serious-discussion

[light horizon]

I mean, sure...? What does that have to do with "the truth of arguments" or whatever

[placid shadow]

I don't know if you're trying your hardest to engage in faithful debate?

i think

I'm sorry if this is provocative.

[light horizon]

Oh I mean I'm for sure not because I usually don't take the other person seriously enough to consider what I'm doing a "debate"

[placid shadow]

Okay thank you

[foggy meadow]

I figured you'd like it, but it doesn't matter.

[shell bloom]

help anyone, is it because I stressed too much that I have lot of white hairs

[placid shadow]

That was the case for me.

I recommend cutting yourself a lot of slack and just relaxing.

Being carefree

[shell bloom]

im still so young

[placid shadow]

Stop worrying so much, its ok to worry a little

[shell bloom]

idk is it because of finals

[placid shadow]

same i was 8 when i got white hairs

[shell bloom]

I had it when I was 12

[placid shadow]

Could be

You should relax

[shell bloom]

it super hard for some reason

[placid shadow]

Its ok

It's not easy to just start relaxing, but you should try, for your own health.

[shell bloom]

I’m so anxious about everything though

My parent and grades and other factors

[placid shadow]

Same, but realizing everything is fine helps me a lot

[placid shadow]

Yeah, in today's world there's so much to worry about

but, that doesn't mean stress is okay

[shell bloom]

yeahh

I’ll try to stop stressing and worrying

[placid shadow]

awesome, i wish you the best

and same really

[shell bloom]

thank you

[placid shadow]

You're welcome!

[timid bronze]

Bro America is a joke compared to this

America’s hospital food cannot compare 😭

[placid shadow]

That's awesome!

[vast wraith]

this is wild

yt has been feeding me a lot of videos abt pregnancy and its not good for me 😭

[timid bronze]

Sorry if me sending this caused anything

[vast wraith]

nono dw its me who keeps clicking on them

[jovial ember]

Why is it not good for u?

[timid bronze]

Whatever it is though, I hope it gets better ❤️ :((

[vast wraith]

guh they’re often lovely but also extremely dysphoria inducing

[jovial ember]

Ah

[fast owl]

hi biche

[thorn kelp]

WHAT THE FUUUICK

HOSPITAL FOOD?

NAAAH

WE GET LEFTOVER WAR RATIONS

[toxic dagger]

Luxury

America is for the rich

[turbid sedge]

Hi fiscussy 2

[turbid sedge]

Sarangay oppa 🥺

😭😭😭😭

[hidden isle]

highkirkenuinely i cannot believe the yash x yeet x saini x wb x wb x flux x convergence x mxrgd x measure2 x arjun gc happened @tough stratus

[tough stratus]

Did tm learn nothing from our session ✌️

[rose ridge]

tm in big 2026 ✌️

[tough stratus]

Ts still meta twizzler

[turbid sedge]

WTF IS THIS

[torpid bay]

[tender rover]

Also, if I posted this in the wrong channel, please direct me to the appropriate one please.

[deep mango]

if you havent yet, definitely reference khan academy, they have comprehensive lists of topics on all those areas

[torpid bay]

[stark palm]

Hello

I have a problem but not specifificaly in maths

I have bad hand writing and teachers warn me

Maths teacher say he have hard time reading it

Any advices on how to improve handwriting ( in stressful situations)

[toxic dagger]

Try practice your writing when You are relaxed, then slowly speed up

Don't just ramp up so fast

[tropic pivot]

in addition to previous advice try to make the letters of same size with similar gap. You can try 4 liner notebook for that too.

[hexed cairn]

suppp

hi.

[timid bronze]

@sonic field @velvet dagger

[stark palm]

I always use notebooks with lines

[stark palm]

I have this problem also with numbers and symbols

[toxic dagger]

Likely to be cooked

[timid bronze]

😭

Nah

This TT user has this turkey has a pet

[civic trench]

been working on a resource for differential calculus (calc 1), with some linear algebra and animations to illustrate the ideas.

i’m thinking of teaching out of it next time i run a calculus course and would really appreciate any feedback on its clarity and usefulness. here’s the link: https://math-website.pages.dev/

[sonic field]

🤣

[wraith magnet]

this is nice but can you add a dark mode 😭

[sour jay]

I love the web page design, what font did you use?

[rocky shuttle]

the final exam pdf file is broken

[old oak]

Exam cancelled 🥳

[timid bronze]

I like this btw!

[magic python]

:3

[latent edge]

good job

[fresh comet]

I have nothing in the way of real feedback, but I like this project a lot c:

it's great that you're creating something like this

please continue!

[civic trench]

fixed it

[civic trench]

working on that

[civic trench]

for math: html-math-method: katex,
text: mainfont: "Charter, Bitstream Charter, Cambria, serif"

working on calc 2 at the moment. do you think discussing taylor polynomials as linear combinations of ${ (x-a)^k }{k \in \mathbb{Z}{\ge 0}}$ is justifiable for a calc 2 student, if one frames it in terms of vector spaces, as i did in the calc 1 treatment?

[fathom swallow]

CantorClosure

[timid bronze]

Omfg.

People who come into my room and leave without shutting the door piss me tf off .

[warm gull]

true

[loud oxide]

Does anyone here want to help me with a Simplex method solver of a 6 unknowns system in an equality like sum(vars times stuff)=constant with inequalities for bounds like 1<=var<=2 or some other constants?

[ocean harbor]

omg same

[worthy shell]

real

[civic trench]

i've added dark mode

[placid shadow]

Does anyone know alternate interior angles?

[timid bronze]

Those pissed me tf off because they came back in physics

[placid shadow]

Oooo

[timid bronze]

Sorry professor but I don't remember what I learned in geometry 🙏

[placid shadow]

I don't remember either haha

I'm doing some relatively basic proofs in geometry, and this is really fun!

[timid bronze]

Heheh

[placid shadow]

🫶

Do you mean my role?

This is high school geometry on Khan Academy, I think it's worldwide curricula.

What do you want?

Why did you say that?

[raw cedar]

💔 sorry oomf

[placid shadow]

Uh

[raw cedar]

i am very jolly today.

[placid shadow]

I hope you enjoy math as much as I do, I don't mean this in a bad way

Same

I really love math

[raw cedar]

are u native english

[placid shadow]

I'd say so, are you as well?

[raw cedar]

no

[placid shadow]

If you mean UK I'm from the USA

Ah, what are you studying?

Right now I'm not studying any math in school, but I'm learning stuff online that I don't know yet, to pre-learn it.

[raw cedar]

like what

[placid shadow]

Are you studying calculus?

[raw cedar]

um, not really rn

[placid shadow]

Ah

[tropic pivot]

What is that property called when two adjacent angles are suppliment?

[placid shadow]

Complementary angles.

They add up to 180 degrees

[tropic pivot]

Very good. I'm gonna slap you.

[magic python]

3:

[placid shadow]

why

[placid shadow]

Hiiiii Car 🩷

[tropic pivot]

Wrong definition of complimentary angles. Second I was asking the property of parallel lines. Let me correct my statement again.

[magic python]

!bnuuy

[quasi jetty]

[placid shadow]

[magic python]

WAIT ITS DEFAULT CHRISTMAS

Mods thank you so much

[placid shadow]

Do you mean supplementary angles?

[magic python]

Anyway, hru aurora?

[placid shadow]

Good hby

hru @tropic pivot

[magic python]

Dry ig, atleast feeling relatively normal today

[tropic pivot]

What is the property called that interior angle sum to 180 on one side of transversal line? I think I'm going to Google it

[tropic pivot]

I'm fine.

[placid shadow]

Yayyy

[placid shadow]

What's it called?

[tropic pivot]

Consecutive interior angle.

[placid shadow]

Interesting, first time I've heard about it

[tropic pivot]

And you're reading parallel lines. Maybe there some other name in your book.

[placid shadow]

I think I'm supposed to already know this stuff, but I'm not sure.

[tropic pivot]

Go to #math-discussion t I will send image.

[placid shadow]

Okay

[placid shadow]

I see now.

Is this a theorem?

[tropic pivot]

Yeah

[magic python]

Oh isn't this normally formatted or proved using the z

Why no parallel indicators tho

[placid shadow]

Cool!!

[tropic pivot]

I don't know

[tropic pivot]

Yup

[placid shadow]

What are those? As in the double line to indicate that two lines are parallel?

[tropic pivot]

They will put arrow on parallel lines to show those are parallel.

@placid shadow

[placid shadow]

Ah

What's it called for angles when 2 angles are congruent/equal?

[tropic pivot]

On parallel lines and transversal or something else?

[placid shadow]

No like this

[tropic pivot]

Two angles are congruent or equal if the measure of their angle is equal. Like angle R and and angle Z are congruent in triangle PQR and XYZ.

[placid shadow]

Does this mean congruent indicator

[tropic pivot]

Yeah, that means it's given.

[placid shadow]

Thanks!

Interesting.

[tropic pivot]

I'm teaching these to 9th standard kids.

[placid shadow]

Nice

[tropic pivot]

Their attention span and focus is very weak. They don't want to study at all.

[placid shadow]

Yikes

[misty hound]

I'm in 9th grade and i feel that too.😭

[timid bronze]

@fresh comet @velvet dagger 🤞

[fresh comet]

vegetable chicken nuggets

[latent edge]

[timid bronze]

I just wish D*mi would get this excited about how much I do for him… and maybe be a little more thankful. He’s already pissed tf off that I took away that… um… numbery theory… combinatoricky… math book thing he’s always reading :/

NOT the end of the world that you can't do math for a couple hours 🥀

[unkempt moat]

Yes it is

I neeed my math hit

[timid bronze]

No!

I'm glad that this youngling isn't addicted to TT, but he needs to take a break from math too!

[unkempt moat]

breaks are good
But I want math to be available whenever I wants

and it is

In my neko head

[timid bronze]

-Rips math textbook all apart and burns it-

GO AWAY MATH!

[unkempt moat]

I’m gonna rip you apart and burn you!!

[timid bronze]

Woah there.. Gonna call 911..

[unkempt moat]

Call them on yourself for burning math!

[timid bronze]

😂 😂

I had a reason to....

[unkempt moat]

NOOO

[unkempt moat]

I’d be cranky without maths too

[fresh comet]

you should give him an iPad instead, that'll be more beneficial for his development

[timid bronze]

LMFAOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO

[latent edge]

No math no yuri and I'd be crashing out

[cyan forum]

Reject postgrad math, become an iPad kid/adult

Totally worth it, trust

[latent edge]

[timid bronze]

I use my iPad more than my laptop in uni

I only use my computer to open practice problems or for lab

[cyan forum]

I mean as a writing tool to replace laptops it's great

[timid bronze]

My ❤️ iPad ❤️

[cyan forum]

I'm just referencing the iPad kids addiction problem xd

[timid bronze]

Ik, I hope D*mi can recover

He loves his stardew valley way too much

[velvet dagger]

[timid bronze]

Ugh here he comes

STOP WORKING ON MATH FOR ONCE

[jaunty oak]

is there a website where i can spam problems for linear algebra like ixl, khan academy

[latent edge]

You can try to think about open ended questions

Not unsolved one but like really hard but doable ones

[timid bronze]

Also @velvet dagger you are so fake

You never taught me discrete math.

[velvet dagger]

I've never even played that!

[velvet dagger]

I WASN'T I was doing data science

[velvet dagger]

RIGHTTTT omg I still need to do that

[fresh comet]

wait

we had a group chat for that many months ago

and then it was left to rot

why'd we never do it

[timid bronze]

Tbf we all were very busy

It was during the s*mester

[fresh comet]

true

[velvet dagger]

Yeahhhhh

[fresh comet]

I honestly forgot that GC existed too

the semester's workload just wiped everything from my mind

[tropic pivot]

Nice.

[timid bronze]

Fr and in the last month I especially said goodbye to everything and told myself I can't take any breaks if I want to be successful 🥀

Can confirm this is false. Give yourself breaks people

[feral gorge]

Smart peeps I would like to learn how to do ODE's and PDE's but I only know calculus 1 at the moment what other prerequisites do I need ?

[latent edge]

Ideally you want to know calculus 2 as well

Calculus 3 too I think if that covers multivariable

That's for ODE

For but PDE it depends on what you want to do

But you can do basic PDEs too after ODEs

Anything more complicated and you need more machinery

[vast wraith]

ive been on a semester long unintended break, have gotten a lot of much needed sleeping and crying done also ig some talking with my gp and a psych

[feral gorge]

Im not sure at the moment they just seem fun to look at , thank you for your help

[vast wraith]

oop but i should sleep byee

[timid bronze]

I hope things get better, I am sorry to hear 😭

Taking breaks is definitely important though, need to have a balance of both

[latent edge]

You can look at the basics of heat equation

[timid bronze]

Gn!

[vast wraith]

im sure they will !

[latent edge]

If you want to look at Navier Stokes... Well good luck on that

[feral gorge]

Like the ∂T²/ ∂²t= "other side that I forgot"

[latent edge]

del u/del t = delta u

[feral gorge]

I just looked it up , why such much ?

[latent edge]

Mamma mia

[tropic pivot]

Is it tough?

[timid bronze]

This is what happens to you in physics exams if you don't ever take a break from your studying

(Thank god your two lowest 2 exams are dropped in that class)

[latent edge]

Studying the equation dor specific stuff might be fine though

[fresh comet]

why would you tell yourself that when you know it's not true

[latent edge]

But like in general these things have open problems

[timid bronze]

Insecurity ig

And an obsession with numbers

[tropic pivot]

My problem is that I'm always on breaks. Currently I'm on break. I don't take breaks between study. I study between breaks.

[feral gorge]

Yea the heat equation seems alot nicer , I want to know how to do that one , what would I need for that ?

[latent edge]

Focus on calculus 2 first

Learn how to integrate things

Also learn series

[feral gorge]

Bahh Allright then back to opencourseware

[fresh comet]

good grief

please try to have a healthy mindset with yourself

[timid bronze]

Cutting back on things that really distract me definitely helped a lot. One of those being Discord

I don't regret cutting Discord completely, but I do regret not giving myself a rest still

If you are always on a break and are trying to study more, you gotta reset your source of dopamine

[fresh comet]

welcome to the mathcord c: @feral gorge

[timid bronze]

Dw about it

I learned the hard way

[feral gorge]

Oh thank you for haveing me

[fresh comet]

better late than never

[fresh comet]

we're happy to have you here c:

enjoy your stay

[latent edge]

You can interpret the equation physically it should be accessible but anything like solving it might not be very accessible with only knowing calculus 1

[tropic pivot]

Currently for me, yes it's discord. I'm getting kind of fomo.

High level of fomo.

[feral gorge]

I most definitely will (i looked at the diff-geo place earlier, stuff was scary)

[latent edge]

But yeah don't get discouraged with prerequisites

Think of it this way: there's tons of math to learn!

[timid bronze]

FOMO is definitely hard 😭

Whenever I delete it, I end up going back. This was me at first

But I just forced myself to keep it deleted and continue to work on making progress. Seeing the numbers go up kept me motivated

[feral gorge]

So true always more to find

[timid bronze]

Brainfart in that last line 😭

[latent edge]

Yeah anyways have fun

[tropic pivot]

I just uninstalled on 19th, yesterday used on Android chrome, then today again installed app.

[latent edge]

PDEs do come with what I do too

[feral gorge]

Allright then mentor person (get teacher-ed hehe)

[feral gorge]

And what do you do ?

[latent edge]

Number theory

[timid bronze]

I left all servers I was chatty in

[feral gorge]

That sounds like it's just about numbers so it will be kind , but its probly super scary

[tropic pivot]

I like this server.

[latent edge]

Lol number theory and kind should not be associated together

[timid bronze]

I'm not saying you have to leave, but I left the servers I was chatty in to reset my dopamine

[feral gorge]

Oh....

What does number theory mean

[tropic pivot]

Yup. I think I will uninstall it now again and will wait for next round.

[latent edge]

For more context though you are looking at functions f satisfying Delta f = lambda f. Where Delta here is the hyperbolic laplacian

If you've seen eigenvalues before this is very similar

Except instead of vectors you have function

[tropic pivot]

But I have youtube next to the app then.

[latent edge]

Let me ask you this first. What comes to mind?

[feral gorge]

My calculus didn't teach this , uhhh I guess I'll try to start at the calc 1 ?

[timid bronze]

This server doesn’t really apply tbf bc I left it (and just rejoined now) early in the semester, but there was another server where I was more talkative (@jagged forge hehe..)

[latent edge]

No you'd learn this in linear algebra

[timid bronze]

Look, you really just need to get started

[feral gorge]

??? Tf is that i thought algebra was done why is there another one

[timid bronze]

No one will start for you and finish your education

Only you can do that

[latent edge]

Mamma mia

[feral gorge]

We did both algebra classes , just call it algebra 3 and let us know it's real

[latent edge]

Yeah anyways linear algebra is about vectors and matrices

[velvet dagger]

Algebra is never done

[feral gorge]

Oh i know those words

[velvet dagger]

Literally an open research topic

[feral gorge]

Hmmmmm ok

[velvet dagger]

So rejoice!

[feral gorge]

What is still left ?

[latent edge]

Right yeah you might have seen these in a physics class or something

[timid bronze]

It is when I'm in the room ❤️

Because that shit needs to fucking shut its mouth 🥀

[velvet dagger]

It will always smile upon you with its beauty

[feral gorge]

Yea that's where the vectors come from

[tropic pivot]

Have a great day then. Bye. Thank you too. Will use discord on pc then. I will not install discord on my phone for next 3 days. Will not use on mobile browser too till that time.

[feral gorge]

Oh you have every role ever

[timid bronze]

He paid the owner for those roles

[timid bronze]

Remember to give yourself breaks tho, good luck on studying!

[feral gorge]

It sounds like the study of different types of numbers , like complex real irrational transindental and more i don't know of yet

[latent edge]

Right yeah since you don't know linear algebra, I also recommend it if you want to look at ODEs and PDEs

[jagged forge]

hi

[timid bronze]

Fym "hi"

[jagged forge]

i just got home after being out with a friend for 8 hours

we walked so much i injured my leg

[timid bronze]

What..are you srs? Is everything ok?

[feral gorge]

Ok so the current bucket list for math to learn is
Calc 2,3
Linear algebra

[latent edge]

Yeah that's more or less on the right direction (this is doing the heavy lifting)

[latent edge]

You can start linear algebra right now

No need to wait for calc 2 or 3

[jagged forge]

yea im ok, just one of my hip flexor muscles is unhappy

[feral gorge]

Oh can I? So it is just algebra 3 why did they name it that

[timid bronze]

Feel better Matt :(

[jagged forge]

tanks

[timid bronze]

Dami are you typing my ban message

[latent edge]

Idk what you learn in "algebra 3"

[jagged forge]

no need for the sad face

[feral gorge]

Idk either but if it has algebra in the name i would assume it's about manipulating things useing identitys I guess this is just all of math but you can understand me right ?

[latent edge]

I'm just going to assume this is not university math so maybe precalc or something

[feral gorge]

Also idk what you'd learn in linear algebra, the other ones also have lines in em what makes this one so special

[latent edge]

Well it's the one subject where I'd consider to be incredibly useful to learn regardless of what you do in life

[feral gorge]

Let him cook

[feral gorge]

You have me intrigued? How so

[timid bronze]

He isn't cooking

[latent edge]

Hmm what are you into?

Have you done programming before?

[timid bronze]

Dami here is your daily reminder

[feral gorge]

Uhh im takeing my second year in it currently so kinda but nothing complex

[latent edge]

There's a funny joke: "all math is either linear algebra or combinatorics. If it's linear algebra then you should celebrate otherwise forget about it"

It's somewhat true

[timid bronze]

https://tenor.com/view/sloth-crawling-slow-gif-9915689

You really are a SLOTH.

[feral gorge]

So what is this special algebra do tell

[latent edge]

Well it's all about vectors, matrices and linear transformations. You can model a lot of things in life with it

[feral gorge]

Mmm this does seem like it could be useful

[velvet dagger]

Eh there's quite a lot. You saw vectors in physics, as things with magnitude + direction, but also you can think about them as points in many dimensions, or just a list of numbers. Then you have matrices, which are functions on vectors.

This connects to the study of systems of linear equations: you've seen how to solve two equations in two variables using substitution and elimination, but what about any number of equations and any number of variables? What if there's no solution? If there are many solutions, what is the geometry? This is linear algebra

What about solving polynomial equations? Can you have something like the quadratic formula but for bigger polynomials? Turns out, this connects to what you could call "an algebraic study of symmetry", which is the starting point of a subject called abstract algebra. Particularly group theory

What if you want to study equations but ask about solutions which are integers? This is (part of) number theory: if you ask the question of which primes can be written as a sum of two squares (e.g. you can't do it for 3, but 5 = 1^2 + 2^2), this leads you to trying to understand whether a number is "prime" once you look at "complex integers". Studying algebra for these "integer-like systems" guys opens up a whole new subject called ring theory (and module theory), which also teaches you a lot about polynomial algebra

Hmmm, okay wait a second we studied systems of linear equations and individual polynomial equations. What if we study systems of polynomial equations? That's algebraic geometry

[feral gorge]

OH MY , HOLY

[velvet dagger]

And this is still 19th century math for the record

It goes way deeper after that

[velvet dagger]

No u

[timid bronze]

?

Your name has SLOTH in it-

[velvet dagger]

The temptation to edit your username and say "So does yours!"...

[timid bronze]

Do it

[feral gorge]

Ah I think i know this first part tho , if you have n equations and each has n variables then you can solve it useing gaussian elimination (I think that's the right term for it)

Oh also I see that "role that does nothing" could I get that one ?

[latent edge]

I can give you a list of things:

In games, you often want to rotate stuff but how'd you do this? Matrices.

In physics you often look at things like speed, force and so on. All of these need a notion of "direction" and some quantity to measure "how much." You can use vectors for these.

[velvet dagger]

This is right! Though I will say, even in that case there's a chance you get no solutions or many solutions rather than just one solution

[feral gorge]

This is true , the questions were very conveniently set up , I was trying to make my own practice problems , did not go well

[velvet dagger]

And there's more you can do than just solving and saying "Okay cool gg", you can look at the geometry underneath as well

Which is a beautiful story

ALLY SHUT UP THERE WAS A DELETED MESSAGE BETWEEN THOSE WITH A REALLY CUTE ANIMAL

[timid bronze]

LMFAOMOMSHKDFHJFDJHKJFD

[feral gorge]

Are you an algebra person or is that just a side branch of what you do ?

[velvet dagger]

I'm kind of an algebra person?

Idk I do a lot of things

Or

I should say what I do touches a lot of topics

[latent edge]

Bro does combinatorics. Scary chad mathematics

[feral gorge]

I want to aks what you do but I'm worried I would get another paragraph description

[velvet dagger]

If you look in the search you'll find so many people give so many different answers to what I do

Depending on who you ask I do combinatorics, geometric group theory, analytic number theory, Fourier analysis, quantum dynamics...

[timid bronze]

Including shit talking me...I've been here for you this whole time SMH

[velvet dagger]

Too late >:)

[feral gorge]

Well your the one that does the things so your answer is the one that matters

[feral gorge]

Oh cool beans then

[velvet dagger]

Jk it won't be giga long because the in depth description is very technical. Above was long but surface level

[velvet dagger]

Sorry it's just too much fun

[toxic dagger]

Can you describe a piece of Fourier analysis that you think is useful

[timid bronze]

I'M SCREENSHOTTING THIS SHIT AND PLOTTING IT AGAINST YOU

[velvet dagger]

Partial differential equations, signal processing

[velvet dagger]

HI SCREENSHOTTING THIS SHIT AND PLOTTING IT AGAINST YOU
I'M DAMI

[timid bronze]

.

Ok.
I'm going to go jump out my window. Bye 🖕

[velvet dagger]

[toxic dagger]

Signal processing in electrical engineering? Nice

[velvet dagger]

Yup!

[toxic dagger]

I also like transmitting wireless messages

[velvet dagger]

Look up "Fast Fourier Transform"

It underlies so much modern tech

[toxic dagger]

Have a good nap 👋

[timid bronze]

..

CRAZY SHIT TO SAY

[velvet dagger]

So, the idea is that you want to study probability. A classic thing people like to say is that it takes 7 shuffles to make a deck of cards "truly random"

Now what could this mean?

[toxic dagger]

Wish you happy anything you do 😀

[timid bronze]

Going to get Dami banned from this server.

[toxic dagger]

Woa okay 😀

[toxic dagger]

Yes, backbone of telecomm

[short acorn]

@north topaz I see you're in the ibo server did you do IB?

[north topaz]

mhm!

[velvet dagger]

The idea is that, if you shuffle a deck, the probabilities give you some high-dimensional vector. There's one vector that represents a "fully random deck", and the distance between these two vectors is a good measure of how random your shuffle is

[feral gorge]

Oh... that sounds so interesting, maybe the avg distance from the starting position of each card remains the same after each shuffle after ?

[velvet dagger]

And it turns out when you run the numbers, shuffling 5 times is barely better than shuffling it at once or not at all

But on the 6th, 7th, 8th, 9th shuffles

[short acorn]

How long ago did you graduate if you're comfortable saying

Oh I should say I did too

[velvet dagger]

It goes from being almost as far as possible from the "fully random" vector to being almost equal to the fully random vector

[north topaz]

2022

[velvet dagger]

So the way you encode this as a vector is a bit sneakier than that, but take it for granted that a shuffle gives you some vector of probabilities, and you can use the distance from a certain vector to study "how random" it is

And then yeah somehow it goes from barely random to almost fully random in a short time window

This is called the cutoff phenomenon. It was discovered in the 80s and was something of a surprise

[feral gorge]

Is it like a 52 dimensional vector ? How would one point and another look from eachother ?

[velvet dagger]

It uses that kinda algebraic/geometric symmetry subject I alluded to earlier called "group theory"

[timid bronze]

Traumatic...

[feral gorge]

How you decide what the vector is sounds hard

[velvet dagger]

Lately people have been studying this for random processes on networks. This uses linear algebra. And it turns out, if you really go deep into things, it turns out to mix a ton of math

[feral gorge]

Like do you just say what it is based on what spot each card is in ?

[velvet dagger]

Group theory, linear algebra, geometry, even... a kind of version on calculus

[velvet dagger]

So imagine there were only three cards. Card A, B, C

[feral gorge]

Yes I can imagine this

[velvet dagger]

There are 6 possible arrangements

ABC
ACB
BAC
BCA
CAB
CBA

[feral gorge]

? 24

[velvet dagger]

If you shuffle a deck completely randomly, then each of the 6 arrangements should be equally likely

[feral gorge]

3 cards now

[velvet dagger]

So that's the vector (1/6, 1/6, 1/6, 1/6, 1/6, 1/6)

[feral gorge]

Ohhhhh

So .... it's got alot alot of things

A 52! Dimension vector

[short acorn]

Oh nice earlier than me

[velvet dagger]

Maybe if you shuffle it once in a certain weird way, you have a 1/2 chance of ending up with ABC, a 1/3 chance of ending up with BAC, and a 1/6 chance of ending up with CBA

So that's the vector (1/2, 0, 1/3, 0, 0, 1/6)

So the distance between that vector and (1/6, 1/6, 1/6, 1/6, 1/6, 1/6) is how random your shuffle was

[velvet dagger]

Yuuuuuup

[short acorn]

Are you graduating next year then(?

[north topaz]

yes, but my uni is playing chaos with my degree

so it's an extra semester basically

[short acorn]

Real

I'm praying they won't do that to me

[timid bronze]

Extra year for me 😁

[short acorn]

Ugh I'd love to chat more but I have to sleep

I'll make sure to say something when I next see you around

Gn 👋

[feral gorge]

Is it for an application or just for funsises ?

[velvet dagger]

The specific work I do is more funsies/the applications are to other things in math

[feral gorge]

Oh nice!

[velvet dagger]

But the overarching umbrella topic does have applications to CS!

Error correction, signal processing, quantum information, and cryptography are maybe one or two degrees of separation away from this

[feral gorge]

Computer science right , gotta make sure this isn't some abbreviation that can be confused

[velvet dagger]

Yup!

[feral gorge]

Hmm Allright then

[civic trench]

hi, i’m working on a dark mode feature—any suggestions for a color scheme that’s easy on the eyes, readable, and visually appealing? (this is what i've got currently)

[shadow girder]

ooh youre making a calculus website

[slow pier]

Apart from the high contrast in the search bar, I like it and also the low contrast on coloured text

[shadow girder]

cold colors work well in the background but it's better to use them for purely visual gui features and keep text monochrome

[civic trench]

yeah (here it is https://math-website.pages.dev/)

[civic trench]

thanks

[civic trench]

got rid of the blue on the right:

[wraith magnet]

I really like the themes available on monkeytype.com

You can see the specific colours they use here on their github as css files
and also an explanation for what each colour means here

Each theme has a background colour, main text colour, and one or more secondary colours, which should be enough for the purposes of a mathematics page (at least one hopes)

[bright hill]

since when was given its real name? lmfao

I remember eric or someone saw this and was like "I object to propagating the stereotype that whites guys have hair cuts"

and that was prolly the sillies thing I heard in all of #『meta-discussion』

[lunar ruin]

Default dark mode for pico css is to me the easiest on the eyes if you want to just throw together something quick and worry about it later.
https://picocss.com/docs/color-schemes

[small dust]

i noticed the same thing recently #discussion message

[trail gust]

@shut thunder @flint pulsar

so, continuing the discussion, how do you measure time?

[shut thunder]

Math is just a tool to define things as we want/serves us

Time is a measurement of things happening with respect to some frame of reference

Usually an arbitrary one

[bright hill]

bonsoir slayla

I hope you're doing well

[trail gust]

Hmm

[shut thunder]

Like, a second is just a thing humanity agreed upon as a useful measurement

[small dust]

,w bonsoir

[shut thunder]

Still, twice as much time is not an arbitrary thing supposing we work in the same frame

[fathom swallow]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by slayyla

[trail gust]

I have a question, if time would be infinite then energy would be infinite right

[shut thunder]

Supposing you assume the universe also is, yes.

But it doesnt really fall from time bein infinite.

[trail gust]

but then, wouldn't time already be infinite? because in 1 second, you can just sort of cut out a lot of models of the reality that has passed (technically infinite)

so wouldn't energy already be infinite because of that?

[shut thunder]

Not necesarilly, and no, subdividing infinitely a measure doenst make the original amount also infinity

Between 0 and 1 there are infinite numbers, but the range is clearly finite.

[trail gust]

yes but that's only mathematically right? in our universe, if we say at 3.01 seconds we have so and so energy, wouldn't energy also be for 3.001 seconds and so and so it will be infinitely present and happening

[flint pulsar]

which system are you talking about?

[trail gust]

universe?

our physical universe

[shut thunder]

And again, time doesnt correlate with energy as measures

[flint pulsar]

and when you are talking about "infinite time" I suppose you mean infinite duration?

[flint pulsar]

anyway this

[trail gust]

why would energy be infinite if time was infinite then? if energy just wouldn't care and be the same 10N even if time existed, then wouldn't it always be 10N? why would energy be infinite if time was infinity then

[shut thunder]

The argument you appeal to is like 3000 years old and clearly wrong

[flint pulsar]

10 N is a force

[trail gust]

well technically speaking if there was a current energy level of the universe

[flint pulsar]

but it's not energy right

[shut thunder]

Zeno's Paradox for the nonexistance of motion, aka, a runner is doing an arbitrarily long run, in some amount of time, it covers half the length, in another amount of time, it covers half the length remaining, etc...

[trail gust]

uh how about this, the force that comes if you concentrate all the energy of a system into one super 100% efficient hitter that hits another particle with all the energy present (and maybe later the energy would diffuse)
the highest possible force then

[shut thunder]

He appealed to motion being impossible since there are infinite subdivisions of time in which an event has to happen, aka, nothing can truly moves

My personal opinion is that Zeno's was smoking some primo shit

[trail gust]

alright, how did you un appeal his idea then...

[flint pulsar]

the problem is that it supposes that an infinite amount of something is necessarily infinite

which is not the case in modern math

[trail gust]

I see

[shut thunder]

Empirical observation of things moving. Algebraically, the sum of infinite elements isnt necesarilly infinite.

[trail gust]

so bigger infinities exist

and different sizes

but here's the thing though

[shut thunder]

On the topic of energy, if you suppose the Universe is infinite in size and seemingly uniform on the big scale, then energy is also infinite

Since infinite mass, bla bla bla

For us humans the problem is that we recide in a limited region of space

[trail gust]

hmm, if universe were to be finite, and time were to be infinite

then

why would energy be infinite

?

[flint pulsar]

but what do you really mean by infinite time

[shut thunder]

That wouldnt be necesarilly true under our current way of seeing energy

[trail gust]

what is the idea behind u concluding that energy is infinite because time is infinite

[trail gust]

time passes on indefinitely

without an end

I'm sure mathematicians would have a hard time doing something real and actual like this

[flint pulsar]

that's normal time as far as I'm aware

[shut thunder]

I didnt say that inf. time implies inf. energy

I said an inf. Size of the universe

[trail gust]

I see

[shut thunder]

In fact, we dont quite consider time to have infinitely passed inside our universe, since the big bang works as an initial condition for all we care

[trail gust]

how is it that we do not already have an infinite size even though it kinda is limited?

[shut thunder]

An infinite size and uniform density implies infinite mass. Which we do associate to energy

[shut thunder]

Its limited for us

We cant reach (much) beyond our observable universe

So we are basically limited to a really small region

[neat lintel]

Would you guys mind if i asked for some tips?

[shut thunder]

On what

[trail gust]

u said infinite elements won't add up to infinity always (such as the 3 dimensional area graph that forms our observable universe and the small units of space in it)
but how do you know that mass in it is not infinite

for example, if u take an atom

it's kinda small for us

but apply something like a zeno paradox for it

it has a lot of mass seemingly

just small compared to us

[shut thunder]

Infinite mass would fill completely our finite region

[trail gust]

how do u know that an atom is not infinity already

and we bigger infinities

[shut thunder]

Since that doesnt happen, ergo, there isnt inf. Mass

[flint pulsar]

what?

[trail gust]

yes but, how do u suppose we are finite? what if we're just bigger infinities

[tender cobalt]

what on earth am i supposed to refer to you as

[shut thunder]

Even if you assume that its all concentrated into a single point, that would imply that there is a black hole big enough (infinitely big in fact) to engulph all our observable universe

[neat lintel]

How to teach yourself math in an optimized and efficient way. I know how ofc, but i'm looking for ways to make it smarter. I figured it out for biology and the sciences-- active recall, memorization, got that aspect all figured out. But I realize I can't do those exact same methods for math, and I only have four weeks to teach myself algebra before i get into a trig class. Time spent studying isn't an issue i'm concerned with.

[shut thunder]

And evenly distributing it wouldnt help either

[trail gust]

I like to think of a thought experiment here, that there's a universe that's soo small that it's practically invisible for us (like really really, if we map the area of it, it would be like not even a dot but soo small compared to an atom)
say if it was in the scale of a quark to our universe size, to it to a quark

but inside it

[flint pulsar]

I mean ok

[shut thunder]

Start a project that forces you to use what you know or learn new things ig.

[neat lintel]

I realize math is a lot more practice oriented but i still need to understand the concepts and they're applications. I've been trying to find good ways to mix both and i've seen some videos of people recommending time spent studying theory vs application of the theory

[trail gust]

it would just work like our universe

[trail gust]

inside it, there would be galaxies and clusters for its own sizes

and earth and towns

but we wouldn't know

neither would they

[neat lintel]

I'm thinking more stuff like time spent studying theory vs practice then repeat etc

[trail gust]

what if, you apply this logic and think that we are way larger than we look

[shut thunder]

Grab a book and solve the problems on your own(?

[trail gust]

or infact, we are infinite

and our mass being finite and literally quantifiable

[flint pulsar]

but wdym "we are infinite"

[trail gust]

isn't true

[trail gust]

@flint pulsar read from here

[shut thunder]

Again im refering you to measure theory

[flint pulsar]

but who is "we"

[trail gust]

our current scale

[shut thunder]

A line (1d object) is infinitely long for a dot (0d object)
And so is a surface (2d) to a line

None of them are infinite as we would normally say it

[trail gust]

atoms, humans, earth, solar system, galaxy, super galaxy cluster duper hyper max destoryer 5000, and so on obeservable universe

[shut thunder]

They just use different measures

[neat lintel]

I shall do that. I'm literally just inquiring abt study structure tho lol. thx anyways

[shut thunder]

If youre on a lower level, khan academy is great too

But for more advanced topics youll have to hit the books

[neat lintel]

I like khan academy for practice but it's very...

slow

with how much information it gives me at a time

[flint pulsar]

do you mean infinite in mass or in size? you need to be more precise
and also I suspect the answer is still: an infinite amount of something is not always infinite

[neat lintel]

I've been using prof. leonard videos

[trail gust]

okay but you aren't actually able to plot a point in our 3 dimensional universe, we have limitations. U wouldn't be able to plot an infinitely thin line too

[neat lintel]

but then again there's no structure with that just lectures yk

[trail gust]

in fact, I'm asking right now, how do you know that you would be able to plot a 3 dimensional space as well

[shut thunder]

A true line is just a part of our universe that we cant construct but we can define as a tool

[trail gust]

(Even though we're in 3 dimension, how do u know we're not infinite)

[trail gust]

well how do u define a line?

[shut thunder]

Like, if i ask you a direction, you clearly wont be thinking of a 3d platform through which ill walk, you just think of a straigh line

[trail gust]

That's really rough measurement tho

I'm asking if there exists a possibility for us to define a 2 dimensional line

in our 3 dimensional space

[shut thunder]

We have defined distance as a measure in meters, which reflects as a real life amount, which is what we use for lines

[trail gust]

to me that possibility seems 0 (for a true 2d line)

[shut thunder]

Lines are 1d btw

[flint pulsar]

2 things:

• infinite in what? you really need to be more precise.
• you need to keep in mind that this is the real world: saying "what is my mass was actually infinite" is meaningless because it would be 1) useless 2) not the case since we define mass to be measurable (thus not infinite)

can I ask what class you are in?

[trail gust]

well I know you can do that, but there's also seems to be a physical limitation in our universe.
Imagine, you have 2 particles, in between them u can construct a line as in distance

but

in our 3 dimensional space

you can't really construct an EXACT true line though

[trail gust]

that's accurate to the distance

[shut thunder]

Again, measurements we have dont really reflect into something real. Temperature, distance, time, energy are just a way for us to predict events

[trail gust]

that's perfectly precisely 1dimensional

[shut thunder]

You just can define it as is

You dont have to build the bridge

[trail gust]

you don't

but

I'm saying you can't just define as it is

let me be more clear

[trail gust]

if there was a true distance between those 2 classical point like particles, our limitations in our 3 dimensional space, would just be so that we can't literally define the line to point blank accuracy

[shut thunder]

Whats a line (segment) between two atoms? Simply an imaginary connection defined by the position of the two atoms where one points through the shortest distance to the other.

[trail gust]

what does that mean? that means we also cannot define ANY line to point blank accuracy

[shut thunder]

And also, distance also isnt an absolute

[trail gust]

well we ignore all of that

2 fixed particles

and an observer with power

[shut thunder]

Space curves, nothing can be truly defined in position, etc...

[trail gust]

well we talk about 3 dimensional space first

and then talk about all the other mad stuff

[trail gust]

Here ^

I think you don't get the intuition of what I mean

one sec

[shut thunder]

If you can define the position of 2 points, somehow, you can define the line

Which in reality we cant even define position

[valid token]

👍

[flint pulsar]

@trail gust are you taking into account things that come with relativistic or quantum effects, or should we use 3d euclidean geometry only?

[trail gust]

@shut thunder can u come #help-44｜stanley-🌲-v2-dans I can't send pics here

[shut thunder]

In this ideal world can we define two points?

as in, measure their position

[flint pulsar]

pls answer

[trail gust]

I believe that even if you define positions of actual 3 dimensional particles

with point blank accuracy

it isn't possible for you to construct a 1 dimensional/ 2 dimensional

line

[shut thunder]

If you can numerically define them, then yes, you can numerically define a line.

[trail gust]

with point blank accuracy

[trail gust]

no I don't think u can

[flint pulsar]

why not: be clear

[trail gust]

in 3 dimensional space

in any 3 dimensional space

alr here

[shut thunder]

$pt + q(1-t)$ with $t\in[0,1]$

[trail gust]

#help-44｜stanley-🌲-v2-dans message

[shut thunder]

being p and q vectors in euclidian space*.

and t just a variable.

[trail gust]

if u see this picture

[flint pulsar]

*R if you want it to be a line

[trail gust]

you see 2 particles

fixed

we have their position perfectly

this is 3 dimension space

now if u see the observer

and in front of what he's looking at

there's a supposed to be, 1 dimensional line

[flint pulsar]

the line exists independantly of whether you look at it

[shut thunder]

Then yes, there is a definition for the line
Its the collection of all points strictly between them

[trail gust]

yeah I'm just making it uh understandable

[shut thunder]

In euclidian space at least.

[trail gust]

right right I don't argue on that

[trail gust]

But here's the thing

[shut thunder]

There isnt anything beyond that definition for a line

[trail gust]

This observer

[flint pulsar]

it's independent of whether you can measure it if we're talking strictly about geometry

[trail gust]

He tries to narrow his equation

of the line's position

to 100% accuracy

but he just can't

[shut thunder]

Again, we are talking about geometry, and if we have 2 fixed points in space as point (x,y,z), then theres a strict definition for the segment between them,

[shut thunder]

Specificly, all the points of this form:

[trail gust]

if u take a cuboid instead of the line for visual purposes, in between those particles

for visual purposes

This observer

Has to narrow down infinitely many lines

inside of that cuboid

region

to get the correct true line

it doesn't have to be a cuboid but

there's a region where he has to eliminate other lines

[shut thunder]

Then youre not defining a line, youre talking of a completely different object defined through a lot more information.

[trail gust]

alright let's say you have a line

perfectly

stray

straight*

1 or 2 dimensional line

okay?

and here's my task

place it in 3 dimensional space

and tell me the co ordinates of where it's placed

[shut thunder]

.

[trail gust]

or perhaps, tell me where exactly it's placed

[shut thunder]

If we assume 3d space is also a collection of infinite points, there are points that are in between the two

And others that arent

The ones that are, define the line, the ones that arent define "not" line

That an object is part of an infinitely small region of a bigger space doesnt stop it from existing in said bigger space.

[trail gust]

that's possible in your dreamy paper written 3 dimensional space

[shut thunder]

if you dont agree with that, then the idea of 2 points also doesnt make sense

[trail gust]

3 dimensional space is more complex than what you would think

[trail gust]

nah I do agree with that

the problem is

you aren't able to find the centre

[shut thunder]

You can tho

[trail gust]

to map out where the line would lie

[trail gust]

oh really

define me a centre

in our 3 dimensional space

I give u nothing

but void

and ur eyes

[shut thunder]

Again, do we know the two points that delimit the line?

[trail gust]

we do

we sure do

what next

[shut thunder]

(p+q) / 2 defines the midpoint

[trail gust]

okay

I give u a midpoint

what next

[shut thunder]

Again, if you want to operate under classical rules, then you can define a line in 3d space

Areas too, and volumes

[trail gust]

yeah classical rules none of the relativity complexity

[shut thunder]

(p+q)/2 is just a special case of. pt + q(1-t)

[trail gust]

what next, u have a midpoint and 2 points that's perfectly defined (you have a definition of their positions)

[trail gust]

Ah special case I see, I see

I have a problem though

I wanna reach the other particle

and I'm at point 1

and I see infinite directions around me

which one do I go?

if u do have a line that's perfectly 1/2 dimensional

[shut thunder]

You can still choose the one that will define the correct path

[trail gust]

u should know which one I should go

[shut thunder]

In fact, thats what vector substracion does

[trail gust]

how do I choose that with this equation?

[trail gust]

what does this equation tell me about the direction that I should go from point 1

because I wanna do something called constructing a line

here I'm a one/zero dimensional point that just wants to find it's next true brother

[shut thunder]

p and q being the points that define the position,
q-p is the direction that indicates the direction of q from p.

If you want it as an angle, you can in fact get it

[trail gust]

I don't suppose angles work well in 3 dimensional space do they

[shut thunder]

Ever heard of polar coordinates?

[trail gust]

no

what are they

[trail gust]

I see

q-p

[shut thunder]

Any cartesian space (euclidian geometry) can be described as a length and a set of angles.

If we are in 2d space, you need 1 length and 1 angle.
3d, 1 length, 2 angles, etc.

[trail gust]

ah I see, so u give me the direction to go first, and then that direction is like a 2 dimensional plane where u give the me the angle then

alright

[shut thunder]

And theres a clean transformation between the two

[edgy ether]

🤔

[trail gust]

if p is 0,0,0 and q is 5,0,0

then q - p

hmm

[edgy ether]

-5 😁

[trail gust]

-5, 0, 0

here's a problem tho

now where exactly is the direction of x axis and y axis

[shut thunder]

q - p here is 5,0,0, not -5,0,0

[edgy ether]

x,y,z

[trail gust]

ah right well

[trail gust]

what about this?

[shut thunder]

x,y,z is defined in the same space as (5,0,0) and (0,0,0) are

[trail gust]

yes

I do understand that

but

where exactly does the x axis go

[shut thunder]

It doesnt really matter

[trail gust]

in our 3 dimensional space

[shut thunder]

(5,0,0) and (0,0,0) are formed by their own orthonormal vectors

[edgy ether]

it would be -5 if its delta x

[shut thunder]

In the same measure you define the two points

[trail gust]

I see it doesn't? so are u saying that u can't reach the correct destination if there was one, with this equation

[trail gust]

How about this, I can deeper my end of the argument

let us say

you don't need to reach the already destined point

u make ur own journey yay

[shut thunder]

Nope, im saying that it doesnt matter how you define xyz, only that its consistent between the direction vector and the position vectors

[trail gust]

now here's the plot twist

when u reach

the next point

at 5,0,0

god knows how much is 1 unit btw

[trail gust]

the situation is the same

where is your x axis and y axis and z axis towards

[shut thunder]

after moving yourself a total distance of 5.

[trail gust]

wait u reach the other particle?

Hmm

I thought we were moving point by point here

[shut thunder]

You dont even need to be able to tell that, if you correctly know the two points, everything between them is properly defined.

[edgy ether]

biktor

[flint pulsar]

real

[trail gust]

really?

are u saying me that

[edgy ether]

whart are u ltaking tbboutr

[trail gust]

you can go to an already destined and positioned point

[shut thunder]

And yes, you can move an infinite amount of points while apparently moving through a finite distance.

[trail gust]

from point 1

without making ur random weird journey

[trail gust]

I suppose you're saying me that we can just construct a line between 2 points if we know their positions

but here's the problem

when u wanna contruct a line to the other point

in 3 dimensional space

[shut thunder]

define "construct"?

[trail gust]

what does our equation tell about WHERE the x and y and z axis is

[trail gust]

uh

u move towards

[shut thunder]

If we are talking about the mathematical object

[trail gust]

that point 2

[shut thunder]

This is quite literally the construction

[trail gust]

okay

it is

[shut thunder]

change any arbitrary amount in the range t, you end up somewhere in between while in the line.

[trail gust]

but this only works if u wanna construct ur own random path and ur own random line

[trail gust]

I have point 2's position already

[shut thunder]

Nope, that defines the only line.

[trail gust]

there's no "only" line

for point 1 , the x axis can be towards it's right hand side

[shut thunder]

yes there is. Theres no 2 shortest straight lines between two points

[trail gust]

for any other brother of it, x axis can be towards the slanting up right (from its eyes btw) side

[shut thunder]

If you want a curved line, then you can define it too.

[trail gust]

and it won't match

[trail gust]

I would talk about this before moving into more complex topics

[shut thunder]

if p and q are defined correctly for their pov, then the line is also defined correctly.

[trail gust]

here u go, how do u know that p and q are "correctly" defined from the point 3's co ordinates

what does the equation tell

in terms of 3 dimensional co ordinates/space

[shut thunder]

Nothing to tell us, but you asked for the condition where we treat this as an euclidian geometry.
If you cant define the points from their perspective, then you shouldnt be able to definite for us.

If you want a more accertive way anyways

Define the position of 2nd guy as a point too

[warm umbra]

Welcome to the server @trail gust

[shut thunder]

and you can translate between the two person

hi yeet

[warm umbra]

Hey twin. 🥹

Are we talking about three dimensional coordinate systems?

[shut thunder]

doesnt differentiate between euclidian geometry and irl physics

[trail gust]

I see, I thought we were having 0,0,0 as co ordinates of every point of its down. didn't realize mathematics was so incapable that it requires a fixed definition for both of the points in one frame of reference for it to actually do anything

[shut thunder]

You arent at 0,0,0 for me, since im at 0,0,0 from my pov.

the magic of translations

[trail gust]

how about

we talk about you as a point and me as a point alright

[shut thunder]

If you want an absolute 0,0,0, define our position with respect to it and also the points

[trail gust]

you're at 0,0,0

[shut thunder]

Then it becomes an universal thing.

[trail gust]

I'm at 5,0,0 from u

okay?

I just told u the co ordinates

now throw a ball and hit where I lie

Now..... PROBLEM? YEAH THAT'S RIGHT, you don't know where the x axis is towards

[shut thunder]

yeah, i know

if youre (5,0,0), then the axis is exactly alligned to where you lie.

[trail gust]

where is it, tell me a bit humanly, is it towards ur right hand or towards your left hand or towards ur right leg

[trail gust]

yes I know I'm at 5,0,0

[shut thunder]

if i want to rotate i can too, (5,0,0) will change and become some other point

[trail gust]

but which direction's 5,0,0

[shut thunder]

5,0,0

[trail gust]

I don't think you're getting the idea here

[shut thunder]

(5,0,0) - (0,0,0) gives me your direction

[trail gust]

alright

if it gives u my direction

tell me

[shut thunder]

theres only one direction

[trail gust]

do I lie towards your right hand side

[shut thunder]

If i rotate, then the point will also rotate.

[trail gust]

or towards your left leg side

[flint pulsar]

The axis is defined BEFORE you give the position

[trail gust]

tell me this

[shut thunder]

Go look into what a rotation matrix is

If i want to flip 180º around yz, now youre at -5,0,0

From my perspective, the direction vector always precisely tells me where you are

[flint pulsar]

Does he even know what a matrix does

[trail gust]

oh I see, knew mathematics was so incapable that it could not even find the axis when a child gives it perfect co ordinates of 2 points

[trail gust]

yeah

I do

[flint pulsar]

Ok good

[shut thunder]

Like, if i want i can define x to be exactly where you lie

[trail gust]

but the problem in 3d space is, u have many 2 dimensional planes and u don't know which one to pick

[shut thunder]

It could be y, or z too.

[flint pulsar]

What do you think coordinates are?

[trail gust]

how do u know which one to pick?

[shut thunder]

Whatever you want

And then define the point around the one you chose

Thats why knowing the geometry youre working with is important

[trail gust]

I give u 5,0,0 okay? you're at 0,0,0 , but this is 3 dimensional space and the x axis can be towards your right hand side (for human purposes) or towards your left leg side or towards your head side

and no equation tells me which side it would be

and how do I define this "axis" Even if I want to

[shut thunder]

Gang is not being able to understand how basis vectors work

Ever seen ijk as vectors?

[trail gust]

I see

so u can't just know where it would be if I just told u 3 numbers x, y, z

you need to me to tell which direction each would be from ur perspective

[trail gust]

how can u tell me then

tell me

[shut thunder]

Your three numbers lie in the "plane" you already defined.

[trail gust]

I give u 5,0,0 but u dont decide where the point would lie

I already have a point fixed

u have to reach that exact point

tell me how do u know

where the point is

right hand side or left hand side or where

I just gave u 3 numbers

5,0,0

Tell me now

[shut thunder]

Youre at 5 in the x axis

My x axis that is

5i if you want

[trail gust]

can u point out this x axis in terms of which direction it would lie in terms of ur body?

I'm sure it's a kindergarten question

so tell me

[shut thunder]

I say that straight up in front of me

Cause i wanna

[trail gust]

alright

but YOU'RE wrong

[shut thunder]

Lmao

[trail gust]

I already kept the point at left side

and u didn't find it

u said in front of u

I gave u what u wanted, 3 numbers 5,0,0

[shut thunder]

Then it isnt at (5,0,0) for me

[trail gust]

how do YOU decide what is your x axis

you're just a human

[shut thunder]

Its arbitrary

[trail gust]

this isn't actual matter and particle laws

[trail gust]

it's not, if someone else tells particle 1 5,0,0 the particle 1 would be in awe to pick a direction

[flint pulsar]

The problem is that you define a point by its coordinates before giving the axis/basis vectors, when the definition of coordinates is precisely "the amount of each unit vectors needed to reconstruct your original point". So the answer is that you cannot find a point given its coordinates without specifying the axis.

[shut thunder]

Youre the one that said that we define 0,0,0 where i am.

[trail gust]

The particle doesn't have bias like u

picking front or any direction

[trail gust]

right

I do

I do

but like direction is different mate

[shut thunder]

No it isnt

[trail gust]

u don't know which direction x axis lies

[unkempt moat]

Yeah if you’re at 0,0,0 then for all intents and purposes 5,0,0 and 0,5,0 and 0,0,5 are all the same

[trail gust]

you have infinite directions around a point

I don't understand why you don't get my point

how about this

[shut thunder]

I chose one and you gave me a direction, you dont choose for me what the basis is.

If you dont know the basis, you cant define the point

[sleek sable]

woah nice discussion

[shut thunder]

0 clue whats going on

[trail gust]

I see

[sleek sable]

nice pun

[sleek sable]

"to confuse the enemy, you must confuse yourself"

[trail gust]

no but

if u say yourself 5,0,0

what is the basis of where you will define the x axis as

[shut thunder]

(5,0,0) is 5 in my x, 0 in my y, 0 in my z

[trail gust]

As a human, u have bias to say it as "front of me"

but as a particle

what is the basis of which direction it will pick as x axis

if it knows it has to move 5,0,0

I don't involve in anything here

I don't give it anything

It does Self propulsion but where?

[shut thunder]

If i rotate 90°, then my x and y can switch alligment, and now its 0 in my x, -5 in my y, 0 in my z

[flint pulsar]

Can I try?

Mr stokes theorem

[trail gust]

u can rotate 90 degrees, but towards which direction? right or left?

u as a human can say right or left

but it as a particle

how would it know

right or left

where does ur equation tell right or left

we're talking about particles here

and u don't have a nice frame work