5 ms·

> Because humans can't visualize more than 3 dimensions. It's awfully hard to prove that real-world things are impossible, especially if there's no objective m

by JadeNB 2y ago

> Because humans can't visualize more than 3 dimensions. It's awfully hard to prove that real-world things are impossible, especially if there's no objective measurement of whether they've been achieved. (For example, if I tell you that I can visualize more than 3 dimensions, then how could you verify or disprove that?)

epidemian 2y ago
> For example, if I tell you that I can visualize more than 3 dimensions, then how could you verify or disprove that? I don't really know. The first thing that came to my mind would be to ask to draw/model different cross-sections of a 4D object ("cross-volumes"?). We can visualize 3D objects, and therefore can draw 2D cross-sections of 3D objects relatively well, and relatively easily. Like, sections of a human body, or a house. So, maybe someone who can visualize 4D objects in their head could also model 3D "cross-sections" of that object at arbitrary "cuts". And we could check if those 3D radiographies are accurate, because we can model those 4D objects on a computer, and draw their 3D cuts. Just a simple idea. I'm sure there could be other ways of probing this.
- JadeNB 2y ago
  > We can visualize 3D objects, and therefore can draw 2D cross-sections of 3D objects relatively well, and relatively easily. Many people can draw cross-sections reasonably well, but I can't. Nonetheless, I believe that I can visualize 3D objects.
  - wongogue 2y ago
    But you can still draw the concepts of a cross section, right?
    - JadeNB 2y ago
      > But you can still draw the concepts of a cross section, right? I'm not sure what that means, but my inability to draw is astounding.
- quuxplusone 2y ago
  > We can visualize 3D objects, and therefore can draw 2D cross-sections of 3D objects relatively well, and relatively easily. I don't think that's true. For example, consider a regular octahedron: take a parallel pair of its faces and bisect the octahedron between those faces. What's the resulting figure? What happens to the figure as you tip the plane? I mean, obviously the task I just set isn't impossible; and with a little reasoning anyone can give the answer in a few seconds; but it feels too me like the answer is not simply intuited merely by the virtue of our being 3D creatures. Sure, part of the difficulty stems from that the octahedron (to most folks) is both less familiar and slightly more complicated than the cube. But the same applies to the hypercube!
UltraSane 2y ago
Humans have had tremendous evolutionary pressure to develop excellent 3D visualization abilities. Humans have had exactly ZERO evolutionary pressure to develop 4D visualization abilities. If someone claimed to be able to visualize 4D the exact same as they can visualize 3D I wouldn't believe them. Maybe there are some kind of tests that could be done to prove it?
- teemur 2y ago
  My low, low priority side project has been to make a VR app that lets you (create and) move around 4d environments. I'm pretty sure that navigating even moderately complex 4d environment can be used as some kind of proof for 4d visualization/intuition capabilities. Level 6 on my toy maze game has all of 4 tesseracts within the maze tesseracts and after some hours of playing, I am still completely lost there. If someone wants to have a look, feel free (but it is hard. You need time. If you do not have vr headsets but want to have a look, you can install browser add-ons thet let you simulate vr headset and controls): https://www.brainpaingames.com/Hypershack.html https://www.brainpaingames.com/Hypershack.html I have been planning to write a Show HN any day now for months, but maybe someday.
  - UltraSane 2y ago
    Some cool examples of 4D games https://4dtoys.com/ https://4dtoys.com/ https://store.steampowered.com/app/2147950/4D_Golf/ https://store.steampowered.com/app/2147950/4D_Golf/

by JadeNB 2y ago

epidemian 2y ago

> For example, if I tell you that I can visualize more than 3 dimensions, then how could you verify or disprove that? I don't really know. The first thing that came to my mind would be to ask to draw/model different cross-sections of a 4D object ("cross-volumes"?). We can visualize 3D objects, and therefore can draw 2D cross-sections of 3D objects relatively well, and relatively easily. Like, sections of a human body, or a house. So, maybe someone who can visualize 4D objects in their head could also model 3D "cross-sections" of that object at arbitrary "cuts". And we could check if those 3D radiographies are accurate, because we can model those 4D objects on a computer, and draw their 3D cuts. Just a simple idea. I'm sure there could be other ways of probing this.

JadeNB 2y ago
> We can visualize 3D objects, and therefore can draw 2D cross-sections of 3D objects relatively well, and relatively easily. Many people can draw cross-sections reasonably well, but I can't. Nonetheless, I believe that I can visualize 3D objects.
- wongogue 2y ago
  But you can still draw the concepts of a cross section, right?
  - JadeNB 2y ago
    > But you can still draw the concepts of a cross section, right? I'm not sure what that means, but my inability to draw is astounding.
quuxplusone 2y ago
> We can visualize 3D objects, and therefore can draw 2D cross-sections of 3D objects relatively well, and relatively easily. I don't think that's true. For example, consider a regular octahedron: take a parallel pair of its faces and bisect the octahedron between those faces. What's the resulting figure? What happens to the figure as you tip the plane? I mean, obviously the task I just set isn't impossible; and with a little reasoning anyone can give the answer in a few seconds; but it feels too me like the answer is not simply intuited merely by the virtue of our being 3D creatures. Sure, part of the difficulty stems from that the octahedron (to most folks) is both less familiar and slightly more complicated than the cube. But the same applies to the hypercube!

UltraSane 2y ago

Humans have had tremendous evolutionary pressure to develop excellent 3D visualization abilities. Humans have had exactly ZERO evolutionary pressure to develop 4D visualization abilities. If someone claimed to be able to visualize 4D the exact same as they can visualize 3D I wouldn't believe them. Maybe there are some kind of tests that could be done to prove it?

teemur 2y ago
My low, low priority side project has been to make a VR app that lets you (create and) move around 4d environments. I'm pretty sure that navigating even moderately complex 4d environment can be used as some kind of proof for 4d visualization/intuition capabilities. Level 6 on my toy maze game has all of 4 tesseracts within the maze tesseracts and after some hours of playing, I am still completely lost there. If someone wants to have a look, feel free (but it is hard. You need time. If you do not have vr headsets but want to have a look, you can install browser add-ons thet let you simulate vr headset and controls): https://www.brainpaingames.com/Hypershack.html https://www.brainpaingames.com/Hypershack.html I have been planning to write a Show HN any day now for months, but maybe someday.
- UltraSane 2y ago
  Some cool examples of 4D games https://4dtoys.com/ https://4dtoys.com/ https://store.steampowered.com/app/2147950/4D_Golf/ https://store.steampowered.com/app/2147950/4D_Golf/