#serious-discussion
1 messages · Page 114 of 1
Sounds like info hazard with extra steps
But all the stories about them are fun
Yes, info hazard is the basis for it. Memes and antimemes are both infohazards
Nah its Euclid only
Interesting
My other favorite is the one about the forest which cannot be given a permanent name
what was this one’s name
was Larry the old man or was Larry 096
ah no that’s 106
radical larry
Larry is such a funny name
Oh the other absolutely incredible one is this
https://scp-wiki.wikidot.com/scp-5005
About a town built on a piece of land floating outside spacetime
The SCP Foundation's 'top-secret' archives, declassified for your enjoyment.
Just so well written
SCP jelly thingy
today i thoght
if there was another univers where is it now?
and whe cant see all of our univers
so waht if after the part whe can see is just more un our univers and after that a big black void and after that the old univers
and so it could go on
and infinet circle of universes
What if there really was a fourth spatial dimension
maby
But everything we can observe is stuck in 3 dimensions
but if there was maby there is also a 5 a 6 and so on and on
Like microbes trapped between two panes of glass under the microscope
And stuck in 2 dimensions
you mean "whe are all in a simulation"?
do you know the experiment of 2d billy and 3d sientist?
Flatland?
yes
if whe pass a ball tro the 2d land for billy its just a point that starts little then big and gehts little again
and then disapears
so he cant see the ball just a shadow
and that would confirm your "alian simulation" theory
cus if they are in 4d whe could see them
If we were truly in 4D we should see more parity inverting transformations
no whe are in 3d (1d + 2d) but if there is somfing out there that is in 4d (1d + 2d + 3d) whe couldnt see them
cus whe cant see wahts beond the point of 3d
In 4D, 3D reflections are just rotations utilizing the additional dimension
I think I can make it irl and just call it 4d then?
just like from 3d -> 2d
but for us a 2d world is flat wich in a point the 3d world is 3d but waht could the 4d dimension be
and how would our world look like in 4d?
is it also just flat?
Opinions on where the complex numbers really lie on a graph.
just like Cartesian?
ima just gona put it on paper and it all makes sens
heyy, quick question:
I was taking a look o cases in which newtons method (calculus) fail, and I was told that in order for the precision to be good, the "second derivative should not be too big". Why is that?
Is anyone here a pro in maths but in French?
un pro en mathématiques
,iamstudying
Gave you the studying! selfrole.
#pika
not entirely sure what this is referring to. do you have a bit more context?
if the derivative at the point of consideration is 0 (i.e. if youre looking for a local extremum) and the second derivative exists, then the convergence is linear with error determined by the second derivative
so it will converge slower in such a situation if the second derivative is large
but it'll still converge eventually
Does anyone know any good resources about practical numerical differentiation with regularization? Most papers out there describe the theory of different methods but they don't provide any algorithms. Something like "you have n samples of a noisy function, here's how to estimate the derivative at each point" would be nice.
any numerical analysis book
I've checked a few but couldn't find something solid. Any suggestions?
Yes, in fact this is true forever. Every Geometric Algebra is isomorphic to the even subalgebra of a Geometric Algebra 1 dimension higher
reminds me of how the permutation groups are generated by transposition
The fun series of examples (if I remember correctly) is
$C \ell_{p,0}(\bb R)^+ \cong C \ell_{0,p}(\bb R)^+ \cong C \ell_{0,p-1}$
wraithlord_kograduate
Which starts with Cl_1 having an even subalgebra of R, Cl_2 having an even subalgebra of the complex numbers (Cl_0,1), and Cl_3 having an even subalgebra of the quaternions (Cl_0,2)
What's the difference between permutation and transposition
whe talked about 4d
and i just toght
waht if 4d is another kind of world ore univer and whe are inside of that univer
ore whe take an example on the multivers theory
where whe could say there is a univers in the multivers that is all just in 4d
a “transposition” swaps two elements and that’s it
Gotcha
so teleportation?
uhhh sure, that works lol
...
no
okey
hmm okey so basikly ur puting stuf from point a to point b?
yeah, sort of, but you can’t put multiple things into the same spot
well yes
but thats also interesting
when i could teleport a human and i teleport him intro a wall
waht would happen?
ore whe use any other objekt
well if you did it with a permutation, the particles of the wall would be exchanged
so you would have wall where the human used to be
and human where the wall used to be 
nice
but waht would be other way to transport stuf besides that?
i mean whe could try to destory a objekt intro evry singel atom and transport the atoms to another point
but i like bothe
well ask a physicist
nah i just like making questions
qithout questons there are no answers
so mathe canot be without a question
wat we got goin on
ludi wants to know practical methods of teleportation
practical? as in why we would want to do it? or like workin methods?
sorry that's practical reasons
wat u tryin to teleport for?
if ludi doesn’t ask these questions who will 
he is shouldering the weight of humanity’s future
do you want to teleport?
but would it tho?
so yet whe cant
waht?
you sure it would really be nice to?
sure
i mean i dont need to pay for travel anymore
i just say where i wahnt to go and i geht there
whe could save trilions on traveling
you mean that it will be swapt with me?
well waht about teleporting a human intro a wall?
would he replace the wall?
ore would the wall replace him?
well you question teleportation
so let's talk about it
let's say that if we teleport a man into a wall
yes
that "wall" switches with the man
is it just that part of the wall or the whole wall itself?
ore would the wall and man become one?
that's a good question
hmm well i would say when that it would be just a part
but if whe do manage it now evryone would geht a teleport device
thats like handing out bombs
hmm
waht whe could do is replace ariports with trave teleportation stations
so nothing could go wrong
your scientists were so occupied with whether or not they could, they didn’t stop to think if they should
so there might be issues with the idea of teleportation as you've described it.
well i gusse thats right even if whe can whe dont know waht it could do to our body after a long time
it could give us a new type of canzer
I think it's pretty obvious that if we want a man and a wall to switch, that's gonna cause problems. But for your description of just the portion of the wall switching with the man, a physicist might tell you that they NEED this to happen, and that they DON'T need the man and the wall to become one. Can you see why?
yes i sure can see why
the main question is "waht if"
i mean if you could you wouldnt teleport intro a wall
yes whe dont quit know
if the think of it as teleporting not swaping the man and wall becoming one would be wery much likly
cus i dont know waht schould be there to remove the wall
well there's lots of thoughts on these types of things. A physicist might also tell you that switching a man with a portion of the wall would be impossible, even if we could make the switch.
that sounds about right
but why?
well it wouldn't necessarily have to be a physicist, it could be some other gentleperson with the same knowledge base
questioning to question is fine. but your question has an answer, it's time for another question, why not reveal the answer ya?
here's a thought... what happens to your bloodstream if an oxygen bubble appears in it?
dude i know a fart about waht where talking about and i dont see any big diffrents betwen our answers
well nothing big i say
just a friendly discussion happening 👀
u sure?
well how big is the bubble?
👀
I hope you don't mean an embolism...
I do
i mean if whe say the buble if a big as a blood cell then i would say theres no bigi
teleportation
cus it is important to ask
it is
Okay idk the context I jus jumped in

you can make questions about evrythink even if you know the answer
someone said teleportation and I got excited
it's just good to do

a friend of mine and I go back and forth like this all the time, he's got his phd in physics. it's a fun time
Teleportation...
what about it
well whe took the question waht happens if whe teleport a man intro a wall
LOL
...
Oh ok now I understand
Intro the wall
We totally not shooting a video
I mean well. Unless you can somehow manage metabolism you can't really keep life intact in teleportation like that
Here's a cool idea. Let's say we could teleport this way: Take an object, shrink it to a point mass, then move it through time to our spot in choice and enlargen it. If we could put a protective bubble around that individual, that would eliminate the chance of any "air bubbles" simulatenously appearing in our bodies as a result of teleportation
that comes with problems too tho
also good if i teleport somwhere would the air on the spot i teleport just be all in my body?
But yeah speak of teleportation of gold from the rich coffers oh yeah I'm all about turning it into black holes and point masses
that would be another good question, so like, if we teleport to one spot, would all of the air just move out of the way? I guess it would depend on how the teleportation works
i dont think working with point masses is the right way to go
i mean whe are talking abou swaping atoms not transporting them
Well for that you need to assume all your atoms tunnel through and nothing remains which obv isn't tru at all
Just board a bus. That's how you teleport in real life
Stop living in the Argand plane
I think quantum tunneling is a thing now:
It is obv
well another way whe could teleport is to vaporate our body in all his atoms and dna coppy them and destroy them and rebuild them on another spot
well idk abouy it being obvious...
That is a lame idea ig
I'm sorry to say that Ludi
You just need to copy DNA of one cell
Not all atoms
np it'S all just questions whe dont have the answers to yet
Cells*
we'd somehow have to preserve our psyche
yee sry i forgot 
Also then again. Without prerequisites having DNA is useless
Like you need a whole functioning machinery and differentiated cells to do the job
but also waht would happen to our dna wile teleporting
Or atleast stem cells
i mean whe could mutate
And then again. You'll have lost your memory and you'll be reborn
yee thats also right
that's what I wonder about. imagine having to put a brain back together
I mean we trying to teleport atoms and you're teleporting a whole complex molecule
damm this think is tricky
It's not gonna even remain
DNA is enough big
It stretches long enough
I think six times to the earth and moon... wait I gotta check it
maby
From the earth to the moon*
also waht would happen to your brain if you teleport you hole body
but besides that i would say that it makes more senze to teleport the hole body then to teleport just a part of it and rebuild the rest with new atoms on the oter side
damm
and whe just need i to copy the body
but whe are our brain and not our body
so whe dont know what quick could happen to our brain
and what if people with problems like aids ore cancer teleport?
will it just geht worse?
Well I mean the teleportation discussy seems fun but again there's no point in teleporting half the human body
cya
And since you can't teleport the whole...( idk ask area 51 )...
wait what if whe dont use that to teleport but besides creat a wormhole to the place whe wahnt to go?
that would be much more easy
when whe could know how to make wormholes that is...
"feets", "miles"
Not even gonna read
sorry ti tag you but is it oket if I ask you a question?
Each human cell has around 2 metres of DNA. Let's say each human has around 10 trillion cells (this is actually a low ball estimate). This would mean that each person has around 18 trillion metres or around 18 trillion kilometres of DNA inside of them. The Earth is about 150 million kilometres away from the sun.
Thanks harpre

why is arithmetic this bad ?
how bad?
He dosnt have to numerically quantify it though
He could say something like "more bad than X"
Buy the dip 
Oh my god, I thought that was Workday for a second, and looked at the price.
Are videos like this actually useful? https://www.youtube.com/playlist?list=PLTa2m6WeLW_8oif19IFXvxVJHy_MEM1ZU
It seems like they just want you to shove things into your head without knowing why
how to solve this problem:
"Just use this formula"
the trunk of an elephant?
oh
Hi chat
I present to you
$\int \frac{\sqrt{\sin(x)}}{\sqrt{\sin(x)} + \sqrt{\cos(x)}} dx$
help me
integrate? how bout you integrate yourself into society
u/u+(1-u^2)^.25 -> 1/1+((1-u^2)^.25/u) -> another usub?
looks sorta like 1/1+x
actually nvm
based
Help me guys
no way josé
!help
To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.
Lol
@solar hawk would you have kids?
you can make a decent income child selling
yea
What on earth is that
but tbh probably bad rates unless your kids are max market value
minmaxing your baby's build you get 7500 after ~9months
Mans actually gone clinically insane
thats 27 USD per day amukh
I'm not reading that
I'm gonna read the mathematical model of glucose tolerance curve instead
That bettrr
probably
@solar hawk so i was told that the role was only for people who have been active/very active
Ye
and that the vc was for the minecraft server
Ye
i wanna use the vc for math related stuff
Nobody uses it for that tho
We just talk about math or desmos and stuff
Ok just wait for it then
Yoy willl prolly get it soon anyway
Prolly by the time it comes
what is the requirement for active?
Being active
The bot will assign it
Automatically
what bot?
If you talk in math channels it happens faster
@quasi jetty
workin on it
planning on it
But if you lose the boost you lose access
Whys there army everywhere
ohhh
neato
Pretty untypical for Sunday
well i wanna boost the server but dont got nitro soo :< (ill probably be able to relatively soon)

Just get active role it’s prolly easier
انا ليس بفلسطيني
well i can only insert myself into so many conversations (with math at least)
yeah but then someones gonna roll up and be like ☝️ 🤓 erm math only bucko
and im even less knowledgable in phys than math
cuz im tryna learn math and chem first lol
Only if you're doing it in math-discussion
fair
I feel so scared looking at the army
Or at the police for that matter
oh
I could just be on the disappeared person lists next day for that matter
i wanted to learn arabic for a little bit but i decided not to start learning it
im gonna learn german when i start college
Well. I'm not an Arab native
So I learnt Arabic a little..
For like... the Quran
And for talking a bit in Quranic Arabic
It's very plain and considered without a dialect
YES I WANTED TO FOR THE SAME REASON
I think it's called فصحي
i wanted to study islam but i need to study christianity and judaism first since islam bounces off of it a bit
i at least need to read the torah before studying islam
oh and the gospels
I see
I've studied little comparative religion in my free time
Especially Hinduism and a bit of Christianity
Imma log off anyway
Bye
Not a good time to talk
indeed, there are k! permutations for each combination
so divide permutations by k! and you get the number of combinations (which is the binomial coefficient)
... read wut suremark said
I mean nCr is literally nPr/r!
I have no idea what you're talking about
nCr (“n choose r”) is another way to write the binomial coefficient
I am on this chapter of book I start read now
LIBRETEXTS 
help guys whats 1-1 i need it for my homework
injective
ok
1 - 1 is
ty
$$1 \cap 1$$
help me
suremark
what thing
I forgor
like 139.5 i think
like set subtraction?
literally me when
uhhh what
yk
no i don’t know what you mean
basically

bro really just be yapping
wtf
whatever im going to bed
yappington
Should I skip this chapter?
Hey did you order a PDF from LibreTexts'
Which book is it]
order?
I just pressed the download pdf button
Ik half of the book ig
no nvm
OH WAIT WUT\
I thought u needed to pay
Yayy
I can study celestial mech now ty so much Brandon
Somehow For some reason this book is supposed to be completed in a year ( two semesters )
I'm sure someone can do it two weeks
what is this textbook and what math are you intending to learn
oh I didn’t scroll down
formal logic is a pretty useful thing to learn imo and not hard
and definitely for a discrete math course
I will read it
Is it possible to master from pre algebra to statistics and probability in 1 year? I have entrance exams in one year 😭
Yeah, if you're dedicated enough
sorry if this isn't the appropriate channel to ask, just let me know! I would really appreciate some help.
I'm trying to do grad applications but I'm getting really hung up on the requirement for recommendation letters, especially from math faculty.
- background: my ugrad has been rocky (abuse from some people, had to take a break) and in my fixative autism, take on way more than is reasonable. Now I'm an average B student in mathematics but higher in my other subjects I guess because how much more effort math takes me. I haven't really talked much to the instructors I've had for classes since a lot of them were late grad students or postdocs in other subfields (they're also not at my university anymore) but the professors that I've talked to, about my and their research interests, I wasn't able to complete the classes of because of my break, and on top of that it's been a couple years since talking.
- is it appropriate for me to ask the professors that I've talked to about research for recommendation letters? I'm absolutely terrified of asking because inconveniencing others makes me feel horrible about myself and I'm pretty sure that they'd say no or not even remember me.
- is there really any hope for me to go on in pure mathematics? it's been my passion since my preteens so I'm a bit heartbroken with the situation I've gotten myself in.
- I've also been trying to go through some of the university's faculty's research (though it's definitely difficult). Would it make more sense for me to wait on my applications (so take another gap in my academic history) and talk to some of the professors to see if they'd be willing to work with me on a project?
sorry again for being a downer and for all the text. I'm just feeling really down and lost, and hoping that someone can help me get on a good path. I've talked to my advisors but they're not very helpful. I get the feeling that they think that I'm not good enough because of my university's prestige.
thank you. : )
What did I write here?
.
Best place for this is the #graduate-applications channel (graduate applications, you probably don't have access to that until you get the undergraduate role from #info )
I guess I can give some input. Math grad schools don't really care about "gaps" in your educational history as much as long as you use that time doing something (working, learning, doing research). Lots of students in math grad school are on nontraditional routes. There's no such thing as "behind".
What I will say is that realistically they will care about consistent B's in math classes and recommenders who don't know you very well. In-major GPA and recommenders are the parts they usually consider most. A math phd is really greuling, not much fun, and adversely affects a pretty large proportion of grad students' mental wellness. So this does sound like a situation where taking some time to both strengthen your application (to stand out against the pretty good but not stellar in-major GPA) and to build direction and self-assuredness could be helpful. Meanwhile, it's good to remember that in the US a lot of math phd programs start with 2 years of taking courses (like a masters) which can be a nice transitional time. So the rough stuff isn't all that imminent
Can someone please help me in #probability-statistics if you understand basic probability?
by formal logic do you mean all the various axiomatic/deduction/rewriting systems or just basic predicate logic?
idk if you can validate formal proofs just by shallow understanding of the latter
you'd also need the foundations
What’s formal logic vs regular logic
does anyone know any websites that have information (relatively in depth) on different topics like trig and combs
Yes
"formal" comes from the fact that you study the "form" rather than the "content" of an argument
just like the number "2" is an abstraction from pairs of stuff like "two apples" and "two pears", "formal logic" is an abstraction of everyday logic to turn it into something that can be studied and reasoned about
Thanks
well, you can translate common arguments into predicate logic without going all the way, like using a proof assistant language or something. i think it is useful to learn, to give you a better sense of what rigor feels like
eg you can translate a statement like “x is in the intersection of the family U_i” into “for all i, x is in U_i” and other sorts of things
it’s sort of like unpacking the terminology and seeing what it means at a more basic level, which can get rid of confusion for beginners
CVB/
@acoustic yarrow to answer your question no, the only ap's offered at my school are exclusive to 10th graders, and im an 11th grader and i have not taken those ap classes
??? why would it just be for 10th graders that is silly
because the ap classes replace the regular hs class
they have AP us history and AP english
those are literally the only two ap classes offered at my school
Damn that sucks
You can still the take ap test tho
yeah but thats alot of work to go through with my school counselor when i could just go through my school's cis program
What cis
it's basically ap but better i'll explain
Chs ?
How can it be better if nobody has ever heard of it
if you get college credit from it then who cares
Ig
so the local community college (i plan on spending my first two years there) allows my high school to offer some of their classes for free. so like you can take a college art class for example, and you're literally enrolled in that college's stuff and taking the college class while in high school
What type of credit is “continuing studies” credit?
and it also gives you extra high school credit too
Like yk how some colleges have those programs
i have no idea
Ok
CIS (College In School)
my high school also haves a program that allows you to graduate with an associates and high school diploma
It’s called CHS for us
exactly
hopefully im taking cis courses next year
My school just hates me so I won’t get to take any 😭
my school requires a 3.0 gpa for juniors and 2.5 gpa for seniors and a certain score on the accuplacer tho im not sure what the score requirements for what classes are
Man. I envy you all. I'm here stuck in India. The education system here is just horrendous.
What about online courses
You can get continuing studies credit like me
It’s pretty easy
I see, can you elaborate?
Ye
So like
Yk how colleges have full programs for bachelors degrees and masters degrees and stuff
And all that
Yeah.
But you can also take individual courses
So
Well idk how it works for
People who aren’t in HS
I assume it’s easier
Well I am in HS.
Like the 3rd time we've had this convo.
Oh
But you are probably already more advanced than this
You could try like
Some of those accept international
Ik this one does for sure
The highest level they do is abstract algebra tho
What do you think
Look at this one first
That's alright. I haven't done real analysis + complex analysis and just started with abstract algebra so it would be fine.
Yeah that’s great
You can apply for it soon
The semester is almost over I think
It ends in December so applications will open up then
If you can’t afford it I think they have financial aid idk
I don’t think I’ll be able to pay for it next semester
Is there any prelim test for registration or...?
Also yeah, was about to ask, how much is it?
You just gotta explain your pre reqs for the course you apply to
It’s like 30 bucks or smthn to apply
1500 for a semester
I think that’s like 2 and a half rupees
Thousand
Obviously
Hmm. That's definitely affordable, but I gotta convince my parents.
Oh
*Lakh
Yeah the system here is funky. Around 100K rs.
Core
Oh I meant to submit the application
LOL.
I mean yeah the application cost is around 2500Rs. I thought you were talking about the tuition fee lol.
lol
Nah I can’t do multiplication that big in my head
It’s like 80 rs is a dollar right
Last time I went to India it was 64
Henlo
Well I have visited in between but I didn’t check the rate
I underestimated it to be like early 2000s and got really confused.
lol
It's 83 now. Gotta love inflation.
The rupee is losing faster than the dollar then I guess
Yeah.
Gotta love calculus
lul
Venezuela exists
Hello
How are you doing tonight? 👀
Haha. They should just switch to the dollar now, would save a lot of hassle.
RuneScape gold is more stable then Bolivar
Too lazy to study but also scared of test
Oh wait btw rage
Hmm
To take the exams you will need proctoring
What test if I may ask 👀
Idk if you still get credit if your parents/friends do it
Linear algebra is the most worrying, but also bio ig
Are you in high school? 👀
My plan now is to get into IMO, IPhO or IChO, get some sort of recognition from universities, and get out of here.
IMO?
What year (year? I think it's year?)
9th, freshie
International Math Olympiad.
Icic
13-15
15
We have a different system in here sorry these 9-15 grade system is weird
Oh that's cool!
Same here.
@deep mango thank you! I'll post there as well. : ) makes sense, appreciated! do you have any recommendations for building one's application?
honestly the scariest part of doing a phd is the people for me.
For example I am gonna finish vocational school before I turn 20
So starting uni at 20 🙏
Oh.
No no
Vocabulary
They teach you a trade in the school primarly
After you graduate and pads national exams you get a technician title in your field
Yeah that might be another name
My friend went to a trade school for art
I am eligible for "technician programmer" after I finish this school
Or like a sorta trade school
:o u liek cs ?
Probably best and worst choice of my life
By myself or in this school?
School
In this school last thing I learned was that I cannot depend on the materials provided by the teachers regarding my career
Oh that was way back
Ik
If my parents ask, "How is this going to help you at all in your future?"
What can be my possible answer?
We are preparing for school leaving exams
My parents friend is studying cs at my dream school and she said she is learning about compilers
i forgot what you answered with the first time, how did you learn calculus?
It will look good on applications
That's cool!
Well
I like low level the most
First I watched 3b1b “essence of calculus” on YouTube
Then I started using Kahn academy until my textbook arrived
And then I grinded that during school
Yep. Now I just gotta erode their IIT mentality and hopefully I would be able to convince them.
And then after I passed the test in the back of a book I pushed everything out of my mind and forgot about it
Imma dip, goodnight!
I just learned algebra 2 from a book that was a bit above algebra 2 and then went on hole patching mode
If that makes sense
G'night!
Gn!
So like, it covered some precalc but it didn’t cover it all, so I would just do math and see stuff I didn’t know and search it up and learn it
so you essentually know conceptual calculus but if i threw a random integral at you you couldnt compute it?
Like trig identities
I could
That's pretty much me but for everything before calc.
lol yeah
so are you at like a calc 1,2, or 3 level?
I hate peooke watching me work
in regards to calculus specifically i mean
Well the book covered calc 1-2 and then I watched like 75% of a calc 3 course
So like
Somewhere in calc 3
well thats conceptually
Like I can program gradient descent but I forgot stokes
And computationally
oh cool
But higher math is pretty conceptual
im currently at algebra 2 level computation and conceptually im in calc 1 lol
I mean you don’t usually write out all the pairs of (integer, natural) to prove Z has the same cardinality as N
Ykwim
but idrc about conceptual understandings if i cant actually do the math
where do u see shuri
i know that an integral is just the area under a curve (when it has a bound) but if y you actually threw one at me i'd just stare at it lmao
I never seen anyone else use it
Can you differerwntiate
yeah im siding with eclipse here, the proof is in the pudding
That’s conceptual though
Well conceptual understanding goes hand in hand with computations and abstraction, if you lack in one, you're incomplete with the others.
I guess it depends on what I meant by conceptual
i mean i know the constant and power rule lol
thats abt it
But like when I say “computational linear algebra”, I mean multiplying matrices
Do you know the limit def of a derivative?
Like I took a computational LA course once and that’s what it was like
oh for sure 100%
i do not consider myself to have learned something unless i can pick up a textbook and complete problems from it successfully
and watching videos is not gonna get me there
dy/dx = 2x
Well I mean there was problems
oh yeah i "discovered" it for myself by accident one time (i play around with functions alot)
It's the lim of f(x+h)-f(x)/h as h approaches zero
so you did do calc 3 problems then
Awesome. Now using this you can derive the derivative of any continuous function, so after learning the proofs, just memorise the results. So you're both computationally and conceptually sound.
And forgot a lot of stuff but I remember the important things to me
theres a lot more to it than what i said its actually a long story (but im super proud of myself for it, i essentially accidentally stumbled upon that formula)
Like I can integrate 2d shapes if you give me some bounds and stuff
I could but it was sketchy
Though this does require you to be good at limits.
Like I could but I didn’t understand what I was doing
They didn’t explain the jacobian
It was just there..
yeah no one does in a typical multivar class i think
I could open up the course notes and memorize it again though
i mean they teach you how to do 3x3 determinants
Yeah but I just didn’t understand why it was there
sounds about right
Sounds hard
The equiv linear algebra course covered it
in a nutshell tho i noticed that the rate of change of x^2 was changing and so i noticed that i could manually approximate the rate of change on x^2 between two points it by hand
but that was too slow so i had troposphere help me generalize it and i got f(x+1)-f(x) but that only approximates the rate of change between x,y and x+1,y so suremark essentially called me out on that
so he kinda pushed me a tiny bit which led to me generalizing it to f(x+h)-f(x)/h
then i tested making h really small which led to the derivative of that point
so in a sense i derived (not the math kind) the limit def of a derivative from my initial observation which im SUPER proud of (thanks to suremark and tropo for helping with that)
like the jacobian matrix?
Eclipse to didn’t do my problem :(
matrix of all partials
I mean
oops sorry lemmie go to it
It wasn’t like that they didn’t explain ANYTHING
They just said
When moving to polar form put this infront of the differential
It’s called the jacobian
well im explaining it to you right now
no idea, i only understand d/dx
you dont need differential forms
Ok
amukh do you want to know what diff forms are?
it's the scaling factor when you convert an infinitesimal volume in one coordinate system (dx dy) to an infinitesimal volume in another (dr dtheta)
Something about the dx on the end of the integral maybe?🤔
Oh shit
Woah, that is definitely pretty cool! I remember when I was being introduced to calc I accidentally discovered taylor series by approximating functions in this "cool way" I found lol.
It makes so much sense
What functions derivative is 2x
Work the power rule backwards
The power rule is x^n = nx^n-1
This function is 2x^1
omg yeah it definitely feels satisfying when you have a math question, and you answer it, and discover that your answer is something special like omg
Why? What does the matrix represent
ik the power rule
Like why does the matrix scale like that
so you have a function f(x, y) = (r, theta) which converts cartesian to polar
Jf [dx dy] = [dr dtheta] is the jacobian
if you perturb x and y by a small amount, dx and dy, it tells you how much r and theta are perturbed
I'm perturbed by my headache
Yeah
i could derive d/dx 3x^3 + 2x^2 + 3x lol the power rule and constant rule isnt very tricky and it could easily be taught in like an 8th grade algebra class
Yea do it backward tho
Determinant is the scale factor
Power rule takes you from the original function to the derivative
How do you get from the derivative back
yeah ik thats just the anti derivative
but that is literally all the calc i can do
(for now)
That’s what integrating is tho
anyways i need to go finish my paper ill be back here when im done (theres not much left)
That’s what I’m sayin
a couple of things
one thing is volume change under change of basis
this is useful a lot of times in diff geom
$\frac{d}{dx} x^2 = 2x$, $\int 2x dx = x^2 + C$
amukh1 | Jay, Wraith Obsesseddd
well the matrix itself doesnt represent the volume change, but the determinat of it does
The matrix inflicts it tho
The determinant is the scaling factor from the domain to the range right
Because of what the matrix did
Why
its useful for finding equilibrium states of a system of ODEs
the system of ODEs is the jacobian matrix
it can also be used for generalized versions of gradient descent
Generalized to what?
if the function you are minimizing has multiple variables and some other assumptions
reminds me of some robotics stuff i used to be interested in
say you want to move your end effector by de where e is the position of the end effector
and say your parameter vector is theta
J dtheta = de
so simply do dtheta = J^-1 de
now you know how to tweak your parameters to move in the right direction
actually i think you have to take the pseudoinverse but yeah
close enough
since the effector can't move in an arbitrary direction, J is singular, but taking the pseudoinverse gets you as close as possible under least-squares or something
yea
An interesting thing is that derivatives and integrals are defined strictly independently of each other
ftc moment 
But ftc ties them together
there is probably something else that ties them together too
but thats all i know about
cus question about when you can commute integral and differential operators def comes up sometimes
So |determinant| equals volume just by virtue of obeying the properties of finding the volume of a parallelpiped?
it's linear in each side (makes sense), alternating (degenerate parallelepipeds have 0 volume), and uhhhh the unit parallelepiped has volume 1
that characterizes the determinant
i finally finished it
i didnt put much effort into it tho since i dont really care about forgers tbh
its for my forensics class (it's due tomorrow)
It's because that is what defines the determinant
The determinant requires the outermorphism
The determinant is the scaling factor of an outermorphism evaluated on the pseudoscalar
whsg an outermorphisms
The pseudoscalar is most easily expressed as a parallelopiped
Cool
In this short, I show how outermorphisms can lead to an incredibly simple definition of the determinant. This definition is simple both geometrically and algebraically, and it is incredibly useful.
Discord: https://discord.gg/3Zj59zA2Rg
Patreon: https://www.patreon.com/sudgylacmoe
Patreon Supporters:
Christoph Kovacs
David Johnston
Jason Kil...
In this short, I show how to extend linear transformations to arbitrary multivectors using the outermorphism. The outermorphism extension of a linear transformation is useful for many things, such as an almost trivial definition of the determinant.
Discord: https://discord.gg/3Zj59zA2Rg
Patreon: https://www.patreon.com/sudgylacmoe
Patreon Su...
I'll take the shorts
Watch in opposite order
Bro?
Lol my b
i was in the middle of reading yours lol
Geometry algebra?! lol bro I’m stupid asf u can’t do that
oh boy
Bivector 💀
wraith obsessed
doesn't know what a multivector is
amukh how are you just hearing about this
you bring shame to the wraith clan
I even unsubscribed cuz it was too hard
How?
Cuz
His videos are like 1 star difficulty
Cuz I thought it was linear algebra right
If that makes sense
So I was dissapointed
To see it wasn’t
It’s not tho it’s geometric slyness
Algbra**
There are two ways to look at it, either Geometric Algebra is an extension of Linear Algebra which subsumes it and reframes it,
Or Geometric Algebra is a part of the Linear Algebra toolbox and thus is Linear Algebra
In either case, by using GA to reframe Linear Algebra, it again is Linear Algebra
But he was very clear that he was talking about GA the whole time
He proved the properties of the wedge and Geometric product to use them instead of matrices and determinants on his homework he says
And yes it has vectorspaces
Of course it does
Ah yes one star difficultylooks up bivector
Area*
A bivector is an oriented area
Bro how do you have that definition memorized word for word
You actually fr be knowing GA
A vector is an oriented slice of a 1 dimensional subspace
Which makes it an oriented line segment
A bivector is an oriented slice of a 2 dimensional subspace
what is a line segment?
it's very simple, just take the quotient of the tensor algebra on V by the ideal generated by terms of the form v * v - Q(v)
Which makes it an oriented area
Finite section of a line maybe
Oh yes mhm
Do you require initiation Cali
I'm scared
Sludgy wacamole
Sudgylacmoe looks like Clifford
A line segment is a portion of a line defined by two points within it
Let $p_1, p_2$ be points within the line $l$, so that $p_1 \vee l = 0 = p_2 \vee l$
wraithlord_kograduate
Then the line segment $\ell_{p_1}^{p_2} := {q \in l \mid \norm{q\vee p_1}\infty + \norm{q \vee p_2}\infty = \norm{p_1 \vee p_2}_\infty}$
Is the set of points on the line whose distance to the bounding points adds to the distance between the bounding points.
wraithlord_kograduate
The big red dog??
The Geometric Algebraist
Geometric algebra vs algebraic geometry
Does anyone here own the ti-84 plus ce python edition?
the what
i am losing my fucking mind rn with khan academy
if i get a problem wrong and i click on the explanation is basically says fucking nothing
and i have to solve the absolute riddle of an explanation they give me and try to apply it to another problem
and big shocker i get it wrong
omg i finally solved all the riddles
you wont solve this riddle though
what are all of the nontrivial zeroes to the riemann zeta function?
I don't consider any of the zeros to be trivial.
There's actually a lot more to them once you get to know them.
okay, find all of the zeroes then
No.
Nah I just brushed my teeth.
sphinx allows you passage
oki dont worry ill eat it for you
nom
yummy cookie :>
Does that mean you solved the riddle? Someone call up the committee. World's youngest Field Medalist.
lmao
Maths research contains a ticking time bomb. You just know some day some cracked 14 year old will get a field medal and we'll see a wave of resignations throughout all of mathematics. Naturally, this will not impact larger society in any noticable way.




