Please explain like I’m actually 5. I’m scientifically illiterate.
In: 172
A tesseract is a 4 dimensional cube.
If you think of a square drawn on a piece of paper as 2 dimensional and then a box as 3 dimensional, a tesseract is the same thing projected into 4 dimensions.
It’s hard to visualize as we’re not wired that way, but there are some [decent examples](https://en.wikipedia.org/wiki/File:Tesseract.gif) of this expressed in 3 dimensions.
Draw a dot. That’s a point. It’s zero-dimensional – you can’t pick any spot on it, it’s just a single spot.
Add a second point to the right and connect the two. You’ve just made a line, a one-dimensional object. **One** dimensional, because if point A is at 0, and point B is at 100, then you only need **one** number to choose a point on the line. This line is defined by two points, one at each end.
Now take that line and move it down, connecting the endpoints via two new lines. You’ve just made a square, a two-dimensional object. **Two** dimensional, because we now need **two** numbers to define a point in the square – one for how far left/right we are, and one to for far up/down we are. This square is defined by four points, one at each corner, and contained by four lines.
Now take that square and pull it out of the page, connecting each corner of the original square to a corner of the new square. You’ve just made a cube, a three-dimensional object. Three dimensional, because three numbers define a point inside the square – left/right, up/down, and closer/further from the page. This cube is contained by 6 squares (one for each face), 12 lines (each edge) and eight points, one at each corner.
Now take that cube and move it into a fourth dimension, connecting each corner of the cube to a corner of the new cube. You’ve just made a **tesseract** (finally!), a four-dimensional object. Four dimensional, because four numbers define a point inside the tesseract – left/right, up/down, closer/further, and thataway/thisaway (or whatever you want to call movement in the 4th dimension). This tesseract is contained by eight cubes, 24 squares, 32 lines and 16 points.
It’s an object with higher dimensions than a normal object.
For example, a normal object has only three spatial dimensions: length, width, and height. These are the three dimensions of ordinary space.
But it’s possible to imagine a space with 4 dimensions. The 4th spatial dimension would have to be perpendicular to the other three. That means you wouldn’t be able to see it in 3-space. Only a portion of it that was super-imposed (like a projected image) on 3-space. We can mathematically describe it, but not directly see all of it.
This can be seen in lower dimensions more easily. What does a cube look like in 2 dimensions? Well, it depends on the angle, but kinda like a square. You see this in the real world all the time with shadows. The shadow of a 3d object is a 2d projection of it.
So a tesseract is more than 3 dimensions and we can only see a shadow of it in 3 space because we aren’t capable of sensing higher dimensions directly.
A square is a two-dimensional shape where each edge had the same length.
A cube is the same for three dimensions.
A tesseract is the same for four.
Line = 1 directions (positive x, or negative x)
Square = 2 directions (+x, +y and -x, -y)
Cube = 3 directions (+x, +y, +z, and -x, -y, -z)
Tesseract = 4 directions (idk but there’s the same as 3 but with whatever a fourth one would be in this fourth dimension too)
One overlooked fact that may help with visualizing a tesseract is that each dimension is at 90º of each other; if you take a line and move it in a direction at 90º of their original one (up/down from left/right), you create a plane with 2 dimensions.
If you take this square and move it at 90º from the plane, you create a cube in the third dimension….
…Now take this cube and move it in a direction 90º from the third and you’ve arrived to the fourth dimension (and so on and so forth)
You can “preview” higher dimensions in a lower one if you make the move at 45º in the other ones, for example you can move a plane 45º in X/Y and now you have a “shadow” of a cube in 2 dimensions, if you move a cube 45º in all three X/Y/Z dimensions you get a 3 dimension shadow of a teseract, which is the popular image of a cube inside another cube, If we were able to see the forth dimension, all sides, interior and exterior would be of the same size and at 90º
Trippy, right?
Imagine a bookshelf with a single row of books. This is a line, or the 1st Dimension. You need to know how many books from the side to count. So, if you have 100 books, you’ve found it after counting 10 from the left.
Next is a full book shelf. You need to know the which shelf it’s on then you need to know how many books to count in. This is the 2nd dimension. Your book is now on the 3rd shelf from the top, 10 books from the left.
Now, we move to a single story library with multiple rows of shelves. This is the 3rd dimension. You need to know which row your bookshelf is in, then which shelf it’s on, then how many to count in on the shelf itself. Here we have our book in the 12th row from the front, 3rd shelf from the top, 10th book in.
Finally, we have a multistory library. We first need to know which floor our row of bookshelves are. This is the 4th dimension (or our tesseract). You first go the the 2nd floor, move to the 12th row from the front, 3rd shelf from the top, 10th book from the left.
You could continue this by adding multiple library buildings, etc. to continue up the chain of dimensions. This isn’t a perfect analogy, but a good way to put multiple, dimensions into concept.
Imagine moving your pen on a piece of paper. That paper is 2D. What happens if you stop moving your pen up or down and only allow left and right movements? You get a line (1D).
What happens when you restrict left and right movements too? You get a point (0D).
Mathematically, moving left and right is done by changing the x coordinate. Moving up and down is done by changing the y coordinate. Freezing one coordinate moves you down a dimension. It works in 3D too: if you freeze the third coordinate while traversing a cube, you get a plane.
So now, you could just say “Well what if we had 4 coordinates?”. Geometrically, there is no way to fit a fourth axis. But coordinates really are just bundles of numbers so why not have 4 instead of 3 numbers? If we apply the coordinate freezing trick here and freeze the fourth coordinate, we lose a dimension and get a cube. Some people say that a 3D cube is the shadow of a 4D cube and this is what they mean. Its in the same way that a 2D plane is the shadow of a 3D cube: you get the shadow by removing a dimension, and you remove the dimension by freezing a coordinate.
So what we can say is: you can think of 4D points as a bundle of 4 numbers. That fourth axis doesnt really fit into our coordinate system, its abstract. But by freezing movement along that axis, you move down a dimension and get a 3D slice of the 4D object. In this case, the slice of a tesseract is a 3D cube.
A tesseract is to a cube what a cube is to a square. So a 4-D shape with cubes on each “face”. Hard to picture
I think other posters have done a good job explaining conceptually what a Tesseract it, but maybe you’re also wondering what [these well know 3D tesseract models are](https://media.printables.com/media/prints/146580/images/1383071_9e6af9d4-08d9-4d1a-a9d8-e3ef93b5b503/thumbs/inside/1280×960/jpg/88693291339c588951373115531ede4a_display_large_14.webp)?
Well, in our 3D space shadows are 2D right? So if you imagine holding a hollow cube up to the light [it would make a shadow like this](https://i.stack.imgur.com/A3rfx.png).
In 4D space shadows are 3D! So if you held a hollow tesseract up to the light in 4D space the shadow would be that 3D model of a tesseract.
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