The first video in a multi-part series on understanding and visualizing the 4th dimension, from a mathematical point-of-view. We'll understand where a 4th di...
Wasted my time watching this. 23 minute video that repeats itself so often there’s only ~30 seconds of information. It feels very AI-generated. And it is not possible to “visualize 4D”, the video does not prove otherwise.
3 spatial dimensions + 1 color dimension (grayscale)
2 spatial dimensions + 2 color dimensions
etc
And that’s not even counting projection. All the time we interact with 3D data that’s projected to 2D (almost every photo you’ve ever looked at). There are similar ways to project 4D to 2D.
(Not defending the video or anything, just pointing out that visualizing higher dimensions is something we know about for ages.)
I took a shortcut when typing that, quoting the OP instead of further explaining. It is definitely possible to visualize 4 datapoints, but not 4 spatial dimensions. The only way to do so is to project to lower dimensions or take a lower dimension slice and display that. That works for 2D slices/projections of 3D objects because we already have a full understanding of 3D. It does not work for 2D projections of 4D objects, similar to how “flatlanders” couldn’t make sense of a 2D or 1D projection of a 3D object.
Wasted my time watching this. 23 minute video that repeats itself so often there’s only ~30 seconds of information. It feels very AI-generated. And it is not possible to “visualize 4D”, the video does not prove otherwise.
It’s possible to “visualize” 4d with projections to lower dimensions. This video is just bad at explaining.
Sure it is.
And that’s not even counting projection. All the time we interact with 3D data that’s projected to 2D (almost every photo you’ve ever looked at). There are similar ways to project 4D to 2D.
(Not defending the video or anything, just pointing out that visualizing higher dimensions is something we know about for ages.)
I took a shortcut when typing that, quoting the OP instead of further explaining. It is definitely possible to visualize 4 datapoints, but not 4 spatial dimensions. The only way to do so is to project to lower dimensions or take a lower dimension slice and display that. That works for 2D slices/projections of 3D objects because we already have a full understanding of 3D. It does not work for 2D projections of 4D objects, similar to how “flatlanders” couldn’t make sense of a 2D or 1D projection of a 3D object.
I see. Yeah, obviously the world only has 3 spatial dimensions, so you can’t represent 4D data spatially.
My general point is that we have additional senses that we can use to represent additional dimensions. And that totally counts as “visualization”.