quickfur wrote:Epic post
Marek14 wrote:Fill the 3-sphere with water, add some currents along the ringpoles, and you can have an interesting story even with 3D creatures
Keiji wrote:quickfur wrote:Epic post
Excellent work, quickfur! I can finally visualize this now thanks to your image and explanation.
The topic on 4D planets described the concept of time- and climate-zones. [...]
Mrrl wrote:I'm not sure that you will have polar day of polar night somewhere of the planet. After a half of the day every point on the planet will be on the opposite side of the sphere (is it right?), so almost everywhere we'll have equal day and night duration. [...]
Keiji wrote:quickfur, do you mind if I add all this amazing information about glome subdivisions to the wiki?
If that's okay, I'd appreciate if you could upload the images yourself (using :AddFile and "files from other websites") so that they get the right authorship information and you can choose a license for them.
quickfur wrote:currently my brain cpu power is being hogged by a background process trying to calculate the cells of the CRF polytope with 4 square antiprisms.
Keiji wrote:quickfur wrote:currently my brain cpu power is being hogged by a background process trying to calculate the cells of the CRF polytope with 4 square antiprisms.
If it even exists
I'll wait until the images show up, and then re-read the topic and write up either a big section in the Glome article, or a separate page on 4D planets, or both.
quickfur wrote:Keiji wrote:quickfur wrote:currently my brain cpu power is being hogged by a background process trying to calculate the cells of the CRF polytope with 4 square antiprisms.
If it even exists
Unfortunately you're right, it doesn't exist. Or at least, it does exist but is non-CRF because some of the tetrahedra are non-uniform.
I'll wait until the images show up, and then re-read the topic and write up either a big section in the Glome article, or a separate page on 4D planets, or both.
OK I've uploaded all the images in this topic.
I highly suggest a separate page on 4D planets, although the subdivision stuff can go in the glome page. After all, the 4D planets stuff is pure speculation, and besides, not very realistic speculation given that stable orbits don't exist (or can't possibly maintain themselves without some kind of fiat).
Marek14 wrote:quickfur wrote:[...]
I highly suggest a separate page on 4D planets, although the subdivision stuff can go in the glome page. After all, the 4D planets stuff is pure speculation, and besides, not very realistic speculation given that stable orbits don't exist (or can't possibly maintain themselves without some kind of fiat).
Stable orbits could exist if the 4D realm was just a "slice", i.e. if it was squeezed between two hyperplanes That would work, wouldn't it?
quickfur wrote:Marek14 wrote:quickfur wrote:[...]
I highly suggest a separate page on 4D planets, although the subdivision stuff can go in the glome page. After all, the 4D planets stuff is pure speculation, and besides, not very realistic speculation given that stable orbits don't exist (or can't possibly maintain themselves without some kind of fiat).
Stable orbits could exist if the 4D realm was just a "slice", i.e. if it was squeezed between two hyperplanes That would work, wouldn't it?
Not really, unless you're saying that the gravitational force is confined to a hyperplane, and so its flux decreases as an inverse square instead of an inverse cube. Besides, if you're confined between two hyperplanes, you're back in 3D.
Marek14 wrote:[...]Yes, that's what I'm saying. And there's a difference between a 3D and narrow 4D. The planet could still be 4D.
Another solution might be if the star was an infinitely-long spherinder (or a spherinder of finite length, if one dimension was circular). That would make the flux inverse square as well, wouldn't it?
quickfur wrote:Marek14 wrote:[...]Yes, that's what I'm saying. And there's a difference between a 3D and narrow 4D. The planet could still be 4D.
But in that case what happens to gravity at the confining hyperplanes? Does it get reflected? Absorbed? And would space have a discontinuity there?Another solution might be if the star was an infinitely-long spherinder (or a spherinder of finite length, if one dimension was circular). That would make the flux inverse square as well, wouldn't it?
But if the star was a spherinder, wouldn't it eventually collapse into a 3-sphere under the force of its own gravity?
Also, even though gravity would be inverse square, it won't result in a periodic orbit in general, because the planet will just spiral along the length of the spherinder with a constant displacement along the spherindrical axis. EDIT: The projection of the planet's movement would be an ellipse, but its actual motion would be aperiodic.
Marek14 wrote:[...]It wouldn't collapse since gravity would be the same at each slice. And the aperiodic motion of the planet wouldn't be important - the important thing is whether the conditions on the planet would be stable, and the distance of planet from sun would be bounded.
Of course, not taking into account the energy output of the infinitely long star
For some reason, this reminds me of one of the more crazy fantastic world I thought of: a torus-shaped star with planets as smaller toruses. The star passes through the central hole of the planets, each planet passes through the holes of its moons, etc... Gravity is hacked to be perpendicular to the surfaces, of course Different planets have wildly differing diameters, so they can pass through each other.
quickfur wrote:Marek14 wrote:[...]It wouldn't collapse since gravity would be the same at each slice. And the aperiodic motion of the planet wouldn't be important - the important thing is whether the conditions on the planet would be stable, and the distance of planet from sun would be bounded.
This can only be possible if the star is an actual infinitely-long star. Any finite-length star will eventually collapse into a 3-sphere because its ends will feel gravity towards its center.
quickfur wrote:Marek14 wrote:[...]It wouldn't collapse since gravity would be the same at each slice. And the aperiodic motion of the planet wouldn't be important - the important thing is whether the conditions on the planet would be stable, and the distance of planet from sun would be bounded.
This can only be possible if the star is an actual infinitely-long star. Any finite-length star will eventually collapse into a 3-sphere because its ends will feel gravity towards its center.
Yes, one without planetary systems, without all day-and-night stuff, with the life on the surfaces of cold starsquickfur wrote:All of this just means that we need to forget about our 3D-centric stars and planets type of system, and imagine a truly native 4D system.
Mrrl wrote:Yes, one without planetary systems, without all day-and-night stuff, with the life on the surfaces of cold starsquickfur wrote:All of this just means that we need to forget about our 3D-centric stars and planets type of system, and imagine a truly native 4D system.
Keiji wrote:I'm curious to learn more of this alternate universe of yours.
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