So greater the mass lower the acceleration
#serious-discussion
torpid hull
toxic schooner
what
torpid hull
:/
neat lintel
Plz forgiv, I'm shaking the rust off. ^^;
toxic schooner
u cant say that this will be the mass and this will be the acceleration
ur units are totally wrong
a cant be 1/r^2
that would have units of L^-2
torpid hull
It would be GM/r^2
neat lintel
But anything to the power of a negative exponent is just the reciprocal of that exponent. . .
neat lintel
Wait.
But if F = GM1M2 / r^2
why can't we arrive to the conclusion that GM1M2 = m
since F = ma?
torpid hull
O_o
Why
Oh i think you got it wrong
See the force that GM1M2/r^2 give is the force that both bodies with masses M1 and M2 apply on each other
So you apply GM1M2/r^2 on earth and earth does the same
But in case of earth, Mass = Massive
So F= Massive Mass x Acceleration
Acceleration= Force/ Massive Mass
Acceleration= 0 approx
In your case,
Mass = low
F= Low mass x Acceleration
Acceleration= High
neat lintel
Ooooh, I see what I did wrong.
I looked at it as F = Ma and F = G M1.M2 /r^2 and therefore Ma = G M1.M2/r^2
I believe that is a logical fallacy if I'm not mistaken . . .
torpid hull
So whenever someone says what's your importance on this planet, you can proudly respond with I keep this planet at its correct place.
neat lintel
hey, I guess I do!
Now I can prove it using science.
So if Kanye West or any other egoist ever asks me "Who are you." I'll reply :"The man who keeps the world in place, and I can prove it using science. Can you?"
torpid hull
Epic comeback
torpid hull
I looked at it as F = Ma and F = G M1.M2 /r^2 and therefore Ma = G M1.M2/r^2
Yeah that Ma would either be M1 or M2
Depending on what youre calculating the acceleration for
neat lintel
OOOOOO
torpid hull
The body with mass M1 or the body with mass M2
neat lintel
and r^2 is just the radius i.e. the mass of the object, yes?
torpid hull
Distance between the 2 objects
torpid hull
In the case above it would be radius of earth
Because distance is always calculated from centre of masses of the objects
torpid hull
You would make a killing every finals week.
😂
neat lintel
Come to think of it. . .
I would make a killing every finals week.
I know exactly where students fall short in calculus and what problems they end up botching on midterms and finals week.
ugh. . .But no, I'm already doing too much as it is. . .
And I'm balancing it so badly that I'm losing customers on all fronts.
torpid hull
Well you'll eventually manage.
neat lintel
Yeah, it's been 5 months. But, I just finished undergrad. So it's alright to screw up a little.
Besides, I'm moving away from dog walking as fast as I possibly can.
torpid hull
What's your undergrad degree
neat lintel
Computer Science.
Right now I'm on coursera learning full stack development, I learned a lot of theory but not enough application.
torpid hull
Good luck
neat lintel
Thanks!
I actually have a contract to fulfil to make a website.
Its why I'm doing full stack on coursera, you see.
torpid hull
Oh nice.
neat lintel
Guy loved my proposal, but he wants to see more websites made.
My contact inside and I agreed on 4 months to build some stuff.
I don't know HOW I'm so lucky, but somebody on Coursera made an encryption algorithm course.
I itemized encryption and had NO idea how I was gonna learn it. XD
torpid hull
Alright gotta go man
neat lintel
What real analysis textbook did yall like most?
neat lintel
I haven't gotten to Analysis yet, but everybody always recommends that Blue and Yellow one to me. You know the one.
fair mural
i’m aware that it’s a joke, but it’s funny that i can think of two analysis books that fit that description off the top of my head
neat lintel
The blue and yellow one with the minimalist cover.
toxic schooner
What real analysis textbook did yall like most?
i was reading though apostol, and i loved it
its very nice
(apostols analysis, not calc)
sick burrow
model theory is so cursed
like
Compactness and Lowenheim-Skolem are two of the most cursed and morally false theorems I've ever encountered and they're used in like every proof
bronze pelican
The picture is ultrafilter magic
bronze pelican
dense belfry
you have to think about the stone space of your theory (or rather the lindenbaum tarski algebra associated to it)
sick burrow
you've never been wronger gamma
That's a strong statement coming from you
I've seen the proof that compactness is just topological compactness of stone spaces if that's what you mean (though I don't remember it off the top of my head)
And ok maybe from the right perspective the theorems make sense. But like their consequences are so stupid
"Given any integer I can find a larger integer QED there exists a nonstandard model of PA" - statements dreamed up by the utterly deranged
What is picture that you have where these theorems make sense
dense belfry
The picture is FOL has limitations in it's expressibility
And these theorems are capturing that failure
You can't finitely say that a model of PA is standard is what that statement means
If you want logic to work how you want it to you need more expressibility
And there are logical systems like that
Lol my keyboard isn't working rn
I'll give more details later I guess
But also I'll give you a sheaf theoretic interpretation of the completeness theorem if you want
Because I think it's really nice
light needle
yes i want that
sick burrow
Same
sick burrow
What's that
light needle
sick burrow
Ooh looks interesting
Not sure if I'll have the time though, at least not for a while
I'm doing an REU this summer and then I'll have grad school applications
light needle
oh i see
sick burrow
Oh is this like HoTT stuff
dense belfry
They are very intuitive
And not as scary as you probably think
I'll show you some natural sheaf structures that arise in logic later
About to leave my house
empty stratus
https://www.math.ias.edu/~lurie/278x.html
KIWF
empty stratus
And not as scary as you probably think
I'll believe it when I see it. xD
(is terrified)
neat lintel
(apostols analysis, not calc)
Ahh nice!
dense belfry
@light needle read that with me
light needle
<@476552746581884958> read that with me
Sure
light needle
Well it’s summer so p much all the time oof
bright hill
What real analysis textbook did yall like most?
(that's not exactly a lie so I haven't read any other analysis book 
)
hushed turret
and you're on chapter 2 
muted venture
Does anyone know any sites where i can find some 3x3 matrix problems so i can practice LU decomp?
vivid halo
I'll believe it when I see it. xD
if you know what functions are you can understand what a sheaf is
seriously it's not that hard
fair mural
tell me right now then 
sleek wing
"it's not that hard"
fair mural
wikipedia makes it seem otherwise
neat frost
"it's not that hard"
WEW
sleek wing
my notes are making it seem otherwise
neat frost
Noted
fair mural
alggeom
vivid halo
wikipedia makes it seem otherwise
this is wikipedia problem not sheaf problem
bronze pelican
Quantum sheaf cohomology
fair mural
Quantum sheaf cohomology
maybe in 3 years at best
worn garnet
Is anyone familar with the process of academic awards ? I have like a ~2.8 yet I was given award by my math depart for academic excellence the dean called me hardworking why even bother handing me something at the point my class rank isn't even that high
limber thunder
it's relative to every particular prize really, there's no general criterion for "academic awards"
surely your department has specific criteria for that excellence award
either that or the dean simply has their reasons to consider you for that award
worn garnet
I had managed to improve over a couple of semesters I was told by my academic advisor I qualifed but like I haven't even taken any grad courses yet
nor have hit every undergraduate math course
limber thunder
it's relative to every particular prize really, there's no general criterion for...
that's also why it's hard to say whether e.g. such an award will have weight on your CV or admissions — but I guess it's worth mentioning
limber thunder
I had managed to improve over a couple of semesters I was told by my academic ad...
that's fine, I doubt people expect (most*) undergrads to take grad courses anyway
which year are you in
worn garnet
- I learn and move at a very slow pace every other person in my program is already at grad level by now
worn garnet
which year are you in
Senior
limber thunder
oh
worn garnet
I'll have to do summer semester and then i'lll be done
worn garnet
that's also why it's hard to say whether e.g. such an award will have weight on ...
Oh that reminds I acutally got a another award form last semester it was the Shabanni book fellowship
worn garnet
@limber thunder + the dean callled me a hard-working student I was told that at least in the world of physics/tcs recommendation letters that word can be a kiss of death
limber thunder
it might be if your grades aren't that good
I can't say I know much about physics academia though
aside from what my friends tell me at times
worn garnet
I can't say I know much about physics academia though
i'm actually aiming for math grad school of some kind then industry
sick burrow
this is wikipedia problem not sheaf problem
Marh server repeatedly saying sheafs are simple and easy to understand while also not explaining them
sick burrow
light needle
I’ll explain once I get to desktop
sick burrow
Sure you will
fair mural
Marh server repeatedly saying sheafs are simple and easy to understand while als...
this but unironically
if something so complex sounding is actually so simple to understand just explain it yourself lol
light needle
i mean its not complex sounding, and no one has any obligation to explain it to you.
that being said ill start my explanation
fresh oriole
consider a topological space, and a set of all possible pairs (U, f) where U is an open set, and f is a continuous real function on U
all those pairs are a sheaf
light needle
So a sheaf is suppose to model functions that are determined "locally" on some space X
so something like continous functions to R would be a sheaf, as continuity is a local property.
Lets make the exact defintiion
Let $X$ be a topological space, a presheaf of abelian groups (or rings, or vector spaces, etc) on $X$ is
-
An abelian group $F(U)$ for each open $U\subset X$
-
For every $V\subset U$ of open sets, we have a restriction map $\rho_{UV}:F(U)\longrightarrow F(V)$
and you need $F(\varnothing) = 0$, $\rho_{UU}= id_{F(U)}$ and $\rho_{VW}\rho_{UV} = \rho_{UW}$
flat harbor
enumerate
light needle
im fixing it smh
flat harbor
uwu
fathom swallowBOT
JohnDS
light needle
Ok so i want you to try to interpret this rn
wrt what i said about modeling function spaces
who asked for the explanation again lol
@sick burrow
grizzled grove
F(U) has to be abelian group or it can be ring or vector space as well?
grizzled grove
Why would someone attach so many rings on each open set of topological space
Is it like someone wants to do smooth manifolds shit?
light needle
well the uses of it comes in later, but roughly speaking it allows you to measure the difference between what something looks like locally vs globally
sheaf cohomology makes this precise but this isnt something we need to worry about rn (that one is actually hard lol)
for now we will just try to understand what this means
and why this is modeling function spaces
light needle
well i want you to tell me your intuition
grizzled grove
About what
light needle
what is F(U) suppose to represent, what is rho_UV suppose to represent etc
sick burrow
hm
grizzled grove
F(U) is supposed to represent locallly a structure better than the just topological space available on X
Second condition is just way of passing from bigger set to smaller subset etc
hushed turret
i mean, im kind of led on by what you said about global/local but id guess the restriction maps are a way of zooming in on what your object looks like on a smaller scale
sick burrow
so like would F(U) be for example continuous functions on U?
light needle
sure
so yeah like, F(U) is supposed to be some space of functions
and then rho_UV is supposed to be restriction in the usual sense
ancient flame
F U
light needle
and an example? let X be any top space and F(U) cont functions U->R
grizzled grove
But when we are doing such general definition what other options we have for F(U) except for continuous or smooth or analytic etc type funxtions
light needle
this is a presheaf of R-vector spaces right
sick burrow
right
light needle
the rho_UV ofc are restrictions
and think about why all of what i asked makes sense
like rho_UU=identity
or F(empty)=0
or composition working
sick burrow
yeah that all makes sense
grizzled grove
this is a presheaf of R-vector spaces right
R vector space? Isn't it just Functionals. Continuous map from U to R
light needle
sure but it forms an R vector space under pointwise operations right
sick burrow
doesn't it form more than a vector space?
you have pointwise addition, multiplication, and composition
sick burrow
why not?
grizzled grove
Okay yeah..they do have this nice structure.
light needle
U->R
light needle
yeah like most function spaces have some type of nice structure
this is what a sheaf is trying to capture and like
generalize
so we comfortable with presheaf?
grizzled grove
Okay you got a nice R algebra for each open set and there is some compatibility as well
light needle
yeah you can do the restriction of functions and this is an R-alg homomorphism
from F(U)->F(V) where V<= U
ok so so far we kinda only capture that you are some type of functions
we dont necessarily capture a, local property so to speak
grizzled grove
We don't have R alg homo yet I think
light needle
like continuity is special in the sense that if you know something is locally continous everywhere its globally continous right
and same for most of the special type of function you know probs
so lets try capturing this
grizzled grove
What is something which is locally true but not globally?
light needle
boundedness for example
if you take F(U) to be all bounded functions U->R for example
boundedness locally def doesnt mean boundedness globally right
grizzled grove
f(x)=1/x is not locally bounded right?
I kinda want some concrete example of this phenomemnon
I think orientation is not local phenomenon? Right. So we can't talk about it.
light needle
So let $F$ be a presheaf on $X$, and ${U_i}_{i\in I}$ an open cover of $U$, we have 2 things we want now
-
Locality, if we have $f,g\in F(U)$ and $f|{U_i}=g|{U_i}$ for all $i$ then $f=g$ in $U$. Here $f|{U_i}$ is shorthand for $\rho{UU_i}(f)$.
-
gluing, if we gave a collection of functions $f_i\in F(U_i)$ and we have they agree on intesections, i.e $f_i|{U_i\cap U_j} = f_j|{U_i\cap U_j}$, then there is a $f\in F(U)$ with $f|_{U_i} = f_i$ for each $i$.
fathom swallowBOT
JohnDS
light needle
ill let u guys absorb this
grizzled grove
This feels like some unique analytic continuation kind of stuff
light needle
f(x)=1/x is not locally bounded right?
if you want take like, id:R->R, this is locally bounded in the sense that around each point there is a neighborhood of which it is bounded in, but obv it is not globally bounded
grizzled grove
if you want take like, id:R->R, this is locally bounded in the sense that around...
Thanks
light needle
is condition 1 not redundant?
Good question let me find 1, its honestly usually 2 you need to worry about
sleek wing
pasting theorem type beat
flat harbor
well definedness isnt smth u can always take for granted
grizzled grove
But i wonder how would we remember this definition as easily as we remember definition of group or ring
light needle
yeah like keep in mind while the intuition for these are a generalization of function spaces
these objects can be as abstract as you want
ok we will put a pin in the counter example for part 1 for now
cause i dont wanna go through my book searching for one oof
light needle
nice
but is it clear how these like, describe function spaces?
the two sheaf conditions,
dense belfry
Okay so locality is a quotient condition
grizzled grove
No it will be clear to me if we know of some presheaf which is not a sheaf
light needle
try F(U) = bounded functions U->R as i said before
check it doesnt satisfy the gluing condition
dense belfry
So let's just assign to every open set the same set of global functions
So when you restrict to an open set, you will have many copies of the same functions
When you restrict in a sheaf, locality quotients the set of sections (the functions on the open set) so copies are identified
grizzled grove
try F(U) = bounded functions U->R as i said before
You mean taking the identity function and then since we are unable to find globally bounded function so point 2 is not validated.
light needle
yeah
dense belfry
So in particular you can just take the presheaf which assigns to each open set the set of all globally continuous functions on a manifold (in manifolds you can always extend a continuous function on an open set to the whole manifold) and interpret that set of functions as the restriction of the function to your open set
And that will satisfy gluing but not locality
grizzled grove
Well then we are kinda leaving out lot of interesting things such as bounded functions space when we go to sheaf. But Do we have a good example of something which is not a presheaf as well?
dense belfry
SSK do you understand my example?
Oh John I told you I would tell you about interpreting the completeness theorem as gluing
So here's the sheaf setup
light needle
yes but prob not today im near the end of my sleep lol
hushed turret
i am long past the time to be awake
light needle
fair lol
hushed turret
trying to make sense of this but my brain is not in gear lol sorry
grizzled grove
Let me try to say what i understood. You mean to say we cannot extrapolate to the full manifold? Because if we can then can we end up in two different functions?
light needle
but yeah like the upshot is sheaves are just generalizing what it means to be functions that can be determined locally
dense belfry
No I'm saying that that's just an example where locality isn't satisfied
dense belfry
Hmm actually maybe this example doesn't work
grizzled grove
The point 1
dense belfry
hushed turret
we do a little trolling
dense belfry
There's a slight subtlety I have to think about here lol
light needle
i mean to be fair also in practice we never really worry about condition 1 lolz
its just condition 2
ok
my book has one
hushed turret
bronze pelican
👀
grizzled grove
I think point 1 may make difference in non nice topological spaces
bronze pelican
What we doing here
hushed turret
explaining sheaves
grizzled grove
I think point 1 may make difference in non nice topological spaces
Like not Hausdorff etc
dense belfry
Okay so two functions which agree on every open subset but don't agree globally
light needle
Suppose $X$ is a riemann surface. let $$F(U)= O^\star(U)/ exp(O(U))$$ $O^\star (U)$ is the holomorphic functions $U\longrightarrow \bC^\star$ and $O(U)$ the usual holomorphic functions
fathom swallowBOT
JohnDS
bronze pelican
A sheaf is a generalized covering space 
dense belfry
light needle
this doesnt satisfy locality
you need to do some modding out ig
to violate condition 1
light needle
yeah i didnt really want to go in my book cause this might have too much like
geo prereqs
oops
bronze pelican
**JohnDS**
hushed turret
Suppose $X$ is a riemann surface. let $$F(U)= O^\star(U)/ exp(O(U))$$ $O^\star (...
i cannot really parse this, but thanks for trying
grizzled grove
But what is a good example of not a presheaf
grizzled grove
**JohnDS**
Exp() here must be some crazy stuff
light needle
its just complex exponential pointwise
bronze pelican
This is a pretty weird class of functions
light needle
its like, how far away are my functions away from having a log i guess
dense belfry
Okay so imagine the topological space consisting of the natural numbers plus 2 points at infinity
bronze pelican
Nonvanishing holomorphic functions modulo exponential of holomorphic functions
sick burrow
also r <@381174875215364109> <@907309366502359170> still around
sorta
I'm around but spacing out
bronze pelican
Idk how to think about this
light needle
its like, how far away are my functions away from having a log i guess
probably this
dense belfry
So the situation with this is I want each natural number to be an open set
bronze pelican
probably this
On any simply connected domain, every nonvanisheing holomorphic function has a holomorphic logarithm?
light needle
hmm good question i think this is true?
hushed turret
anyway im gonna go to sleep it's 1:44 AM 
light needle
like yeah its like, integrating some closed form
hushed turret
gn yall
light needle
which is exact bc simply connected?
flat harbor
sweet dreems
grizzled grove
Are we all nocturnal humans here
pastel temple
not by choice, not by choice...
bronze pelican
This is actually an equivalent condition for the domain to be simply connected. If every nonvaninshing holomorphic function has a holomorphic logarithm
light needle
interesting so F is somehow measuring number of holes
bronze pelican
I see
dense belfry
Have a good night twice
light needle
too bad its not a sheaf we coulda done some fun stuff with it
bronze pelican
Its not a sheaf?
light needle
yeah it doesnt satisfy locality
light needle
as a counterexample to locality
bronze pelican
Whats locality here
light needle
if u agree on a open cover on U then u agree on U
bronze pelican
interesting so F is somehow measuring number of holes
Yeah if you think about it, whats a hole? When you can map a circle to the unit circle in C. And thats not gonna have a holomorphic logarithm. So 
light needle
yeah this also intuitively makes sense
dense belfry
I cannot think about such things
dense belfry
grizzled grove
It's requiring quite geometric intution
But what is difference in locality and gluing
light needle
gluing tells you you can glue together local info, locality tells you this will be unique
grizzled grove
I see
dense belfry
Locality is saying "if a global section exists, then it agreeing with another global section on an open cover implies they are the same function", gluing says "if I have a bunch of sections defined on a cover and they agree on intersections, then there is a global section obtained from gluing things together"
dense belfry
Yeah when you take values in rings
light needle
sure a space with a sheaf of rings is called a ringed space
bronze pelican
if u agree on a open cover on U then u agree on U
How does this fail for F?
dense belfry
So in the case of logic the rings you take value in are boolean rings
light needle
so take a non-simply connected set and an open cover by simply connected sets
every f agrees on the restrictions cause they r 1 on the restriction right
but not every f is the same ofc
grizzled grove
Sheaves are used in logics too?
light needle
yeah
bronze pelican
That makes a lot of sense
grizzled grove
I thought it's just algebraic geometry oriented
light needle
yep
lavish isle
chef
bronze pelican
Sheaf chef
light needle
infact one of the fathers of like, category theory, maclane, wrote a book on using sheaves in logic
so it was kind of there from the get go
bronze pelican
Its like the opposite of a sheaf. It captures global data
light needle
yeah its a wierd object
dense belfry
So open sets get assigned to the boolean algebra of formula modulo equivalence on the set of complete theories that are described by the open set
grizzled grove
But ultimately aren't we just doing some sort of generalized functional analysis with abstract objects
dense belfry
Boolean algebras/boolean rings are exactly associative algebras over the field with 2 elements
bronze pelican
So long as we are talking about sheaves, I like to mention a really good example of a sheaf is a covering space
dense belfry
So that's what the sheaf you get is
light needle
oh this sounds cool emma
bronze pelican
So long as we are talking about sheaves, I like to mention a really good example...
Sections are actual sections of the projection map
dense belfry
You can also have your sheaf take values in algebras over a complete boolean algebra (which is what boolean valued models does)
light needle
espace etale 🙂
grizzled grove
dense belfry
Sections on an open set are consistent theories with respect to that open set, global sections are consistent theories
Completeness let's you glue locally consistent theories together to get a globally consistent theory
Stalks in this interpretation are just the boolean algebra 2
They aren't this in general though
Lol
I'll give more detail when John isn't tired
light needle
yeah oop
dense belfry
Anyway John imma hit you up for categorical logic in a couple of days I think
light needle
nice yeah
dense belfry
I also have a really cool book called toposes and local set theories
That we can look at a little
light needle
do u like the idea of reading outloud in vc, thats how i usually do this stuff, leads to richer discussions
grizzled grove
Where are number theory discussions 🧐?
bronze pelican
grizzled grove
Is Keith conrad teaching ?
light needle
yeah i think so
grizzled grove
Nice
grizzled grove
Idk they will upload on yt
Like they did for previous
I watched a few lectures from 2020 version I think
light needle
Nice
bronze pelican
Yeah maybe email them asking for an update
light needle
Yeah I’ll do that before I go to sleep probs
still lance
What do you guys use to take notes with? I've been using physical journals and while they've been fine I've been accumulating a lot of them for various subjects and topics. I feel like physically writing helps me remember stuff, but I was interested in any recommendations in general or stuff related to stuff used to take notes for math. I've also had the same issue with doing problem sets which have led me to accumulate notebooks. I'm interested in any recommendations or any organizational tips.
pastel temple
a4 paper and lots of sheet protectors
grizzled grove
Scan them all and keep it in online drive
velvet dagger
Yknow they changed the date if the event
What
The website still says June 6-12, when is it now?
Oh hmm
still lance
a4 paper and lots of sheet protectors
like should I take the pages out the journal and use sheet protectors?
how would I organize it?
pastel temple
oh, for what you've written so far i don't know, scanning and printing them sounds inefficient but i lack sleep and i can't think of anyhting better
for new things that you will write from now on, having free sheets of paper that you can organize however you want is pretty convenient tho
still lance
oh, for what you've written so far i don't know, scanning and printing them sou...
Some stuff I've already written down, but I was also asking about in the future because I got a lot of topics that I plan to study
still lance
for new things that you will write from now on, having free sheets of paper that...
how would I organize the sheets of paper since I would be accumulating all of these sheets?
how do you properly store them?
charred mortar
Plane tickets in general have become far pricier
pastel temple
how would I organize the sheets of paper since I would be accumulating all of th...
in a uhhh
charred mortar
I’ve seen flights that were literally over 5x what they used to be
still lance
in a uhhh
wouldn't it create a similar situation in which I would have a bunch of binders instead of journals?
vivid halo
What do you guys use to take notes with? I've been using physical journals and w...
loose leaf paper and then type up the parts that are actually worth saving
still lance
loose leaf paper and then type up the parts that are actually worth saving
how would i type up my math notes should i learn latex to do that?
also how would i organize it across multiple accounts if I type it up?
vivid halo
yes learn latex for this
most people either use overleaf, which is an online latex editor, or download a latex editor to use offline
overleaf is kinda slow and annoying but it's nice if you have multiple people working on the same document and want stuff synched to the cloud
latex does have a bit of a learning curve but it's not that bad, you get good and fast with it with some practice
this site helps: https://detexify.kirelabs.org/classify.html
since a lot of the learning curve is just knowing what the right command is for common math symbols
still lance
this site helps: https://detexify.kirelabs.org/classify.html
thanks for the help
i was just wondering if you felt there was a difference in your ability to learn and grasp concepts with typing things up vs. physically writing notes
i feel like part of the reason i haven't made the jump to taking online notes was because i've had good results with writing it down although i definitelt plan to look into this and evaluate how it fits me
vivid halo
yeah there is definitely a difference for me
the main benefit of handwriting instead of typing in terms of retention is that handwriting forces you to slow down, so you're processing the information at a more reasonable rate
that said for most things I feel like I have to do both handwriting and typing. Usually handwriting as a first pass and then typing as a second
the benefit of typing things carefully in latex is it forces you to write something fairly polished and complete, with the benefit that you end up with documents that you can share with people if you finish them
also has the benefit of being able to edit easier
still lance
that said for most things I feel like I have to do both handwriting and typing. ...
so do you usually handwrite your notes and then type them up?
also does this apply when you're doing psets in which you write them and then type it up?
vivid halo
when I have to do psets I just type them up from the beginning
since it's a lot easier to be able to go through and edit your solutions while you're working on them
and yes depending on what papers/books I'm working through I'll usually handwrite notes and then type them up as a second pass
bronze pelican
New emote concept: blursed sully
neat frost
Blursed surly
charred mortar
blushed sully
vast surge
New emote concept: blursed sully
What would blursed sully look like?
light needle
blursed i imagine
bright hill
Ah yes, the floor is made out of floor
unreal ore
69 looks nice. 420 also looks nice. But can this be called "nice"?
,w Famous people who born on 4/20
fathom swallowBOT
deep mango
neat frost
Andy Circus
fair mural
oh god
brave wraith
this is correct right?
unreal ore
Yes
brave wraith
ok
unreal ore
Yes
torpid hull
yes right?
Yes.
bronze pelican
this channel lmao
i love this channel https://www.youtube.com/shorts/MOYB1JUhWWY
I cant stop laughing
cyan goblet
math edits are hilarious
bronze pelican
https://www.youtube.com/shorts/DDtoQkCFj-c
@jovial ember you gotta watch this
surreal sapphire
why the copyright of pursuingstacks
cyan goblet
meme theft is no joke these days
bronze pelican
I cant get over "The tale of Naruto Uzumaki" played while flashing through images of Grothendeick
hushed turret
that is brilliant
gray loom
Is anyone just able to rewrite this or something
I have no idea how it's wrong
I've done all kinds of little tricks to get the numbers to match with the video that tells me the answer
It even tells me the formula
But I have no idea how it's wrong
It's impossible
I can't tell if the video is wrong and I'm just going fucking insane
The first selection should be .00514 but it's just not
And the total should just be .0255 but it is obviously not
toxic schooner
https://youtu.be/K8EQ626Lr3Y
interesting channel lmao
toxic schooner
FUCK NOOOOOOO
fair mural
time to delete 15 messages
toxic schooner
ok i have 69417 now
what do i do for my 69420th message (Someone ping me with something nice)
maiden nest
3n+1 = 1
frigid lark
Well I missed my 1337
surreal sapphire
shyshu never posting again waiting for a good 69420
sick burrow
Talking about mathematical logic while cuddling call that forking and spooning
bright hill
shyshu never posting again waiting for a good 69420
@toxic schooner post blushy sully
alpine kindle
bright hill
ally is here 
neat lintel
this is correct right?
fun fact : log_a(b) = b^a
hushed turret
hi ally
how r you
odd narwhal
fun fact : log_a(b) = b^a
What
neat frost
neat lintel
No I did that wrong. . . .
Fun fact : inv(log_a(b)) = b^a
Because logs are just the inverses of exponentials.
neat lintel
I haven't touched calc in awhile, but I remember that from self-study.
that makes no sense
Okay. . . .?
neat frost
Fun fact : inv(log_a(b)) = b^a
If you define a function f(x) = log_a (x) the inverse is a^x, not x^a
neat lintel
Ahhh~ gotcha, misremembered.
Wait, I remember now.
@neat frost That's not quite right either.
I forgot the log_a(b) = y and therefore it should be b = a^y
Inversions are just taking the outputs and swapping them with inputs with the inverted function.
So if you had f(x) = log_a(x) your input is x and your output is why.
y*
meaning, the input of its inverse b^(y) gets the ouput x.
toxic schooner
<@416884645976604685> post blushy sully
fuck no jfc
never
i guess i will just do a catthink for the 69420th message
dont have any other ideas, and no one pinged me with a good one
surreal kindle
according to cnn 80% of Russias population support the assault on Ukraine
They must be held at gunpoint or something xd
bright hill
according to cnn 80% of Russias population support the assault on Ukraine
I think discussion of the russion-ukrainian conflict is still prohibited
surreal kindle
I think discussion of the russion-ukrainian conflict is still prohibited
oooh
frigid lark
Maybe confess to Slurp as your 69420th message
bright hill
neat lintel
I think discussion of the russion-ukrainian conflict is still prohibited
smart, honestly no good can come from talking about that now at this juncture in this chatroom.
neat frost
neat lintel
As long as the admirer isn't abhorrent, just take the free ego boost.
neat frost
Shyshu is too old for me anyway 
neat lintel
Bad luck for Shyshu, I guess?
On the bright side : An older guy likes you. Good for you! (Edit: Older man sounds weird. . .)
fair mural
Shyshu is too old for me anyway <:whatcanisay:916931197794394162>
you and him are like the same age
neat frost
you and him are like the same age
Nah he’s older
frigid lark
what age gap is ok?
neat lintel
what age gap is ok?
I mean, older guys who attract younger women seem to attract specific types of younger women if Robert Greene or kidology are correct.
neat lintel
you and him are like the same age
Never talk about a ladies age! smacks hand with spoon
Okay, a movie that finally has actual code ; I'm totally watching this.
neat lintel
Hey, meme at my parents and aunts, they are the ones who drilled this into me. lmfao.
neat frost
boomer
bright hill
Good morning slurp
neat frost
Good morning DarQ, how did you sleep?
neat lintel
I'm awake because insomnia woke me up at fucking 3 am.
And now I'm hopped up on Vyvanse and adderal.
neat frost
I'm awake rn by sheer force of will and obscene amounts of caffeine
You need more caffeine then
bright hill
Sotrue
bright hill
<:flonshed:629835071465062410> boomer
Wait
Does that mean I'll be a boomer in a few days?
neat frost
Yesh
neat lintel
Yo, zoomer @neat frost stop overusing that term, or its eventually going to mean nothing.
neat frost
Don’t tell me what to do normie
They’re all boomers
And they must become self aware
neat lintel
Don't tell me what to tell you what to do, freak.
neat lintel
WHAT!?
neat frost
WHAT DID YOU JUST CALL ME, NORMIE
neat lintel
I CALLED YOU A FREAK, FREAK.
neat frost
FCKIN NORMIE
bright hill
If we're all boomers than you're a child
neat lintel
HECKIN FREAK
HMPH
Also, since we're not allowed to talk about the Ukraine crisis here : https://www.youtube.com/channel/UC5_npTvQVSZ28Kc8wvffPew watch this youtube channel for updates.
Mr. Friedman has taught me a lot about geopolitics with this channel.
Though, his videos are on the lengthy side.
neat lintel
If we're all boomers than you're a child
We ain't boomers, we're bloomers : https://www.youtube.com/watch?v=n6RoesnNDBM&ab_channel=MonkMode
wary relic
Hi, I'm writing a report about quantum computing. I know this may be a little hard to understand without context, but does the explanation/derivation that I've given here seem clear? I'm specifically referring to how the function in the power of -1 gets turned into +-
neat lintel
Hi, I'm writing a report about quantum computing. I know this may be a little ha...
LMFAO U(H | 0)H
Also, whoever did that Latex should be fired, one left '(' bracket and 3 right ')' brackets???
wary relic
Just realised that the last line is missing the lhs
wary relic
those are angle brackets used to indicate quantum states
they're basically the equivalent of vector notation
wary relic
it's not a class tbh, it's my CS dissertation
neat lintel
Masters or PHD?
wary relic
thanks
neat lintel
Yeah, I've got some studying to do.
bright hill
toddler.
neat frost
How's your back, old man?
bright hill
you need calcium for a back as healthy as mine
neat frost
no
neat frost
you need calcium for a back as healthy as mine
no witty comeback needed for such a dumb message
bright hill
I was playing on your level 
neat frost
no
torn willow
Hi, I'm writing a report about quantum computing. I know this may be a little ha...
Well yea seems clear enough. Btw what does it mean to multiply two kets
bright hill
<:hmmCat:831508801646755850> no
nice
torn willow
Nvm it's tensor product
neat lintel
thanks
Got a github or bitbucket to share? Can use a shot of inspiration for code, you've given me my shot for studying math believe it or not.
wary relic
I do but there's not much on it
neat lintel
Really?
wary relic
I do have what I'm currently working on
it's called shors algorithm
let me send you that
pastel temple
speaking of algorithms
wary relic
Aaaa~ so you're specialty is making algorithms.
pastel temple
is there a formal theory of algorithms?
wary relic
yes there is a somewhat formal theory
torn willow
Oh nice you implemented shor's
wary relic
haha yes
pastel temple
yes there is a somewhat formal theory
complexity/computability?
or something finer
wary relic
complexity/computability?
yes
torn willow
So um so you build these quantum circuits out of quantum gates right?
wary relic
yes
wary relic
complexity/computability?
strictly speaking there's no formal theory to designing algorithms, but there are theories, such as the ones you mentioned, that focus on analysing algorithms
neat lintel
Is Physics, Calculus, Multivariable calculus and Linear Algebra enough of a prerequisite for studying quantum physics?
pastel temple
strictly speaking there's no formal theory to designing algorithms, but there ar...
mfw actually have to think
wary relic
CS students generally start with a topic called "Algorithms and Data Structures" and potentially cover Computability theory.
pastel temple
yeah i'm one such student
calm frost
Is Physics, Calculus, Multivariable calculus and Linear Algebra enough of a prer...
where's linear algeba
torn willow
Is Physics, Calculus, Multivariable calculus and Linear Algebra enough of a prer...
Linear algebra
torn willow
LA,stats and physics should be enough
pastel temple
lambda calculus and turing machines are very cool but it doesn't say anything about designing algorithms like you said
wary relic
Complexity theory comes later, usually at Masters/PhD level, I think
torn willow
lambda calculus and turing machines are very cool but it doesn't say anything ab...
Well designing algorithms is a skill
wary relic
lambda calculus and turing machines are very cool but it doesn't say anything ab...
yeah designing algorithms is more of an art xD
torn willow
It's part of engineering more than cs
Although cs gives you some inbuilt algorithms
It's upto you to incorporate everything and make a good algorithm
neat lintel
There is a point where Engineering and Computer Science intersect, no?
Kind of like a not all humans wear sandals situation?
torn willow
Kind of yea
You have some core algorithms
You incorporate principles from those into your algorithm
I don't think you can study "how to make algorithms" ,you can however study existing algorithms and learn to reduce your problem to one that is solved
For example,Sorting is important because a big chunk of problems are reduced to sorting
torpid hull
There is a point where Engineering and Computer Science intersect, no?
Problem solving
neat lintel
Problem solving
Yeah that too.
pastel temple
aggressive common sense
torn willow
Sometimes,I just want to forget I do cs
All the good algorithms are a mix of math and ingenuity
pastel temple
i'm a """cs""" student but i don't feel like i can call myself that
torn willow
The only good parts of cs are implementing some cool thing
Like OSes and Networks
That's my opinion
waxen lily
counter strike student
pastel temple
What about making Google?
what you really mean is making money, in which case i agree
that's a good part of cs
torn willow
Studying cs won't help you design algorithms smh
Practicing to design algorithms will
calm frost
do you think that is it possible to tackle advanced probability(measure based) without having done naive version(like ross)?
neat lintel
what you really mean is making money, in which case i agree
No, I mean implementing some cool thing.
neat lintel
Hey, to be fair? It's a GOOD assed recommended system.
wary relic
All the good algorithms are a mix of math and ingenuity
legit my feels
pastel temple
tfw dijkstra is a physics graduate or something
wary relic
when you look into it, most algorithms are created by mathematicians
torn willow
neat lintel
Aren't all algorithms literal mathematics but implemented?
torn willow
Ok actually physicist by training
wary relic
but tbh at the academic level the line between mathematics, cs, engineering and even physics can get quite blurry
such as for example in quantum computing
torn willow
Yea true
wary relic
worst thing about being a CS student for me is never ending impostor syndrome
torn willow
Why do all the cool people not have a cs degree
torn willow
Everyone who is a prominent computer scientist is either an electrical engineer, mathematician or physicist by training
neat lintel
Why do all the cool people not have a cs degree
uhhh~ I have a cs degree and I know I'm the shit.
But then again, I'm taking a light starting job so I can study and do modeling, so. . . . .
torn willow
Actually, That's probably because cs is such an young field
atomic hornet
Everyone who is a prominent computer scientist is either an electrical engineer,...
Not necessarily really
In theory areas ya
pastel temple
rename computer science to computer usage when??
neat lintel
cool people don't need to learn javascript
I mean, what else do you do at faang companies?
pastel temple
CRUD science
torn willow
I mean, what else do you do at faang companies?
Actually important stuff?
wary relic
personally I think CS should be split into "Applciations of Computing" and "Computer Science", or "Theoretical CS"...
torn willow
Like how do you optimize X query
neat lintel
optimize X query?
pastel temple
I mean, what else do you do at faang companies?
probably some really really complicated distributed algorithms or something
torn willow
I think FAANG work will be optimising some really specific thing
neat lintel
probably some really really complicated distributed algorithms or something
When the companies were in their infancy? Sure, but most days you're just implementing algorithms to fix bugs or implementing new features.
torn willow
Yea probably CRUD science
neat lintel
From what I understand, architects need to go through a lot of politics before they make anything (which means its going slow...LOL)
pastel temple
They probably still do a bunch of rnd tho
neat lintel
Bro, listen. . .You aren't doing RND fresh out of college.
Unless you're a genius, you're just NOT.
and even a 22 year old genius has an underdeveloped frontal lobe.
torn willow
What
neat lintel
Google it. . . .
pastel temple
Maybe like if you go far back enough in history to where mathematicians had the official job title of herbalist or whatever, eventually everything involved in the current cs landscape will mesh together and create math 2
neat lintel
You're not considered a full human before 25 for a reason.
torn willow
idk sounds like bullshit
wanton panther
its true
neat lintel
idk sounds like bullshit
uhhh. . .Okay?
atomic hornet
Most people ik that got jobs at faang after college said it’s p boring
A few left and decided to get a phd
wanton panther
your fluid intelligence is still developing till the age of 25, after that it starts dropping
pastel temple
You're not considered a full human before 25 for a reason.
Does it mean when I get to 25 I will never become less stupid from that point?
neat lintel
your fluid intelligence is still developing till the age of 25, after that it st...
Ehhh, there is a grey area there.
neat lintel
Does it mean when I get to 25 I will never become less stupid from that point?
Well, I'm not a neuroscientist but I will share what I know.
pastel temple
I'm almost 25 bro...
neat lintel
The general wisdom is at 25 you are as smart as you are going to get, and you are on the decline from there. HOWEVER . . . .
wanton panther
Does it mean when I get to 25 I will never become less stupid from that point?
no, it just means that it'll be harder for you to learn new things
neat lintel
When you consider most CEOs or leaders of industry are old, you have to really question that.
wanton panther
no, it just means that it'll be harder for you to learn *new* things
it'll take longer to pick up new skills
neat lintel
Now, according to this book I read : Late Boomers, a German University conducted a study in which older people were taught new things and new grey matter was formed.
A child can obviously learn faster than an adult, but an adult can learn without restriction as long as one keeps their emotions in check.
Further : There seems to be a correlation between consistently reading / learning and having a small / no decline.
wanton panther
hmm... i see
wanton panther
Further : There seems to be a correlation between consistently reading / learni...
but the main point is fluid intelligence stops increasing
pastel temple
A lot of musicians i know developed hugely in their 40s
wary relic
There's a podcast run by a neuroscientist called Andrew Huberman. He talks about neuroplasticity in a few of the episodes. Highly recommend.
pastel temple
Well, not a lot, the best really
wary relic
I recall that by 25 your neuroplasticity drops drastically
neat lintel
but the main point is fluid intelligence stops increasing
I am not familiar with that term, so I cannot argue with that or speak to that.
wanton panther
I am not familiar with that term, so I cannot argue with that or speak to that.
it's a big word(that i myself don't know very well) that basically just means how quick you can learn new skills/knowledge
neat lintel
I recall that by 25 your neuroplasticity drops drastically
Idunno about that, bro. I'm gonna be 30 in a few days and I'm learning more / smarter than I have EVER been.
pastel temple
My brain shall soon turn into an ice cube
wanton panther
Idunno about that, bro. I'm gonna be 30 in a few days and I'm learning more / sm...
yea that's crystallised intelligence. That keeps increasing forever.
neat lintel
it's a big word(that i myself don't know very well) that basically just means ho...
Well, I guess until I read the studies that prove it, it would be best that I just see myself as an anime character that keeps getting stronger.
wary relic
Idunno about that, bro. I'm gonna be 30 in a few days and I'm learning more / sm...
I'm only quoting what I heard. I believe that it's possible to keep learning (you don't completely lose neuroplasticity throughout your life)
pastel temple
I've always been a terrible learner
wanton panther
Well, I guess until I read the studies that prove it, it would be best that I ju...
lol nice. going through training arcs
neat lintel
lol nice. going through training arcs
Going through a bit of a villain arc right now tbh.
Then again, that probably has more to do with my erratic sleep.
Calling my insurance today to go to a sleep center.
This sleep basically keeps me at 40% at all times.
wanton panther
at what time do you sleep?
neat lintel
I slept at 9 pm last night.
Woke up at 3 am today, so that means I went through a light sleep cycle for some reason.
Thing is : This is NOT the first time this has happened.
3 weeks ago, I did nothing but play Elden Ring for a week and I slept well that whole week.
The week after that I slept well again.
But I haven't really touched Elden Ring or any game since then. It's been work work work.
I think my body is trying to tell me to take a break? But I wanna do the sleep study just to be sure.
wanton panther
Hmm...stress sounds like a plausible cause
neat lintel
If its stress, then I need something besides gaming to de-stress.
Because I am NOT drinking to de-stress.
neat lintel
That's the neat part. . . .
My body FORCES a LOT of naps in the afternoon lately.
I still feel my jaw clenching unconsciously.
And it takes a huge bite out of my day.
Started meditating regularly again.
10 minutes Mon-Sat , 1 hour on Sunday.
wanton panther
does meditating help with the sleepiness?
neat lintel
No, that sleepiness mostly because of the Vyvanse / adderal combination pushing me to a crash.
When I started adderal, the daytime napping was a fucking plague.
12 noon - 2 pm napping until 5 or 7.
And if that happened? FORGET sleeping at night, lmfao.
And no, the stims aren't the cause of insomnia.
My insomnia started at 28 after I did 3 months of nofap if I'm not mistaken.
Maybe before that?
wanton panther
hmm....if the stims and the nofap are all normal to you then i'm inclined to believe it's mostly the stress that's the cause
like your brain just needs some rest
neat lintel
Probably.
So, I'm going to let myself game after I finish making this product for my side hustle.
I'm SO close to being finished and its the BEST looking thing I've ever made.
My customers are gonna fucking love this.
wanton panther
what is it?
neat lintel
p/m me, It's not something I can go around telling everyone about you know? (It's not illegal, before you get any ideas)
wanton panther
lol ok
torn willow
I guess toc
pastel temple
i'm in epic burnout-mode
a bit of it self-inflicted
i have to learn some things i don't care about but i actually WANT to learn a bunch of other things
but i can't, physically, do it at anything above snail pace
wanton panther
i have to learn some things i don't care about but i actually WANT to learn a bu...
saaame
I've got a chem test in a week but i've been developing some major interest in psychology recently
it's one of the dopest things i ever learned about
pastel temple
like what?
wanton panther
like that crystallised, fluid intelligence thing I was talking about
that's psychology
pastel temple
right
wanton panther
and obviously there's also content about mental illnesses(which I do read up into) but I mostly want to learn more about development
wbu, what are the buncha things you wanna learn?
torn willow
Well,I had an interest in psychology until I realised it isn't very developed
Like I don't think theories in psychology can be held up to the same level of scrutiny as in physics or chemistry
torn willow
wbu, what are the buncha things you wanna learn?
Well,Math and maybe some physics
I am looking to specialise in things that I find useful tbh
wanton panther
Like I don't think theories in psychology can be held up to the same level of sc...
well, physics and chemistry are much more rigorous
pastel temple
wbu, what are the buncha things you wanna learn?
Music, maths
wanton panther
I am looking to specialise in things that I find useful tbh
oh noice. Useful like?
wanton panther
Music, maths
cool. What kinda math tho?
pastel temple
cool. What kinda math tho?
I don't really know, probably fundamental things like set theory and number theory
torn willow
Basics like topology and real analysis
pastel temple
And whatever comes after that when it's time
wanton panther
Basics like topology and real analysis
topology is one of the basics? Damn....
wanton panther
And whatever comes after that when it's time
i see
pastel temple
I believe having intuition in those two will make a lot of things easier for me
toxic schooner
Shyshu is too old for me anyway <:whatcanisay:916931197794394162>
firstly, no i dont like you, and secondly, we are the same age man
toxic schooner
<:flonshed:629835071465062410> boomer
graceful glade
How are you
Better than you at maths hehhehehe
torpid hull
Better than you at maths hehhehehe
Hmmm cocky
graceful glade
Test me
torpid hull
Some other time
torpid hull
Well... Im Australian but I don't think that it means anything
torpid hull
Automatically +1 points for me
So you might recheck the sign of the one that you added to your points. It might be negative
graceful glade
Okay
Uk>Australia
Im so good at inequalities
y>2x+7
Y=mx+c
I've got Maths test tomorrow
waxen lily
Well... Im Australian but I don't think that it means anything
its bedtime
bright hill
firstly, no i dont like you, and secondly, we are the same age man
bruh
torpid hull
its bedtime
For me it's about 3am
bright hill
@neat frost you tricked me
waxen lily
For me it's about 3am
about <t:1651503658:f>?
torpid hull
Sleep time.
bright hill
slurp is older than I am and they were calling me a boomer
toxic schooner
bright hill
they said they were a girl but I'm not sure what they're pronouns are
neat lintel
bright hill
neat lintel
WHY IS IT SUMMER IN THE SPRING
neat frost
firstly, no i dont like you, and secondly, we are the same age man
WHAT? UNTRUE
Everyone has a crush on me
Also youre most definitely a boomer and I most definitely am not
bright hill
slurp, you're a "she" right?
neat frost
Also you are older than me DarQ
neat lintel
its hot outside
neat frost
fckin boomers
bright hill
Also you are older than me DarQ
toxic schooner
Everyone has a crush on me
no.
bright hill
I'm super confused rn
neat frost
why
bright hill
slurp don't do this to me
graceful glade
Hi
bright hill
I literally have 2 brain cells left
neat frost
what have i done to confuse you now?
no.......
bright hill
what have i done to confuse you now?
*vaguely gestures at everything*
neat lintel
are you unfunny on purpose ?
graceful glade
vaguely gestures at everything
neat frost
Omfg
graceful glade
Are you unfunny on purpose?
toxic schooner
but.... <:sad:532803514892812288> no.......
sorry slurp, someone had to tell u
graceful glade
Sorry slurp, someone had to tell u
neat frost
whyd you have to do me like that Galwa
toxic schooner
they said they were a girl but I'm not sure what they're pronouns are
also slurp, would u clear this
neat frost
also slurp, would u clear this
no
neat lintel
hold on i'm joking
stark charm
neat frost
I like your pfp
thanks, me too