense

so its like you have this much in a mol

[alpine kindle]

yeah

it's "per mole"

that's the unit

[old sequoia]

so it have dimension

[alpine kindle]

yes

[mint raven]

But a mol could just be a number, no?

[alpine kindle]

maybe arbitrarily

[alpine kindle]

it could be
but usually it's treated as a unit with dimension

[mint raven]

That’s even more silly lol

[old sequoia]

well to be fair distance also is artbitrary. i have live 4 unit distance away from you

that units could be km

or miles

[alpine kindle]

take it up with the scientists

[mint raven]

I would if I could

[old sequoia]

since it is something we used to measure something with it has dimension

same with no of particles in a mol

that logic works??

[mint raven]

(the meetings are in French and I don’t speak French) /hj

[old sequoia]

same with temperature

i guess

[mint raven]

Temperature is strange and I don’t understand it

[old sequoia]

me neither lol

but im guessing same logic applies

i can google but i think its a measure how cold something or how fast particles are moving or energy they possesed

[mint raven]

I heard something about “joules per bit” being a unit of temperature

[old sequoia]

bit?

[mint raven]

Yea

[old sequoia]

thats new haha

[mint raven]

Apparently 1 bit ≈ 9.57*10^24 J/K

[old sequoia]

right

then basically joules per bit is K

in disguise

[mint raven]

Yea sure but I have no idea how this is true though

[cloud dagger]

Are there any websites or communities where someone can contribute to amateur maths research mainly for people who are generally interested but are not in university?

[untold sapphire]

Suppose you weigh 60kg on Earth. How many kg do you weigh on the moon?

A. 10kg. In the given context, a "kilogram" implicitly refers to the weight of a kilogram on planet Earth.
B. 60kg. Both a person and a kilogram on the moon are lighter by a factor of 6, so you still weigh 60 times the weight of a kilogram, or 60 kilograms.

[fervent oyster]

C

[wet mortar]

"weigh" and all of a sudden it's implicit

[untold sapphire]

If you don't like the wording you can propose your own

I don't understand your critique

[wet mortar]

wokeness in full effect

[glass peak]

A kilogram in isolation doesn’t impictly mean the weight of a kilogram on earth. But as soon as you said “you weigh 60Kg on earth” it becomes implicit is my reading

[untold sapphire]

Ah, okay. Yeah, I seen now.

[gentle stone]

Actuarial science or mathematics in banking? Which one has the greatest prospect?

[pulsar finch]

book that explains w lambert function?

[raven plaza]

Bprp

[vast surge]

I don't know any specific books, but the subject that you want is called "Special Functions". A quick google search for the Lambert W in particular showed me this chapter: https://web.archive.org/web/20101214110615/http://www.apmaths.uwo.ca/~djeffrey/Offprints/W-adv-cm.pdf. Depending on what you want to do with it it may or may not be useful; also check out the listed references.

[pulsar finch]

tysm for the resources but I wanted to ask aswell for some well regarded references for learning about gamma and beta functions aswell

[old oak]

This is unrelated to the subject, but may I just say the current nickname is one of your best

[vast surge]

Thank you!

I put more effort than I'd like to admit into these puns.

[old oak]

Worth it!

[vast surge]

Gamma function you can find resources on in just about any complex analysis text that covers analytic continuation. It's one of the classic examples.

If it's a graduate level intro CA text, it'll cover it.

Alfhors, Conway, Stein & Shakarchi, Rudin R&C all come to mind immediately as probably having something relevant

[pulsar finch]

ty 💙

[vast surge]

I've only seen the beta function in my undergrad probability textbook (Sheldon Ross 9th edition) in the context of the beta distribution.

Someone else may have a better resource on that one. I imagine it might also appear in some special functions books.

[velvet dagger]

Lol yeah beta distribution was vaguely in front of my face once I'm a probability context but I never remember it or why anyone cares

[old oak]

The Wikipedia article on the W function links to a 32-page article about it, that would be a good starting point (and the article should include references to other works)

[old oak]

https://en.wikipedia.org/wiki/Lambert_W_function#References It's the first reference

[vast surge]

So the website wikipedia cites is dead nowadays, but I earlier gave a wayback machine link to it

[pulsar finch]

I saw gamma function I think as part of one of fresnel integrals I saw somewhere I think, since I dont know contour integration, I just want to read about it more because seems very different to what I have seen so far

[old oak]

Fun fact, I use it at work (in an actual application), because we do Thompson sampling

https://en.wikipedia.org/wiki/Thompson_sampling

[vast surge]

Contour integration is worth learning, then getting annoyed by all the obnoxious computations, then not touching again until it comes up in something more interesting.

Any of the CA books I referenced should cover it in great depth.

[velvet dagger]

Yeah contour integration is the lame part of complex analysis

[vast surge]

(Not sure if you can tell but I've just been grinding annoying contour integrals for qual prep and I am mildly annoyed)

[old oak]

I think it's a very cool method but it would probably lose its luster if I had to do it a lot.

[vast surge]

It is indeed a very cool method that has quickly lost its luster because I've had to do it a lot.

[red notch]

Is it true that the number of natural solutions to $ax+by=c$ is $\lfloor c/\gcd(a,b)\rfloor +1$?

[fathom swallow]

kevinhardy2

[quasi jetty]

To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.

[coarse bridge]

you confirmed it yet?

[old oak]

One of these days someone will have solved Collatz but no one will take them seriously.

Comedy option: this has already happened.

[vivid halo]

it's usually pretty obvious lol

[coarse bridge]

like you mean filtering out nonsense ones by skimming thru it

[vivid halo]

you barely have to skim most of the time, you can look at most crank work for like 5 seconds and be like "yeah a crank wrote this"

[coarse bridge]

fair enough lmao

[vivid halo]

when it's obviously from an actual mathematician sometimes it can just take a while to find mistakes

but people don't usually claim big results without checking it and having other people read it first

like usually it gets sent to a handful of experts in the area to catch "obvious" mistakes and if they don't catch them then such things often get released

and most of them time those papers only get written after lots of conversations with other experts in the process, like much before things get completely written up

[elder grove]

Guys what is n € Z again

[vivid halo]

so that helps catch mistakes too

[coarse bridge]

like ∈?

[elder grove]

Ye i dont know how to do the sign haha

[coarse bridge]

means n is an integer

[elder grove]

I know but dont it mean it can be a negative too?

[vivid halo]

yes integers can be negative

[elder grove]

Yeh but then this question makes no sense that I have

[pulsar finch]

Terry tao i saw the other day that for example said for riemann hypothesis all proofs that do not contain number theory are already discarded iirc https://youtu.be/t908N5gUZA0?si=AKUIk7EAM79THKvf

Minute 58:50

[vivid halo]

no but you can usually figure this out easily

[elder grove]

Show that for all n ∈ Z 5 is a divisor of 2^(3n) -3^(n)

Like lets say I put -2 in its literally gonna be a fraction

[vivid halo]

then probably whatever text you're using doesn't know what an integer is

[elder grove]

Indeed

Thats what I'm saying

They prob meant N not Z

[coarse bridge]

N: Natural
Z: Integers
Q: Rational
R: Real
C: Complex

[vivid halo]

Probably they meant N and it’s a typo

Typos happen a lot

[coarse bridge]

oh you meant instead of Z

yeah

[vivid halo]

Loads of published papers have typos

[coarse bridge]

mightve meant to say Z+ as well

[pulsar finch]

how did this happen

more specifically the equality in the middel when doing induction

[clever slate]

Hello, good day. Please does anybody wish to start a rigorous journey in undergraduate math (using texts like spivak, Axler's LADR, ...). I am about to, and I'll love to have someone with similar interests to journey with.

PS: I'm currently pursuing a math degree (2nd year), but it's not rigorous and satisfying enough.

[uneven tinsel]

I am creating a new set of numbers called Ultra complex numbers which is bigger than set C and denoted by U

[visual breach]

<@&268886789983436800>
They also posted on #discussion

[sudden gorge]

Hi, my friend and I are developing a new algorithm and a new number system, but we need some help and are looking for talented individuals. If you think you can assist us, please reach out to me via DM.

[harsh coral]

Send

I wanna do some

You can use them for everything it just depends if it’s worth using 💀

[neat lintel]

https://youtu.be/xvFZjo5PgG0

[frigid dust]

WHat would be a synonym for asymptotic behaviour

[molten frost]

I'm not sure there is one

And why would you need a synonym of it?

[frigid dust]

For coherence of my thesis

But I'll just either try to avoid it or accept it if there is no other synonym

Thank you!

[storm sage]

long-term behavior

[trim quiver]

Could someone help me out with this one tiny question

I just want confirmation

[ocean harbor]

!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/

[jovial ember]

Not the right channel, but just expand out the 5(5^n - 4n - 1) and add to 16n and u get -4(n+1) - 1

Hi kenzy

How r u

Oh that was like 3 hours ago lol

[granite crag]

https://rintintin.colorado.edu/~vancecd/phil201/Searle.pdf

"My response to the systems theory is quite simple: let the individual internalize all of these elements of the system. He memorizes the rules in the ledger and the data banks of Chinese symbols, and he does all the calculations in his head. The individual then incorporates the entire system. There isn’t anything at all to the system that he does not encompass. We can even get rid of the room and suppose he works outdoors. All the same, he understands nothing of the Chinese"

If someone has memorized every Chinese word, the grammar rules, the exceptions to the grammar rules, and cultural conventions and are capable of holding a conversation in Chinese then I would argue they understand Chinese. John Searle seems to think they don't. Why?

"Actually I feel somewhat embarrassed to give even this answer to the systems
theory because the theory seems to me so implausible to start with. The idea is that
while a person doesn’t understand Chinese, somehow the conjunction of that person
and bits of paper might understand Chinese."

Yes. Just like how no individual neuron understands Chinese but the brain of a native Chinese person as a whole does. I really don't understand what point he's trying to make here.

[pulsar finch]

I figured, ty!!

[storm sage]

Yeah I always thought this argument was dumb and don't understand how it came to be so famous

[granite crag]

Me too, I'm just struggling to steelman the opposing argument.

Like I don't even know what his definition of understanding is

[dire flicker]

I think Searle tries to say you are given a script of every possible conversation you'll make with a Chinese speaker and are just expected to say the things you're supposed to say in Chinese without giving much attention to what they actually mean. Then that would not count as understanding Chinese, it would count as being very good at following instructions.

whereas if you did understand Chinese, you could change your lines in the script and the conversation with a native speaker could still go flawlessly.

[fresh comet]

👋

hello!

[dire flicker]

hi!

[fresh comet]

I know you!

[deep mango]

Right, its not really about understanding the syntactic rules

Its about ascribing meaning to the patterns you observe

(Semantics)

[dire flicker]

from the uni discord or in real life?

[fresh comet]

the discord

I know almost nobody in real life

[deep mango]

Theres a difference between "understanding how to form sentences in chinese" and "being able to act accordingly to a sentence spoken to you in chinese"

[dire flicker]

yeah exactly

[deep mango]

Also i think theres a sort of built in spectrum of the experiment here

Like

He doesnt really go into this but in reality the person in the room is probably putting together bits and pieces of meaning, some of them will be inaccurate extrapolations, some of them accurate founded on feel instead of logical deductions

But is still largely unable to follow any kind of big picture ideas being communicated

And loses out on a large percentage of the details

Meaning and understanding arent "yes" or "no"

[granite crag]

The number of possible conversations is uncountably infinite. It would have to be generalized to a set of rules to truly be complete.

[granite crag]

I think they're isomorphic

They do not understand if and only if there exists a question they would get wrong