What's a good read for getting a better understanding of the idea of 4 or more spatial dimensions?

like a spike

jewish person*

the modern computer was invented by a white person in n.s. germany

>wins an US presidential election with all the political establishment and mainstream media against him
Sounds pretty smart to me. You could just leave it at "wins US presidential election" and I don't think it describes a single dumb person.

Probably because a jew taught him. White people are plebs.

it's a popularity contest

It is very easy actually

...

if you think you could somehow judge my visualization to be correct or incorrect, then you must be under the impression that you could recognize a correct visualization.

how come you believe it is possible for you to review, if you dont think its possible to construct?

youtu.be/HECI4QK_mXA?t=43s
0:43 is for you.

I'll know it when I see it

these so far are not 4 axes all orthogonal to each other

>Rudy Rucker

Great author, although he did spend a bunch of time in that shithole known as Geneseo.

>you cannot visualize R^4
(1,0,0,0)
(0,1,0,0)
(0,0,1,0)
(0,0,0,1)

>algebraic=visual

You can't imagine four dimensional space, your brain is 3d and ONLY 3d. You can't actually imagine 2d space either: If you try, you'll see a flat plane, but that plane sits in a 3d space.

Put a square in the xy plane centered on the origin.
Rotate it about the z axis.
What do you see in the xy plane?

The concept can be generalized to higher dimensions. Instead of it being a square, it would be a cube.

algebra=geometry

>muh perfection
No you idiot, nothing about perception is perfect, by your retarded standards we can't perceive in 3 dimensions either because our brains extrapolate from two 2D retinal images.
You don't need a literal orthogonal W axis to be able to see what it's like to have shapes with four dimensions. You just need to approximate the idea with the appearance of four axes as though they were orthogonal.

Not user, but you do need 4 orthonormal bases. If not, then you just have extra lines in 3d.

It's like saying the projection of a vector onto a plane tells you what the original looks like. This is only true if you have a feel for the norm, which nobody does since you can't see in 4d.

Any Linear Algebra textboox

You have never seen a 3D object then because your brain just extrapolates from two 2D retinal images.

I'm tired of this meme. It's just as bad as the color thread.

I drew them for you, did you not see them? Here it is again
(1,0,0,0)
(0,1,0,0)
(0,0,1,0)
(0,0,0,1)

It is a meme, and it's the same meme as "you can't visualize 4 dimensional objects."
That's the point. You're expecting perfection for the 4 dimensional question when our perceptual systems are already using hacky workarounds to make 3 dimensional visualization work. Nobody is perfectly perceiving anything of any number of dimensions, all perception is based on pragmatic imperfect trickery.

The visual cortex is programmed to perceive three dimensions.

It infers three dimensions using 2D retinal images.
ncbi.nlm.nih.gov/pmc/articles/PMC21082/
>Information generated by the eyes is ambiguous. Everyday we have to make decisions (about the size and distance of objects, their form, and whether they are moving) based on retinal images that can have two or more meanings (1–4). Indeed, because the complexities of a three-dimensional world are projected onto a two-dimensional receptor sheet, the interpretation of most retinal images is equivocal.

Yeah, but the visual cortex is still hardwired to perceive three dimensions from a two dimensional retinal receptor sheet.

Damage to specific parts of the visual cortex affect the perception of static and moving 3D objects. The idea that you "train" yourself to perceive 3 dimensions and can thus train yourself to perceive four dimensions is just stupid; it would be like saying you can train yourself to smell methane or water.

If vision is only 2D and it can take 3D objects to 2D maintaining the profundity perception through shadows and stuff, and the sense of touch is 3D, could there be anyway in which we could experience 4D through 3D touching?

haha, such a funny comment. Just exemplary.

to a 2d being, a slice or a projection of a 3d object would be nonsensical, same way we literally cannot visualize a 4d object properly

who came up with the idea of more than 3 dimensions?

mathfags

(((einstein)))

The perception of 3D objects isn't an absolute or direct experience. The fact the hacky tricks that make it work can fall apart with brain damage isn't proof you're getting some authentic sort of 3D perception that 4D perception can never reach.
If we were perceiving "true" 3D you wouldn't be able to detect changes in the same 3D visual perception brain systems you're referencing when a subject is "flipping" between the two different 3D interpretations of an ambiguous image like a necker cube. The brain makes assumptions using less than 3D input and you get an approximation of 3D that lets you move around and interact with your surroundings well enough to get by.
You can approximate 3D and you can approximate 4D, in neither case is it a requirement that you have some sort of pure 100% perfect direct perception of these spaces exactly as they are

Isn't training something, changing these parts?

Also that analogy doesn't work because methane and water don't have smells not only in reality but also not as any artificial model you could define or build so there's nothing to learn in those cases to begin with.
4 dimensional structure on the other hand is definitely something you can define and build artificially, it's a very obvious extension of how 3 dimensional space works, with one additional axis you can define coordinates in terms of.

You're right, but the distinction I'm making is that we live in a 3d universe and can perceive 3d exactly, even through superposition of 2d images. If you visualize something in 4d, it is always going to be skewed. There's no way to get around it. So you can ONLY see 4d as an abstraction whereas you can see 3d directly.

If there really were 4 spatial dimensions in our universe, our eyes could see it perfectly fine.

Every basic linear algebra book.

Since OP asked for understanding, not visualization, I'd say that this is an acceptable answer.

>can perceive 3d exactly
A whole lot of optical illusions wouldn't exist if we were perceiving 3D exactly.

>They cannot visualize 4D Space
I want the brainlets to leave

Lol not even close. White people are unironically the master race.

What I'm saying is that with two eyes in 2d, you can see 2 2d planes.

Say one of the planes is xy, the other is yz. Then you can see all 3 dimensions exactly. Because you can slightly skew a line to trick people is purely psychological.
If there was a 4d, you could see xy,zk for example. You'd truly see in 4d.

Since there is no 4th spatial dimension, the best you can do is see a projection of k onto x,y,z. There is a distinct difference.

>calling out bait and then proceed to get baited
why do you reply to this?

Start with a n=1-dimensional (or even n=0-dimensional if that's easier for you) base case, then let n go to 4 or whatever else you need

The visual cortex evolved to be hardwired to decode the raw input from your 2D retinal sheet to recognize patterns in a 3D world -- no amount of neuroplasticity in the world is going to change that and make you recognize patterns in a hypothetical 4D world with your visual cortex. Sure, you can use tensors and other mathematical concepts as tools to recognize patterns, but that's happening in your frontal cortex and is more abstract than actually perceiving those patterns in your sensorium.

I'd counter your criticism of my analogy about methane and water not having any smells in reality by saying that you can't build a 4 dimensional object in reality either. In fact, if anything, you can create artificial things that "smell" water and methane (think mass spectrometers), but it's impossible to build a macroscopic 4 dimensional object in a 3 dimensional world (even though our world is technically four dimensional and you'd actually be building a five dimensional object if you include time).

I stand by my analogy that trying to visualize a 4D object is as stupid as trying to smell methane -- you simply lack the neurological capacity to do either.

>(even though our world is technically four dimensional and you'd actually be building a five dimensional object if you include time)

If everything around you is moving at around the same rate and in the same direction in a dimension, how can you say that it doesn't exist? How do you explain the effects of relativity and the empirical usefulness of Minkowski space?

Please, elaborate.

lmgtfy.com/?q=is time a dimension

>Taking the first thing google spits back at you as scientific dogma

>my hot opinion trumps scientific consensus

Because the goys are as easy to manipulate as dogs.

here you go

>i don't know what orthogonal means

Thank you.