help-36

[vale vigil]

to the correct original pov of what the exam paper meant by 1,1,1

you have to correct where ur axis is placed in terms of direction

to get the right 1,1,1

now u can argue, that in a world with no other object, not even points

this can be useless

but in a world (3d btw) with any other object (if we forget there are infinite points already and objects aren't necessarily required)

[vale vigil]

this is required, the correct direction to understand the correct location of the point is required

even with the same 0,0,0 or origin

now y'all can talk

[candid pulsar]

ok so you have two problems essentially

[vale vigil]

a, teeny tiny, super tiny, side note: you can't just say "well it's, 6,1,2 in your axis direction when it's 1,0,0 in my axis direction

[vale vigil]

alright go ahead.

[onyx peak]

Well, if we have a fixed coordinate system, then we can describe the location of each point exactly. Of course if you twist the axes or swap them, change them or sth like that, you change the whole system, which was ought to be fixed.

If we wanna communicate position of certain points, we have to agree beforehand on one common coordinate system, with oriented and labelled axes which we will both use.

A good example of this (although not a cartesian system) is the earth and the latitude-longitude coordinates. If I tell you some coordinates, you'll know exactly where on earth they are. Because we agreed on the coordinate system beforehand

TL;DR, you have to fix a coordinate system and not change it, then the coordinates will work

[vale vigil]

if at all

you have a intuition of how 3 dimensional spaces work, and how linear "twisting" works

you'd understand why I didn't "change" anything

when I changed the direction of axises

[vale vigil]

So, for me to explain more clearly

I do not have a vengeful intention behind changing this

and I completely agree with u that we need to have a defined co ordinate system

you'll later understand that's what I'm tryna argue for

[vale vigil]

but

the literal intention behind me showing you that I changed it is

the fact that you.... say it with me... CAN

change it

[candid pulsar]

but.. i) you are unsure how to define the coordinate axes such that the point the examiner calls to be at (1, 1, 1) matches with what YOU have defined

[vale vigil]

when u give this system without a concrete direction

over here, all u gave was which point was 0,0,0 and u gave me basis vectors

and then u gave me a point to locate, 1,1,1

[clear moon]

you yourself admitted that changing the axes doesn't actually change anything. so as long as people agree to your axis directions it doesn't matter what the "true" axes are, assuming you're looking for some sort of universal basis

[vale vigil]

god forbid this mis understanding

[candid pulsar]

that is, you argue that there are infinite possible ways to define the basis vectors, and therefore you are not sure how the grid would actually look like

[vale vigil]

god forbid this mis understanding again

alright

we're back to two minutes of no talking pls

[clear moon]

it's unnecessarily restrictive to want to look for some true established coordinate system, the freedom to change coordinates are useful in all sorts of math

[vale vigil]

to put this into a nutshell, and not confuse u if I actually did something called "changing it"

I was trying to show you, that;
If you give me a point and call it 0,0,0 as the origin, and if u give me basis vectors 1,0,0 - 0,1,0 and 0,0,1 for example.

[vale vigil]

and then ask me to locate or "talk" about a point 2,0,0

then I am ABLE to show 2 different representations

like the ones I showed in the picture

{ SAME basis vectors, SAME origin, JUST twisted the directions of x, y axises WITHOUT any hinderance in the question }

[vale vigil]

I am trying to show u that

[candid pulsar]

but you have seemed to rotate the axes

[clear moon]

it follows from the definition of a basis for a space that any point in that space is uniquely representable in that basis

[candid pulsar]

which is essentially just changing the basis vectors

[vale vigil]

alright so I'm trying to show u that

[candid pulsar]

the axes are a representation of the basis vectors

[vale vigil]

one more minute of silence please

[candid pulsar]

changing them means you are changing the basis vectors

sure

[clear moon]

what you're saying here is "same basis vectors, you're just twisting and changing the basis vectors"

[vale vigil]

pls one more minute of silence

[bold turtle]

Just let him cook

[vale vigil]

what I'm trying to show right now

[bold turtle]

-# Let the kitchen burn

[vale vigil]

is not that " Hey, u gave me an answer, I twisted it and look I got a different answer"

what I'm trying to show right now is

[vale vigil]

" Hey, you gave me a process to find an answer... but why does it look like I can reach two answers with the same process "

[vale vigil]

all of u who have doubts regarding me "changing it all"

please calibrate over this

for a good 2 minutes of ur life

I did not change anything

I ended up with an answer

with the same conditions y'all set

and I ended up with a different, perfectly right answer

that's what I'm tryna show

it's self contradictory therefore you need an absolute direction for x, y and z axis in terms of a line equation of where they are

to actually locate a point

[vale vigil]

^^^

[onyx peak]

Okay, if we talk concretely, I fixed origin (0, 0, 0) at London's ground. My basis vector (1, 0, 0) goes to Birmingham and (0, 1, 0) goes to Norwich, (0, 0, 1) goes to say 10km above london. I think, that means that (1, 1, 1) will surely be 10km above Lincoln, is that wrong? If so, could you tell me where your second answer would end up being?

[clear moon]

if you let e1 = (1,0,0), e2 = (0,1,0), and e3 = (0,0,1), you can write (2,0,0) as 2 * e1 + 0 * e2 + 0 * e3. what's the second representation? in other words, how else would you write (2,0,0) as a * e1 + b * e2 + c * e3?

[valid carbon]

https://tenor.com/view/british-gif-26077384

[vale vigil]

I need this, I need this idea of the axises going to a definite direction (here called Birmingham, norwhich and st. Albanese)

but in 3 dimensional space

you did not define me a direction

for this x axis, y axis and z axis

[vale vigil]

therefore my friend, even though the length "between origin and Birmingham" can be the same

the destination may not, given the process you are given with

[bold turtle]

The destination's BIRMINGHAM ffs

It does not matter the coordinate system involved; the destination is clear

[vale vigil]

listen if I obtain a different x, y, z axis directions

the destination wouldn't be Birmingham

[bold turtle]

The maths does not contradict itself here, because you're using a different description

[vale vigil]

it would be the ocean

[bold turtle]

Okay so

When we switch basis vectors, there is a way to convert from one basis to another

This is the fundamental property of linear algebra

[vale vigil]

you are allowing me to take a different direction for these axis, by not stating the direction you want it to be in so (u can say x direction for x axis, but like it would be the same even if I take a different position pls understand this)

I can't be more clear to you

[bold turtle]

Yes, and I'm being as clear to you in kind

[vale vigil]

you are not teaching me that here, I'm not converting the basis vectors

[hasty mist]

how civilised and learned

[vale vigil]

I'm not converting the basis vectors to different one

[candid pulsar]

ah

[vale vigil]

do u understand this?

or do u not

[candid pulsar]

so if you change the basis vectors

[bold turtle]

Er... but you are LITERALLY DESCRIBING THIS without knowing it

[vale vigil]

no no

I do not change the basis vectors

[candid pulsar]

the destination noted by (1, 1, 1) changes

[bold turtle]

Yes, yes

[vale vigil]

oh.. my God

okay

[candid pulsar]

thats literally what you are saying

[vale vigil]

shall we have

5 minutes of silence

[bold turtle]

If you're changing where x, y, z are pointing on the outset, I hate to break it to you, but that is literally the fuxking definition of a change in basis_

[vale vigil]

for my dead brain cells

to gain back life

[valid carbon]

alright we're all leaving

[vale vigil]

please

let me explain you with pictures

just don't talk please

[clear moon]

what would you call your rotation and twisting that you're trying to do

[vale vigil]

point that is already defined

it is called 0,0,0 the origin of a co ordinate system which in near future, u will construct

[vale vigil]

these are 3 basis vectors

that u are given, respectedly for x y and z axis

Alright

This is what you are given

ALL of u be clear, these are very important for u to understand me

Next;

I'm going to start the process

of finding 6,7,8

@clear moon @valid carbon @bold turtle @candid pulsar

we found the point

taking any direction of x, y, z we did not care

okay?

[vale vigil]

do u agree with this?

[valid carbon]

i just wanna point out

[vale vigil]

DON'T SAY ANYTHING

[valid carbon]

good 'yay' drawing

[vale vigil]

do you AGREE WITH THIS

[bold turtle]

...Sorry, I actually don't agree with this

[vale vigil]

oh

u don't agree that we found the point?

[bold turtle]

No, I don't agree that we didn't care about x,y,z

[vale vigil]

sorry

my mistake

we did care for the x, y, z

[valid carbon]

wdym you cant just agree with him

[vale vigil]

but not in terms of hereC's serpant's direction

[bold turtle]

Right, so this is going to change your argument, don't you see that?

[vale vigil]

we agreed with x, y, z in terms of placing the point / locating the point

[bold turtle]

Sure

[vale vigil]

and hereC's serpant also agrees with this

[bold turtle]

why are you speaking in the 3rd person

[vale vigil]

We didn't take a point that's like 10 kilometeres far away nf say it's 6,7,8

we actually measured everything and like.. took the correct 6,7,8

[vale vigil]

to explain u

without messing up

[bold turtle]

Also, you know coordinates are written with brackets, right?

[vale vigil]

now DO YOU AGREE that we found the point?

[vale vigil]

do u agree now

it alings up with 6 units of x

or basis vectors for more convenience of mathematical ocd

[bold turtle]

7 of y, and 8 of z, yes

[vale vigil]

yep

do u agree?

that is perfect

[bold turtle]

Now, you zip it for 5 minutes

[vale vigil]

NOW we're back to silence of 5 more minutes

[vale vigil]

NO NO NO

u stop here this is the most crucial part

pls

[bold turtle]

So you shouldn't have pinged us BEFORE you were finished.

[vale vigil]

u agree that we found a point with a conditions PLS STOP TYPING NOW

[vale vigil]

no I needed to know

if u agreed

u do, now lemme show u some other thing

[bold turtle]

Look, a few people had agreed to give you 5 minutes to explain yourself; so don't try and ping us before your argument is done. Lay out your ENTIRE argument, without pausing for whether someone has to AGREE with you, because otherwise you're just getting frustrated whenever someone explains to you why that is a hurdle.

Please, by all means, continue - but DO NOT PING ANYONE UNTIL AFTER YOUR "THESIS" IS DONE.

[vale vigil]

what if

we took the point like this?

both of THESE answers are valid

we didn't change the first answer to get this

I REPEAT

I REPEAT

[hasty mist]

Truly one of the drawings in the history of all drawings

[vale vigil]

WE DID NOT

WE did not change the first answer to get this

We got this answer of our own

We did not twist the first answer to get this

[valid carbon]

this is getting to spam levels of heading font

[vale vigil]

we just took any arbitary directions of x, y, z axis for our own sake, that just... was different than the first answer's

[clear moon]

why are we big now

[valid carbon]

yeah no stop that

[vale vigil]

Please dont care about that rn

the more important thing is see what I'm saying

" I did not twist the first answer "

[valid carbon]

i can read normal sized fonts

[vale vigil]

" Even though this looks twisted, this is a completely valid answer that we got on our own"

" You would have agreed to this, if I sent this instead of the first answer"

" This being different doesn't make 2 points by the way, it just says we could have gotten any right answer "

" Please don't confuse this with thinking I changed and twisted it myself, I did not have an answer for this second version already that I twisted... I literally made it based on the question "

" And therefore the part where I finish off is saying that.... in 2 dimension, this would have been the same if it actually aligned up with 6,7 of 2d plane"

[vale vigil]

" But in 3 dimension we get different points because we did not define the direction of the axises, which hereC's serpant believes that it's impossible to do so and math fails fundamentally "

[vale vigil]

" Ending off, if u did not get anything cleared, re read all of this from here, if still not... go ahead and type"

@bold turtle @valid carbon @candid pulsar @onyx peak
You don't need to reply to my ping rn, just read everything and if u still did not get anything, please reply then. it will be better for us

[bold turtle]

-# SO STOP PINGING US, I TOLD YOU THIS.

-# IF YOUR ARGUMENT IS NOT FINISHED...

[candid pulsar]

okay wait im not sure how you're confused/not confused in 2D

can you go through this entire thing in 2D just for the record

[vale vigil]

I do not want to flood the chat to explain to your autisti- sorry for the different use of English, that I finished the argument and if u read it properly bi- sorry for the misuse of English language, you would understand that u pinged u after I finished my argument

[vale vigil]

Actually, I believe I have a mis take there

[bold turtle]

Okay, this is far enough.

<@&268886789983436800>

[vale vigil]

I don't think it really does in 2d as well

[valid carbon]

<@&268886789983436800>

okay waes

[vale vigil]

all I want is

[valid carbon]

i wonder what the 'bi-' is lol

[vale vigil]

before a punishment

delete these chats after #help-36 message

and let someone learned, to reply everything

I believe strongly that

someone will understand

without a mis understanding

[valid carbon]

hi hayley

[barren hound]

I think we've reached the point of establishing that this server is not going to be able to help you diagnose and remedy your core confusion, unfortunately

[vale vigil]

you are laughing in a child's face when he's asking a question for knowledge and you are harrassing him and then complaining that he got angered because of you, all u can do is just walk away and say " Don't involve me in this "

[vale vigil]

wait please just read

what I said

I'm actual and in good faith

[bold turtle]

THEN DON'T JUST INSULT PEOPLE.

[hasty mist]

Even someone as learned as I must concede that I am unable to assist with your confusion. It truly lies beyond the reach of my considerable intellectual apprehension.

[vale vigil]

#help-36 message

[valid carbon]

i did plenty of good faith discussion yesterday

HOURS OF IT

[vale vigil]

Please read it from here

[vale vigil]

And then this

This is the major part

[valid carbon]

oo hi ann too

[vale vigil]

how about I say a sorry to you

and u forgive me and we forget about this

I will not do such thing

anymore

I just was tired

[valid carbon]

uh huh

[heady moon]

take a break

[vale vigil]

yes I will not, I'm here to just gain knowledge please don't mis understand me

[heady moon]

its been 3 days

[valid carbon]

maybe youll be given a break

[vale vigil]

no but we are on the best straw of the talk right now

[clear moon]

i'm unironically convinced that talking to chatgpt would help you way more than anyone in this server could lol

[vale vigil]

I can't leave it at this when I've spent hours of countless explaining to u what my question is

[tired walrus]

ayo that use of "autistic" as an insult ain't cool at all mate

[vale vigil]

and when these few minutes of

[heady moon]

we can move to threads so can continue later

[valid carbon]

blud thinks calling people autistic in the math server is an insult

[vale vigil]

no but like... it would take someone 5 minutes

to end this argument right now

that's the stage it is in

[candid pulsar]

uh huh

[heady moon]

i doubt

[clear moon]

does ending the argument mean agreeing with you

[barren hound]

While people have been very eager in helping you with this (and some have been what I would call overeager), I don't think the medium of discord chat will be an appropriate venue for this. I would encourage you to find someone that you can talk with in real time, with the aid of a physical piece of paper or whiteboard and possibly a beer if age appropriate.

I will also insist that you not use autistic as an insult, and that you not call us bitches; if you continue to do things like that we will need to take more drastic action.

[old quarry]

guys why dont all of u become this active when i open a help channel 😭😭

[valid carbon]

try being entertaining

[clear moon]

i think you need to ragebait us more

[robust mulch]

homie im helping you already, lets go back there

[heady moon]

https://tenor.com/view/dicaprio-leonardo-dicaprio-django-meme-leonardo-gif-19141321

[vale vigil]

I am very confident that I will end up with the right answer in the next 5 minutes (after re presenting what I showed just now), I will put at sake of everything, I will not talk anything other than the discussion, I will not make comments no matter the situation, please let me present my question for the next few minutes

[barren hound]

no, this is not an appropriate way to talk to a student here

[vale vigil]

if I still end up in mis understandings or hate discussions, then I will do so as you wish but please give me a last chance here

[barren hound]

right; you can, but after today i want you to find someone irl to talk to about this instead, because this server will not be able to help you with this

[vale vigil]

alright

I give u my word

[bold turtle]

Okay, so this part - you're claiming that this is [A] different or [B] the same as changing the basis?

Let's start with this part for now.

[valid carbon]

(i feel like she doesnt mean you cant ask questions just... more grounded? ones?)

something like that.

[bold turtle]

And there is in fact a right answer here

[vale vigil]

thank you, I want to claim that it is different than changing the basis. we are not changing a basis at all, we are in fact, getting a new different answer but that's a different basis than the one we could have taken as an answer

[bold turtle]

Sorry, you've lost me at the first hurdle then

You've got a second answer that's in a different basis, you're saying?

[vale vigil]

in indirect words, changing the basis was not the part of our motive here, I was trying to show you, we can get 2 different answers with the same initial question, without caring about the other answer

[vale vigil]

infact, not only 2 answers, we can get infinite answers and that's why -- need for direction to be defined

yes.

[bold turtle]

Okay, so, here's the thing.

[vale vigil]

and the major point being, these answers were not dependent on each other

[vale vigil]

yep

[bold turtle]

If your answer is in a different basis, congratulations, you have changed the basis.

This is what changing the basis is, by definition.

[vale vigil]

we never got a basis to begin with

[bold turtle]

Correct; we've had to establish one.

[vale vigil]

hold on for one sec

[vale vigil]

all of these "different basis" answers, are not that we "changed the basis from an answer"

I'm telling you that... we can get a different answer itself

we don't need answer

from the point of the question

we define a basis of our own in each answer because the question doesn't give one

[bold turtle]

Weirdly, and you're gonna have to bear with me here, I'm actually going to pull up a map from the HITMAN series, because I think it's going to be the best way to explain this to you, unironically

[vale vigil]

ant this is why, we are able to get different answers

not by changing the basis of an answer, but by creating one ourselves

and the basis is obviously gonna be different to most of the other answers (this isn't something mathematical but like...)

[vale vigil]

Alright

[bold turtle]

Here is the Berlin map from HITMAN III.

If I use the terms "map-up", "map-down", "map-left" and "map-right" to describe moving up, down, left and right (respectively) along the map as shown, would you agree that the DJ Booth is to the map-left of Agent 47 here?

[vale vigil]

Yes

[bold turtle]

But is it West of 47?

(be very careful here; there's something in the first image that would help you)

[vale vigil]

yes

[bold turtle]

You sure?

[vale vigil]

I'm sure

[bold turtle]

Look at the bottom left here

[valid carbon]

okay thats a very hidden compass

[bold turtle]

I'll grant you that, yh

But it is there nonetheless

[vale vigil]

it would be east then

[bold turtle]

You can be a bit more specific

Supposing that North was facing map-downright?

[vale vigil]

south east?

[bold turtle]

yee

[vale vigil]

okay

[bold turtle]

But, do you see how "South East" does not match "map-left" in name only?

[vale vigil]

I do

we have infinite directions not just 4

[bold turtle]

We've had to use the context that this map has been devised in the first place to deduce any comparison

Whenever you have a question in coordinate geometry, the map is the question

A well-written question provides you such a map to begin with, by default

[vale vigil]

it seems like the other way around; you deduced a map and you gave an object in it only 4 directions to move to when there's infinite directions it should be able to move to be able to access everything around it

[bold turtle]

Since when did I deduce this map?

[valid carbon]

...noooo

[bold turtle]

I've been GIVEN this map to start

[valid carbon]

do you know what deduction is

[vale vigil]

that's a well written map

[valid carbon]

imma plug more another roof here

[bold turtle]

Yeah, and the game has given me this map

I didn't theorise it

[vale vigil]

The only problem was with moving buttons being only 4 directions

[valid carbon]

https://www.youtube.com/watch?v=MJrYwh6WyF8

[vale vigil]

I don't see what you're asking me here

[vale vigil]

what does this mean?

[bold turtle]

You're working under the false assumption that a question does not give you basis vectors to define a coordinate geometrical space

They definitely do

[vale vigil]

I'm not working under the assumption that a question does not give me the basis vectors at all

[bold turtle]

When a question gives you coordinates, for example, such a basis is inherently implied

[bold turtle]

This strongly suggests you ARE working under such an assumption

[vale vigil]

I'm just working under the assumption that a question does not give me the basis vectors's direction

[vale vigil]

read my next 2 messages carefully;

[vale vigil]

Basis vectors;

[bold turtle]

Suppose if I gave you some coordinates, say the origin (0,0) of a 2D map (two dimensions are simpler for you to get this concept properly)

[vale vigil]

We did take the basis vectors as it is for both of our answers, we just took different relative directions of those basis vectors

[bold turtle]

This inherently already implies there is an x-direction and a y-direction, and that they are non-parallel, so that they cover the space

This is already what we mean by "giving coordinates"

[heady moon]

sorry bout that @barren hound @vale vigil
i meant burnout can sometimes fuck your mind so taking break is a good idea

[vale vigil]

two dimensions don't properly capture the necessity of a relative direction for the axises

[bold turtle]

Having a dimension by DEFINITION does capture a relative direction

Else, it is NOT a dimension

You MUST understand this before anything else in this discussion.

[vale vigil]

as I told here; I am not arguing that x and y and z do not convey their basis vectors,

[bold turtle]

This is why they're described with vectors, by the way

And not scalars

[vale vigil]

what I'm trying to show you is, in which direction they point out, matters

[bold turtle]

And what I'm trying to explain back to you is, when you define a dimension, it already HAS a direction implied

[vale vigil]

@bold turtle if u see here, there's 3 coloured lines that are basis vectors

let's say they have an arbitary direction, without the loss of generality

[bold turtle]

Is this in 3D? even despite me saying that working in 2D would make this easier for you to get?

[vale vigil]

It's 3d

[vale vigil]

these are 3 more basis vectors, that.. quite infact.. are just as linearly spaced as the first 3 ones, and also, we have the same point of origin here

but if u try to form a point

or a vector

they'll end up in different positions

that's why I argue direction matters, the axis's direction should matter, in 3d space

I'm just waiting for you to ask me a question like "you just flipped it, you obviously changed it "

[bold turtle]

you just flipped it, you obviously changed it
is not a question, for starters;
but if I DID respond with this, your point seems to be that you disagree that this is true?

[vale vigil]

and for you to think I'm gonna give an answer like " well 3d space is symmetrical right? soo like for an object that's seeing this graph out of this... theyd be like............ different positions so you're obviously wrong, it wouldn't matter if I flipped it"

but nope, here's my actual response

[vale vigil]

I flipped nothing, you didn't define/denote an answer to begin with, I just took a, perfectly, valid, real, correct answer that formed with the initial questions

( the initial question was about the origin's location of which point it is, and the basis vectors, and the amount of linear spacing, like how the graph is)

based on this I took this answer

[bold turtle]

But look, the initial question inherently gives you a basis the literal moment they tell you any coordinates

[vale vigil]

yep

a basis x, y, z

but not which direction it points to

[bold turtle]

Right

[vale vigil]

so this answer is completely valid

is it not?

[bold turtle]

Look

[vale vigil]

why does this seem flipped to u when the first answer didn't

what would have happened if I showed u this as the first answer

these are literally derived from the same question

I can't be more clear to advocate for a need of direction of the axises to be relative instead of x, y, x direction

[bold turtle]

When we say a coordinate (2,5,6), we're inherently saying that relative to an origin and some notion of a unit, we have a point "2 units in the x-direction, 5 units in the y-direction, and 6 units in the z-direction from the origin"

Do we care where specifically the literal x-, y-, and z-axes are?

[vale vigil]

yep

[bold turtle]

not really

[vale vigil]

nah

that's just confusion

[vale vigil]

right but the point you see is that even though this looks like x-, y-, z- of the original answer

you fail to understand, that, THIS is also an original answer

[bold turtle]

It.. actually isn't

[bold turtle]

Because you're playing in the same court as the question

[vale vigil]

there's nothing saying that, axises situated this way is the original answer

[bold turtle]

Firstly, the plural of axis is axes

[vale vigil]

we derived this answer from question yes

[vale vigil]

but we derived this also from the same question

yeah, just different direction of axes

[bold turtle]

"Derived" how?

[vale vigil]

the question didn't specift the direction of axes

[vale vigil]

just like how we derived this

[vale vigil]

you tell me in mathematical language how we derived this

I'll copy paste it for the other answer

it would be the same; valid and correct

[bold turtle]

No, the onus is on YOU to tell me how; it's YOU who said we "derived" these in the first place

[vale vigil]

we never had an answer to depend upon for the direction of the axis

[bold turtle]

You're working under the assumption that our mouths are yours

[vale vigil]

so, we had a question

that said everything, including the basis vectors and point of origin

and said to find a point x, y, z okay like 5,6,7

from it, can we derive a valid answer as this?

[bold turtle]

Then your answer, (5,6,7), whatever it may be, already uses the same basis

[bold turtle]

It now reads "5 units in the x-direction, 6 units in the y-direction, and 7 units in the z-direction from the origin"

[vale vigil]

in here just imagine a point a bit right side to the white line (I can draw it if u want)

can we get a valid answer like this

[vale vigil]

yep

[vale vigil]

is this a valid answer then

[bold turtle]

Why do you think this is invalid, first?

[vale vigil]

I do, not.

I do not

that's valid

[bold turtle]

So then we're all good; the maths hasn't broken down, do you not see that?

[vale vigil]

I didn't say the system was flawed

I said the system didn't apply to that

and if u continue with me on 3 dimensional space you'd see where I'm arguing from

[vale vigil]

okay how about this, maths hasn't broken down as of now

as of this point in our discussion

maths hasn't broken down

cool?

now if you hold on with me , can I ask you this question

[bold turtle]

If you decide on changing where x-, y- and z- point in the first place, do you not agree that (2,5,6) and (5,6,7) still refer to relative points, that both still mean:
"2 units in the x-direction, 5 units in the y-direction, and 6 units in the z-direction from the origin"
and
"5 units in the x-direction, 6 units in the y-direction, and 7 units in the z-direction from the origin"
?

[vale vigil]

I do not decide on changing the points to x-, y-, z-

please bear with me to know why

Alright

So, there's a point we need to find. 5 units in the x, 6 in the y, 7 in the z

I've constructed a graph to plot this out

[vale vigil]

@bold turtle this point reads 5 units in x direction, 6 units in y direction and 7 units in z direction

so, is this correct of the question "find 5,6,7 with all the units"?

[bold turtle]

Where each direction corresponds to which basis vector colour there?

[vale vigil]

yeah I mean, I've drawed it horrendously, but it should

[bold turtle]

That's not a yes no question

[vale vigil]

Yes

[bold turtle]

I'm asking you which colour is which of xyz

[vale vigil]

Yes

I mean.. they correspond very well to 5,6,7 co ordinates

take yellow as y, red as x and white as z direction

[bold turtle]

Okay, so - this is not a good question, to start. Wherever did you come up with this? /genuine

[vale vigil]

they're exactly as such; 5 times red's length in x, and 6 times and 7 times in y and z

[vale vigil]

why is this not a good question to start? they've given the position of the point of origin and basis vectors

and asked us to plot out the point 5,6,7

we can just ignore the fact that most of the points are not plottable with a finite data

also we ignore our error fact

and assume the point we plotted is 5,6,7

[bold turtle]

Look, knowing whether it's a good question or not takes years, if not decades, of experience, and it's not really that easy to explain why, suffice it to say that it's a poor question.

[valid carbon]

Pictured here, Waes:

https://tenor.com/view/elrond-lotr-lord-of-the-tings-lord-elrond-3000years-gif-13229890

[vale vigil]

if that's your feeling, I can accept that, but it is a question no matter what. if the question is flawed you tell me with proofs

its a euclidean 3d space

[vale vigil]

going back here (if u couldn't point the flaw in the question

[spring haven]

"this isn't a good question because i'm smarter than you"

[valid carbon]

well more like intuition

[vale vigil]

is this correct? we Derived a point 5,6,7 true to it's co ordinates

Then is it a correct representation and have we correctly located the point

that we were asked to

have we?

[bold turtle]

Questions can be flawed; and at this point we're delving into philosophy, not maths, so bear with

[valid carbon]

it's not a good question because it doesn't mean anything-

[vale vigil]

it does

[valid carbon]

You might as well say 'find (5,6,7) with all the chicken sandwiches'

[vale vigil]

it means to show u something and for you to stop it by saying it's a bad question makes it inable to serve it's purpose

u dont just say it's not a good question without understanding it's purpose

right now if I tell u "there's a need to define a relative direction for axes"

you just would say "what, this person is nonseical"

and when I try to give the intuition, by taking u to the necessary question first

[bold turtle]

Listen, you can make something "sound" like a good sentence, but it be completely nonsensical.

[vale vigil]

you say "what, this is nonsensical I'm not going further"

[valid carbon]

points dont have units

[valid carbon]

.

[vale vigil]

5,6,7 is a point

accept it or not

it's a 0 dimensional point

u can't put 3d objects in it

[valid carbon]

points are 0 dimensional.

they also dont have units

[spring haven]

what do you mean when you say 5,6,7? that statement itself requires a basis to make any sense

[vale vigil]

fight me a mountain, 3,6,7 can only be a point in a 3d euclidean space

[valid carbon]

can you find (5,6,7) with all the chicken sandwiches

[vale vigil]

The basis is the co ordinate system

with basis vectors

1,0,0
0,1,0
0,0,1

and with a origin 0,0,0

[spring haven]

okay sure

[vale vigil]

we know the origin's location

[spring haven]

and what point are you making

[vale vigil]

now we're needing to locate 5,6,7

all I'm asking is

[vale vigil]

is this a correct representation

of locating it

the point perfectly aligns with 5,6,7's position

[valid carbon]

Sure then I guess.

[bold turtle]

It is a representation of describing a coordinate-triple, yes

[vale vigil]

so have we located the point at 5,6,7

alright cool

cool now bear with me

[valid carbon]

you can make pictures

[vale vigil]

bear with me, I'm not finished yet

[spring haven]

drawing a 3D thing in 2 dimensions is gonna cause some confusions anyway, I'll take your word for it

[vale vigil]

we have a point here

[valid carbon]

ill do you one better

[vale vigil]

this also matches with 5,6,7 perfectly

so is this a correct representation of 5,6,7?

[valid carbon]

no it doesnt

[spring haven]

if you change your basis vectors to point in the opposite direction

[vale vigil]

we just changed the directions of x, y and z axis so that it would

[vale vigil]

yeah

I did do that

[spring haven]

fundamentally it's a different point, it's like you flipped your whole space

[vale vigil]

no hold on here

u dont talk that high level stuff yet

[valid carbon]

https://www.youtube.com/watch?v=P2LTAUO1TdA

[vale vigil]

Tell me this

is it a valid point 5,6,7 now?

[valid carbon]

you can't talk about high level stuff without talking about high level stuff

[spring haven]

in a different basis, yes

[vale vigil]

yes?

now here tell me

[valid carbon]

If you talk about change of basis (even without knowing it), you'll get a reply about... change of basis.

[spring haven]

any point can be made to have coordinates 5,6,7 in an appropriate basis

[vale vigil]

Alright I think it's time to stop your words, I have a really, beautiful thought experiment (it's literally this but like a story please don't think I create something else nonsensical here, unless u do after reading it)

[spring haven]

time to stop your words is crazy

i'm using that next time

[valid carbon]

https://tenor.com/view/first-time-meme-movie-james-cameron-western-gif-17538858

[bold turtle]

@vale vigil
I'm telling you this right now:
you need a lot of experience, and that includes possibly hundreds of worked examples, on 2D coordinate geometry.

You might think this irrelevant, and maybe people your age might think so too. However, the vast, VAST majority of the concepts you're trying to grapple with in 3D exist in 2D and they can be explained in 2D as well. To this end, however, you need to put in the effort to go through these examples AND answer questions on these topics, and a lot of them.

This is not me gatekeeping you - it is your own lack of experience and underlying knowledge that is limiting your grasp on this. I can appreciate that this is tricky as a concept, but that's because you need much more solid foundations like this. To use an analogy, you're trying to fly a rocket to the Moon here, yet your rocket doesn't even have wings.

[valid carbon]

(i dont think rockets have wings waes)

[bold turtle]

Not the point.

[valid carbon]

(sure but the more you know)

-# fins i think

[bold turtle]

I personally will not entertain this discussion any further than I have done, which I think was far more than I would have liked myself to have done.

[valid carbon]

Yeaaah same, possibly

hopefully

I'm just going to reiterate some resources that are good:

1. Another Roof.

2. 3Blue1Brown

3. ...KhanAcademy

You have homework.

At this point you're mostly just wasting people's time. It is now on you to do some due diligence on your part and read through the resources people have given you.

[vale vigil]

So, there exists a 3 dimensional euclidean space, with a lot of objects, perhaps more than 2 3 dimensional objects for your sake of understanding.
Now, we have 2 humans trying to communicate via different rooms (different rooms just meaning; they can't see each other, and just read words or talk words, they can't show anything) .
What they're trying to communicate is really silly: person 1 , whom we call Billy, is operating a space ship that has no windows to see, actually let's assume we have just 2 3 dimensional objects somewhere floating in space, cool with that?

Now, Billy is trying to fly his spaceship to person 1 , whom we'll call silly.
Silly can see everything as Billy is coming towards him, silly can use co ordinates and mathematics to explain Billy everything.

The task is really simple, silly sees an object, that if billy's spaceship hits, Billy dies.
That's why silly has to say the co ordinates of that object, with respect to billy, we ignore a lot things, like 3 dimensional objects not being points, and time;
let's suppose that Billy and like his spaceship, is one point at 0,0,0 and we are given basis vectors as well, and the object is a point as well, now all silly has to do; is convey billy the point's exact location so that billy understands the exact point where it is, and doesn't die

[vale vigil]

And as far as this multi-hour discussion, we have concluded that different directions of basis vectors (not different basis vectors here, just different directions of basis vectors) would give us different points of location for the same co ordinates in 3d space

[vale vigil]

So @valid carbon and learned person @spring haven , our task is to help silly find the appropriate basis so that even billy can know where to not go by his own pov via co ordinates

[vale vigil]

keep in mind: the appropriate basis is not something like the correct numbers, it's the correct direction of those basis vectors

[hushed sequoia]

Please stop pinging people who left the conversation

[spring haven]

you've introduced a lot of layers of complexity here

[vale vigil]

oh alright

[hushed sequoia]

Should people want to answer, they'll do it on their own

[spring haven]

such as the fact that the spaceship is moving

[vale vigil]

ignored that

ignore everything like that, it's a thought experiment but u get the idea

points, co ordinates, correct direction of basis vectors

[spring haven]

also "different directions of basis vectors" just means changing your basis, so I don't understand the distinction you made there

[vale vigil]

alright

[vale vigil]

how is it changing your basis?

what does basis even mean

is basis "basis vectors"

[spring haven]

and that's the problem, you fundamentally don't understand what you're talking about

[vale vigil]

is basis "the number of dimensions x, y, z.... n"

[spring haven]

a basis is made up of basis vectors

[vale vigil]

no I do I'm just confused with your wording of it

[vale vigil]

right

so would u consider

1,0,0
0,1,0
0,0,1

a basis?

[spring haven]

yes that's a basis

[vale vigil]

this basis, is it 1,0,0
0,1,0
And 0,0,1?

suppose we wanted to keep the basis vectors as those

is it a basis

I mean is it a valid basis sorry not if they are the basis

[vale vigil]

Is this a valid basis

if I wanted to keep vectors as

1,0,0
0,1,0
And 0,0,1

[spring haven]

there's a distinction you need to make between vectors and coordinates. The problem is that, in R^3 (which is 3D euclidean space) they look pretty much identical

[vale vigil]

I'm asking right now that, is 1,0,0 basis vector of x, 0,1,0 basis vextor of y and 0,0,1 , basis vector of z

[spring haven]

Vectors do not change with whatever particular basis you choose. They are simply points

Coordinates are how you describe a vector with respect to a particular basis

[vale vigil]

be able to form this

[vale vigil]

yeah

[vale vigil]

"with respect to a particular"

a particle axis

[spring haven]

a particular basis

[vale vigil]

right my bad

and the basis vectors, with respect to a particular axis

right?

[spring haven]

the problem in R^3 is that you can't really describe a vector without coordinates

unlike other vector spaces

which I suspect is part of where your confusion is coming from

[vale vigil]

are u saying that

[spring haven]

what this means is you cannot describe any direction mathematically other than by giving its coordinates in some basis

[vale vigil]

this, with the basis vectors being 1,0,0 0,10 001

is impossible in R^3?

are u saying this?

[spring haven]

no?

[vale vigil]

so are u saying that

this with the basis vectors being that, is possible in R^3?

just say yes or no if u want to, no need to clear my confusion on some other topic which I may not have a confusion of

[vale vigil]

this particular thing specifically

[spring haven]

I don't understand your question

[vale vigil]

it's a yes/no question

[vale vigil]

is this basis possible

with the vectors being

1,0,0
0,1,0
0,0,1

for 3 dimensional euclidean space

[vale vigil]

those directly correspond to x axis y axis and z axis

[spring haven]

yeah sure

what would those vectors be then

in your basis

like (-1,0,0) (0,-1,0) and what looks to be some other random vector

[vale vigil]

those would be scalars of our 3 vectors

-1, 0,0 is a co ordinate where our vector is scaled by -1 * basis vector of x (we ignore 2 zeros of x here)

[vale vigil]

and doing the same multiplication

for both of the other basis vectors

dot products probably

but it's NOT what we care about right now

[vale vigil]

All we care is, if this is possible with basis vectors being 1,0,0
0,1,0
0,0,1

then

is THIS possible with basis vectors being 1,0,0 0,1,0 and 0,0,1

[spring haven]

what is "this" and what do you mean by it being possible

[vale vigil]

same 3d euclidean space

[spring haven]

you've just drawn some vectors on some axes

[vale vigil]

that visual representation of the graph/co ordinate system that originated with those (we took an arbitrary direction for each of the axises)

[vale vigil]

not on some axes

it's x, y, z

but essentially not the same as your desmos

[spring haven]

x,y,z are just labels

[vale vigil]

alright

it's 3 axes

and those 3 vectors are the basis vectors

corresponding to each of the axes

good now?

[spring haven]

sure

[vale vigil]

then how about now

over here

Same setup, is this possible now?

1,0,0
0,1,0
And 0,0,1 as basis vectors

and those 3 dimensions are corresponding to these vectors as their basis vectors

is this setup possible and factual in 3d euclidean space as well?

just tell me a yes or no

[spring haven]

sure

[vale vigil]

cool

these are, solely decided by the relative directions of where u keep the axes towards

that's why in one set up its towards the top right (in visual space)

and in one set up its to the bottom left (in visual space, I know about 4 quadrants by the way.. in actual visual space these would be at top right and bottom left tho)

[spring haven]

I don't get why you're not doing this experimentation in 2D, it would make drawing the figures way easier

and doesn't really change anything substantial

[vale vigil]

no you wouldn't understand it

the point being that, we need a third object

[vale vigil]

To observe this for what it is

if we don't have a third object

bottom left, would be as top right (I mean... it would be flipped for our view, but it's not the graph that's flipped, it's our view that's flipped)

[vale vigil]

but if we do have a third object that doesn't care about this graph

[spring haven]

ok I'm done with this lol, it's clear you don't actually care about what people are saying

you're just acting obtuse and degrading

[vale vigil]

this is why, you wouldn't understand it in 2d space

actually it's not why u WOULDN'T be able to

[candid pulsar]

thats not how mirror images work..

[vale vigil]

this just an explanation of why third object is necessary

[vale vigil]

it's not a mirror image

it's a showcase that, in 3d space, if we flip the direction of the graph

then the position would be different

and we can't allow the position to be different than what we mean

[candid pulsar]

yeah what does flip mean here then

[vale vigil]

it's not actually getting flipped

but like

[craggy plank]

I’ll give it a try, are we still discussing the original question?

[vale vigil]

it's a different representation

[vale vigil]

nope

[vale vigil]

of a system... uh alright how do I say this

[candid pulsar]

looks poorly defined though
the bottom one seems like a water reflection across the orange line, but the top one is just rotated 180 degrees for no reason

[vale vigil]

look at this, over to the left side; u have x being the horizontal line, y being the vertical line (for u, this is actually 3d space and there's z also but I'll make it more comfortable)

and we already have the basis vectors
1,0,0
0,1,0
And 0,0,1 even though I didn't draw them they're there, and also the point is at 5,6,7 and it sticks true to being at the correct location of 5,6,7 with those basis vectors

[vale vigil]

over to the right, even though it looks flipped, it's quite literally the same because everything in the graph is being flipped

but to an outside, observer, who is in the same 3d euclidean space

[vale vigil]

by the way this applies to the right side also, the point that u see is at 5,6,7 to it's co ordinates when the basis vectors are the same numerically as the left side

[candid pulsar]

its not the same after flipping.

[candid pulsar]

this is where the confusion began

[vale vigil]

yes but I'll talk about this in a second

I already know that

you'll understand what I mean, hold on

[vale vigil]

but to a third object theyre different, why?

because

the direction of axes matters

[vale vigil]

if a person 2 talked to person 1 about the left side's graph

but person 1 thought it was the graph like it is in the right side of the picture

then person 1 would have a wrong understanding of the point

[vale vigil]

And this is where u come in

"it is not the same after flipping" Can u redefine this statement?

[vale vigil]

because, to me, I don't see any original answer that we flipped to get the second answer

I see infinitely many answers that we ORIGINALLY got, from the question itself; which didn't specify the direction of the axes

[vale vigil]

we didn't flip anything

the question itself literally didn't gave the direction of the axes

ant dont confuse the question here

[vale vigil]

This is the question

[vale vigil]

This is the question

but

these people don't talk about direction at all

I've been arguing here

for 22 hours or more

no one gave me a direction, they said it doesn't matter

BUT IT CLEARLY DOES

you need to know how the axes is situated even if u have the numbers of what axes is situated

I need this direction

in 3 dimensional space even more precisely

[vale vigil]

because there's infinite directions for a point to go; infinitely different points that are gonna be located, with the same numbers called basis

all of the answers are ORIGINAL

NOTHING IS FLIPPED

the question needs to imply the direction, otherwise it is incomplete!!!

and what my purpose of making this thread is

to argue that, the direction is impossible to define

because u have a paradox of defining another x, y, z and how it would be situated to construct the line for the perfect direction

and more and more

[vale vigil]

Alright, I'm gonna stop here PLEASE READ FROM HERE ANYONE WHO'S GONNA COME FORTH ON

I perfected my argument

I believe........

[candid pulsar]

okay so if you want a reliable coordinate system and basis vectors to plot your points on
then you can assume the basis vectors to be perpendicular to each other and in the directions as specified in the diagram below

for your convenience and to anyone with whom you're going to discuss 3d geometry with

[vale vigil]

that doesn't work

we literally can get a lot of answers just with that

and by the way, we're not even changing the origin for the third object's pov

[vale vigil]

Alright, I'm gonna stop here PLEASE READ FROM HERE ANYONE WHO'S GONNA COME FORTH ON

[candid pulsar]

no we cannot..

just fix them in those directions in your mind

[vale vigil]

if u see my picture... do u realize both of them follow the same property of perpendicular angles

[candid pulsar]

what is this property of perpendicular angles

[vale vigil]

that y axis is perpendicular to x axis

and that basis vectors

[vale vigil]

to be perpendicular to yadayadayada... This is correct but u can literally just change the direction of it and it would follow same property

[candid pulsar]

but the coordinates you got with the first set of basis vectors would be different in this new system

[vale vigil]

they would be numerically same

wouldn't they

[candid pulsar]

no.. you would have a negative sign

3, 4 becomes -3, -4

not the same

[vale vigil]

nope because you're changing the direction of positive and minus as well

so in the new direction, the place where it should have been positive with the current directions, it would be negative, and vice versa

so 3,4 wouldn't become -3, -4

u literally changed the axes as well

the quadrants (positive, negative, positive positive etc..) change with u

[candid pulsar]

this is not true

3, 4 means that

[vale vigil]

lemme give u an explanation

[candid pulsar]

you are using 3 times the x vector and 4 times the y vector

once you flip both your vectors

you need to use -3 times the new x vector and -4 times the new y vector

to get to the point you started with in this new system

[vale vigil]

@candid pulsar

u see this?

this is what you've defined

now

[candid pulsar]

ok this is coherent

go on

[vale vigil]

what if I do this?

do the quadrants not move along with me?

[candid pulsar]

correct

[vale vigil]

and

the point is numerically the same

as the first point

correct?

[candid pulsar]

say any point on the top right of the origin is the point you say

[vale vigil]

Just see here, I've already given 1,2

[candid pulsar]

and the point remains there even in this new system

[vale vigil]

it's the same numerically as in this representation where u gave, both of them are 1,2 right

[vale vigil]

we can ignore the fact that we got this from an old system

[candid pulsar]

you are rotating the point here

[vale vigil]

this can be an entirely new system

[candid pulsar]

the point remains there

[vale vigil]

we can ignore that it's rotated

we literally can create this ourselves

not required to link it with an old system

therefore, it is 2 systems

having numerically the same point

but they're different in direction for a third object viewer

[vale vigil]

This is what I meant

when I drew this

numerically same, spatially different

direction MATTERS that's why

[candid pulsar]

what do you mean by numerically same

numerically relates to numbers

[vale vigil]

The point would be 1,2 in the first system

the point is still 1,2 in the second system

it did not become something like -1, -2

[candid pulsar]

then they are not the same point

[vale vigil]

+1, +2

[candid pulsar]

the point denoted by what you say as 1, 2 would not be the same

[vale vigil]

yes but they're numerically the same in terms of co ordinates

It wouldn't become another number

[candid pulsar]

but two different points

[vale vigil]

both of those systems's point would still be +1, +2

Even though they'd be in different locations

because, we have imagined a different direction

[vale vigil]

for the axes

[candid pulsar]

yeah since you are using another coordinate system to define 1, 2

[vale vigil]

if we imagine one single direction

[vale vigil]

we're not using another co ordinate system like u think

we just changed directions linearly

And no question ever specified about directions

[vale vigil]

if we imagine one true direction, we can't change this at all and imagine more than one answer for 1,2 in any system

I appeal for any of the learned persons <@&286206848099549185>

to tell me how we'd define that true direction

[candid pulsar]

ok so the same way in 3d space you know that they are perpendicular but youre not sure in which way

[vale vigil]

they're perpendicular

literally both of the systems follow same properties

their axes are situated in different directions

that's it

they're perpendicular

and follow everything, like same basis vectors

[scarlet sinew]

? wtf did i just walk into

[candid pulsar]

if you want to comfort yourself then say x is ponting to the right in the plane of paper, y is pointing to the top in the plane of paper, and z is pointing at you

[vale vigil]

The fact that their axes is situated in different directions

[candid pulsar]

you can invoke the real world in this case to fix your thoughts

[vale vigil]

I'll comfort you by this now, this is real world what im talked about;

[scarlet sinew]

he’s talking about you btw
i have no idea what ‘real world’ you’re on based on the convo im reading here

[vale vigil]

@candid pulsar This is what u imagined, a perpendicular axis stuff

[candid pulsar]

sure..

not exactly that way

but those are perpendicular too i guess

[vale vigil]

@candid pulsar and this is what I imagined, keep in mind this is not the "flipped version" Of that

this is an entirely, original version, that I don't need that for me to generate this

BUT

if u look at the numericals

[candid pulsar]

yeah i get it

[vale vigil]

you will have literal same numericals

[candid pulsar]

numerically the same point

[vale vigil]

yeah u do now

and that is why

I argue that

[candid pulsar]

but at a different place

that is why

[vale vigil]

yep that is why I argue that the direction of the axes

matters

[scarlet sinew]

im getting fucking lobotomized by this chat dude

[vale vigil]

none of these other people understood me

[candid pulsar]

you can imagine it in this way alone

to fix your thought

[vale vigil]

That is where rigorousness breaks and it doesn't become mathematical

[candid pulsar]

so when you are trying to imagine (5, 6, 7) for now just think (5 to the right, 6 to the top and 7 towards me)

[vale vigil]

saying it's to the "right" isn't valid

you do understand that right?

[candid pulsar]

well yes

[vale vigil]

it's not

[candid pulsar]

but for your standards its more than enough

[scarlet sinew]

how is that supposed to matter

im assuming that you’re sticking to the og question of “can a line exist as an equation in a 3D space”

[candid pulsar]

and you would feel better working with this till you get a good exposure of vectors and other stuff like that

[vale vigil]

mathematically if it was valid, we didn't need to construct equations for line, we could've said " Oh a bit slanty slanty over here, and a bit top left over there and a bit"

[vale vigil]

respectfully, I think it's not

[vale vigil]

here

lemme show u this

[vale vigil]

it matters now isn't it

[scarlet sinew]

are those fucking runes

[candid pulsar]

yes maths is confusing like that

[vale vigil]

there's a third object that cares if u change it into a wrong perception of direction of axes

[vale vigil]

no

[candid pulsar]

that is why we are trying to imagine things like that with simpler and easier-to-understand real world notions

its not always easy to go full abstract mode

sometimes you need a crutch

[scarlet sinew]

basically wtf is going on here

[candid pulsar]

why do you even have 3d geometry in 9th grade lmao

[vale vigil]

we are 3 dimensional, and this is real world 3 dimensional. we are much more closer to this than we are to the weird bending of black holes (for our perception)

For us, it's almost always a Euclidean 3d space

which is what we're talking about here

how do u think I got these questions without knowing any of the vectors text book knowledge?

[candid pulsar]

yeah but we need an easy to understand way to note points

[scarlet sinew]

okay so basically your question is

can a line in 3D euclidean space be represented as an equation right

[vale vigil]

because we literally live in 3d and ur mind could think so

[candid pulsar]

what do you think you would understand in the real world

go to the right

[vale vigil]

well yes

[candid pulsar]

or go to (1, 2, 3)?

[scarlet sinew]

3d vectors

[vale vigil]

u do realize that... There's a lot of "rights?

[candid pulsar]

what about "move to YOUR right"

thats easier to understand

[vale vigil]

@scarlet sinew hold one 2 minutes let me reply to this person

[vale vigil]

@candid pulsar

all the yellow lines (and more)

are considered to be "towards your right"

all the red lines and more to your left

[candid pulsar]

towards YOUR right

what is your right hand

[vale vigil]

so which one exactly is "move towards your right"

[vale vigil]

LITERALLY we are situated in the middle

imagine it like that

that semi green line's center is where we are

so which one of the directions is "towards your right" in that yellow lines

[candid pulsar]

in the right perpendicular to you

[vale vigil]

?

yes but all of those yellow lines are directions of "right"

u need co ordinates to describe the correct right

[candid pulsar]

only one of those "right"s are perpendicular to you

that right

the perfect right

[vale vigil]

And how would u say something that's perpendicular to a 3d object?

how do u explain someone what perpendicular is

to them?

hmm? maths has already done this really rigorously

by co ordinates

sure, human intuition has a right too

but

it's literally crumblingly undefined

[candid pulsar]

..and thats enough for your purpose for now

[vale vigil]

I'm not gonna argue with u anymore on what my purpose is

thank u

[scarlet sinew]

[vale vigil]

I'm going back to replying to the other people

[candid pulsar]

sometimes you are asked to guide through elementary math with rules and intuition

and only after you reach a decent level of knowledge are you asked to wrack your brains

[scarlet sinew]

blurple what are ur thoughts about this convo so far

[candid pulsar]

im entertained

[scarlet sinew]

im lobotomized

[vale vigil]

3d vectors

now

in which direction

would these vectors be?

basis vectors at least

in directions of their axises right?

[scarlet sinew]

in whatever’s positive in the respective axes?

ig?

[vale vigil]

yes

now

what direction would their axises be?

[scarlet sinew]

spreading out from a center

[vale vigil]

in what way? u can define something like perpendicular 90 degrees from each other

but in what way

HOLD ON DO NOT SPEAK YET

[candid pulsar]

yes this is a weird question but it is true

you cannot say what direction they are in with the English we work on for now

[cyan kayak]

Please be polite to helpers. And I would hope that helpers are also being polite to you.

[scarlet sinew]

how tf would i know
look the way axes point dont matter right

[vale vigil]

oh sorry about that

[vale vigil]

they do matter

[candid pulsar]

best description you can give is, x-axis is in "this" direction, y-axis is in "this other" direction, and z-axis is in "this third other" direction

[vale vigil]

they really matter

[candid pulsar]

but they are fixed in space

[scarlet sinew]

in representation

okay sure

[candid pulsar]

just that you cannot describe them with English or any other language properly

however, it is much easier to use words like up, right, and towards

[scarlet sinew]

then i expect you to define them mathematically

[candid pulsar]

so thats what we go with at the start

[scarlet sinew]

that’s describing from a static POV

[candid pulsar]

and then let you in the details once you are comfortable

[scarlet sinew]

yea

[vale vigil]

they legit matter... if they don't, I can pick 2 answers and say " Hey these look like 2 different lines even in co ordinates and positions to me, so the equation didn't tell me which of the infinite lines I should pick even though it told me something like the measurmeent, it still led me to nothing than the original question: which of the infinite lines am I describing"

[candid pulsar]

well yeah they are fixed in space

i just

cant say HOW they are fixed

and the best to do as consolation at this point is

convention

like what ive been saying

[vale vigil]

that means I can pick any 2 or more arbitary positions where I can keep them fixed

[vale vigil]

and u have my reply from here

[candid pulsar]

correct, and there are several such options

you can take one of them

and work with your problem

[vale vigil]

so how is that different then saying "hey I know a line exists, I just don't know where it is okay

[candid pulsar]

the easiest to go with

[vale vigil]

I thought u were real and the truth and rigoroys

[candid pulsar]

is convention

[vale vigil]

is this all u got? a rough "idk"

[candid pulsar]

but theres a limit to human capacity

sure if you are a multidimensional god

[vale vigil]

you are not the one to define human capacity