[Boards: 3 / a / aco / adv / an / asp / b / bant / biz / c / can / cgl / ck / cm / co / cock / d / diy / e / fa / fap / fit / fitlit / g / gd / gif / h / hc / his / hm / hr / i / ic / int / jp / k / lgbt / lit / m / mlp / mlpol / mo / mtv / mu / n / news / o / out / outsoc / p / po / pol / qa / qst / r / r9k / s / s4s / sci / soc / sp / spa / t / tg / toy / trash / trv / tv / u / v / vg / vint / vip / vp / vr / w / wg / wsg / wsr / x / y ] [Search | Free Show | Home]

How do l imagine 4 dimension functions? Seriously l can't.

This is a blue board which means that it's for everybody (Safe For Work content only). If you see any adult content, please report it.

Thread replies: 66
Thread images: 10

File: 1480972374225.jpg (33KB, 238x250px) Image search: [Google]
1480972374225.jpg
33KB, 238x250px
How do l imagine 4 dimension functions? Seriously l can't. How would you imagine a 4 dimension sphere like this for example? 1 = x^2 + y^2 + z^2 + w^2
>>
You shouldn't be able
>>
>>9148622
>4 dimension sphere
There's your first mistake, let go of what you know of all other dimensions.
>>
>>9148622
think about 3d cross sections
>>
>>9148622
To grasp the fourth dimension, try pointing with your finger along its axis.

Protip: any direction you point is along its axis
>>
>>9148622
>4 dimension sphere like this for example? 1 = x^2 + y^2 + z^2 + w^2
That's an equation, not a sphere.
[eqn]\left\{x \in \mathbb{R}^4 \ \vert \ 1 = \langle x, x\rangle \right\}[/eqn] That's a sphere.
>>
File: 1477524009337.png (226KB, 450x431px) Image search: [Google]
1477524009337.png
226KB, 450x431px
>>9148717
>>
>>9148622
Get me some 4 dimensional graph paper and I'll show you
>>
>>9148622

You don't, your brain works in 3 dimensions (of space) and ONLY in 3. Try and imagine a 2d world, like Flatland. Guess what? You're seeing it from the perspective of a 3d observer, because your brain literally can't "do" 2d.
>>
>>9148717

No, idiot. The axis of the fourth dimension is ORTHOGONAL to the axes of the other three, just as height is orthogonal to width and depth. Now, go ahead and point your finger along an axis that is orthogonal to the three you're familiar with. I'll wait.
>>
>>9148622
A three dimensional circle is a hollow sphere
A four dimensional one is filled sphere
>>
>>9148824
There is no possible way to point your finger without it being in the direction of 4D, unless you know how to stop time? OP is a confirmed troll and a brainlet for saying that was wrong..
>>
>>9148833
This is actually how l imagine it

Can someone confirm
>>
>>9148835

Obviously we are talking about dimensions of space you mouthbreathing fucktard.
>>
All you need to create a 4-dimensional function are 4 independent variables. This happens all the time in real life. Maybe your decision to buy something is based on money on-hance, desire to have it, distance from the shop, and amount of gas in your car. Four things. It doesn't have to have anything to do with physical space and there's no point visualizing it as physical space. You want to visualize a 4 dimensional function? Easy: 1 = x^2 + y^2 + z^2 + w^2. That's a visualization of a 4D function. And it's pretty easy to understand what it means: it's the set of variables whose metric distance from the origin is equal to 1.
>>
>>9148833
>>9148837
This is bs. Like >>9148840 said all variables have to have a metric distance from the origen = 1. Obviously a filled sphere has a smaller radius the deeper you go in
>>
>>9148840
>>9148849

That's just how to work with multiple dimensions, not how to imagine them as OP requested.
>>
https://youtu.be/uDaKzQNlMFw
This didn't really help me but maybe it'll help you.
>>
>>9148851
I imagine 4 dimensions: I imagine a four-
dimensional hypercube around a fixed point. The fixed point is $0. The halflength of the hypercube is the amount that dinner costs. And the four dimensions are the amount of money that 4 different people are going to pay towards covering the cost of dinner.

Sounds to me like you two just lack imagination.
>>
i just imagine the cartesian product of 2 complex planes
>>
>>9148893
Care to elaborate
>>
>>9148896
think of one complex plane
then another one
>>
>>9148622
I'm gonna bomb a truthbomb on you absolute retards in this thread. I don't think you're ready to handle it.

There is a way to get a glimpse of the fourth dimension and the answer is to imagine a scalar function on a 2-manifold in 3D. You can imagine any 4D construction by parts this way so to speak.
>>
>>9148868
>I imagine a four-
>dimensional hypercube

No you don't, because that's impossible. Also, your advice to help OP with visualizing 4+ dimensions is to say "lmao dude just, like, imagine them, dude!"
>>
>>9148622
There's actually a pretty cool video on trying to imagine 4 dimensional shapes, this channel in general is really good when it comes to mathematical topics in general

https://youtu.be/zwAD6dRSVyI
>>
>>9148839
So youre illiterae. Huh, now I feel bad for being so short.
>>
>>9148622
If I were to imagine this using the 4th dimension as time, I would picture this as a sphere with decreasing radius over some arbitrary time frame measured from 0 to 1.

However, it is pretty difficult to imagine 4 tangible and independent dimensions.
>>
>>9148622
Think about a sphere changing through time, so that time is the fourth dimension. To picture the value on any particular w point, determine the sphere that correlates to it. Just as you can picture a line as a series of dots, and you can picture a 2d shape as a series of lines, and you can picture a 3d shape as a series of 2d shapes, ypu can picture a 4d shape as a series of 3d shapes.

Alternatively, you can picture a 4d shape as a 3d shape made by xyz, a 3d shape made by xyw, a 3d shape made by xzw, and a 3d shape made by yzw, a multi angled view.
>>
>>9148922

That's just a hologram, dope.
>>
File: maxresdefault (8).jpg (52KB, 1280x720px) Image search: [Google]
maxresdefault (8).jpg
52KB, 1280x720px
>>9148622 #
When there is an entire video by 3blue1brown with 27 min on YouTube about visualizing higher dimensions.
https://youtu.be/zwAD6dRSVyI [Open]
There are no excuses for any Brainlet to not understand how to visualize shit in higher dimensions.
>>
>>9148833
NO

If you get a "slice" of a sphere, you get a circle.

Likewise, if you get a "slice" of a hyper-sphere, its a sphere.
>>
>>9148821
>You don't, your brain works in 3 dimensions (of space) and ONLY in 3.
No. You're capable of imagining all sorts of things that have nothing to do with the scope of your own body's structure. We're not anywhere near the massive size of a galaxy or the tiny size of an atom, that doesn't mean we can't think about them either. If you can mathematically model it you can come up with some mental intuition about it.
>B-But you'd still just be using 3D thoughts!
No, your thoughts don't have spatial dimensions in the first place. You don't have literal pictures in your brain.
https://www.youtube.com/watch?v=YTRm1-7BvH8
>>
>>9148777
>4D graph paper
Try 3D graph paper. You can still get a great understanding of a shpere on regular 2D graph paper with some shading, so it should stand to reason that you could make a representation of a Hypersphere on a 3D grid pretty well with some shading. But yes to get a true hypersphere one would need a 4D grid just like to get a true sphere one needs a 3D grid.
>>
I simply imagine a 3-dimensional function over time. So a bit like a wavy piece of cloth.
>>
>>9148996
What the fuck are you talking about.
>>
Here's your answer.
>>>9149389
>>
>>9148839
He said fourth though
>>9149296
You can even kind of depict a 3d projection of a 4d image on 2d. The good old "draw 2 squares and draw lines between the respective corners"
>>
File: 1502330780467.png (260KB, 620x640px) Image search: [Google]
1502330780467.png
260KB, 620x640px
>>9149268
>dude you can think in more than 3d because you just think in 4d, it works because there arent literal dimensions

if i imagine a photon what im imagining is placed within a 3d framework regardless of what i do

accept that your neural architecture prohibits you from think in any way other than 3 dimensions and get over it
>>
>>9148622
Not a sphere. Just the product of a sphere rotated about its center in R^4 with a "radius" of 1 centered at the point (0,0,0,0)
>>
>>9151776
>if i imagine a photon what im imagining is placed within a 3d framework regardless of what i do
https://link.springer.com/article/10.3758/PBR.16.5.818
>Here, we show evidence that people with basic geometric knowledge can learn to make spatial judgments on the length of, and angle between, line segments embedded in four-dimensional space viewed in virtual reality with minimal exposure to the task and no feedback to their responses. Their judgments incorporated information from both the three-dimensional (3-D) projection and the fourth dimension, and the underlying representations were not algebraic in nature but based on visual imagery, although primitive and short lived. These results suggest that human spatial representations are not completely constrained by our evolution and development in a 3-D world.
>>
>yes the best you can ever do is imagine shitty projections and cross-section
>you will never even so much as imagine four axes all orthogonal to each other
>>
File: aXm7845xjU.jpg (55KB, 650x650px) Image search: [Google]
aXm7845xjU.jpg
55KB, 650x650px
think about how like it look when you crossy eye

then do a switch in the imagination and you see it like 4D hypercube 4D really for real its real

so cool!!!
>>
>>9151966
I know that feel man
>>
>>9148622
Simple: imagine n dimensions, then set n=4
>>
Imagine the sphere extending inwards twice, overlaping itself.
>>
File: 4D Solve.webm (3MB, 500x556px) Image search: [Google]
4D Solve.webm
3MB, 500x556px
>>9148622
You don't have to imagine it, nobody can and nobody asks you to. But what you can feel familiar with is the maths of 4D, or playing with the 3D shadows of 4D, stop obsessing over something that's impossible
>>
>>9152006
XD
>>
>>9148835
The fourth dimension never really was time.

Before it was more like 3 spacial dimensions + 1 time dimension.

Once you accept there are more than 3 spacial dimensions, time's position gets bumped up.
>>
>>9152270
>Implying time isn't a spacial dimension and we are "falling" trough it at a constant rate
>>
File: 1475234707543.png (945KB, 1015x697px) Image search: [Google]
1475234707543.png
945KB, 1015x697px
>>9152285
>>
wormhole
>>
That's actually a 3 dimensional sphere
>>
>>9148622
Imagine it variating in time
>>
>>9149079
>>9148993
>>>9148622
time isn't a spatial dimension

these explanations are all just obfuscations and misleading or over-sell what they claim to be able to visualise.
>>
yessssssssss
>>
>>9152254
a 3D rubics cube is made by stacking 3 *3 *3 little cubes so a 4D rubics cube is made by stacking 3*3*3*3 little hypercubes

whatever that shit is it is not a 4D rubics cube
>>
>>9148671
this unfortunately
>>
File: 1494723137687.jpg (16KB, 338x338px) Image search: [Google]
1494723137687.jpg
16KB, 338x338px
An additional dimension doesn't practically coincide with our current understanding of physics. This is just speculation on what's inside your neighbor's house when you've never been outside and you also have no windows and you are blind and everyone you know and love has left you with a caretaker who has to describe to you how your own home looks.
>>
File: One over z cubed plus one.jpg (399KB, 1871x1898px) Image search: [Google]
One over z cubed plus one.jpg
399KB, 1871x1898px
>>9148622
really sci? nobody mentioned complex functions? fuck you highschool turds suck dick

visualizing complex functions (functions f: C->C) requires 4 dimensions, it's usually done with 2 dimensions and two "color dimensions"
https://en.wikipedia.org/wiki/Domain_coloring
>>
>>9152285
>implying we're falling through at a constant rate and not accelerating
>>
>>9148622
Think about the a general n-dimensional sphere. Then set n=4.
>>
>>9153244
^Literally this desu. You're brainlet supreme if you let a minor issue like super-tertiary dimensions be a limit to your capacity for imagination.
>>
>>9148622
Read about it
http://www.urticator.net/maze/notes.html
>>
>>9148748
Did you just assume R^4's topology?
>>
>>9153598

I identify as a hyperbolic 3-manifold embedded in R^4.
>>
Think of 3D, but every point has a color.
Thread posts: 66
Thread images: 10


[Boards: 3 / a / aco / adv / an / asp / b / bant / biz / c / can / cgl / ck / cm / co / cock / d / diy / e / fa / fap / fit / fitlit / g / gd / gif / h / hc / his / hm / hr / i / ic / int / jp / k / lgbt / lit / m / mlp / mlpol / mo / mtv / mu / n / news / o / out / outsoc / p / po / pol / qa / qst / r / r9k / s / s4s / sci / soc / sp / spa / t / tg / toy / trash / trv / tv / u / v / vg / vint / vip / vp / vr / w / wg / wsg / wsr / x / y] [Search | Top | Home]

I'm aware that Imgur.com will stop allowing adult images since 15th of May. I'm taking actions to backup as much data as possible.
Read more on this topic here - https://archived.moe/talk/thread/1694/


If you need a post removed click on it's [Report] button and follow the instruction.
DMCA Content Takedown via dmca.com
All images are hosted on imgur.com.
If you like this website please support us by donating with Bitcoins at 16mKtbZiwW52BLkibtCr8jUg2KVUMTxVQ5
All trademarks and copyrights on this page are owned by their respective parties.
Images uploaded are the responsibility of the Poster. Comments are owned by the Poster.
This is a 4chan archive - all of the content originated from that site.
This means that RandomArchive shows their content, archived.
If you need information for a Poster - contact them.