Like this comment if you're from the 4th dimension.

6:20 The spiritualist movement totally liked the Fourth Dimension, so much, that German humorist, author, painter and inventor of the Graphic Novel Wilhelm Busch (1832 – 1908) wrote in his graphic novel Clement Dove, the Poet Thwarted: "... and moves as Muse's free son into the poet's dimension, the fifth, as the fourth is now occupied by spirits anyhow."

14:54 bro just gave a abridged version of Naruto and it had me dying 😂

You can think of a tesseract as a 4D shape that casts a shadow in 3D. That shadow is that funny layered rotating cube-thing from the video. It’s in 3D because that’s the part of it not in the 4th dimension you can see. A good example is a normal 3D cube that casts a 2D shadow (of 2 squares connected by lines) on the floor since the floor is 2D and can only take in a 2D slice from something 3D. So therefore, a slice of a shape is similar to its shadow, meaning that a 0D point is a slice of a 1D line, which is a slice of a 2D square, which is a slice of a 3D cube, which is a slice of a 4D tesseract, and so on.

One thing that’s interesting is that if a 2D being actually existed, we would see its exterior (basically a curvy shape made from a line) but also its inner organs (like a 2D heart, mouth, brain, etc.) all at the same time. Taking that to its logical conclusion, a 4D being wouldn’t just be able to see us the way we see each other (exterior skin, clothes, hair, etc.) but also all of our insides at the same time. Kinda gross but I guess that’s a biologist’s dream lmao

So as a child who grew up with the metal dome I can state that they where in fact dangerous as if you fell through the bars on the way down you could very easily break a bone. They switched to rope because you can’t get a limb trapped as badly and if you do it is more likely to stop your fall without snapping a bone.

1. Apple (not even close)
2. Orange
3. Grape

4:53 You’ll get used to most aspects of the 4th dimension pretty quickly, if you just study it. Analogies (like those provided in Edwin Abbott Abbott’s ”Flatland”) and pattern recognition are a good start.

Also; when Mathematicians and Maths-nerds (like myself) talk about ”the 4th dimension”, we specifically mean: ”4th SPATIAL dimension”. For me, time is just a manifestation of, how we experience motion, change, and the order of events.

12:25 A tesseract is a 4-dimensional block that’s bounded by 8 3D-cubes (2 per axis), in just the same way, as a cube is bounded by 6 2D-squares (2 per axis), and a square is bounded by 4 1D-lines (2 per axis). It can be thought of, as an extrusion of the 3D-cube, along the 4th W-axis, in just the same way, as a cube is an extrusion of the square, along the 3rd Z-axis. Notice that the wireframe projection of the tesseract is basically 2 cubes, with their corresponding vertices connected by lines (edges). That is a straight-forward analogy of a drawn image of the cube being 2 squares, with their corresponding vertices connected by lines (edges).

High school math teacher here. I introduce 4D by going to animation flip books and walking back a dimension. Say you make a short movie of stick figures. Your characters can move up, down, left, and right in space. But they actually experience another dimension as you put the flip book together. To you, the book gains depth, which for you is a third dimension of space. But to the stick figures, that depth is time. As they progress from page to page, all their 2D spatial objects are still there but they are all moving together through a third dimension that  is basically a progression of their actions. In essence, they can only conceptualize the third dimension as a temporal movement rather than a spatial dimension. But as a 3D creature that created the flip book, you can see each 2D frames separately and you can see their progression in time as movement through the 3D spatial dimension through depth.

So now we move forward. Our own reality is a flip book. From moment to moment, our reality is moving. To us, the movement is time. But it is in reality a fourth spatial dimension that isn’t movement at all. Someone of that dimension would see us in the same way that we see characters in a flip book. Each time we look at a particular flip book frame, we’re looking at a slice of their reality that stopped along a line of depth for which they have no concept. Our 3D world is essentially a slice of reality along a fourth dimensional line for which we have no concept.

Also…

1) Apple
2) Orange
3) Grape.

It's normal to not be able to imagine 4-D objects.  The best I can do describe it using language is...  you know how the area of a 2-D square makes up the surface of one side of a 3-D cube?  Now (do your best to) imagine the entire volume of a 3-D cube being the 'surface' of one side of a 4-D tesseract.

5:00 Mr. Terry has me wanting to read Flatland again...

Orange.
Apple.
Grape. Ugh. Grape.

2:51 Is that Tropico-music, though?

1) Orange 2) Apple 3) Grape

2:50 Yeah; one of the first, I bet. I have heard his name, a few times, but I don’t know much about him. But I could totally see him in the same generation and group of people, with Ludwig Schläfli, et al.

It's easier to use the term "hypercube" than "tesseract". They're synonyms and "hyper(3d object)" tends to be used to refer to whatever 4th dimensional object one wants. Basically, you'd not see an actual 4 dimensional object, but, you would see its shadow as a 3d object. If a hypercube is stationary, its shadow would look like the picture on the book. A cube inside of a bigger cube, connected at the corners. The 3d animation is what happens if the hypercube starts rotating in one direction. Grape, orange, apple. Not so much a fan of apple, and sometimes Orange is a bit too acidic.

12:28 Tesseract is conceptual explenation shadow of a 4D cube in 3D. Like how you can draw a cube a 3D object into paper, a 2D drawing.

Fun fact: he is the great grandfather of Geoffrey Hinton: the godfather of AI, the coinventor of neural networks and the recipient of last year's noble prize for physics.

13:00 So, does ”Kata” correspond to the direction of the hilt, and ”Ana” to that of the blade; or vice versa 🤔?

As I get older, I am approaching these theoretical physics concepts more with the filter:  Does this affect how I do my taxes?