The pyramids in the background are called Cubic Pyramids. They have a cube for their base and 6 'sides' (square pyramid cells) to them for a total of 7 cells.
i'm probably way late to say any of this but anyway you _almost_ had the right idea at 33:23. it's helpful to go in volume view and think of the slope as having a forcefield that's gonna push you in the opposite direction, thus curving your path -- only the forcefield is actually just gravity. i had an easier time with slopes after figuring out that way of conceptualizing it. if you do go on to the later levels then a few things i think are also pretty helpful are switching to metered putts so you can dial shots in accurately (i switched on the first course i think because i was having such bad accuracy with physical, it might have been partly due to inconsistent FPS on my computer but that could just be cope), turning on "ghost colors" so you can see what parts of the projection are "above" or "below" you, and actually using the 1/2 keys (looks like on controller it's L3 and R3, aka clicking the sticks) to toggle visuals and only look at the volume -- on a few of the courses the background can make it really hard to see the projection well enough to make any sense of it, imo other people are right, ofc, that rotating the view around when the ball's already moving won't do anything, but another thing that might take a bit to understand is that holding click and moving the mouse left and right when setting up the putt (dunno what the gamepad equivalent is, sorry) doesn't actually change the trajectory either. in volume view you can hold click, move the mouse left and right and see that that just tilts the view -- it's exactly the same rotation (like the tutorial says, the line that comes up represents what will be visible to you when you switch back to slice view, so it does affect what angles you'll get afterward when you just aim without holding click).
34:33 You make some beautiful observations! Yes, it does that, and I think it’s because all of those hills are connected in the same way the sides of a cube are connected 2D cubes (squares). Also just in the same way a you can reflect a 2D creature by just continuously rotating it in the 3rd dimension, you can reflect a person, a shoe or anything 3D by continuously rotating it in the 4th dimension. If you like your mirror self more and wish you looked like that to others, or lost your right sock then just borrow the 4th dimensions way of transforming objects for an action then
4D isn’t just a theory, it’s just the math continuing in the same pattern. Point, square, cube, hypercube and so on. Higher dimensions are just a case where the math is simple, but visualizing it isn’t. Farmers can use higher dimensions for calculating minimal farming prices because you can use a new direction (orthogonal to the others) for each variable because it makes the math easier and a minimum would be a combination of those creating a higher dimensional shape where you use 4D logic. There are tools mathematicians use like turning shapes into networks, where you can say this point is connected to those points therefore that side of the higher dimensional shape is next and connected to those other sides. In AI language models words and other tokens get a point in a high space where there is a direction (not necessarily orthogonal to the others) for masculinity because waitress - woman turns into waiter. A circle is every point which is the same distance from a single point in 2D within every combination those two directions (up-down right-left) so a 3D equivalent of a circle is a sphere (up-down right-left forwards-backwards) a hypersphere is every point the same distance away from a single point in 4D (up-down right-left forwards-backwards ana-kata). And the logic continues even though with think holograms are complete, final and holistic it doesn’t mean it has to be final since there could be more dimensions. The political spectrum on a 1D axis only has one variable even though we might try to spread other aspects to each side in a linear or non linear way, shouldn’t economy and authority get two different axes, because they are separate things? Well we could continue like that until we have a high dimensional space with up to the right and ana more authoritarian and less local and so on to find where you are on the political landscape
I find that thinking about the relationships between 2D and 3D does help a bit with understanding the relationships between 3D and 4D. Many things are similar, just a dimension higher. But thinking directly about 4D is still not something I can do, and I kinda doubt many people (if any) can, we're just not wired to think like that.
As far as game design and math goes - it's just one more dimension of space. The computer can simulate it even if it doesn't exist in real life. Instead of x, y, z it does w, x, y, z.
Bruuuh🤣 at 22:11 you said you'd shoot the ball and then quickly change your view so you can "catch the ball on the way back down" The level is always the same, it doesn't matter what your perspective is. You're not changing the level when you do the 4d magic rotation stuff, you just start seeing the level from a different view.
The pyramids in the background are called Cubic Pyramids. They have a cube for their base and 6 'sides' (square pyramid cells) to them for a total of 7 cells.
i'm probably way late to say any of this but anyway
you _almost_ had the right idea at 33:23. it's helpful to go in volume view and think of the slope as having a forcefield that's gonna push you in the opposite direction, thus curving your path -- only the forcefield is actually just gravity. i had an easier time with slopes after figuring out that way of conceptualizing it.
if you do go on to the later levels then a few things i think are also pretty helpful are switching to metered putts so you can dial shots in accurately (i switched on the first course i think because i was having such bad accuracy with physical, it might have been partly due to inconsistent FPS on my computer but that could just be cope), turning on "ghost colors" so you can see what parts of the projection are "above" or "below" you, and actually using the 1/2 keys (looks like on controller it's L3 and R3, aka clicking the sticks) to toggle visuals and only look at the volume -- on a few of the courses the background can make it really hard to see the projection well enough to make any sense of it, imo
other people are right, ofc, that rotating the view around when the ball's already moving won't do anything, but another thing that might take a bit to understand is that holding click and moving the mouse left and right when setting up the putt (dunno what the gamepad equivalent is, sorry) doesn't actually change the trajectory either. in volume view you can hold click, move the mouse left and right and see that that just tilts the view -- it's exactly the same rotation (like the tutorial says, the line that comes up represents what will be visible to you when you switch back to slice view, so it does affect what angles you'll get afterward when you just aim without holding click).
34:33 You make some beautiful observations! Yes, it does that, and I think it’s because all of those hills are connected in the same way the sides of a cube are connected 2D cubes (squares). Also just in the same way a you can reflect a 2D creature by just continuously rotating it in the 3rd dimension, you can reflect a person, a shoe or anything 3D by continuously rotating it in the 4th dimension. If you like your mirror self more and wish you looked like that to others, or lost your right sock then just borrow the 4th dimensions way of transforming objects for an action then
4D isn’t just a theory, it’s just the math continuing in the same pattern. Point, square, cube, hypercube and so on. Higher dimensions are just a case where the math is simple, but visualizing it isn’t. Farmers can use higher dimensions for calculating minimal farming prices because you can use a new direction (orthogonal to the others) for each variable because it makes the math easier and a minimum would be a combination of those creating a higher dimensional shape where you use 4D logic. There are tools mathematicians use like turning shapes into networks, where you can say this point is connected to those points therefore that side of the higher dimensional shape is next and connected to those other sides. In AI language models words and other tokens get a point in a high space where there is a direction (not necessarily orthogonal to the others) for masculinity because waitress - woman turns into waiter.
A circle is every point which is the same distance from a single point in 2D within every combination those two directions (up-down right-left) so a 3D equivalent of a circle is a sphere (up-down right-left forwards-backwards) a hypersphere is every point the same distance away from a single point in 4D (up-down right-left forwards-backwards ana-kata). And the logic continues even though with think holograms are complete, final and holistic it doesn’t mean it has to be final since there could be more dimensions. The political spectrum on a 1D axis only has one variable even though we might try to spread other aspects to each side in a linear or non linear way, shouldn’t economy and authority get two different axes, because they are separate things? Well we could continue like that until we have a high dimensional space with up to the right and ana more authoritarian and less local and so on to find where you are on the political landscape
I find that thinking about the relationships between 2D and 3D does help a bit with understanding the relationships between 3D and 4D. Many things are similar, just a dimension higher. But thinking directly about 4D is still not something I can do, and I kinda doubt many people (if any) can, we're just not wired to think like that.
7:01 I think your problem is that you're forgetting about height when you're using volume mode. It still exists even if you aren't looking at it.
22:11 Dude's trying to change the direction of the shot after he already hit the ball! 💀💀💀
heads up: you can't actually change your trajectory (or the level itself) by rotating your 4D view
Wait until you get to the last world…
As far as game design and math goes - it's just one more dimension of space. The computer can simulate it even if it doesn't exist in real life. Instead of x, y, z it does w, x, y, z.
That’s a good way of putting it. Since computers need to be told what physics are to begin with, just adding one more dimension isn’t far fetched.
"Alright kids, this is your brain on drugs"
I don’t encourage it, but playing this game while on drugs would be be a trip and a half.
Bruuuh🤣 at 22:11 you said you'd shoot the ball and then quickly change your view so you can "catch the ball on the way back down"
The level is always the same, it doesn't matter what your perspective is. You're not changing the level when you do the 4d magic rotation stuff, you just start seeing the level from a different view.