4 Dimensional graphs?

[Anonymous No.5363794]

Hi /sci/ excuse my ignorance i am a youngin' but I love math

OK, so when you graph a problem containing x and y
(for example "x/y")

the output at any point in the chart (any combination of (x,y cords) can be input to get an output
call z the output,

now use z to plot a 3d graph, you've warped a 2d graph into 3d space to visualize z.

pretty simple stuff so far, no problem

But..

what happens if I take a problem with x,y and z and want to plot the output of that.

(example x/y^z)

coords x,y,z

Can i see this in 4 dimensional space?
If not how can I plot it?

there just be a way, I am so curious to see this, I feel like there is so much hidden in the world beyond this dimensional constraint, I feel like so many mystery's of the way the world works will start to be unraveled, if I can just visualize this

[Anonymous No.5363800]

no.... you cannot see in 4 dimensions >___<

[Anonymous No.5363803]

the fourth variable could be color or something, but it would have to be transparent and you would have to be able to move the graph around and see it from different angles to visualize the function. Another option is level surfaces, where you take f(x,y,z) to be a constant and plot all the points (x,y,z) that have the same value, and then you do that for different values. Or you could take one of the variables to be constant and graph the figure on a 3d axis omitting that one, as if that were a cross section of the function

[Anonymous No.5363806]

the movie cube 2:hypercube touches upon this issue. I'd recommend watching that to gain some insight.

[Anonymous No.5363813]

I'm new to this sort of idea, based on theoretical physics, maybe try to conceptualize a 5th dimension?

I forget who makes the theorem, but it's based upon singularity and the idea of universal expansion

[Anonymous No.5363824]

It's a whole research domain. "Data visualization" and "Dimension reduction" are your keywords if you want to search for that.

[transfer student from /fit/ No.5363825]

you see that three dimensional graph in op?
>no you don't
yeah it's only a two dimensional representation of three dimensions
and because we can only see in three dimensions we can't visualize anything more than that
>inb4 time and centipedes with babbies on one end and geriatricbrahs on the other
>no

[Anonymous No.5363836]

>>5363824
thanks, sounds like something I might be interested in getting into later in life, I will read up everything I can on it

[Anonymous No.5363842]

>>5363825
I get your thing with the immediate jump to time as the next dimension, but you could also graph a fourth dimension by displaying a plot of 3 of the variables for successive values of the fourth.

And now that you've mentioned that the 3d graph at the top is a 2d representation of a 3d graph, I am reminded that similar algorithms can be done to 4 dimensions, producing something you can look at but which is really hard to get your head around

[Anonymous No.5363945]

>>5363813
i hate current /sci/

[transfer student from /fit/ No.5364056]

>>5363842
my point was that you can account for as many dimensions as you can manage, but you'll never see a 4 dimensional space
or in other words
graphs have no necessary relation to reality
>so tread carefully