Why is it so hard to imagine 4D objects
In: Mathematics
Because we see the world mostly in 2D. We infer 3D from context and to a minor degree by stereoscopic vision (seeing slightly different images from our two eyes lets us determine how far things are). 4D objects require us to really SEE 3D- to know what’s inside a closed box just by looking at it. To see the form of an object and not just its exterior. This is tough to wrap our minds around.
Try reading FLATLAND by Edwin A. Abbott for the classic book trying to understand dimensions
Because you have no reference frame. You can make out the 3D object from a 2D Shadow because you’ve seen 3D objects projected onto a 2D plain. But you’ve never seen a 4D object so your brain can’t imagine how a 4D object should look like based on a 3D Shadow
Simply because we don’t experience it on a day-to-day basis.
It would not be dissimilar to trying to explain 3D to a 2D stick figure. Say there is a stick figure who lived his whole life on a piece of paper. He can go up, down, left, and right, but his world ceases to exist past the front and back of that piece of paper. Now try to explain a 3D object to him. If you could pass a 3D object through the paper, such as a pencil, he could see the “slice” of that pencil that is currently in the paper, but there is no way for him to actually see the whole pencil in 3 dimensions at once, and it would be very difficult for him to accurately imagine it, let alone explain it to someone else.
We are like that 2D stick figure trying to figure out the 3rd dimension. Since we are 3D and have never seen or experienced 4D, it’s very difficult to imagine it, and any representations we come up with of a 4D object are only in 3D, just like the 2D “slice” of a 3D pencil would be to a stick figure.
Isn’t 4D just a 3D object moving (the time component)? I can easily imagine a box rotating.
The cerebellum has (a neural analog of) purpose-built hardware to efficiently process 3D scenes. When we imagine or manipulate 3D objects, we don’t do this with logic, reason, and faithful analysis. We just deter the entire computation required to the cerebellum, sort of like computers offload graphical computations to the purpose-built graphics card, rather than computing it on the CPU.
This circuitry is not learned. It’s inborn. We didn’t invent it. It evolved. Some parameters of it can be changed, because brains are pretty plastic, but to a very limited degree. In the ancestral environment, you never encountered 4D objects, so there would be no reason to evolve brain areas to compute 4D scenes, so you have to compute it using your general-purpose reasoning facilities, which is going to be way slower if even possible, for pretty much the same reason why an otherwise powerful computer wouldn’t be able to run a modern 3D video game without a graphics card.
I like think of it this way. Think of a point representing 0D object. Now draw a 1D line. You can fit an infinite amount of 0D points on a 1D line no matter how short you make that line. Now draw a 2D surface. No matter how small that surface you drew, you could fit a 1D line of any length by folding it into that surface. Now imagine a 3D object. Every 2D surface can be folded into that 3D object. Now imagine a 4D object – no matter how small you think that object is, it can hold everything in this universe within it.
This is what makes it hard for me, anyway, to imagine.
Imagine if 2-D characters on a comic book page were sentient and aware that we, the readers, existed.
How would they possibly comprehend a creature of depth?
It’s not possible for 3-D creatures like ourselves to interact with that 2-D world. If we were able to insert a finger into that world by touching the page, they’d only see the interaction point as your finger goes the 2-D space. At most, they’d see that interaction point, with the internals of that finger showing through, blood veins, capillaries, bones, as it passes through the 2-D space.
So, in this case, imagine it as a 3-D space and a 4-D creature. We simply cannot comprehend such a thing.
Imagine a cube which is a 3D object.
Now imagine another cube inside of it with corners that are connected to every respective corner of the cube inside of it.
That is a Tesseract.
https://en.m.wikipedia.org/wiki/Tesseract
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