help-36

[candid pulsar]

then this would be easier and more rigorous

[vale vigil]

I don't believe u are

[candid pulsar]

bro is not saitama

[scarlet sinew]

js stick to conventions bro

[candid pulsar]

we are bound to have some sort of mental capacity

[tranquil pine]

Hi who need help

[scarlet sinew]

backread

[candid pulsar]

and the majority of human population use.. this convention to make sense of the 3d plane

[vale vigil]

I believe that you are not replying to me in ways mathematics would be considered real

please do not engage more

[scarlet sinew]

you arent even

??

[vale vigil]

wouldn't look good on your behalf

[vale vigil]

I'm asking questions and you're saying "well hey we don't know. But like humans have a limit right"

[candid pulsar]

yeah no at this point we might need @God to look in here please thank you

[vale vigil]

bro

have you even started college 1st year

or are you still in school

to speak about mathematics like this

?

[scarlet sinew]

have you finished 9th grade lil bro

[vale vigil]

are u someone who knows the subject

[heady moon]

brodie this not going in right direction

[candid pulsar]

enough for this argument at the least

[vale vigil]

yeah, I just don't want people who say I don't know to my questions to indulge here

they literally have a choice to not talk when I'm the one asking for help and not them here

[candid pulsar]

look the answer to your question is

yes, there are infinite possibilities

just choose the one the lot goes with

thats all

[scarlet sinew]

yes we have your answer to your question and that is 3d vector equations RELATIVE TO THE AXES and youre somehow turning this into an argument about directions and shit

[vale vigil]

look you're saying me " We humans don't know that, only God can"
and I don't believe this because you may not have studied mathematics enough to be able to qualify to say this

[scarlet sinew]

and now you’re doing ad hominem

[vale vigil]

<@&268886789983436800>

[heady moon]

crazy

[scarlet sinew]

says the guy bringing ad hominem while asking for help lmfao

[candid pulsar]

im saying that its better for humans

[steep hatch]

Why am I summoned

[candid pulsar]

as we have learned with evolution

[turbid spear]

What the hell happend here

[quasi rapids]

haiii :3

[heady moon]

to endts plz

[quasi rapids]

take a chill pill everyone

[candid pulsar]

just go with what your teacher suggested as convention

[scarlet sinew]

close plz

zzz

[candid pulsar]

its not my fault youre being adamant

[steep hatch]

Have you considered just blocking the OP and moving on with your day?

[vale vigil]

look, I was going through my questions peacefully and back and forth and so; but these both people, suddenly started saying me "look we don't know that, only God can, what your purpose is...." WHO ARE THEY TO DEFINE MY PURPOSE LMAO

[scarlet sinew]

idk im just susceptible to ragebait
my bad 💔

[vale vigil]

they have a literal choice not to help me if they don't know this subject

[steep hatch]

Can you point me to the message in question

[vale vigil]

I don't even think they studied an actual course on the topics they're talking about

[vale vigil]

To say maths doesn't know it

[vale vigil]

Ye sure

[scarlet sinew]

bro ragebaiting atp

[steep hatch]

@heady moon that's not helpful

[heady moon]

k srry

[vale vigil]

.

[candid pulsar]

he does not accept it when i say its easier for him to work on a convention in paper and not just simultaneously visualize all possible coordinate systems like a god

he says its not rigorous enough to assume a coordinate system

[heady moon]

i drawback from now on

[vale vigil]

"you can take one of them " what is that supposed to mean? that just wrong on so many levels, we're talking in a maths environment here and not about what u feel

[steep hatch]

I think blurple is just using a common analogy that you're not understanding and hence are taking offence with

[faint edge]

This is not a productive way to respond.

[vale vigil]

and how do u know u can take any of them and that maths didn't already make a correct path

or procedure

[vale vigil]

well yes I'm just explaining the situation

to the moderators here

I didn't want this to be like this

[faint edge]

Blaming things on peoples feelings, telling them they can't participate if they don't meet whatever arbitrary educational qualifications etc

That's not cool homie

[candid pulsar]

there are some things in math you need to sigh on and move on

not all in math can be perfectly justified for

we have learned with experience that this has sufficiently helped us

[vale vigil]

right but like... This is not a chat discussion mate... he's not even telling it like "I feel like" he's telling it to me like it's the mathematical truth, and this channel is help channel for a reason... people who know come to explain questions, people who don't come to ask

[candid pulsar]

as math develops, we will justify everything

you can confirm with other fellow members if this is acceptable

[vale vigil]

this just shows you're telling me math hasn't developed enough to define the co ordinate system like that yet

[faint edge]

This IS a chat in the sense of a discussion. The topic is about math but it's still a conversation and you are still obligated to act civilly.

[scarlet sinew]

how is visualising everything at the same time supposed to make it simple to understand

[vale vigil]

but math realistically.. might have already

and u just didn't study it yet

in your education

and I don't think you answering it to me as the "TRUTH" instead of how you feel like makes the situation civil

[faint edge]

For higher dimensions lines you can define lines f(t)=tm+b for m and b two vectors and t a scalar.

Fwiw

[candid pulsar]

well you didnt either

[faint edge]

You don't need to pick a coord system. You are however kinda just hiding that a system of equations is around the corner

[vale vigil]

yeah but like that equation needs to have a definition of which direction the axis would point in

if not; this and this would be the same numerically

[faint edge]

In what sense?

[vale vigil]

here

[scarlet sinew]

equations are relative to axes not how they look or what they’re pointing at brochacho

[vale vigil]

These both would be the same numerically

[faint edge]

Once you want to explicitly write out equations of lines I suppose.

[vale vigil]

but to a third object, this changes real position and they're not the same

[candid pulsar]

yeah i think you just want to hide behind more and more complicated math in efforts of justifying your rigor

[faint edge]

I don't see why that's an issue though. You pick an origin even in the xy case.

[vale vigil]

u can pick an origin

but

[candid pulsar]

that is why i want you to pick a coordinate system

[faint edge]

y=mx+b measures x and y relative to the x and y axes.

[candid pulsar]

and work with it for now

you are overthinking this

[vale vigil]

which direction would the x, y and z be towards

[candid pulsar]

in particular directions

[vale vigil]

if the question or the supplier literally doesn't give the direction

[faint edge]

You already do this in the xy plane case is my point

[candid pulsar]

yeah and this is where convention comes in

[faint edge]

So I don't see why it upsets you in higher dim

[vale vigil]

we can pick any direction and we would have different objects that we construct in space

[vale vigil]

no, in just 3d space

[candid pulsar]

convention.

[faint edge]

We do it in 2-dim as well though.

Why is 3-dim an issue?

We even do this on the number line.

[vale vigil]

yes in 2 dimension u dont have a problem as big as this much which 3d

[faint edge]

You have the exact same problems in 2-dim

[vale vigil]

my brain doesn't visualise 2d as much as it does in 3d

lemme show u some visual representations

[candid pulsar]

that is why you are asked to follow convention for now

[scarlet sinew]

seriously if you want to define axes as, say x points to the sun or y points to Saturn (if that’s what you mean by defining axis directions), it literally doesn’t change the line’s equation

like

at all

[candid pulsar]

do you remember how x is to the right and y is to the top in a 2d plane in general for simplicity

it could have been in any direction

[vale vigil]

If u see here, the blue stuff is just the third object seeing

and numerically, the left side point would be the same as the right side point (say 5,6,7 as the co ordinates with same basis vectors)

[scarlet sinew]

mathematics don’t give a shit about visual representation or about “directions”

[faint edge]

Related point, even on the number line you make choices of convention like this.

If this upsets you you should also be upset that you have to pick an origin, a distance between notches and a direction every time you visualize the number line.

[vale vigil]

this is not a rule and the fact it not being a rule is what I'm making a major thing in my argument

[vale vigil]

Picking an origin piint

point*

[faint edge]

Nobody disagrees that these things aren't rules

[vale vigil]

doesn't upset me

[candid pulsar]

its okay

sometimes it doesnt matter

[vale vigil]

because, for a third object, u can just define an object as a point as a 0,0,0 origin

[candid pulsar]

you dont need to rigor everything up

[vale vigil]

right?

[faint edge]

"Object" is kinda vague.

[candid pulsar]

survival is more important than trying to have a perfect visualization of 3 dimensional space

[vale vigil]

Point

[scarlet sinew]

why do you want to make directions matter

?

[vale vigil]

alright how about this, I take u to a step of sequences with drawings

[scarlet sinew]

look even if i have a cube with three lines on top of it no matter how i spin it’s mathematically the same

[faint edge]

Part of why coordinate systems are useful is that we can rotate and stretch them in convenient ways to match various contexts and that we can transform back and forth between them.

[vale vigil]

you'll understand it way better than this

[candid pulsar]

look we get that they can be in any direction in space

[faint edge]

The number line analogy to this issue is that you can rotate the number line any which way you want. Conventionally we depict the number line horizontally. There is no real reason why we need to do this.

[candid pulsar]

and yes spatially different

but just

fix ONE of those

and work from there

[vale vigil]

now if y'all could, see my words for the next few minutes

[vale vigil]

Over here, you have a 3 dimensional space, with basis vectors 1,0,0
0,1,0
And 0,0,1

then you have a point as u can see, at 5,6,7

right. now my idea is, we can get a different set up but with the same origin

just like this:

[candid pulsar]

yes yes we can

[vale vigil]

the point is the same numerically

[faint edge]

Yes, you can rotate and scale without changing the origin for ex

[vale vigil]

now

[candid pulsar]

but fix one of those

you are focused more on the "choosing" part, and less on the "working with the coordinate system" part

the latter is what you need more

fussing on this does no good

[faint edge]

The points exact coords depend on which set of axes you measure with respect to.

[vale vigil]

Alright now, theoretically, this change shouldn't affect anything at all... but here's a twist, it does

[faint edge]

But it does change things

[vale vigil]

because there's a third object in the 3d space

[candid pulsar]

and that moves with the system too

?

[vale vigil]

the blue is the third object

and the points are different if u change things like this

[faint edge]

This diagram is nonsense to me.

[candid pulsar]

here the coordinate system is not reasonable

[faint edge]

Can you make it clearer what it means to you?

[vale vigil]

I mean it's kinda really hard, but if u pick the first picture that I showed as the left hand side, and the second picture which I showed in the right hand side

then u note down the observations of our third object

[scarlet sinew]

okay so basically the third object is fixed in space and not relative to the system

[vale vigil]

it would be situated at different points in space

[scarlet sinew]

is that what you mean

[heady moon]

you mean position of 3rd object?

[vale vigil]

no

[vale vigil]

no, the 3rd object is viewing this

And

[vale vigil]

This

[vale vigil]

Would become different to this

[faint edge]

That didn't make things much clearer to me.

What is the red line supposed to be?

[scarlet sinew]

[scarlet sinew]

im assuming seperator

?

[candid pulsar]

is THIS what you mean?

[vale vigil]

the red line just distinguishes the two scenarios

u dont have to take it too literally but like

[faint edge]

Kk what about the green crosses?

[heady moon]

ok basically what we are doing is we fixed blue object and rotated the axes?

[vale vigil]

the green crosses... are the axes.. I'm sorry for that drawing

[faint edge]

No worries

Blue ones are also axes and green dots are pts in the green axes coord systems then?

[candid pulsar]

okay now can you confirm if this was what you meant

[vale vigil]

and if u seem the other one after the right line to be kinda flipped: I did mean it to be different, but with the same origin

[vale vigil]

no I meant to draw eyes with the blue one

the blue is the third object seeing all this

What I meant to show was:

to the third object,

[scarlet sinew]

@vale vigil

[vale vigil]

Seeing this

[faint edge]

So kinda like what blurple said?

[vale vigil]

would not be the same as seeing this

[candid pulsar]

yo bro just CONFIRM

[scarlet sinew]

okay we get it

[faint edge]

Christ calm down

[vale vigil]

kind off

perhaps

but now

do u not see a need to define the axes's direction

[heady moon]

can someone pin his 3 drawings

[candid pulsar]

sorry but this is the 25th copy of the 3d visual he sent

and it made no sense

[vale vigil]

when talking about any co ordinates or any objects made via this system

[scarlet sinew]

so basically this or

the orane thingy is ur “third object”

[candid pulsar]

i thought redrawing would make his point easier to see

[faint edge]

It is worth being aware of the fact that visualizations of a mathematical object are not the same thing as the actual object.

[scarlet sinew]

true

[vale vigil]

well not exactly, they're in the same space and to be in fair words with you, the flipping or changing isn't actual, I meant to show that u can interpret the same co ordinates in a lot of ways, and that's why I need it to have a direction

[heady moon]

^ if you are considering usual physics type pov

[faint edge]

So, what I mean is we draw lines and pictures to visualize things, but those pictures may be different from the actual object.

[vale vigil]

well what's interesting

[scarlet sinew]

so if the system and the third object (ill call observer now) is in the same space

that literally just

[vale vigil]

so do u mean to say

[scarlet sinew]

changes the observer’s position relative to the system

[faint edge]

If you have an equation of a line in the plane, you don't at all need to pick axes or anything like that.

[heady moon]

orientation you mean?

[faint edge]

It already implicitly sorta carries that info regardless of how you draw it.

When you want to actually sit down and draw, then yah, sure you gotta pick some axes.

[vale vigil]

Do u mean to say these both points are in the same place

[vale vigil]

wait, where is the line then?

[scarlet sinew]

relative to the system yes

[vale vigil]

from which origin did the line generate?

[faint edge]

Well in the xy plane the origin is (0,0)

[scarlet sinew]

for xyz it’s (0,0,0)

[faint edge]

It's not a visual thing

[vale vigil]

I don't think you're seeing the point here, the idea what I'm saying doesn't actually flip the whole graph...

IF you realistically flip the whole graph, then u would actually have them to be at same points, but like my idea is to show that they CAN be intreperted like this, in a million different (infinite) ways

[scarlet sinew]

more like interpreted from a million POVs

[vale vigil]

in 3 dimension, it's a thing where we have to denote from existences

so we have to " Define a point that exists in 3 dimension at co ordinates 0,0,0"

[faint edge]

Basically nothing changes about what I said in the 3d case

[vale vigil]

otherwise how are u able to tell me it exists in 3d at all? by saying "let dimension be 3?

[scarlet sinew]

tf

[faint edge]

Formally this is basically wrapped up in specifying what R^3 is

Or in 2d by defining what you mean by R^2

[heady moon]

so what is the problem then

[faint edge]

I want to point out something as well

[vale vigil]

Hmm, the actual problem doesn't come in 0,0,0 , it comes from defining which direction the axises would be situated towards (in what setup, indirectly)

because if u don't define that

u can interpret it in a lot of ways

like I showed u

[candid pulsar]

yes but only one of them is enough

[vale vigil]

and u wouldn't know which line they're talking about

[scarlet sinew]

directions are a visual thing, and like doot said earlier it’s not a mathematical matter to define

[candid pulsar]

and as for your contradiction

[vale vigil]

yes but u wouldn't know whic

which

[faint edge]

Okay, but interpreting it for the sake of drawing pictures is irrelevant to the actual math

[candid pulsar]

yes, something might change between you and the points

[faint edge]

Beyond just intuition and drawing pretty pictures I mean

[candid pulsar]

but no one cares about your pov

only what is happening in THAT system is of interest

[faint edge]

In 3d computer graphics, just specifying triples of points is not enough to draw a scene.

[vale vigil]

how so? drawing pictures is what representation means, didn't we get to the axiom of "there can be a line between 2 points" by these same drawings?

[vale vigil]

well yeah

[faint edge]

So you are right that for the purpose of visualizing, you do need more info such as camera orientation+position, screen dimension info etc

[vale vigil]

oh

well

[faint edge]

Because representation =/= math

Well sorta

At some point we get a little philosophical about it I guess

But the actual math we want to do is formal stuff in R^n

[vale vigil]

how did u get to the axiom of there can be a line between any 2 points then? without representation, can't u just say " The probability of the line going to the other point is 0 because there are infinite points in between "

[faint edge]

Why are we taking euclid as fact here?

Euclid's geometry had many problems.

[scarlet sinew]

yo spot the difference mathematically real quick

[vale vigil]

well

[vale vigil]

can we not do this by just saying let x, y, z be any Real number? then we can get all co ordinates to be meaningful

[faint edge]

Wanna also point out that this is not hard to derive in R^n. You just interpolate points. Take a,b two points and pick r(t)=at+(1-t)b as your line.

[faint edge]

R^n is n-tuples of reals. It already does that.

[vale vigil]

I see

[faint edge]

You aren't wrong that there's some important stuff here as far as coord systems and translating between them.

[candid pulsar]

and its easiest to fix one of those easier-to-see POVs and work with your problem

[faint edge]

This is INCREDIBLY useful all throughout physics, cs and probably a billion other subjects.

[vale vigil]

all in all, this just tells me maths cannot show me a line to my eyes in any 3 dimensional world that has any sort of visual representation or detection of co ordinate systems

[candid pulsar]

but you can work with it in some way or the other

[faint edge]

That seems like the wrong takeaway imo

[scarlet sinew]

the 3d vector:

[faint edge]

The math itself, kinda sorta can and kinda sorta can't.

[vale vigil]

because like... if u give me basis vectors, the co ordinates of a point that exists, and then even the origin's true position 0,0,0

[faint edge]

Math has nothing to so with things irl besides us basing things off irl stuff.

If you want your math to be tangible irl, at some pt you have to leave the realm of pure logical gymnastics

[vale vigil]

I could interpret this point to be in infinitely different positions

depending on how

I interpret the axis direction

[faint edge]

You wanna draw a line? Well you need writing tools, stuff to write on etc and you must cope with the fact that the object you draw may not be a perfect representation of the line you intended.

[vale vigil]

well sorry my net lagged

[vale vigil]

hmm

[faint edge]

Yeah, this is true.

[vale vigil]

but it seems troubling that

even if we had an all powerful being that ignored all those imperfections of our physical world

even in a mathematical 3d world

u wouldn't be able to show it

this just seems wrong on so many levels... do u see where I'm coming from

[faint edge]

Part of why cartesian coords are useful is because we can overlay them (imperfectly) onto many different real world scenarios to some extent.

If we just had only one fixed global coord system everybody used, that would be incredibly inconvenient.

The whole notion of coords is not to far off from us just laying a system of rulers on everything.

[vale vigil]

no I don't mean it like that

let's have a really simple case

of 3 points

[faint edge]

Measurements are useful. Rulers are useful. If you glue a ruler to the ground so it can't move it becomes less useful.

[vale vigil]

one point's the observer, one point's the origin

and another point is what we need to find

the observer point gets the measurements as; origin at 0,0,0 basis vectors at so and so

[faint edge]

Yes relative coordinate systems are a thing.

[vale vigil]

and I would still be able to conclude the point is everywhere sort of

[vale vigil]

wait

but how

do u convey that the point is at one place

with a relative co ordinate system

can u teach me this relative co ordinate system idea

[faint edge]

You pick a coord system that you measure the position of the pt wrt

[vale vigil]

okay

[faint edge]

Think of it this way, you fix one set of axes, but you can simultaneously fix another set.

You can measure positions of pts wrt either.

[vale vigil]

wait is pt is a line or a point, in time.

[faint edge]

This is actually also very useful in 3d graphics btw

Pt in 3d space

[vale vigil]

yeah is it the origin or any point in the space?

[faint edge]

Sometimes u wanna measure wrt the camera, the player position, the position of some other object etc

[vale vigil]

or a line

[vale vigil]

hmm

[faint edge]

The "origin" in this context is a point relative to a particular coord system.

So if you have two coord systems saying origin by itself is just vague.

[vale vigil]

I see

[faint edge]

A simpler example: you can have two rulers at once lol

If I say "the 1 inch mark" which one do I mean?

It is unclear.

[vale vigil]

wait I don't understand this representation tho, if u have 2 origins, then what would the co ordinates of one point be?

if it's 2,4,5 here

and 3,6,7 there

[faint edge]

They are relative to coord systems as well.

[vale vigil]

yeah but how do we use it? like do we merge it into one single, co ordinate with an idea, or do we just take both of the co ordinates

or

[faint edge]

When you write (1,2) in the xy plane for example you mean 1 unit along the x axis and 2 units along the y axis for ex (if you have multiple xy axes this is vague)

[faint edge]

Wdym by use?

[vale vigil]

I mean.. how is the depiction done? for one co ordinate system it's done as 3,2 or x, y, .... n

[vale vigil]

hmm

something that doesn't make sense to me is that

[faint edge]

Well you can just overlay the two sets of axes on a single diagram. It might become complicated but it's not impossible to do.

[vale vigil]

if u can pick any direction of x and y axis to be situated as, and all of them would give different, realistically speaking, answers of points in space

then how do u define this co ordinate system to be an actual existing theory at all?

if u can't prove it exists in one place

[faint edge]

Why do you think a coordinate system is a theory? What does theory even mean to you?

[faint edge]

I mean, are you equally unsettled that if something is to your left and you turn around it will be to your right? Or that an object can be to the left of you but to the right of somebody else?

[vale vigil]

I mean sure, u do it via 3,2 = 3,2 but wouldn't something in 3 dimensional space ideas come and contradict this saying 3,2 can be interpreted in infinitely many ways even with just one origin and since it's 3d space, it did not be equal to every other point being the same, if so, 3d space wouldve collapsed into 0d one single point

[vale vigil]

yes but

this would be solved

[faint edge]

Well we can just represent points in the two coord systems differently.

[vale vigil]

if the user specifiied the direction

[faint edge]

There's no shortage of tuple notations.

[vale vigil]

Of which the axises are situated in

via a line equation

showing direction

[vale vigil]

hmmm

[candid pulsar]

point is that it doesnt matter for the needs of the examiner and you as well

and you can work

[vale vigil]

but if u have a problem to depict it as one single point in one co ord system itself

[candid pulsar]

with convention

[faint edge]

Say I call (x,y,z) pts the points in coord system one and [x,y,z] pts the points in coord system 2

[vale vigil]

which 2 points would you pick for each

[faint edge]

Okay, so now you are forcing a choice of one coord system.

I want to make it clear that this is a choice and we do not have to do it

[vale vigil]

see how about this, I get 2,3 2,3 2,3 and infinitely many 2,3s but visually, since I took different 1d axeses, these wouldn't overlap in space even though they're same in numbers

[faint edge]

But typically in lin alg you learn about transformations and such

[vale vigil]

so which of these 2,3s would u pick for the other system to measure

actually, a drawing would show this the best

[faint edge]

So you would provide a map that sends (x,y,z) pts to [x,y,z] pts and such

[faint edge]

Point being you just need a way to translate pts in one of the coordinate system to pts in the other.

[vale vigil]

hmm i get that but

[vale vigil]

talk about it in terms of here

Over to the left, u have co ordinate system #2

it's deciding which point it wants to measure

[faint edge]

This is too vague

Let me give you a different example

[vale vigil]

over to the right, the blue ball is just all the different possibilities of the axises that can be made with one origin

[faint edge]

Say you pick a coord system

[vale vigil]

and each of those would create a different point but name numerically

that's why I put many points instead of one

[vale vigil]

hmm yes

[faint edge]

Say I go "nah ur coord system sucks, I want my own!" So I set my origin at (2,0,0) and then orient my axes the same way you did yours (just shifted).

I can translate points in my coord system by just subtracting 2 from any x coord to get a pt in ur coord system.

We can do similar things with rotations, I can even scale my coord system differently.

[vale vigil]

so

essentially you're telling me that

you would have one single point

for both of those

with a specific setting of the direction of their axises

[vale vigil]

not just numerically

even in spatially

[faint edge]

In this case I would have two different origins. One for each coord system and some orientation of the axes for each coord system.

Lets also say I use the [x,y,z] notation for my pts and you use (x,y,z) notation for urs.

[vale vigil]

hold on

[faint edge]

My [0,0,0] is now your (2,0,0)

[vale vigil]

are u saying this

they're 2 different co ordinate systems

and they share their own points in the first system

[faint edge]

Yes if you mean we can set up a bunch of different coord systems simultaneously

[vale vigil]

but if u bring them specifically

u can get both of their co ordinates to match ONE point

in visual space

[vale vigil]

I see

but this seems like really impossibly hard

[faint edge]

Idk what u mean

[vale vigil]

have u discovered a method to do this easily?

[vale vigil]

just watch the picture

[faint edge]

No explain it

[faint edge]

Again, you would learn more about this in linear algebra

[vale vigil]

and see that, if u place the cyan co ordinate system in a place where the white co ordinate system intertwines with it so that, both of them have a common point that in terms of co ordinates is the same

[slate narwhal]

maybe the only piece of intuition I can give you is that a 7cm object is 7cm regardless of whether you measure the thing from the 0cm mark (in which the object extends to 7cm) or the 5cm mark (in which the object extends to 12cm)
object's still 7cm either way.

likewise, suppose a point on Earth is at sea level, 0 deg lat, 0 deg long.
then I say, fuck the current lat/long/alt system, I'm defining my own!
0 degrees lat is now the south pole, and 0 degrees long is where I am.
does the point change locations? no! but I describe it a different way because I am using a different coordinate system.

coordinates are references, not absolutes!

[vale vigil]

like I'll explain it simply okay

[faint edge]

Stuff like rotating, translating and scaling coord systems is very easy to do via matrix multiplication. Your computer can do thousands of coord changes every minute.

[vale vigil]

let us say

you have an arbitary direction for x, y, z

in co ordinate system one

[vale vigil]

now u pick any point say 2,3

and now forget about this

you have an arbitary direction for x, y, z for co ordinate system two

and now say u pick any point 3,6

now, if u situate these two co ordinate systems in. One single 3d space

I mean... overlap them or something

the chance of their point aligning, is well eh miscleaneous

BUT

there can be a point in the merged 3d Euclidean world

where co ordinate system 1's 2,3

[faint edge]

Why are we worried about overlapping these points?

[vale vigil]

shares the same space of co ordinate system 2's. 3,6

[faint edge]

You pick two coord systems and two arbitrary pts. They may not be the same pt. Why is this a problem?

[vale vigil]

essentially, this would make them be able to define a point at one single co ordinate

without having to worry about the directions of the axises

[vale vigil]

actually

now that u say that

how are u "measuring" this point?

[faint edge]

"Measuring" with respect to what?

You have two coord systems.

What are you measuring relative to?

[vale vigil]

with respect to each of the co ordinate systems

[faint edge]

The same way you'd do in one coord system

[vale vigil]

yes, how do u know that the point is so and so co ordinates in each of them

[faint edge]

Just ignore the coord system you aren't using.

[vale vigil]

in one co ordinate system, I usually define 2,3 as a point that exists in a space like this;

[faint edge]

Nah

Think about it, (2,3) in a particular coord system is RELATIVE to the axes.

[vale vigil]

and if it's real world and I have to locate the 2,3 I give up my hands because locating a 0d object is impossible in 3d world without mathematically saying it exists

[faint edge]

You don't define (2,3) after the fact.

[vale vigil]

Hmmmmmm yes

[faint edge]

You pick a coord system and that tells you what (2,3) is

[vale vigil]

wait

wait

u don't need the co ord system first

u already pick a point and ask " Which co ord system gives the answer of 2,3 for this"

right?

[faint edge]

I think that's kinda different.

Say you have a sheet of paper

You can draw a pt

[vale vigil]

is pt a point

or what is it

[faint edge]

Then draw axes and ask what are the coords of my pt

[vale vigil]

is it a line

[faint edge]

Yeah pt=point my bad

[vale vigil]

hm

[vale vigil]

but

I can legit... draw INFINITe of those

[faint edge]

But before you draw the axes it doesn't make sense to ask what the coords of your point are. The coords are measurements relative to the axes

[vale vigil]

I mean.. pt can be, 3,6 9,8 10383,-0.000002

whatever it wants to be

how do u take one absolute thing

[vale vigil]

yeah

yeah that's true

[faint edge]

Okay, and? There are infinitely many choices of pts axes etc? Why is this bad?

[vale vigil]

wait

what is your bias

to pick one then

[faint edge]

Like why pick one?

[candid pulsar]

everyone is comfortable with it

[vale vigil]

you're asking what the co ordinates of the point is

so u have to pick one

[candid pulsar]

and you can discuss with others coherently

[vale vigil]

out of the infinitely many co ordinates

[vale vigil]

what else can u do?

[candid pulsar]

that is called convention

[vale vigil]

other than not picking one

[faint edge]

A common thing that happens in physics

[vale vigil]

hmm

[faint edge]

Is that one coord system makes your calculations much easier to deal with than others

[vale vigil]

yeah

[faint edge]

You are right that you have many choices

[vale vigil]

pretty much

[faint edge]

But some choices are less practical in a given context than others

[vale vigil]

less practical

I wonder what that means for mister maths who doesn't care about visual representations or inconveniences

[scarlet sinew]

aint no way this convo still ongoing bro

[faint edge]

Say you wanna calculate something about the rotation of the earth for ex. Why set the origin so that the earth lies at (1000000000000000000000,0,0) as opposed to so that the origin lies at the center of the earth?

[vale vigil]

well, sure

[faint edge]

Okay, so it's a bit of a misrepresentation for me to see math doesn't care about visuals

[cyan kayak]

This is also not taking into account other schemes for specifying coordinates, like spherical, cylindrical, etc.

[vale vigil]

you can get a nice origin that takes up less ink in your paper

[faint edge]

We care about them insofar as they help as understand and solve problems.

[faint edge]

Not just that

[vale vigil]

I see

[faint edge]

Like the actual computations can become much simpler

[vale vigil]

yeah true

[faint edge]

You can often cook up a coord system with more convenient angles and distances for doing actual computations is what I mean.

[vale vigil]

hmm

alright

let's move on in the idea

you select a point pt

but what next.. if u can pick a nice co ordinate like 0,0

then?

[odd violet]

hi again

[faint edge]

Idk what ur asking?

[vale vigil]

you said this is in relation to two co ord systems

but we've only gotten one

where's the second one

[odd violet]

Why is all of this going on again

[faint edge]

Sorry I'm still unclear. We pick a coord system and a pt, then we pick another coord system? Then what?

I'm assuming we've overlapped the two coord systems as well?

So, now we wanna measure the position of our pt in both coords?

[vale vigil]

well

but

how

[candid pulsar]

you were the guy starting the two systems talk

[vale vigil]

do u measure this point

[faint edge]

You do it the same way you do if you only had one coord system

[vale vigil]

From the other system, other than 0,0 system

[faint edge]

You just have two representations for the pt.

[vale vigil]

yeah but, by this wouldn't u get another point

[faint edge]

You will get another representation for the point

[vale vigil]

you wouldn't define the same point of the origin/ this pt of co ord system 1

[faint edge]

If I call you by a different name do you become a different person? Lol

[vale vigil]

how so, I mean do u just see and plot out the graph " If we take another point as centre as another co ord system, then this looks like it's at about 3.9,3.2 that seems about right "

[faint edge]

We are in 2d?

[vale vigil]

is there not a mathematical formula that constricts the point's location to an exact

[vale vigil]

I mean same for 3d

[faint edge]

Lets just do 2d since it is easier. The same reasoning will apply in 3d.

[vale vigil]

do u have an invisible graph around u and a trust worthy eyes that tell u they're at about this co ordinates

[faint edge]

Say you draw two sets of axes on the same sheet and a 3rd pt

[vale vigil]

or do u have a function

[faint edge]

Call the pt p

[vale vigil]

yeah sure

alr

[faint edge]

Lets write coords in the fiest coord system as (x,y) and in the second as [x,y]

[vale vigil]

Hmm

okay

[faint edge]

If we want to know what x y make p=(x,y) we look at the axes of the first coord system and measure the distance along the x-axis and y-axis of the first coord system to get to our pt p.

If we want to know what x y make p=[x,y] we look at the axes of the second coord system and measure the distance along the x-axis and y-axis of the second coord system to get to our pt p.

We could even do this problem in 1d

[valid carbon]

oh wow

[vale vigil]

hmm did u define that both of these cord systems have the same basis vectors

[faint edge]

They don't

You should think of basis vectors as defining the axes of a coord system

In this case we have two diff sets of bases. One for each coord system.

[vale vigil]

well if u have 1,0
0,1
For one and like 293848383948,0.1
And vice versa for another
Then measuring the point thinking you've got the same units would be wrong right?

like saying the point is 2,3 in regards to cord system a

[faint edge]

You have to be careful though

[vale vigil]

and 3,2 in regards to cord system b

would just be...

[faint edge]

We have two different ways to represent our basss vectors

*basis

[vale vigil]

2 units of a mountain and 3 units of an ant

[vale vigil]

hmm

[faint edge]

So for example (0,1) and [0,1] need not be the same

In fact our two bases will be {(0,1),(1,0)} and {[0,1],[1,0]}

[vale vigil]

ahhh u became sneaky here

[candid pulsar]

its more of "this way" and "this other way" rather than trying to match their "numeric values" up

[faint edge]

And these sets may genuinely be different

[vale vigil]

Ahhh i seeee

there was a different bracket

I thought it was the same

[faint edge]

Yes (1,0) means 1 unit along the x axis IN COORD SYSTEM 1

And [1,0] means 1 unit along the x axis IN COORD SYSTEM 2

[vale vigil]

I seeeeee

[faint edge]

(Sorry for caps spamming)

[vale vigil]

that's pretty funny lol

[faint edge]

The key point here is our coords are relative to whatever axes we measure them with respect to

It's a little silly but it's also kinda deep and important lol

[vale vigil]

hmm whats the idea of getting these cords in 2 different systems if u can't merge them them like... why can't u just take the better one out of these 2 systems to get the point's location

I mean... these cord systems aren't related to each other right

like their axes are not dependent on each other

[faint edge]

So, I was trying to sorta get at that with the 3d graphics example

[candid pulsar]

and thats.. convention

[vale vigil]

so why the requirement of 2

[vale vigil]

hmm I see

OHHH

[candid pulsar]

you only need the most commonly used one in many cases

[vale vigil]

right right because like

in camera and cinema shooting and stuff, u don't see the same picture of the care or something from every side

ohh this like a physics thing

[faint edge]

Say you wanna render a scene with a house and you wanna render a dog with birds spinning around its head. You have the global coord system, say you place the origin at the house

[candid pulsar]

better way to visualize it yeah

[faint edge]

For rendering the birds it would be a lot easier to draw them relative to the dog tho

So set a second coord system with the origin at the dog

[vale vigil]

well id only imagine why a cameraman would place cameras via co ordinates instead of seeing where his setting would be lolll

perhaps in simulation maybe

[faint edge]

So long as you can translate this back into world coords (or whatever coords you are using) this is very useful

[vale vigil]

Yeah

it is

[faint edge]

But you see that these kinds of situations can get very convoluted and we can come up with many other examples of course

Choosing coords are exactly that, a choice.

[vale vigil]

hmm

a question over here

shouldn't this idea be created for something like computers

because in real life, we'd never be able to do anything 100% precisely

[faint edge]

This is used in computer graphics like I said lol

Well computers aren't 100% precise either ofc

[vale vigil]

I imagine it's a different world and atomic principles don't work for computer things, although they maybe the exact same things but I still don't get the idea how programming exists in atoms... ifywim, it seems non natural

[vale vigil]

well

[faint edge]

I tend to think of it as the real world being much messier than what we deal with in math.

This extends even to computers. Ieee floats aren't actually reals for example.

We use them as a way to represent reals

But that doesn't mean they are the same thing.

[cyan kayak]

As I mentioned casually yesterday, 100% of numbers are number that we have no way of representing in the real world. They require an infinite amount of information to specify. The numbers we deal with are a tiny tiny fraction of the more "interesting" numbers.

[vale vigil]

yeah me too, every morning I really get amused by the strange feeling of touch of a rug, I mean... we can just be synthetic something that really just happened like a cause and effect of forces putting particles in a specific way

or we can not, and be something surreal

The most mathematical example to real worlds

might be computers

[vale vigil]

hmm

[vale vigil]

but

if it's impossible

[faint edge]

Computation is its own bag of worms. Computers on a theoretical level can not do everything we can do in math. Computers irl can do less than what our models of computation can do.

[vale vigil]

then why are we focusing on a subject that's just not possible to do

I thought maths didn't focus about physical real world problems... so why categrozie this as maths and not physics

[vale vigil]

hmm

[faint edge]

Eh all of these subjects overlap in various ways

[cyan kayak]

Real numbers are important because they have no "holes." A property that is critical when we talk about calculus.

and continuity

[vale vigil]

I see

[faint edge]

Math, computer science, engineering, physics, none of them exist in a vacuum. They interact.

[cyan kayak]

For instance, the following function is continuous if we consider only the rationals.

f(x) = x if x^2 > 2, x-1 otherwise

but "clearly" there is a discontinuity here

[vale vigil]

well, maths seems a weird way for dimensional objects to interact.. because it weirdly removes out things like colour, methods of differentiating between void and objects, and a lot of stuff that... may just exist in all real 3 dimensional worlds that can ever exist.

Why is colour not part of maths?

[faint edge]

You can model color

[vale vigil]

I mean...

it's entirely photons

and eyes

[faint edge]

I mean, if you think about it color is a real world thing.

So idk if you can do much better than modeling it.

[vale vigil]

but like

[cyan kayak]

There are very complicated models for colors that take into account human perception

[faint edge]

We have analogous situations for things like force

[vale vigil]

what if we're the only real world that's possible and a world without colour is, in physical nature impossible to exist

then wouldn't maths be talking about a non existent world

I don't get why real world and maths have to be seperate

[faint edge]

Idk dawg that's above my paygrade lmao

[cyan kayak]

There's nothing about math that says it has to model the real world.

[vale vigil]

after all, the real world is just one of the worlds that maths theoretically should be able to model

[faint edge]

I mean, they aren't separate in some ways and they are in others

[cyan kayak]

you can model imaginary worlds with math

[vale vigil]

hmm

[faint edge]

Math is sometimes called a "rational" science.

The idea is (roughly) that we're trying to work purely in logical terms

What happens irl is a separate concern.

[vale vigil]

well I see a lot of philosophy for some reason... are there infinite things to discover, then why discover at all.... are there finite things to discover, then how will you know / what will u do after u discover everything..... Can logics break ? Then how do u know if a logics are truly profound even if u wait for trillions of years

[faint edge]

You are asking several different things here

For the logic question

The history of logic is full of people developing various logical systems and debating how effective they are

[vale vigil]

hmm

[slate narwhal]

the first two questions seem to have nothing to do with math and more to do with how humans categorize things and the nature of humans to explore more anyway

[faint edge]

I tend to take a view that I would consider kind of a logical pluralist pov.

There are many systems of logic one can use. They all have different pros and cons.

Math in particular tends to use a specific system of logic

[valid carbon]

We have three laws.

[faint edge]

Mostly because it works well for the types of questions mathematicians care about.

[valid carbon]

That's mostly it.

[vale vigil]

has there been times where logic literally broke and went into 0 effective?

[valid carbon]

well axioms i guess

[faint edge]

If you read up on folks like cantor russel and godel you will find some interesting things along these lines

There are a lot of cases where things in logic weren't what ppl expected.

[vale vigil]

hmm

what makes u so confident that people aren't wrong now, just like how they were wrong before

[faint edge]

Well I wouldn't claim to be confident about much in general.

[vale vigil]

well

[faint edge]

I think with respect to logical systems you are guaranteed logical correctness only insofar as your logical system does what you think at does and only insofar as you used it correctly.

[vale vigil]

can u be truly 100% confident about it

[faint edge]

I doubt it.

[vale vigil]

if not, then why keep doing this that's seemingly endless

[faint edge]

Well on one hand because it is interesting

On the other because it is useful

[vale vigil]

well yes

[candid pulsar]

hey its working out fine till now

why stop

[valid carbon]

'I do not know if there's possibly some way in which the 3 laws (which are very rudimentary) might break'

[vale vigil]

well I mean... why spend life in agony or anxiousness about finding answers

[valid carbon]

'Therefore logic is not worth studying'

[faint edge]

Have you heard about the consistency of arithmetic, zfc and stuff like that?

[vale vigil]

when countless generations have died

without knowing them

[candid pulsar]

🖋️ 🔥

[vale vigil]

not really

[faint edge]

If not you might like reading about those things

[vale vigil]

I see

[valid carbon]

someone get this guy Camus /hj

[vale vigil]

Also, what are some of the other interesting topics like the ones we discussed a few minutes prior?

I just wanna get my head imagining an empty 3d space void

[cyan kayak]

I mean, you could argue that maybe math axiom that we use now are inconsistent and we'll eventually find a way to break all math, but until that point, we have a tool that has some interesting things that are useful and applicable to real life, and many other interesting things we can imagine. Worrying about maybe all math will break is rather useless, because it's working right now, and if it breaks later, we'll just amend the axioms to fix the issue.

[vale vigil]

and this stuff, like co ordinates, measuring things etc..

[vale vigil]

hmm

[valid carbon]

It's also not broken yet.

Unless you have counter examples to any of the 3 laws... ?

[faint edge]

I think even with consistency type qs you're still kind of stuff with a "with respect to what" question.

For ex gerhard gentzen proved consistency of PA within zfc iirc

Hopefully I'm not butchering that

[cyan kayak]

my understanding of inconsistency problems, is that eventually you'll find a way to prove A and not A for some proposition A, which then breaks everything

[faint edge]

There are various strengthenings and weakenings of pa that people have been studying consistency of for a very long time

[cyan kayak]

and if our axiom set is one of those, then we just need to choose different axioms.

[faint edge]

I think there are weakened versions of arithmetic that supposedly can prove their own consistency without any weird paradoxical shenanigans.

You still are in a position where you have to answer "consistency of what" and "relative to what" for these kinds of qs.

[vale vigil]

well my idea was that.... you guys might have been missing something in broad daylight all this time, like a logic itself that you didn't apply to theories (a logic like if a exists, then a doesn't exists is false or something like that)

[faint edge]

There are multiple choices of foundations you could pick to discuss pa in.

[vale vigil]

when was the last logic that's significant discovered

[faint edge]

People study logic now

I study logic lmao

[vale vigil]

Oh lol

[faint edge]

Though I do computability in particular

So more pure logic stuff is not something i'm willing to claim to be competent in.

[valid carbon]

!occupied

[final saddle]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[vale vigil]

I have a question;
You would say a is not true if I believe something b as an axiom right,
But if I believe the opposite of b, then a would be true,
But if I believe an axiom that if something leads to something then it is false,
Then wouldn't a be false according to my axioms,
And if I believe another axiom that leads to a contradiction, how are u going to tell me that my ideas contradict so they're false?
Because I can believe that, if any ideas contradict, then they would be true

And if I take these axioms, I would have an absurd world, can u still compute this?

[faint edge]

"You would say a is not true if I believe something b as an axiom right"

Idk. Why would I say that? Lol

[vale vigil]

I mean.. if uh, b says a is not true in some way

for example b says no dog exists

a is a red dog

a does not exist

something like this

but I change the rules of what I believe

then wouldn't my world still be a logical world

[valid carbon]

Why don't you, like, study basic logic?

[faint edge]

You can assume contradictions.

Nobody is stopping you.

[cyan kayak]

I think what he's pantomiming at is if you have some axiom set B, and this axiom set B implies not A, then if we have some other axiom set B' (which is somehow the "opposite" of B), then would that imply A.

And the answer to that question is there is no way to construct B', because 'opposite' doesn't have a meaning in this context.

[faint edge]

You're just stuck in a situation where (if you have "enough" logical oomf in your system), then you can just prove anything you like.

[valid carbon]

That wouldn't be terribly good of an axiom set would it

[faint edge]

Have you seen the proof that 0=1 implies russel is the pope?

[vale vigil]

well if I believe something that doesn't has meaning is always required to be able to be construct and stuff like this... then id have it well

[vale vigil]

lol.. I don't know about proofs much

but I think it's all related to the

axioms that you believe

[cyan kayak]

math isn't about belief. it's about rules. The axioms are the rules we adopt to play our game of math

[faint edge]

https://www.nku.edu/~longa/classes/mat385_resources/docs/russellpope.html

[cyan kayak]

we can adopt any set of rules we care to, just some make the game more fun than others.

[faint edge]

It's a pretty easy to read informal argument/story

[vale vigil]

right, but a major limitation is like... putting all the axioms that are significant, to your base...
I mean different people have different things of what they consider axioms are, some believe good about stuff like abortion, some bad about stuff like abortion

so my question is

what would consider to come as an axiom in your book of logics

[faint edge]

Tbf axioms are just assumptions. They can and irl often are things people earnestly believe.

[cyan kayak]

what the hell does abortion have to do with any of this?

[candid pulsar]

how did we come to social studies lmfao

[vale vigil]

just an example of, how a lot of people can have a lot of different beliefs

and logics should include the significant axioms most humans believe

[faint edge]

Maybe you are assuming too much about how logical other people are.

A lot of people like to think they are logical

But idk if ppl really are

[slate narwhal]

(see: how many people think they are above average)

[faint edge]

I mean, I try to be logical but I would not say I am perfectly logical, consistent, etc.

[vale vigil]

no but, you and many others study logic as a subject right, but like what's the criteria of the axioms that you believe

if many people, believe many different axioms of the same idea

[faint edge]

Idk If I'd be willing to commit myself to laying out some criteria like that.

[vale vigil]

what's the criteria that decides which one you're taking

[cyan kayak]

I just objected to how prescriptivist the position sounded. Making it explicitly about "what you believe" rather than "just some rules" makes it sound more profound, which is never very good in these kinds of discussions. We can also make axioms about things we do not believe just to try them out.

[faint edge]

It doesn't do me much good in the immediate sense if I do. I could be wrong. My feelings may change.

[vale vigil]

hmm i see

[faint edge]

Sometimes you do wanna pick careful logical foundations for things.

[vale vigil]

just some rules yeah, but you're not getting far if u dont think about what/where did the rules come from or how would they come to

there's only so much u can do about solving a cube

[cyan kayak]

you can get as far as the rules allow you to.

[vale vigil]

you can do a lot more if u think a cube has other purposes

[cyan kayak]

you're conflating a lot here

[vale vigil]

well it was an analogy, kinda bad but

[faint edge]

Thinking about these things is different from committing to them

[vale vigil]

you gotta think out of the box sometimes

[vale vigil]

hmm

right

[scarlet sinew]

holy…

also hi guys how’s the convo going

[faint edge]

We can think about law of excluded middle without being like "law of excluded middle is something I 100% believe is true all the time"

[vale vigil]

true

[vale vigil]

but, I don't even think the main problematic task is thinking about those laws,
The main thing is, a lot of the times.. the rules u already believe may not say whether or not to accept a new rule, or reject it

[scarlet sinew]

getting a bit philosophical here are we

[faint edge]

I think ur lost in da sauce

[vale vigil]

I don't suppose your axioms have an opinion towards if having 700 unicorns in a dream would be correct or wrong

What is your opinion on that?

actually

[scarlet sinew]

the concept of axioms having an opinion…

[vale vigil]

I'm lost here

[faint edge]

Idk seems like I don't have much of a reason to worry about that until it becomes an actual issue that affects me.

[vale vigil]

I don't think I should worry about it right now too

well

[faint edge]

It's fine to think about diff axioms and how they play with other logical notions.

I just don't personally see a point into committing myself to believing things I don't know are true.

[vale vigil]

it just came so in this conversation cause someone told me on a debate server a few days ago that, both a unicorn and laws of non contradiction don't have proofs, but u believe one more because it's true, and just like that god is something u beli- so and so..

[valid carbon]

well

[scarlet sinew]

urm

[valid carbon]

that escalated quickly

[vale vigil]

what are some other major things that you study?

[valid carbon]

https://tenor.com/view/escalated-quickly-anchorman-drinking-gif-5112090

[vale vigil]

I wanna get to have more experience on mathematical concepts

[faint edge]

Most of the logical laws and ideas come from ppl observing things irl and trying to construct some kind of understanding of things.

[vale vigil]

just like co ordinate systems and I know one more that's called differential geometry

[vale vigil]

hmm well yeah mine too

[faint edge]

This is a process that has happened for basically all of human history

[lime nebula]

oh my

[faint edge]

You construct a model, other people come and critique it. They construct their own models etc etc

[vale vigil]

I would think and have a major opinion on a child crying

[lime nebula]

Pre-uni measure theory back again?

[scarlet sinew]

asking if 3d linear equations exist escalating to funni debate

[vale vigil]

but I wouldn't for 2 micro bacterias getting photons of a train

[faint edge]

Idk if this is a debate so much as herec thinking about logic

[vale vigil]

I wanna know that someday soon lol

but I don't know where to start

[faint edge]

I do think herec would prob get a lot out of studying more logic and math. Maybe some lin alg in particular.

[cyan kayak]

HereC, do you still have a specific question, or do you just have a lot of random thoughts vaguely related to math that you want to air to the internet and see what sticks?

[vale vigil]

well, I have a good feeling towards it

[scarlet sinew]

linalg is an okay path for him imo

[vale vigil]

lol uhm, this was kind of in between of taking a break from all that hours of talking

but I guess I don't have a question right now

[slate narwhal]

!done

[final saddle]

If you are done with this channel, please mark your problem as solved by typing .close

[vale vigil]

I can probably close this now

[scarlet sinew]

aight

it was fun

[vale vigil]

Yeah

[valid carbon]

Well

either it was

or it wasn't

[cyan kayak]

law of the excluded middle!

[vale vigil]

thanks for y'all

[valid carbon]

(im 100% confident come at me)

[vale vigil]

lol

[scarlet sinew]

even though i got a little bit ragebaited lol

[vale vigil]

.close sorry for that

[lime nebula]

What if it was and wasn't at the same time

[final saddle]

Channel closed

Closed by @vale vigil

Use .reopen if this was a mistake.

[candid pulsar]

https://tenor.com/view/reaction-epic-shocked-happy-yes-gif-16462261

great run though

[valid carbon]

Law of noncontradiction!

[candid pulsar]

ggs

[final saddle]

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[bold dust]

A bag contains 4 red marbles and 2 blue marbles, and 2 marbles are drawn at random with replacement. The ratio of the probabilities that 0, 1 or 2 red marbles are drawn is a: b : c in simplest form, where a, b, and c are positive integers with no common factor large than 1. What is the value of 100a+10b+c

[bold dust]

i dont know how to start

I think 2 choose 2 ways for 0 red marbles, 4 choose 1*2 choose 1 for 1 red marble, and 4 choose 2 ways for 2 red marbles

[craggy plank]

Looks good to me

But they’re looking for probabilities

You might need to modify the current information to proceed

[leaden moon]

consider each case

[heady moon]

1st two are correct where as for the third one we need to consider replacement

so 4choose1 * 4choose1

[bold dust]

oh ok

[tired walrus]

then the first one's also wrong

also we may stop writing nC1 instead of n

[heady moon]

oh right

[bold dust]

wdym there's only 1 way for no red marbles to be chosen

[tired walrus]

2*2 ways for both blue, 2*4 for one of each, 4*4 for both red

[tired walrus]

it's WITH replacement

you draw one, record its color, put it back, then draw one again

[leaden moon]

All of that over 8*7 ways of choosing

[tired walrus]

no, 8*8

[heady moon]

2coose 1 * 2 choose 1

[tired walrus]

because. again. WITH replacement.

also i will again say writing nC1 instead of n is quite silly.

[heady moon]

😢

[bold dust]

where do you get 8*8 from?

[leaden moon]

With replacement

[bold dust]

you mean 6*6?

there's only 6 marbles

[leaden moon]

Explanation here

[heady moon]

yeah right

[leaden moon]

My brain got messed up sometimes

[tired walrus]

what? are we gonna have to always pretend to write (number)C1 because "the number of ways to choose 1 object out of n" is somehow fundamentally different from "n itself"?

[heady moon]

k

writing C makes easier to understand as sometimes people get confused js numbers (has happened bfore)

[leaden moon]

$\left( \begin{array}[c] & n \ 1 \end{array} \right)$

[soft zealot]

1 divided by 0 equals Infinity

$\left( \begin{array}[c] & n \\ 1 \end{array} \right)$
```Compilation error:```! LaTeX Error: Illegal character in array arg.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.49 $\left( \begin{array}[c] &
                                n \\ 1 \end{array} \right)$
You're in trouble here.  Try typing  <return>  to proceed.
If that doesn't work, type  X <return>  to quit.```

[tired walrus]

$\binom{n}{1}$

[soft zealot]

Ann

[tired walrus]

much easier

[leaden moon]

Ty :)

[bold dust]

wait how do you put it in ratio form?

i have the possiblities but idk how to put it as abc

[leaden moon]

$\frac{\text{amount of ways that satisfies the condition}}{\text{amount of possiblities}}$

[soft zealot]

1 divided by 0 equals Infinity

[leaden moon]

In ratio form: $a$, $b$, $c$ are just integers

[soft zealot]

1 divided by 0 equals Infinity

[leaden moon]

So you might need to do some algebra

[tired walrus]

actually you dont

you know the denominator is the same for all three

why not simply clear it to begin with

[bold dust]

i got ratio 4,8,16 which simplifies to 1,2,4 but 2 and 4 share a common factor of 2 which is greater than 1

[leaden moon]

Ratio: 1 : 2 : 4

[bold dust]

but 2 and 4 share a common factor greater than 1

so idk what the question wants

[leaden moon]

This ratio is already simplified

[bold dust]

yes but it requires for a,b, and c to have no common factor larger than 1

oh wait nvm im stupid

[leaden moon]

[bold dust]

.close thanks for helping

[final saddle]

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Closed by @bold dust

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[fathom meteor]

<@&268886789983436800> scam bot

[final saddle]

Channel closed

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[fathom meteor]

compromised account it seemed, unfortunate

[final saddle]

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[zenith violet]

umm so like im trying to assign different defensive multipliers to pokemon based on their typing, so like =SUMPRODUCT(fighting column, steel column) gives me 15.5 so like do i do 15.5/18 = .861111 and then do HP * Defense / (.86111) (where higher values are better) or do i just do HP * Defense / (.5 * (19.5 + 15)) or HP * Defense / (.5 * (19.5 * 15))

im trying to understand which method would be mathematically correct. my bren hurt

https://pokemondb.net/type (using this chart)

[desert mantle]

well all of them calculate some number. but its unclear what you want that number to mean

I dont see where you pull the 19.5 and 15 from?

[zenith violet]

well eventually theyll be ranked but its just supposed to evaluate how defensive they are. 19.5 is the fighting column added together and 15 is the steel one

blank space means 1

essentially pokemon with better typings (like steel) should get a higher defensive rating than pokemon with bad typings (like ice) because of the damage multipliers to different types differ

[desert mantle]

well your 15, 15.5 and 19.5 already do that

lower number=better

[zenith violet]

ya but i also want to factor in it's HP and defense stats

[desert mantle]

you would also have to factor in spdef

[zenith violet]

well i have 2 columns: 1 called physical tanks and the other special tanks. physical will use defense and special will use sp def

[wind vessel]

I think it's also important how defence influence dmg taken

[desert mantle]

I dont quite know how the damage formula works

[wind vessel]

You could do for instance do "on average, what procentage of HP does 100dmg take?"

[zenith violet]

uhhh lemme look it up

[desert mantle]

say you attack the mon once with every type with a physical attack with base power 100 or so

and then check with how much hp it survives

[zenith violet]

https://bulbapedia.bulbagarden.net/wiki/Damage

[desert mantle]

from some standardized mon with/without stab. whatever

[zenith violet]

im less concerned with how much hp a pokemon has left rather than how much % of it's hp is left

so hp and defense can be weighted equally

intuitively, higher hp and defense make it more defensive, and better typing multipliers make it better but idk how to make an accurate formula

[desert mantle]

hp*def/15.5 would be fine

its not like there is a "correct" answer here

[zenith violet]

oke leme try it

1 min

yeh i think this works thx

.close

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[final saddle]

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[tranquil pine]

HI hi

[tranquil pine]

i have many hella other tries but all ended up w indeterminate forms

i guess this one is the best one ever although im not really proud of it

[obtuse hedge]

Where did the times 0 come from

I got -infty and ended it there 🤔

Oh I see it now

[tranquil pine]

well i dunno when u change the 1/x to X
i did both 0+ which gave me -inf yes
and weirdly did 0- too

[tranquil pine]

could u tell me how u did so

[obtuse hedge]

I realized the way I did it was wrong 😂

But taylor series may be a good workaround here

[half raptor]

@tranquil pine Nice username

[obtuse hedge]

\begin{align*}
\lim_{x \rightarrow \infty}x^3(e^\frac{1}{x+1} - e^{\frac{1}{x}}) 
&= \lim_{x \rightarrow \infty}x^3(\sum_{n=0}^\infty\frac{1}{n!(x+1)^n} - \sum_{n=0}^\infty \frac{1}{n!(x)^n}) \\
&= \lim_{x \rightarrow \infty}x^3(\sum_{n=0}^\infty\left(\frac{1}{n!(x+1)^n} - \frac{1}{n!(x)^n}\right)) \\
&= \lim_{x \rightarrow \infty}x^3(\sum_{n=0}^\infty\frac{x^n - (x+1)^n}{n!(x+1)^nx^n}) \\
&= \lim_{x \rightarrow \infty}x^3(0 + \frac{-1}{(x+1)x} + + \frac{x^2 - (x+1)^2}{2(x+1)^2x^2} + \dots)
\end{align*}

[soft zealot]

Coolempire93

[obtuse hedge]

We can see that calculating any further terms will have > x^3 in the denominator, so any further terms will -> to 0

And this limit is simple to resolve as $-x^3/x^2 \rightarrow -\infty$

[soft zealot]

Coolempire93

[final saddle]

@tranquil pine Has your question been resolved?

[lyric obsidian]

augh.....

\qty......

[drowsy epoch]

well done

[final saddle]

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[jagged flare]

how does min(a,b)<sqrt(10)<max(a,b) imply that the leading digits follow the leading digits of sqrt(10)

er wait

nvm

.solved