People can think in the 4th dimension, but only with help. Give someone a variety of chiral objects and ask them which two are mirror images of each other, and they almost certainly will be able to do it. Since actually perfectly transforming the objects requires using a 4th dimension, one might say that it requires some sense of the 4th dimension to be able to make the correct comparisons.
This example borrowed from Steven Pinker’s How the Mind Works.
I read somewhere once that Minkowski claimed that he could visualize four-dimensional space. I’ve also read that Einstein claimed to have tried many times and failed.
Approximately how long did it take you, and did you do anything special besides taking normal physics courses and doing problems that involve 4 dimensional objects?
The film Donnie Darko has about the best representation of four dimensions as is possible for the layman to interpret. Of course, trying to actually figure out the plot of the film may drive you instance, but these are the risks you take in science.
How do you get five? With a rotation? I can imagine four pretty easily, but I can’t even start on five. On the other hand, I can represent it topologically as a large number of dimensions, suffering only the tedium of repeated calculation. I don’t have much use for that these days, but so it goes.
Stranger
I’ve often heard time described as the fourth dimension… if so, surely anyone can visualise in 4D by simply imagining a 3D object changing as it ages (like the head on the Anubis statue at the start of The Mummy?
Of course, I’m not a physicist, so I realise it probably doesn’t work that way. Interesting topic, though!
Uh…I think Chronos is yanking our chains. :dubious:
Or, let me just add that I’ve been trying for over thirty years and can’t do it.
This is non-sense. It is not even wrong, because even wrong statements make sense.
Math is a hell of a drug.
I really got into reading up on the fourth spacial dimension a few years ago. I have 12 links, and I’ll share a few. Hope they help:
4D notes
Hypersphere
Higher Dimensional Geometry
Steroscopic Animated Hypercube
Thomas Banchoff
Well… I have a kind of a mental construct for visualising hyperspheres up to 6D without much difficulty. I’m not claiming it is very useful, but here goes.
A 3D sphere is easy to visualise. We meet them all the time.
For a 4D I imagine taking 3D cross-sections. I think of the kind of slider i might move with a mouse. As I slide the slider a sphere appears, grows larger then gets smaller again. The radius of the sphere would form a semicircular envelope if positioned perpendicular to the slider.
5D is not so great of a leap from there. My slider becomes a dot within a circle. The dot takes care of two dimensions and I can visualise the 3D cross section.
6D and my dot in a circle becomes a dot in a ball which takes care of three dimensions and uniquely defines the 3D cross section.
In this way i can mentally travel around a 6D shape. I can travel around teh 5D equivalent of a great circle, visualise poles, meridians, take sections, visualise hypersolid angles and that kind of thing. Again, not terribly useful, but worth the mental trip on bus trips with boring scenery.
On the other hand there are things that I have great difficulty with in 4D. I know taht a plane shape rotates on a point and a solid shape rotates on a line, but even with Wiki’s great rotating tesseract gif I just can’t see the plane that it is rotating on.
Dude…y’know I used to be impressed with you–big science type guy, brain the size of a planet, but now? My illusions are shattered.
It’s so bloody easy to visualize the Fifth Dimension
Aside from that pun, there’s a story by Heinlein ("…and he built a crooked house") that A) is the best attempt I’ve read to try to help you conceptualize the fourth (spacial) dimension and B) is a fun story.
Heinlein had another short story (“Lifeline”) where he helps you visualize a temporal 4th dimension (imagine yourself as a snake made up of billions of stop-motion pictures–the “tail” of the snake is you as a baby–the snake gets bigger/thicker in the middle as you grow and stops when you die (actually decompose, but let’s not quibble). The entire “snake” is all there, all the time–your conscious mind just passes from frame to frame at a one second-per-second rate)
There’s also a fun book (by Rudy Rucker?) that I can’t remember the title of where he gets into the nuts and bolts of life on Flatland.
For example…how do they eat? Everything that eats excretes. But if you have a tunnel through Mr A. Square, you kill him (he’s sliced in half). Does he eat, digest then barf up the remainder?
Could you build a 2-d railroad (yes) and if so, what happens if someone wants to cross the tracks perpendicular to them (they’re screwed).
Etc…I’ll try to find the title.
A question:
Is there a distinction between using time as the fourth dimension and a spatial fourth dimension?
The OP is talking about a spatial fourth dimension.
Thinking out loud here I can imagine using time to take a 2D object and making it 3D. Take a square and move it up. It travels some distance over time and (I am assuming the vertices are remaining connected) in the end you have a cube (or rectangle).
That is easy as I am moving the square at a right angle to itself.
Now, taking a 3D cube and doing the same I fail utterly to picture it. Move the cube through time but you cannot move it at a new right angle to the other three you already have. The result, if I connect all the vertices, are angles that are not 90 degrees from the “old” object to the “future” moved object. I get a 3D representation of a hypercube much the same as a 2D representation of a 3D cube has angles that are not 90 degrees (that cube in 3D all angles would be 90 degrees).
So absolutely not seeing how us 3D creatures could possibly visualize an actual 4D object. I believe it is utterly beyond our ken and what others are doing are tricks that give an impression of a 4D object but aren’t anymore than that 2D cube is a 3D cube.
Why stop at four? These videos do a great job jacking it up to 10 dimensions!
Imagining the Tenth Dimension part 1 of 2 (dimensions 1 to 6)
Imagining the Tenth Dimension part 2 of 2 (dimensions 7 to 10)
Imagining the Tenth Dimension (full and annotated)
Who knows what wondrous superpowers those physicists and mathematicians are hiding from us. Well, at least I hope they’re hiding superpowers, or else I shall be very disappointed in a few years.
I used to spend a lot of time thinking about dimensions. With intense focus I could visualize five and on a few occasions glimpsed six for a fleeting moment. The whys and the implications just aren’t going to fit in a message board post.
For those who want to try, keep in mind that the concept of a 90 degree right angle only applies in three dimensions. I found it useful to assign a color to each dimension to help clarify the mental image.
And yes, quite serious.
This is definitely false.
Ah, you got me. It also apples in two dimensions.
It applies generally in n spatial dimensions as well. See my comment in post #19 for something that’s directly relevant to the fourth dimension.
If you think of time as the 4th dimension, you would have to realize that we are only capable of experiencing one point in that dimension at a time. We have a way to record what happened in points we’ve already been past and can synthesize the whole series of points. A being that truly experienced time as a 4th dimension could move around in time at will and see all events from our past and future in one shot, the same way you can see an entire line though the 1D inhabitants can only see the point they’re at.
Two planes do not intersect in a point regardless of how many dimensions you are in.
In four dimensions, two non-parallel 2D planes lying in the same realm (three-dimensional hyperplane) intersect in a single line, just like they do in our 3D world.
In four dimensions, two non-parallel realms intersect in a plane.
Let P = {(a, b, 0, 0)} and Q = {(0, 0, c, d)}, where a, b, c, d are arbitrary real numbers. {(1, 0, 0, 0), (0, 1, 0, 0)} and {(0, 0, 1, 0), (0, 0, 0, 1)} are the respective bases for P and Q, so both sets are planes. The intersection is the set of points {(a, b, c, d) | a = 0, b = 0, c = 0, d = 0}, so the only common point is (0, 0, 0, 0). The dot product of any vector in P with any vector in Q is a0 + b0 + 0c + 0d = 0, so the two planes are orthogonal.
