How to visualize four dimensions?

Use an interactive model, for instance a three-dimensional image and add a slider to “move” through the fourth dimension.

In essence any movieclip is a four-dimensional model, be it linear and limited in its interactivity.

Hypercube

don’t ask me to explain it.

@fundevogel

What is happening in that video is you are looking at 3-dimensional “cross sections” of a 4-d object. If we wanted to visualize a 3-d object in 2-d in the same manner for example, it would be like taking thin slices of an object, say a sphere, and viewing them one after the other. In the case of a sphere, it would appear as a point that grows into a circle that gets bigger and bigger, and then shrinks back down into a point.

I once saw a site that had a bunch of videos about visualizing 4 spatial dimensions, as well a other mathematical concepts. It was mindblowing. I’ll see if I can find it.

@chocolatechip I’m glad you explained that, someone had broken it down for me years ago but it left me. Probably because I can’t really get my head around 4-d objects. Your explanation reminds me of an exhibit at the Museum of Jurassic Technology.

11 minute Video on 10 Dimensional space
I found this helps and is very entertaining

http://www.youtube.com/watch?v=jMMKceXeExY&feature=related

This is what an actual two dimensional representation of a penteract (5d) looks like.
I draw these things for fun whenever I have paper.
My head broke many years ago….

I once drew an octeract, though since my favourite number is nine I’d much more like to draw an enneract. Infinite dimensions seem like a much more enticing idea then what @talljasperman ‘s video suggests.

Scientists are idiots nowadays.

If your fourth dimension is time, then, as @whitenoise said, viewing a film is analogous to moving through four dimensions, albeit using a two-dimensional medium to represent the usual three dimensions.

If your fourth dimension is something other than time, it gets trickier to visualise.

just add another property that goes in two directions, e.g. heat, black-white, time…

remember that the dimension permeates the object, so its not a 3D object with heat variations only on the surface, but all the way through the 3d structure.

Each point in it has 4 values/positions, one in each of 4 dimensions, x, y, z, heat.

The fact that the obvious part of the world we live in is 4D also makes a good model. Imagine something 3D, which changes over time. What you’ve got to realise is that it isn’t a changing 3D object, but an object that has a 4D shape, one part of which is being shown over time.

You see a 4D object in 3D+time, in the same way a scanner/photocopier sees a 2D object.
Imagine the 1D sensor, sliding across the page, building up a 2D image over time, this is what you do when you look at 3D+time videos of 4D objects.

A few months ago, I stayed up all night reading about this and came across two helpful sites.

http://www.rdrop.com/~half/Creations/Puzzles/visualizing.4D/index.html
http://www.math.union.edu/~dpvc/math/4D/welcome.html

The latter is the most helpful, with many visualizations and explanations of the 4th dimension.

This is how I do it. A circle rotates around a point. A plane rotates around a line, and a space rotates around a plane.

If you think of the fourth dimension as time, I like to explain it like this. A two dimensional person seeing a balloon would see it as “cross sections” of itself. They would see a dot expand to a circle, then a sort of upside-down pear shape, then contract back to a circle, then to a dot, which would then disappear.

Our universe actually exists in four dimensions, but we can’t perceive all of it at once. We can only view it in three dimensional “cross-sections”, that is, individual moments. What we perceive as time is an illusion caused by our incomplete perception of reality.

I’d like to recommend a book called Flatland.

@Rarebear Yes!! But not the movie. :)

@Vortico I never saw the movie—I heard it was awful.

@fundevogel I visualize hypercubes this way: If you take a square and move it in 3 dimensions 90 degrees to the plane of the square, with the length of the sides of the square, you get a cube. Then, if you take that cube and move it in the 4th dimension, 90 degrees from the third dimension, the same distance as the length of the sides, you have a hypercube.

Here’s a book on the fourth dimension I read a decade ago. I really liked it. It references Flatland many times.