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ninalanyon · 61-69, T
If the shadows we are familiar with are two dimensional representations of three dimensional objects does that mean that a four dimensional object casts a three dimensional shadow?
SpudMuffin · 61-69, M
@ninalanyon so something we perceive as a three dimensional object could just be the shadow of a four dimensional object? Slightly mind-blowing!
ninalanyon · 61-69, T
@SpudMuffin Musing on it a little more: would the light then have to be one dimension more than it is already? Presumably three instead of two.
ElwoodBlues · M
@ninalanyon Absolutely! This video attempts to show the 3D shadows of a 4D cube. You can ignore the matrices and just look at the moving pictures.
[media=https://youtu.be/iGO12Z5Lw8s]
[media=https://youtu.be/iGO12Z5Lw8s]
SpudMuffin · 61-69, M
@ninalanyon interesting point. Maybe light exists in all dimensions, however many there are?
GeniUs · 56-60, M
@ninalanyon but we are 4 dimensional; height, depth, width, time (not sure if those are the correct names but you get my drift). The shadow I suppose is the memory of us which isn't even a dimension, or is it? Have I just come up with a new concept? Or is my logic faulty?
* Great and thought provoking topic*
* Great and thought provoking topic*
ElwoodBlues · M
@SpudMuffin I don't know how light would work in higher euclidean dimensions. The video uses a purely geometric projection process (some of the matrices are projection matrices). It's a mathematical way of transforming a collection of 4D coordinates to 3D coordinates that idealizes what an ideal point light source would do, if you know what I mean!
@GeniUs Yes, we exist in a 4D space time continuum, but time is a special dimension that doesn't behave like the other three. I guess you could create a set of 4D coordinates in space and time, and use a projection matrix. But what I think we'd see (in most cases) is points moving in time, not skeletonized cubes like in the video. Certain projections might hold the time coordinate constant and therefore appear all at once, but I suspect they would be boring projections.
@GeniUs Yes, we exist in a 4D space time continuum, but time is a special dimension that doesn't behave like the other three. I guess you could create a set of 4D coordinates in space and time, and use a projection matrix. But what I think we'd see (in most cases) is points moving in time, not skeletonized cubes like in the video. Certain projections might hold the time coordinate constant and therefore appear all at once, but I suspect they would be boring projections.
SpudMuffin · 61-69, M
@ElwoodBlues yes, I see what you mean. The implications are intriguing, but I haven't had enough to drink yet.