This is amazing and looks really fun! I remember reading a short science fiction story once, "Mimsy Were the Borogoves"[1], where small children were playing with such 4D toys, which were found to be educative in unpredictable ways. It really makes me want to try it out. I wonder if it's really the same without VR. [1] https://en.wikipedia.org/wiki/Mimsy_Were_the_Borogoves (watch out, there are spoilers here!)
the bottom of the website includes an illustrated frame and excerpt from that very story
Can someone help me out here?: I can represent 3D quite comfortably on 2D monitors, can there be an intuitive mapping of 4D to a 3D VR view? I know 3D mapped to 2D suffers from occlusions and heavily relies on clues like perspective, shadow etc. But given enough time even a less intuitive 4D view could become intuitive with time, too. edit: found this: https://youtu.be/S-yRYmdsnGs?t=252 even better: https://youtu.be/…
Just like how 3D objects make a 2D shadow (or a 2D projection on a screen), you can make a 3D shadow of a 4D object. https://www.fourthdimensionapp.com walks you through this.
"To deal with hyper-planes in a 14-dimensional space, visualize a 3-D space and say 'fourteen' to yourself very loudly. Everyone does it." – Geoffrey Hinton, A geometrical view of perceptrons, https://www.coursera.org/lecture/neural-networks/a-geometric... * but remember that going from 13D to 14-D creates as much extra complexity as going from 2-D to 3-D
There is a joke that goes like this: A mathematician and an engineer attend a lecture on the 11-dimensional M-theory. At the end of the lecture the mathematician delighted says how much he enjoyed it. The engineer puzzled asks him how anything even makes sense. The mathematician replies "It's easy. Visualize an N-dimensional space, then let N go to 11."
Here's a thought I had watching the bit with 2D man: Actually, the 3D view that 2D man does not understand but which we do understand is... still 2D. My screen is flat. You can use a 2D viewport to render a 3D scene in a way that is natural and easy to understand for us humans: A human watching the 2D scene can very quickly surmise from a glance at the viewport: Which objects are in the scene, and where are they loca…
I think you can't. The problem is that we don't actually see 3D, we basically see 2D twice. This gives our senses enough info to reconstruct a 3D mental image, but the information we gain isn't truly 3D. Actual 3D-sight might include us seeing the inside of objects, what's behind them, etc. We're aided in converting our 2x 2D sight into 3D mental models through the use of color and parallax. In projections on images,…
FWIW this is really not true. (The bit about stereo vision being required to see 3D.)
When I was in college I was fairly decent on the ping pong table, call it high amateur. I also have very very bad vision - -5 diopters in one eye and -6 in the other. At the time I wore contacts and I was also really really poor. At some point I lost one of my contacts and for six months I was effectively blind in one eye for the purposes of ping pong. It took me about a month, but fairly quickly I was playing at my old level without anything close to stereo vision.
Here's a thought I had watching the bit with 2D man: Actually, the 3D view that 2D man does not understand but which we do understand is... still 2D. My screen is flat. You can use a 2D viewport to render a 3D scene in a way that is natural and easy to understand for us humans: A human watching the 2D scene can very quickly surmise from a glance at the viewport: Which objects are in the scene, and where are they loca…
> Can you render a 4D scene onto a 3D viewport [...] I wonder what that would look like.
It would look like VR. 4D toys supports VR already. I tried it but it did not advance my understanding further than the 2D version, although using 3D tracked controllers is definitely a big improvement over a 2D mouse for manipulating 3D objects or 3D projections of 4D objects.
I think you can't. The problem is that we don't actually see 3D, we basically see 2D twice. This gives our senses enough info to reconstruct a 3D mental image, but the information we gain isn't truly 3D. Actual 3D-sight might include us seeing the inside of objects, what's behind them, etc. We're aided in converting our 2x 2D sight into 3D mental models through the use of color and parallax. In projections on images,…
FWIW this is really not true. (The bit about stereo vision being required to see 3D.) When I was in college I was fairly decent on the ping pong table, call it high amateur. I also have very very bad vision - -5 diopters in one eye and -6 in the other. At the time I wore contacts and I was also really really poor. At some point I lost one of my contacts and for six months I was effectively blind in one eye for the pu…
Did you play with only one eye open, or just one contact lens? I have worse vision than you (-8.0, -7.50), and I know that I can still function with just one lens in of needed. You definitely still have stereo vision even if one input is blurred. Your brain does quite a bit of compensation, and I can imagine if you operated this way for months that your brain would be even better at assimilating the noisy information from your "bad" eye.
Here's a thought I had watching the bit with 2D man: Actually, the 3D view that 2D man does not understand but which we do understand is... still 2D. My screen is flat. You can use a 2D viewport to render a 3D scene in a way that is natural and easy to understand for us humans: A human watching the 2D scene can very quickly surmise from a glance at the viewport: Which objects are in the scene, and where are they loca…
The problem is that while everything you see on your (2D) monitor is effectively 2D our brain is good at taking 3D cues (shadows, perspective, parallax etc...) to reconstitute 3D "data" from it. For instance look at 3D rotating cube on your monitor: https://www.youtube.com/watch?v=5E10zYKln3g Even though there's no shading, a bad resolution and zero context anchoring it in a familiar setting you immediately see it as…
This passage from Death's End by Cixin Liu really gave me pause to stop and wonder about what the experience of seeing extra dimensions might be like (here translated to English by Ken Liu): -- A person looking back upon the three-dimensional world from four-dimensional space for the first time realized this right away: He had never seen the world while he was in it. If the three-dimensional world were likened to a p…
Also I loved how a little later in the book, when he gets back into into normal 3D space, he finds it claustrophobic to even float outside of the spaceship, because of his experience in the fourth dimension.
Here's a thought I had watching the bit with 2D man: Actually, the 3D view that 2D man does not understand but which we do understand is... still 2D. My screen is flat. You can use a 2D viewport to render a 3D scene in a way that is natural and easy to understand for us humans: A human watching the 2D scene can very quickly surmise from a glance at the viewport: Which objects are in the scene, and where are they loca…
I think you can't. The problem is that we don't actually see 3D, we basically see 2D twice. This gives our senses enough info to reconstruct a 3D mental image, but the information we gain isn't truly 3D. Actual 3D-sight might include us seeing the inside of objects, what's behind them, etc. We're aided in converting our 2x 2D sight into 3D mental models through the use of color and parallax. In projections on images,…
i would argue that we don't see in any dimension, at least in terms of the physical capacity of the eye. we just take in varying wavelengths of light and those have no intrinsic dimensionality to them per se. the actual manifestation of dimensionality is, at least in my opinion, merely a construct of the brain. while I think it's accurate to represent reality as a multidimensional thing mathematically and formally, i don't know if dimensionality is an intrinsic feature of it or just a way of categorizing our concept and experience of it. either way, the fact of the matter is that the eye merely takes in raw photons and passing messages on to the brain based on the frequency and intensity of the light, and after saying that i suppose i would be willing to admit that the core nature of light and waves in general is two dimensional, since a wave is defined in terms of frequency and amplitude.