I'd like to hear any ideas about what it would be like to be a 4D being viewing 4D surroundings, and other 4D beings.
What would they likely be able to see and perceive?
quickfur wrote:So even while facing the same direction in 4D (and keeping your head pointing up and feet on the floor), you still have 4 distinct orientations you can be in. Or, put another way, you can spin your body around in 4D while standing on the same spot, and facing the same direction, without changing the latter.
quickfur wrote:The Necker Cube is an illusion that is unrelated to the kind of orientation changes I was talking about. The Necker cube illusion is caused by the visual ambiguity introduced by collapsing one of the dimensions during the scene-to-eye projection.
quickfur wrote:This is interesting because as long as the radius is not too far below the 3D thickness of the object, then it behaves "normally", but once its radius becomes too small, it has the risk of "falling over" and acquiring strange properties. So there is a size scale at which things start to turn strange (i.e., 3D effects start to show up). Does this remind you of the real world? Macroscopic objects behave "normally", but once you get down past a certain size, things start to act strangely. Conceivably, this is because objects smaller than a certain size starts to exhibit extra-dimensional properties.
And indeed, this is the idea behind "curled up" dimensions and string theory. When the object is big enough, you don't see anything strange because only their 3D properties are manifested. They are too big to "fall over" in the extra, confined dimensions. But when things get small enough, then the effects of the additional dimensions start to show up. Now they can "fall over" in the extra dimensions, and when we try to interpret the effects from our 3D-centric point of view, we find them really strange. But if we interpret them as the effect of having extra dimensions to "fall" or "rotate" in, then a lot of these effects become quite mundane. That's one of the neat things about string theory.
quickfur wrote:The Necker cube illusion has nothing to do with particles being big or small. It's an inherent ambiguity in any projection-based sight, that is, any kind of eye that sees based on light reflecting off the surfaces of objects. If you're a dolphin with sonar-sense, you'll have a much different experience. The reason for the ambiguity is because you're seeing n dimensions with only an (n-1)-dimensional retina, meaning that information about one of the dimensions (depth) is lost, so some projection images can have multiple interpretations that may not necessarily reflect reality.
quickfur wrote:As for a 4D being confined to a lower-dimensional space -- if he is indeed confined in that way
Hugh wrote:[...]
"In 4D, a shape can be rotated around a plane."
"It must be understood that in 4D a 3-dimensional cube has neither inside nor outside. All points of a cube are as much exposed in 4D as are the points of a square in 3D."
"Vacuously, in a square there is only 1 square that contains a given edge. In a cube, every edge is shared by 2 squares. In a tesseract, 3 squares meet at every edge. Taken pairwise, squares through the same edge define three cubes. Detecting the three cubes seems akin to shifting a view point when observing the Necker cube."
"I found this observation useful when playing with the applet below. What is it about? Travelling in 4D may have a milder effect on a 3D body than turning it inside out. It may only change its orientation."
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