ICN5D wrote:Wow, that's really weird. Never heard of it either. That also determines how high-D beings can hear, or the fact that it won't be as reliable. Or, maybe needs multiple ears for 4-D triangulation. It seems like 3D is the only " normal " dimension, where strange things aren't allowed to happen. Be it self-induced echos or distorted perceptions, 3D is stable. This also makes me think about the concepts with string theory. It's all about undulating waves in high-D space. Not to forget the whole extended/compactified dimension idea. We are huge, so we only perceive the extended, opened up directions of freedom. And right under our noses, the realm of the tiny works in the way of waves sloshing around in extra dimensional spaces. This is what makes planets and solar systems work in a simpler way than atoms and molecules. I forget what the "official " number of D's is, but it might be an even number. Like 26 or something. Revolving around Ramanujan functions, which I have no knowledge about. Sounds amazing, though.
anderscolingustafson wrote:I wonder how a 4d life form would sense the world around it considering how waves work differently in an even number of dimensions and in dimensions above 3d.
anderscolingustafson wrote:If our physical laws work very well in 3d but doesn't work very well when applied to 4d I wonder if that means that a set of physical laws that would work really well in 4d would not work very well when applied to 3d. I mean if our physical laws only work well in 3d then could we come up with a set of physical laws that only works well in 4d but which has disastrous implications when applied outside 4d?
ICN5D wrote:This also makes me think about the concepts with string theory. It's all about undulating waves in high-D space. Not to forget the whole extended/compactified dimension idea. We are huge, so we only perceive the extended, opened up directions of freedom. And right under our noses, the realm of the tiny works in the way of waves sloshing around in extra dimensional spaces.
quickfur wrote:This has far reaching consequences for 4D: assuming that 4D light still takes place via some kind of electromagnetism analogue that produces 4D EM waves, this means that light in 4D does not travel in a single direction, but will have back propagations that causes "echoes"! A 4D flash of light will not appear as a single flash, but as multiple flashes with decreasing amplitude, fading out gradually. This also means that light reflected off objects would behave the same way, thus objects will not have a sharp, focused image, but a blurry "echo-ey" image caused by the repeated back-propagations!
OTOH, if you drop a stone into a pond in 4D, you'll see a single, perfect spherical ripple travel outwards, because the surface of the pond will be 3D. There will be no concentric ripples, and only a single echoing ripple when it hits the edge of the pond. This has the very interesting consequence that ponds and lakes in 4D are likely to be very calm, with only the occasional isolated ripple passing through, quite unlike our 3D ponds where the surface of the water is almost always filled with little ripples.
ICN5D wrote:quickfur wrote:This has far reaching consequences for 4D: assuming that 4D light still takes place via some kind of electromagnetism analogue that produces 4D EM waves, this means that light in 4D does not travel in a single direction, but will have back propagations that causes "echoes"! A 4D flash of light will not appear as a single flash, but as multiple flashes with decreasing amplitude, fading out gradually. This also means that light reflected off objects would behave the same way, thus objects will not have a sharp, focused image, but a blurry "echo-ey" image caused by the repeated back-propagations!
Sounds like the double-slit experiment! A single photon travels through both slits and interferes with itself. This is also thought to occur through the past, a photon mingles with itself in its own past.
OTOH, if you drop a stone into a pond in 4D, you'll see a single, perfect spherical ripple travel outwards, because the surface of the pond will be 3D. There will be no concentric ripples, and only a single echoing ripple when it hits the edge of the pond. This has the very interesting consequence that ponds and lakes in 4D are likely to be very calm, with only the occasional isolated ripple passing through, quite unlike our 3D ponds where the surface of the water is almost always filled with little ripples.
This seems like the way gravity waves propagate. Very interesting stuff!
quickfur wrote:I have this hypothesis that the 3D universe we see around us is actually the surface of an expanding 4D sphere...
I have this hypothesis that the 3D universe we see around us is actually the surface of an expanding 4D sphere...
A stationary object may be relatively easy to see, but a moving object will leave a complex trail of echoing light ripples that will in all likelihood completely distort its image. It will probably appear as a smeared-out image that looks like motion blur, except more persistent and quite disruptive because it will also distort background objects as well.
I have this hypothesis that the 3D universe we see around us is actually the surface of an expanding 4D sphere...
quickfur wrote:Unless, of course, we give up trying to extend 3D physics to 4D, since it obviously isn't working out so well. As far as 4D dimensional analogy is concerned, I'm of the opinion that we should just adopt Aristotelian physics and be done with it. It may not be how 3D works, but who knows, maybe it's just the thing we need in 4D?
Keiji wrote:quickfur wrote:Unless, of course, we give up trying to extend 3D physics to 4D, since it obviously isn't working out so well. As far as 4D dimensional analogy is concerned, I'm of the opinion that we should just adopt Aristotelian physics and be done with it. It may not be how 3D works, but who knows, maybe it's just the thing we need in 4D?
Hence why I came up with my particle system
quickfur wrote:<br abp="664">Hmm. I went back to re-read that proposal, and it's certainly interesting. I'm not sure what the macroscopic consequences of it would look like, though. I was thinking more in terms of taking certain macroscopic properties as axioms, and then working backwards to see what kind of physical laws might have produced that result. Generally, I think this is far easier than trying to design something from ground-up with the hope that the emergent properties will resemble what we want. Emergent properties depend in a very complicated way on the fine details of the underlying system, and it's almost impossible to predict what kind of properties will emerge when you change things around in the underlying system. It's far easier to just shed all pretense and postulate straight-up the desired macroscopic effects as a given, and then trying to rationalize what physical laws may have led to those effects.Keiji wrote:<br abp="662"><br abp="663">Hence why I came up with my particle systemquickfur wrote:Unless, of course, we give up trying to extend 3D physics to 4D, since it obviously isn't working out so well. As far as 4D dimensional analogy is concerned, I'm of the opinion that we should just adopt Aristotelian physics and be done with it. It may not be how 3D works, but who knows, maybe it's just the thing we need in 4D?
anderscolingustafson wrote:I was thinking would the fact that waves would double back on themselves in 4d have any effects on gravity in 4d? Changes in gravitational fields are carried through gravity waves so would the behavior of gravity waves effect the behavior of gravity in 4d?
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