Today I was aked by a friend about viewing objects in 4 dimensions and didn’t really know how to answer. What stops us from viewing the world through a 4D spectrum, and what would it look like?
Thanks
Here’s a image of a Tesseract (4D cube).
In reality what you see there is the shadow a 4D cube would cast.
We cannot see into the 4th dimension (although Chronos and some others here claim to be able to imagine such objects I remain unconvinced).
If you could see in 4D a lot of weird things would become apparent (e.g. you could see inside people’s bodies).
The problem is this…a line is 1-D, a line perpendicular to that is 2-D (a plane), a line perpendicular to the first two is 3-D, a line perpendicular to all those is 4-D. There lies the problem…getting that next line at 90 degrees is not possible for us.
“Spectrum”? If you mean viewing a 4D space, there’s the slight problem that we live in a 3D space. One can extrapolate upwards to a 4D euclidean space, and the math to describe such as space isn’t that much different that that to describe a 3D space. Here’s a link describing raytracing in 4D space and projecting the results onto a 2D screen.
But direct perception? We’d need some kind of 4D sensor and the appropriate brain wiring or whatever. Given the 4D sensor, we could probably learn to interpret things, much as we learn to see 3D space using our 3D eyes.
What’s so unbelievable about it? Is it any less plausible than developing the ability to intuitively “visualize” any other object one has no direct familiarity with? Surely, with enough experience/practice with the relevant mathematics…
3D eyes?
You’re always perceiving things in 4 dimensions. It’s just that you “arbitrarily” carve up one of those dimensions as a mutually exclusive series of 3D snapshots.
I cannot see how anyone can visualize something at a right-angle to the first three.
Someone may get an idea of it, like the tesseract linked above, but it is not the thing itself.
Our eyes are 3-dimensional structures. They have a 2D sensor, the retina, curved through 3D space. A direct analogy for a 4D creature would have a 3D retina curved through 4D space.
I think the OP was speaking of a 4D euclidean space, not the combination of three dimensions of space and one of time.
Flatland is a great book to start thinking about how to visualize the 4th dimension. I have wasted many hours in my life thinking about how to visualize this (most of them while dateless in high school - lord knows why…).
Its a matter of thinking about the 3D/2D equivalent and scaling it up in your mind to the 4D/3D situation.
I have read that and use it to describe to others how seeing in a higher dimension would work and the odd results (to us) that stem from it.
Nevertheless we have an in built handicap in this regard. As 3D creatures we just can’t figure out that last angle for 4D.
Whack-a-Mole, Can you explain why would this happen? What are some of the other weird things?
Thanks.
As mentioned above the easiest way to get a sense of it is to step down a dimension and envision Flatland, a world of 2-dimensional creatures.
To each other there is no up/down. It literally is beyond their comprehension. They would see each other as lines viewed edge on.
So say the Flatlanders are circles and squares. From their perspective their outside lines that define them cannot be seen past.
However, you come along and from your 3D perspective you can see the insides of the Flatlanders just fine (draw a circle on a piece of paper and put some dots on the inside to represent Flatlander internal organs…you see it fine but they couldn’t without cutting themselves open).
Other nifty tricks:
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Not only can you see inside them you could perform surgery on them without cutting them open.
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No jail could hold you if you had access to the 4th dimension. A Flatlander trying to jail you would build a line around your shoes (where you touched their plane). To escape you just step out of the circle. A person in 4D could do the same if imprisoned in a 3D jail.
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To them, you walking they would see you disappear (as you picked up your shoe) and reappear further along. Very magical seeming.
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You could take a sea shell and reverse the spiral if you could access the fourth dimension (just like you could pick up a spiral in Flatland and flip it over to go the other way…something Flatlanders could not do).
A 4D person could see inside a 3D person’s body, not necessarily a 4D body. It’s analogous to a 3D person looking down on a 2D drawing of a person, and seeing everything inside the outline of the drawing.
Excellent explanation. Thanks. If you are not a science teacher, you would be a good one.
I’m not sure how that image equates to a 4D cube. I still see a 3 dimensional object. It’s bascially a wire frame of a donut with it’s skin rotating around itself much like one of those old water snake toys.
It looks cool and all but where do people get “4D” out of this?
Its a 3D representation of a 4D object. As stated above, you can’t directly view a 4D object in 3D space.
Actually, it’s a 2D representation of a 3D representation of a 4D object. Saying that you see it as a 3D object is like looking at a picture of a cube and saying that it’s just a picture of a couple of squares with their corners connected.
You guys have to read the book Flatland, an 1884 “satirical novella by the English schoolmaster Edwin Abbott Abbott.”
I just finished reading it. Crazy weird, but very cool.
True - I was simplifying.
A classic example of 4D weirdness is the Klein Bottle. In 4D space it is a single surface that does not intersect itself. We can only show this in 3D space (or even 2D projections of 3D space) by having the single surface intersect itself.
The usual way to visualise this is to simply draw a 2D projection of the 3D Klein Bottle on a piece of paper and try to imagine the “spout” coming out of the paper.
I actually had a Topology lecture at University where the lecturer actually said “this is much easier to visualise in four dimensions” and meant it. He was a weird guy.