serious-discussion

[vast surge]

Oh god, he claimed that some people (not specifying who) compared him to Wiles, but the difference is that Wiles' first draft was wrong and people found a flaw, while IUT is flawless and the RCS just doesn't understand IUT so he's better than Wiles

[brave hollow]

so its probably a different edition

or smth like that

[vast surge]

Well that's enough of that, I need to go prepare for a lecture I'm giving on one-point compactification of locally compact spaces.

[zenith tinsel]

good luck

[brave hollow]

who would be in audience?

[vast surge]

People learning point-set for the first time

[brave hollow]

so its part of the course? or is it like a talk

[vast surge]

Part of the course.

[brave hollow]

ah ok, good luck :)

[light needle]

teach the C* alg perspective :)

[fast ivy]

What's the C* algebra perspective? Is this related to the fact that when X is a loc. compact space, that when you adjoin a unit to the algebra C_0(X) you get the algebra of complex valued functions on the one point compactification of X (i.e C(X*))?

I remember Baum discussing this in his K-theory talk

But like

[light needle]

mhm

infact all compactifications of X corrospond to "nice" unitizations of C_0 (X)

[fast ivy]

Yeah, I was about to ask this lmao

[light needle]

in particular, stone cech beta X is the same as C_b(X)

[fast ivy]

Can you actually define like

[light needle]

continous bounded functions on X

[fast ivy]

one point compactification in terms of adjoining units.

That is actually neat

Does this work for any space tho?

Or does X necessarily have to be loc compact and hausdorff?

[light needle]

well it needs to be loc compact but not nec haussdorf

you just need uryshon to work

idr the exact conditions under which that happens

[fast ivy]

Neat

[light needle]

the main idea is a theorem of gelfand

[fast ivy]

I should study operator algebras at some point.

[light needle]

every commutative unital C star algebra is isomorphic (by something called the gelfand transform) to C(X) for some nice X (this is actually maxspec of the algebra/or space of chars)

so theres an equiv of categories between compact haussdorf spaces and unital C star algebras

basically

and when you apply that to the C* alg C_b(X)

you get C_b(X) = C(beta X)

[fast ivy]

What topology do you put in maxspec? Is it the same Zariski topology we use for the prime spectrum?

I guess that would be weird, because the zariski topology is usually not hausdorff.

[light needle]

oh its like, the maxspec is the same as the space of characters (continous homomorphisms A-> \bb{C})

and you give this what we call the weak* topology, this just means a sequence of characters converge iff they pointwise converge

[fast ivy]

I thought, maxspec meant like, maximal spectrum.

[light needle]

yeah you can identify the two spaces

like for each maximal ideal M of A

you get a map A-> A/M, and basically all banach algebras that are fields are C, gelfand mazur is the name of the latter part

so you get a map A-> C

[fast ivy]

Alright then, I am actually reading Salamon's func anal book this semester.

[maiden minnow]

yo

sup

nice server idea

[toxic schooner]

mister, u are in uni?

[fast ivy]

But I was thinking about not reading the part on operator algebras

At least not yet

[light needle]

oof

[fast ivy]

Yeah, I entered uni this year

[toxic schooner]

noice!

[light needle]

oh nice

hows uni life

[fast ivy]

Idk, it has the same HS vibes I guess

At least rn

But I am taking some graduate courses too at uni.

[toxic schooner]

if my uni life was the same as hs, i would go insane

[fast ivy]

I am taking riemannian geo and alg. topology.

[fast ivy]

Was it that bad?

[light needle]

nice

[fast ivy]

[toxic schooner]

it is that bad

still not done yet

2 months of hs left

[light needle]

im gonna be doing a riem geo reading group this summer

and then hyperbolic geo next sem

[toxic schooner]

and in the middle of that, and after it, uni entrance exams are going on

[toxic schooner]

[fast ivy]

Nice, I am currently reading Manfredo and Tu's book.

[light needle]

how do you like it

[fast ivy]

What books are you thinking about reading on riemann geo for this summer?

[fast ivy]

[light needle]

well i havent decided eyt

yet

maybe lee

[fast ivy]

Lee is really short and doesn't cover much material, but it is really good for motivating a lot of important concepts.

Specially connections on vector bundles.

Which is core to doing riemann geo

[light needle]

i see

[fast ivy]

Btw John

[light needle]

https://imgur.com/cNwQwwm.png

heres the book me and my friend are think of

[fast ivy]

Neat

Oh, if you like analysis. There's this book that teachs both riemann geo and some stuff about geometric analysis.

[light needle]

oh nice

[fast ivy]

I was thinking about reading it to learn more about flows and stuff.

[light needle]

whats the book

[fast ivy]

Both of these cover like

Some of the core material of riemannian geometry

but then do like

a bunch of stuff related to studying differential operators on manifolds.

Specially elliptic operators and harmonic analysis.

The second book talks about Kahler-Einstein metrics too

I was hoping about reading these once I learn better about PDEs and func analysis.

[light needle]

oh nice

yeah im taking an elliptic pde class next sem

and i might attend the geometric analysis seminar

or join it

[fast ivy]

👀

Neat

So you are actually thinking about giving a talk on geometric analysis?

[light needle]

oh well i dont know exactly how the seminar works

some of them make the students give talks

some of them just have u attend it

[fast ivy]

Ah ok. But in any case, geometric analysis seems to be a very interesting topic, I suppose it might be a fun experience learning a bit about it on a seminar in either case.

[light needle]

ye

[fresh oriole]

that Jost book is tough

doesn't really work as a first encounter with riemannian geo

really interesting though

[stark charm]

Hi

I have two days to give a 20-25min presentation on exponential map and normal coordinates on Riemannian manifolds

If you were to format the presentation what are some topics you would talk about personally.

As it stands I was planning to either introduce both ideas in 10-15 minutes with some of their properties given by propositions in a book by Lee. And then the last 10 on an example

However there are likely more interesting ways of approaching this presentation so I am open to ideas

[deep mango]

The gauss lemma has a pretty cool proof. Maybe you can introduce the definitions and then prove that? Idk if it's too unmotivated

I forget what it lets you show

[fresh oriole]

go into the name isothermal coordinates and talk about the connection to heat

[bronze pelican]

Gauss lemma is important

Like the polynomial irreduciblity gauss lemma right?

No ryc doesn't galois theory

My b

[stark charm]

is gauss lemma the rescaling one?

im guessing no

[deep mango]

Gauss lemma on riemannian manifolds says that geodesic spheres are normal to geodesics.

Yeah

[stark charm]

geodesic spheres are neighborhoods around points on geodesics?

[deep mango]

Specifically, the geodesic sphere of radius r at p is the set of all points of distance r from p

[stark charm]

no lol

it says it right there my bad

g(p,q)=r?

not like this im guessing

[deep mango]

Uhh

[stark charm]

this doesnt make sense

it says radius in TpM

[deep mango]

Yeah. You take the image of the unit ball in T_pM under the exponential map.

Not unit ball

Ball of radius r

My bad

[stark charm]

oh

so exp(B(p,r))_p

[deep mango]

Anyway, there it's g(v, v) = r^2. The points in the geodesic sphere are then exp_p(v) for such v.

[deep mango]

Just the sphere, not the whole ball.

But yeah

This can be equivalently written for small r as the set of points q such that d(p, q) = r, where d(p, q) is the inf of lengths of paths from p to q.

[stark charm]

so this is where straight linedness comes in?

[deep mango]

Yes

[stark charm]

I appreciate you a lot for helping with this

I will definitely mention Gauss’s lemma

[deep mango]

I dont really remember what you use this to prove

[stark charm]

I am curious how this has to do with normal maps also

[deep mango]

(it is a lemma after all)

But the proof is really really nice

And uses normal coordinates

[stark charm]

Oh I see

[deep mango]

The proof of gauss's lemma, that is

[stark charm]

Okay. Small recap. Taking p in M and looking at a sphere S of radius r in TpM. We have that exp(S) is a geodesic sphere. These also equivalently have the property of being vectors v in TpM such that g(v,v)=r^2. The important property is that points q in the geodesic sphere are points with minimal r length paths from p to q.

[deep mango]

Yes

[stark charm]

This allows us to get an analog of straight lines being the minimal distance between two points on a manifold.

Okay I will definitely mention this. Thanks big time once again.

The last topics we talked about were connections on principal bundles

[deep mango]

Oh thats great stuff

[stark charm]

But I am too shaky with these topics but they seem really fun

[deep mango]

I have to do a final writeup for my riemannian geometry class

[stark charm]

Also we kinda speed ran some topics at end of class

[deep mango]

I was thinking of doing that

Yeah

That happens with these classes

[stark charm]

One topic that I want to look more into is Yangs Mills theory

it looked very promising

[deep mango]

That happened with my manifolds class in undergrad. We speedran through riemannian geometry and principal bundles at the end

Lol

So I want to learn it properly now taking riemannian geo in grad school

[stark charm]

I kinda dont feel like speed running is worthwhile

[deep mango]

Definitely

But like

Yeah

I feel so much more prepared learning this stuff on my second run now and have absorbed it super well

Because I saw it all quickly in undergrad

[stark charm]

I tend to have that same experience with most topics I relearn myself

It is making me consider if grad school is really worth it.

Ill apply and see what happens next year

[neat lintel]

Is the pace of important scientific discovery accelerating or slowing?

Oh, I stole that from a Lex Fridman convo so

[fresh oriole]

I feel like groundbreaking physics discoveries have somewhat slowed down from the pace of 1900-1980 or so (which was an absolutely insane era)

Higgs boson and gravitational wave confirmation were big

but theory feels pretty stuck

[modest rune]

Accelerating, although individual fields have different rates

Certain parts of physics do feel kinda stuck

But others are flourishing

[neat lintel]

I really think constructor theories are kind of being undersold

[vivid halo]

I think they're being oversold

physics is kinda stuck though, although we are seeing some hints of stuff beyond the standard model more recently

[fresh oriole]

we have to get past the abomination that is QM

[vivid halo]

QFT you mean?

[fresh oriole]

anything quantum

it's just no good

[vivid halo]

lol

nah, it's fantastic

it's too successful a theory to want to "get past it"

[fresh oriole]

it will prove to be an inconsistent theory of average behavior that works well in special cases

that's my totally uninformed theory

[vivid halo]

I mean yes this is very uninformed lol

[fresh oriole]

down with Bell's inequalities

down with statistical independence

[vivid halo]

"I do not understand QFT therefore it's bad"

[fresh oriole]

it doesn't pass the smell test

[static loom]

cringe

go be a crank somewhere else please we have enough already

[fresh oriole]

the truth hurts

[modest rune]

I feel like there is a lot of physics that has cool progress

[fresh oriole]

hopefully it's clear I'm being mildly facetious

[modest rune]

Like condensed matter stuff

And micro materials

[fair mural]

rip

[fresh oriole]

I have hope that the james webb scope will stimulate some new physics soon

I've been following it with bated breath for some 12 years

only about half as long as the project has been developing

[stark charm]

I understand your frustration

[primal seal]

Wait, what?

[fresh oriole]

no

it's a castle made of sand

[primal seal]

It is certainly correct

Man, stop it

[fresh oriole]

"let's just erase all these infinities, because... something something... yeah, that works!" "let's just not say what the difference between a quantum system and an observer is... that'll work!"

[primal seal]

Try to explain Young’s double slit experiment without the results of QM

There is a definite definition of absolute size

[fresh oriole]

quantum needs help. A lot of help

[primal seal]

It may be incomplete, but everything so far is consistent

Moreover, nature does not answer to any laws of physics or mathematics

[fresh oriole]

no argument there

[static loom]

better get off discord and go help it!

[fresh oriole]

I'm not the guy for that job :\

[static loom]

why not

[fresh oriole]

there are far more qualified people than myself

I wouldn't know where to start

[static loom]

true, you're either born qualified or you aren't

[primal seal]

Much of physics is accurate; QM is correct to the most fundamental levels. I’d be happy to explain anything to you

[fresh oriole]

can you use QM to derive the melting point of aluminum?

[primal seal]

It would be wildly impractical, but I suppose in theory, yes

[fresh oriole]

if that's possible, my respect for QM will go up tremendously

[fair mural]

i can make these jokes all day

[fresh oriole]

I wasn't joking / punning on your name

I'm in pretty good company in believing QM needs a lot of help

[fair mural]

i know

[primal seal]

It certainly can; I’m curious what some of your counter points are against QM?

[split glade]

I'm not a physicist whatsoever, but I am really curious about your stance: could you link some references for me to read about your position?

I didn't realise QM was a controversial thing

[primal seal]

QM is not controversial whatsoever!

People have dedicated their lives to its results and we have electron tunneling microscopes- how can you refute it?

[fresh oriole]

can you outline how that would go? I'm genuinely curious

look, I'm not any pro on quantum stuff. I was a physics major and switched to math in my 2nd year of university. I've tried to keep up with how physics is going because I love it

QM seems to have serious foundational gaps

like what constitutes an observer

how does wave function collapse happen

[primal seal]

Yeah I’m not trying to sound like a dick either

Okay so let’s tackle the question of observation and collapse

A system is defined to be “small” in the absolute sense if a measurement of an observable quantity causes a change of state in the system under observation

[fresh oriole]

what is a measurement?

[primal seal]

A measurement is an attempt to determine an observable of the system

Observable meaning state variable

Momentum, spin, position

[fresh oriole]

this kind of sounds like assuming the framework of QM is correct, but I guess there's not much else we can do to discuss this

[primal seal]

That’s the general definition of measurement

We could be talking about a doctor taking someone’s temperature

[fresh oriole]

I get the naive / intuitive meaning, but I don't think that cuts it formally

why does something get to be counted as an observer distinct from a quantum system, when fundamentally it consists of the same nature of stuff as the quantum system it's purportedly observing?

[primal seal]

Because macroscopic matter is negligibly affected by quantum phenomena

[fresh oriole]

how big does something need to be before it's macroscopic?

[velvet dagger]

Manifold I'm trying to get the idea of what you're wondering about here

[primal seal]

So yes, you could treat the person “viewing” the results quantum mechanically, but you’d get the same results as Newtonian results

[primal seal]

As I said above

[velvet dagger]

Is it like a mathematically formal definition of things?

Or philosophical?

[primal seal]

If the system is non-negligibly affected by the means used to measure it, it is considered “small” (in the context)

So for instance

If I shine a spotlight on a basketball to measure it’s trajectory, the path is unaffected

If I use an electron to determine the momentum of another electron, the state will wildly change

[fresh oriole]

both I guess

[velvet dagger]

I think philosophically there's still probably a lot of controversy of what things "mean"

[fresh oriole]

homies such as Einstein, Penrose, and Weinberg have all expressed doubts about QM

[velvet dagger]

Cue Einstein's whole God doesn't play dice stuff, etc

[fresh oriole]

I'm just full of confusion and doubts about all of it

[primal seal]

Your are 100% justified; the shit is weird as all hell

[velvet dagger]

Now I think there is some mathematical model and it turns out this mathematical model is pretty much the best tested scientific theory there is

[primal seal]

But you can’t denigrate it lol

[velvet dagger]

Except that it plays very badly with general relativity

[fresh oriole]

right. And that's a big problem

[velvet dagger]

So I think quantum is fine in the sense of, once you have the mathematical model and don't ask too hard what that means (which depending on who you ask can be a question of metaphysics), it cuts it ridiculously well modulo the GR problem

As for what this model is, so I've seen epsilon of semiclassical analysis and based on that what I can say is this

[primal seal]

Manifold you may be interested in some of the interpretations of QM

It has nothing to do with the actual mechanics, but rather perhaps how to interpret them

Look up “born interpretation”

[velvet dagger]

Start with classical mechanics

[primal seal]

There’s the Copenhagen interpretation

[fresh oriole]

I like the sound of pilot-wave theory

[primal seal]

Etc..

I’ve got to run but feel free to ping me regarding anything QM related whenever

[fathom swallow]

Several Sloths

[mellow moon]

Symplectic Fourier Transforms comes in

Here is the new challenger

[fathom swallow]

Several Sloths

[fresh oriole]

http://quantum.phys.unm.edu/466-17/QuantumMechanicsWeinberg.pdf

[fathom swallow]

Several Sloths

Several Sloths

[velvet dagger]

So to recap

State space is phase space, a symplectic manifold (think R^{2n})

We have a symplectic form

Symmetries are those which preserve it

Observables are smooth functinos

Hamiltonian flow dictates the trajectory of particles

In quantum mechanics you can do similar things

Oh sorry I trailed off

So so

In quantum mechanics the setting is a Hilbert space H

[light needle]

not forgiven

[fathom swallow]

Several Sloths

Several Sloths

Several Sloths

[fleet cloak]

wait @haughty bear theres actually theoretical cs in this server🗿

the thing i promised you in the other one was here the whole time

#get-advanced-access and then #numerical-analysis

click like the green checkmark

✅

[haughty bear]

tysm

[stark charm]

I am going to learn about quantization soon

[primal seal]

Yeah that’s fair enough. The QM certainly “works.” Interpretations exist, but ultimately they’re immaterial to the actual practicality and precision

[stark charm]

I dont know much about QM but quantizing is very interesting to me

[primal seal]

@violet spade

[modest rune]

I was reading this book called "when we cease to understand the world"

that focuses in large part on like

how much it bothered a lot of people that all this modern science was hard to give physical interpretation to

like not just kind bothered

but viscerally upset

or even enraged

and i so cannot relate to this feeling at all lol

[primal seal]

It’s true. We have literally No intuitive or everyday experiental basis for the results of QM

[modest rune]

i mean like

the world is fucking wack

i struggle to empathize w the idea that it ought to have an intuitive explanation

like its crazy that we understand it at all imo

its way way more surprising that things like QM are predictively useful to me than it is surprising that they are hard to interpret

[fresh oriole]

it's not just that QM facts are weird

they also blatantly don't describe the everyday world, which requires explanation

they describe certain ultra specialized situations in labs very well

there's a very wide gap to bridge

[modest rune]

I mean it describes phenomena that don't influence the everyday world

the GR thing requires some further thought for sure

But like, its not weird that I don't experience quantum phenomena every day

[cyan goblet]

you mean to tell me that when you walk into a wall theres not a chance of you tunneling through the wall?

[modest rune]

maybe not you

im built different

[primal seal]

By this logic you’d also refute special relativity because our watches are sync’d after you drive to the store and return while I wait at home

[primal seal]

There IS a chance

[cyan goblet]

just as that one mathematician devoted his life to finding primes

forgot who it was

i will devote my life to walking into a thin wall

[near fox]

This is not true. Quantized phenomena are actually everywhere in everyday life. A common example comes from visible light. Lights based on diodes or fluorescent lighting uses light emitted according to a quantized light spectrum.

[fresh oriole]

yea relativity is pretty sus too

I kid, I kid

[primal seal]

Yes. Fluorescence and phosphorescence are quantum phenomena, but I guess what I’m saying is they don’t help inspire an intuitive picture of “what’s going on”

Well, let me say “why what’s going on behaves in such fashion”

[near fox]

But this could be said for any competing theory concerning atomic or subatomic objects

[primal seal]

I know, the why is irrelevant

We were discussing interpretations priorly

That’s why I meant there’s Noh much intuitive basis

[fresh oriole]

I'm going to reveal the extent of my ignorance of QM now: could somebody describe to me an experiment that demonstrates the spectacular predictive success of QM?

[primal seal]

Young’s double slit experiment

The photoelectric effect

The spectrum of any atomic gas

[fresh oriole]

I need you to be more concete

Like we can demonstrate the success of Newton's laws by seeing how objects undergo acceleration

[near fox]

These experiments are best read online since you can see good pictures and such

[primal seal]

You want me to explain them?

[fresh oriole]

What's an example of a setup where we apply some kind of QM equation and predict the right result?

[primal seal]

You should try reading the first; they’re fairly simple like @near fox said

I can help though

[near fox]

Most generally, quantum theory came about in an effort to explain the behavior of light

[primal seal]

All of those

[near fox]

Almost every phenomenon related to emission of photons is most satisfactorily explained using quantized models

Or rather, the very concept of photon itself is a quantum concept

[primal seal]

Yes; accepting QM is accepting wave-particle duality

[near fox]

To the extent that we want to see an intuitive experiment similar to those of Newtonian mechanics, the "classic" experiments are the simplest but probably are still not satisfactory, and ultimately that's because humankind for millennia really just had no idea how light worked

In a similar fashion we might question the existence of electrons. I don't think ordinary people have any understanding of electricity as based on discrete particles. Indeed, in the earlier 1800s, electricity was treated more like a continuous fluid.

[fresh oriole]

yeah

what's the simplest example of doing some QM math to solve an actual problem?

even an unrealistically simple scenario

[near fox]

You can use it to calculate the light emissions of hydrogen

[primal seal]

Time independent Schrodinger equation for a particle in an infinite well

[near fox]

Hydrogen emits radiation at very specific, discrete frequencies

[fresh oriole]

but I mean like... that sounds sophisticated. You can use newton's laws to calculate where a constant motion object will move to 1 second later

is there anything at all at that level of elementary?

[primal seal]

QM isn’t deterministic though

You’re not playing an away game

You’re playing a different sport

[fresh oriole]

that's okay

[near fox]

Quantum mechanics is largely about subatomic things, so the only examples are going to be from that scale

[fresh oriole]

what's a toy example of a probability problem?

that it solves

[primal seal]

What I mentioned above is the simplest

[fresh oriole]

what does being in an infinite well mean?

[primal seal]

It means there’s infinite potential boundaries; so the particle can’t tunnel out

[fresh oriole]

ok, so it's trapped and isolated from any other particle

[primal seal]

Correct

And those conditions will allow you to solve an equation to determine the distribution of momentum and position of the particle

[fresh oriole]

now we're talkin

[primal seal]

Not simultaneously though

[fresh oriole]

that sounds good

[near fox]

If you read the first chapter of a standard quantum physics book you should find examples like this worked out in detail

As well as discussion about experimental evidence

[primal seal]

But just to reconcile this with everything else from before

The equation will not tell you the precise position or momentum (whichever you choose to solve for), only a probability of it being in a certain range

[fresh oriole]

I appreciate your little intro

can you recommend a textbook?

[primal seal]

For sure, I enjoyed it

Try David griffiths’ introduction to quantum mechanics

Oh wait

Also

Feynman’s volume on QM is one of the best intros I’ve ever read on the subject

I think it’s volume 3 of the lectures

[cyan goblet]

i use mcintyre qm

[near fox]

I should also remark that the idea of quantum mechanics as encoding probabilities is not the only interpretation of what quantum mechanics is about

Taken at face value, quantum mechanics merely says that concepts like position and momentum are functions and not scalars; it's only when you try to extract a classical state out that you get into troubles

[primal seal]

True, some even interpret it as “parallel realities”

[primal seal]

PS also: it’s somewhat early on because the requisite hardware is unavailable (and likely will be for some time), but quantum computing is a readily emerging field. If anything, most encryption as we know it will be obsolete with the rollout of adequate quantum machines

[orchid lava]

x E R, x not 2pi*n where n element of integer

how dyou write this in

builder notation

[ancient flame]

${x \in \mbb R : x \ne 2\pi n \ \forall \ n \in \mbb Z}$

[fathom swallow]

gmod

[sick burrow]

gmod why are you johnDS now

[ancient flame]

bc im a follower

[vast surge]

#discussion

We're all JohnDS now

[orchid lava]

thank you!

oops

am idiot

[orchid lava]

thank you!

[ancient flame]

lol np

[orchid lava]

how sure are you that it is correct

some guy told me forall should be at the front.

Or can you link me to a page with some complicated examples and how to tackle them with set builder notation.

because I would also like to learn it myself.

[ancient flame]

uh idk it probably could be

idk any websites for that tho

[charred mortar]

I think it’s fine regardless of whether the forall n is at the start or end

[primal seal]

In the final line, I’m not seeing why it’s required that A be nonempty?

Ah wait I got it

It’s needed in the second to last line; otherwise the condition becomes vacuously true and the set “blows up”

[lone carbon]

This is probably the most effort I've ever put into proving something. Feels like I had to invent new math to do it lol

[cobalt star]

i thought of something, it is possible to butcher a function into mapping 1 in to 2 outs by making it return a list

[surreal sapphire]

sure

[cobalt star]

i was not expecting that answer

[surreal sapphire]

more commonly maybe you can have functions into powersets

that return a "set of possible answers"

[cobalt star]

wow

i shall read about these powersets, thanks!

[surreal sapphire]

like, if you want you can do sqrt'(x) = {+sqrt(x), -sqrt(x)}, where sqrt' is my modified function and sqrt is the standard one returning the non-negative one

[cobalt star]

desperately needed function

thats cool

[grave obsidian]

Do you guys have any tips on how to solve word problems

[alpine kindle]

this is what you generally do for multifunctions in Haskell

[cobalt star]

i didnt know haskell had an explicit "multifunction" structure but i do the same when programming and it always slightly annoyed me that functions are taught as mapping strictly one in to one out, which makes them very boring

[alpine kindle]

it doesn't have inbuilt multifunctions
but you can really easily do it with
f :: a -> [b]

where f is your multifunction taking an input of type a and outputting a list with elements of type b

and many the operations defined on lists are based on them being outputs of multifunctions

[cobalt star]

ah i see
that makes sense
i should take some time to brush up my haskell

[alpine kindle]

specifically its applicative functor instance

[cosmic inlet]

I need help in economics specifically microeconomics can anyone help me quickly? I will pay message me

[sick burrow]

[neat lintel]

i can do macroeconomics and you can use a microscope

[cyan goblet]

is this supposed to be some “instagram caption that goes hard” line

[ancient flame]

guys! I got instructor of the month at my tutoring job :)

[deep mango]

🤓

[grizzled grove]

Having hard time to understand why we need sheavea

Sheaves

Reading it for first time actuallt

Actually*

[lime sorrel]

I got a little interested in Economics recently

What sort of Math fields are involved if I join such a university usually?

[leaden torrent]

most people who want to do academic econ nowadays (like, get an econ phd and all that) actually major in math

and focus primarily on analysis and stats/modelling

(while obviously taking econ courses alongside)

[lime sorrel]

no, no phd for me

Also there's no such thing as "major\minor" here; You just do a single field of study kinda
(In fact I wouldn't even have a word to translate that in my native language)

So it's just statistics\modeling cool

[vivid halo]

you need these to properly talk about spaces and functions on them

in such a way that you can glue spaces and functions on them together properly

there are some cases where this isn't strictly necessary (you can get away without sheaves for smooth manifolds and smooth functions on them for example)

but for things like schemes you really need this perspective

[haughty bear]

concentration?

[clever knot]

Congrats 🥳 . I assume you are not the only instructor at this tutor job, is it big?

[ancient flame]

yes I am the only one

jk

[clever knot]

🙂

is it for a school or what?

[ancient flame]

uh idk exactly but about like 50ish employees maybe

no it's a company

mathnasium

[clever knot]

Hopefully you get students who actually want to improve and have not been somewhat "forced" to have tutoring

[ancient flame]

eh about half and half

[clever knot]

idk how i could handle students that don't want to put in any effort

Not sure what you do in those cases

[ancient flame]

there are some who will complete an immense number of pages that we give them and there are some who barely complete one because they just dont care at all

[ancient flame]

it is annoying as fuck

bc I have to handle 2-3 students at once anyway so I can't focus all my attention to one

also it's online tutoring so ya

[clever knot]

Come back to them only to see they have not done anything

[ancient flame]

makes it significantly harder to control them

[ancient flame]

it happens

[clever knot]

one thing to be stuck but another to just think the tutor is going to do everything for you

[ancient flame]

what I want to say: "what the fuck bro have you seriously done nothing this whole time? what are you doing, jerking off or some shit?"
what I actually say: "make sure you're doing your work, I want to see this page done by the time I come back"

[ancient flame]

yeah

and like there's a button to call for help if im not in the breakout room and I think half the time people forget it exists so they just wait for me

and sometimes I may take a while if im dealing with other students

[clever knot]

is there some proprietary software you use or is it just something like zoom?

[ancient flame]

what I want to say: "you dumbass there's a button to call for help"
what I actually say: "make sure if you have questions, press the button to call for help"

we use this site called cranium cafe

cringiest name ever but whatever

[brave hollow]

tutors anonymous

[ancient flame]

it's a good software because it's like zoom but it also has the ability to easily switch to rooms and (most importantly) provide and write on worksheet pages

[clever knot]

seems people on this server are quite aware of the "help" button

[ancient flame]

lol

just not how to use it

[clever knot]

any awkward moments where you don't know how to approach the problems?

[ancient flame]

yes, so I just ask a coworker to help (and yes, it is encouraged to ask for help when needed)

[clever knot]

oh that is cool

[ancient flame]

yeah

the supervisor/manager person idk, he's super cool

super chill

all the employees are high schoolers and college students

mostly college

the supervisor dude is in his like early 30s so he's young

[clever knot]

was it always remote?

or does the service have some local locations

[ancient flame]

so mathnasium is mostly in person

but since 2020 they started offering remote tutoring

I started working about a year ago and I would rather work in center, but it is so much more convenient to work online

the most important thing is I dont drive

and it's just more flexible n shit y'know

[clever knot]

yeah

[primal seal]

I know a franchisee owner of s mathnasium- they pay minimum wageFYI

[charred mortar]

It probably depends from center to center for such a big brand

[neat lintel]

Hey

I'm trying to understand how cos(x) and sin(x) actually give an answer

From basic trig I know that e.g sin(x) = opp/hyp in a right angled triangle

However, sin(x) also gives negative values

How is this possible in the equality? Is there any resource that explains this in a way that a hs senior could understand?

[waxen lily]

very observant! thats because only the first quadrant of the unit circle is relevant for right triangles

if you allow the triangle legs to have negative length then it makes sense

[toxic schooner]

i suppose negative length here would be related to orientation

[neat lintel]

https://commons.m.wikimedia.org/wiki/File:Sine_and_cosine_animation.gif#mw-jump-to-license

Used to be all over the trig pages on Wikipedia but some moron apparently took it off there.

I can hear moron, "nyuhh, it isn't colorblind compatible and the framerate cause epilepsy, not allowed!! take off page!"

[charred mortar]

Alternatively: “this is too handwavy and unrigorous, take it off”

[toxic schooner]

this is what we should show kids

it gives a good idea about waves and the trig functions

[neat lintel]

I mean, what's up there now doesn't explain this guy's question effectively, you have to understand a bunch of notation and shit

Also trig is renowned for being hand waving, that's like literally how it was developed 2,000 years ago

What should we start with euler's identity and understanding complex numbers before you understand numbers because it's a more generalized concept? Ridiculous

[charred mortar]

I’m joking lol

I agree that handwavy stuff is far better for a first go

Get a broad idea and then dive into the details

[torn willow]

Sometimes the subject is so handwavy,that you need rigour

Handwave stuff as long as you can get away with ut

[waxen lily]

👋

[neat lintel]

Thanks for the link. I am however, seeking another explanation without using the unit circle

[toxic schooner]

the only explanation i can think of is, say u keep increasing the angle of which u are taking the sin of, then the orientation of the hypotenuse will become the reverse of what it is was, and hence u get a negative value of sin

[ancient flame]

a bit more for me, I make $11.25/hour, but ik what u mean

[charred mortar]

Out of curiosity what currency is this

[neat frost]

Doesn’t the dollar sign usually mean USD?

[charred mortar]

Probably, but I don’t think it always does?

[toxic schooner]

ryc wtf did u do to ur pfp

[neat frost]

Nothing?

[neat frost]

Oops yeah you’re right

[charred mortar]

Like Australia does too

[neat frost]

And Canada

I forgot

[deep mango]

[neat frost]

I got him before ryc

[toxic schooner]

oh god thats slurp

lmao

[toxic schooner]

dont sully me 😭

[deep mango]

Asking about my pfp before asking why I was unmodded

Interesting

[neat frost]

[neat frost]

Which is more surprising?

[deep mango]

Since im the best mod ever + most honorable server user of all time, it would be really weird if I had a stinky dark blue name.

[neat frost]

Lmfaooo

[charred mortar]

But you do

[neat frost]

Don’t you have a high opinion of yourself

[deep mango]

You're laughing

[neat frost]

You’re a perceptive one

Ryc if you’re the best mod, do me a favor
I cannot allow Shuri to have a better color than me. Could you either remove it or fast-track me for honorable? I’m basically like the best user on this server anyway, so it’s kinda weird I don’t have honorable yet anyway

Thanks I’m advance, I’m sure you’ll pull through

❤️

[deep mango]

Hmm. Curious request.

I do love to troll Shuri.

[neat frost]

Trolling Shuri is debatably more fun than trolling you

[deep mango]

🤨

Well well well

[neat frost]

It’s a good thing ryc trust me

A compliment

[deep mango]

No one is better than me at anything, not even at being trolled!

[neat frost]

True true

That’s why it’s only debatable

[deep mango]

That's the end of your little plot

[neat frost]

If you’d debate it, you’d be wrong

But that doesn’t mean you can’t debate it ryc, it’s a free… whatever idk country

[deep mango]

I won't let Shuri outshine me by my own undoing

Or

Doing

[neat frost]

Nono

You misunderstand

Trust me

This is in your own best self interest

[deep mango]

Trust you

[neat frost]

Trust me.

[deep mango]

Don't you lie to me constantly

[neat frost]

When have I ever let you down?

[neat frost]

No?

If anything weren’t you the one bragging about being a pathological liar the other day?

[deep mango]

I am one, but you are almost as bad

[neat frost]

That is untrue!

I never lie!

[deep mango]

For example "I was just joking around about the egg thing"

Or "I never lie"

[neat frost]

What?!

The egg thing wasn’t a lie!

[torn willow]

Wait there are 2 rycs in chat?

[deep mango]

One is clearly not me

[neat frost]

Wdym?

There is only one ryc.

[torn willow]

Yea I agree @neat frost

[neat frost]

If anyone IS pretending to be me, they will face SEVERE consequences

Identity theft is no joke

[deep mango]

Good idea

[neat frost]

I’m full of them

Speaking of

Slutty flashlight?

[deep mango]

No!

[neat frost]

Yes!

[deep mango]

Why so you people never notice the NAME COLOR

Aargh

[neat frost]

HAHA

I’m gonna trick so many people

And you can’t stop me!

[sleek wing]

I leave for a day

And this is what I come back to

[toxic schooner]

i didnt notice the color

[toxic schooner]

its light blue

[sleek wing]

They’re not even similar shades of blue

Straight up CYAN

[toxic schooner]

exactly

smh

[neat frost]

You’re not even similar shades of blue

[neat frost]

I think wew’s point is that you should’ve noticed the difference….

[toxic schooner]

i mean

i should have

but i dont read names each time

[neat frost]

You should have.

[toxic schooner]

i just have a memory saved with the pfp and name

[neat frost]

I’m disappointed shyshy

[toxic schooner]

as long as those are similar

i wont notice for a while

[toxic schooner]

😭

[toxic schooner]

know me for a little longer

and i will disappoint u more

wtf slurp

i thought we had a deal

[neat frost]

The deal was “I’ll be nice”

But I’m not nice

[toxic schooner]

blocked

[neat frost]

Nooooo 😭

I’m looking through my screenshots of discord convos here

Found a good one

[toxic schooner]

[neat frost]

Ryc is definitely sus

Unfit to be mod, I should be mod instead

[toxic schooner]

[deep mango]

[toxic schooner]

lmfao

ryc what is this

i expected better of u

[deep mango]

It's what type of chicken meat we like!

[median hill]

Wait a minute, there are 2 ryc with same pfp?

[deep mango]

It's not the same

Slurp's is in some ridiculous bunny costume

[inner finch]

hello

[median hill]

Ohh i see

Lmao

[neat frost]

,av

[fathom swallow]

Slurp#0155's Avatar

Click here to view the image.

[neat frost]

This is the TRUE ryc

It’s what he actually looks like

[deep mango]

Your ryc goes to comiccon

[neat frost]

Your ryc goes to parties dressed up as a slutty flashlight

[deep mango]

You're a liar

[toxic schooner]

ik Sure...... whatever u say pal

[median hill]

How much do discord mods make in a month

Ryc question directed at you

[deep mango]

Our stipend is about $400 a month

USD

[median hill]

Tf really?

Gib me mod mnipp

MNIPP

[deep mango]

No, we don't make anything

[median hill]

Huh

Lair

[toxic schooner]

ryc doesnt make anything

all other mods make 7000 dollars a month

[deep mango]

No way... what!

[toxic schooner]

(depending on the number of bans)

[toxic schooner]

i also get paid

i moderate the mods

[deep mango]

WTF

[toxic schooner]

[median hill]

Ohh so more they ban more they get

[toxic schooner]

indeed

[neat frost]

I’ve been getting ryc’s paychecks

[median hill]

Ryc go on ban spree

[toxic schooner]

and that also causes me to get more

[median hill]

That explains

[toxic schooner]

oo

theft

of

about

21k dollaridoos

[neat frost]

@o@

[toxic schooner]

lmao

[neat frost]

I can’t solve this question (╯°□°）╯︵ ┻━┻

[median hill]

What have you tried?

[neat frost]

Crying

[toxic schooner]

have u tried multiplying both sides with 0

that helps

[median hill]

Try differentiation

[neat frost]

It’s not solving an equation shyshy

[inner finch]

do it anyways

[toxic schooner]

did i stutter.

[inner finch]

multiply the hypothesis by 0 and the conclusion by 0

[neat frost]

I don’t think I can differentiate this…

[neat frost]

Did I ask?

[toxic schooner]

yes.

u asked

[neat frost]

There is no hypothesis

[inner finch]

they're essentially words in the free group

[toxic schooner]

subconsciously

[median hill]

Then integrate

[inner finch]

over the set of the alphabet

[neat frost]

It’s fucking probability I can’t do this anymore 😭

[median hill]

Then the answer should add up to 1

[neat frost]

I finished the rest of the hw quickly but this one problem

(╯°□°）╯︵ ┻━┻

[toxic schooner]

the probability of anything happening is 50%.

[neat frost]

No

[median hill]

Unless its a coin flip

[neat frost]

The answer probably won’t be 1

[toxic schooner]

whats the question

[neat frost]

The probability of you getting bitches is far less than that

Gottem

[toxic schooner]

i was going to help you

but not anymore

fuck off.

[neat frost]

Can you do probability?

[toxic schooner]

yes

[neat frost]

[toxic schooner]

unlike you, i actually know my shit.

[neat frost]

Wow

Wow

Is that how it’s gonna be?

[toxic schooner]

send ur question in 10 seconds

and i might consider helping

[neat frost]

I don’t want your help

[toxic schooner]

ur fault for how it ended up

[neat frost]

I’m gonna solve this by myself

[median hill]

But you can’t right?

[neat frost]

[toxic schooner]

the only thing slurp can solve is "how to be annoying"

[neat frost]

Whoa

Wow

True

But wow

[median hill]

[toxic schooner]

😎

[neat frost]

Shyshy wanna question from my algorithm hw?

[toxic schooner]

no

[neat frost]

Good

[toxic schooner]

[neat frost]

I wasn’t going to give you one

[toxic schooner]

i wanst going to ask for one

[neat frost]

Okay

Want a calc q?

[toxic schooner]

not from people who cant solve probability questions.

[median hill]

Depends if its calc 0 give me

[neat frost]

Fuck off

[toxic schooner]

no u.

[neat frost]

You want a probability question so bad?

[toxic schooner]

not anymore

[neat frost]

Good

[toxic schooner]

[neat lintel]

https://tenor.com/view/foss-no-bitches-no-hoes-0bitches-no-gif-24529727

[dense belfry]

Lmao

Tfw inconsistent

[frigid lark]

Shyshu and ryc loving each other.

[toxic schooner]

what

[deep mango]

That's not even me

[toxic schooner]

yeah

lol

[frigid lark]

oh

I just see.

[toxic schooner]

thats slurp

[sleek wing]

turns out 99% of the population is cyan-blue colourblind

[toxic schooner]

[frigid lark]

this looks grey-black to me. Absolutely no blue tone.

[hushed turret]

do we have multiple ryc clones now

[bronze pelican]

Yes

[outer vector]

"i wonder whats under the misc channels, it cant be that unknown to me"
DIFFERENTIAL GROMETRY
PDES
ADVANCED PROBABILITY
NUMBER THEORY
PEDAGOGY (thats the only one i have zero inkling about)

welp, to google i go

[errant furnace]

Jesus 2 ryces

[hushed turret]

there are four, i believe

[sleek wing]

four
PepeLaugh they are unaware

[hushed turret]

i should have said at least four

why are you like this

[errant furnace]

Jesus

[long matrix]

this is brilliant

[deep mango]

[limber thunder]

a lot of people need this sticker smh

[zenith tinsel]

why do you say that

[limber thunder]

because 99% of the time a quick google or wiki search gives a better answer

[sleek wing]

Because the average person has the research skills of a cement mixer

[limber thunder]

to quick questions like what is ___

[limber thunder]

the world if everyone knew how to google:

[old fox]

what does that even mean lol

[stark charm]

Cement mixing is an emperical science so I dont really know.

[sleek wing]

They don’t just need spoon feeding they need shovel feeding

[shut anvil]

@velvet lark Just continuing from the polynomials discussion earlier, you might find some more compact notation useful for understanding the general pattern

[velvet lark]

okay, thanks!

[shut anvil]

Say you have a polynomial with n terms. Your polynomial is a monomial if all but one of the a constants equals zero.

[velvet lark]

i understand‼️ thank you sm

that helped me a lot!

[shut anvil]

Don't confuse this with the degree, BTW. The degree equals the highest power with a non-zero multiplying coefficient

It's not the number of non-zero coefficients

[ancient flame]

me, a tutor: "how much of your homework have you done?"
student: "30"

ah yes because I know if it's 30 questions or 30% or whatever the fuck he meant

[neat frost]

You should! You’re a tutor!

[ancient flame]

ah yes

of course

[old fox]

I find it unlikely be in percent

[wooden flax]

ahh i have tutoring in 19 mins

[eager trout]

Oh my god yo what

This statement itself has revived my interest in geometry

[light needle]

nice

[primal seal]

@light needle I saw you had a live broadcast earlier; I was in public so couldn’t listen in- what was it on?

[light needle]

oh we were just reading some set theory

[primal seal]

Ha, yeah that’s what I thought but wasn’t sure since I only caught a literal snippet

But I happen to be reading set theory currently; is it something you regularly do?

[light needle]

we just started but thats the plan

we are reading kuneths book

[primal seal]

Ah ok, I’m liking Enderton, but if you don’t mind filling me in on when you’re planning to do so, I’ll gladly sit in

I’ll take a look at Kuneth, nonetheless

[light needle]

yeah we just read portions of the book on vc, we dont have a set time so far

we read till pg 21 today

[primal seal]

Gotcha, I’ll keep my eyes out then

[light needle]

ill ping you when we meet next

[eager trout]

Wow using pca is actually surprisingly accurate for voice detection

Never realized pca is actually this powerful

[ripe wasp]

is there any special word for "commutative ring with identity"?

for example a group is a set G with an operation

that satisfies certain properties

and if that includes commutativity we call it an abelian group right

so is there smth like that for commutative rings with identity

[fast ivy]

unital commutative ring?

commutative ring with unity

Those are common to hear.

[ripe wasp]

got it

yep that was what i was looking for

[eager trout]

Uh no

It's in my class

It's such an easy idea that you don't need to write a paper about it

I mean you just assume that each voice input is like a high dimension vector and you use pca and hopefully different words will end up in different clusters

(Of course some preprocessing like making threshold for loudness to align the start time of the words and demean the data to make pca perform better stuff)

And it did not seem promising to me but the end result was shocking accurate

Of course very limited but still very good

[eager trout]

Yeah that makes sense

But that seems difficult

To build a truly general system that can detect anyone's voice

But if you're just building a classifier to differentiate between a finite set of known voices then it shouldn't be too hard

Which is why our model works so well, because we only predict 4 words lmao

[vivid halo]

https://www.youtube.com/watch?v=2i1hrywDwPo

this is the most insane audio thing I've ever seen

[primal seal]

Is that the MIT/Microsoft collab?

[toxic schooner]

holy shit

this is insane

[surreal sapphire]

i read a paper about people doing this from really far away by capturing vibrations in a lightbulb

for espionage reasons

[proper sun]

Guys

what will happen

if normal human

Will go in

black hole

[unreal ore]

S T R E T C H E D T O D E A T H

[proper sun]

Why

E

sad

what if we use

Something

that does not stretches us

[proper sun]

Or if we go really fast in there

with spaceship

[glacial mesa]

whats the best channel for a basic math question

[proper sun]

#math-discussion

[unreal ore]

Good luck when we are inside the event horizon

[proper sun]

what happens next

is stellaris theory True?

[unreal ore]

The gravity is too strong that even light can't escape

[proper sun]

ik And where we are going

With that gravity pulling us

[unreal ore]

I'm not sure

[proper sun]

i think

innerstellar

theory is

true

ima go to There

and

grab gun or knife

so if none comes to save me

i will kill my self

[neat lintel]

. . . .So question about gravity because I haven't studied physics yet.

What happens when a larger body of gravity meets with a lesser body of gravity? (I hope I'm phrasing that right.)

[sleek wing]

no, no you're not. I have absolutely no idea what you mean

[toxic schooner]

what do you mean by meets

[torpid hull]

Meets? Or collides? Or they both become a single body? And it's quite weird to say body of gravity. You need to phrase that correctly.

[neat lintel]

Would it be more apt to say one particle producing a force output of gravity meeting with another particle producing a GREATER force output of gravity?

[neat lintel]

Well, say a starship that produces a field of gravity enters a black hole.

[torpid hull]

Any body with mass will experience a gravitation force.

Both objects will apply equal force on each other

The body with lower mass will experience greater acceleration

Want to know anything else?

[torpid hull]

One example would be the Gravitational force applied by you and the Earth on each other

You both are basically applying the exact same amount of force on each other

[neat lintel]

Well sure, but I'm not pushing the earth towards me.

[torpid hull]

But as Earth has huge mass, the acceleration produced is negligible

[torpid hull]

That's why

F = ma

Your mass is less so acceleration would be big.

[neat lintel]

Mm.

Okay.

Thanks Jack.

Though I still don't understand black holes yet, its a start.

[torpid hull]

Welcome.

[torpid hull]

The black holes have HUGE Densities so it has HUGE mass

[toxic schooner]

no one really understands them

[torpid hull]

Now relate

Black hole form when a dying star crumbles under its own gravity

You yourself get compressed into very very small volume, then you'll also become a black hole

[neat lintel]

And simply making my mass proportional to a black hole would not allow me to survive this?

Also, is acceleration truly negligent no matter what if your mass is too small?

[torpid hull]

Yes that's the reason there aren't very small blackholes. They just evaporate

Gravitational force between any two bodies is
F= G M1.M2 / r^2

Now equate this to F= M a.

[neat lintel]

M = GM1M2