Re: OT: 4D

On Wed, 23 Feb 2005 16:49:31 -0800, H. S. Teoh <hsteoh@...> wrote:
> On Wed, Feb 23, 2005 at 11:34:31PM -0000, Ivan Baines wrote:
> > > Hyperspherical planets are curious things. For one, they can have two
> > > independent spins *simultaneously*. That is to say, one of the spins
> > > can speed up/slow down completely independently of the other.
> >
> > *Can* do, yes, but surely they wouldn't unless acted upon by an enormous
> > force, much like in the 3D world!  Unless there's some truly bizarre
> > consequence of an extra dimension on the laws of physics which hasn't
> > occurred to me. ;-)
>
> Well, any plausible physics of a 4D world must necessarily be
> fundamentally different from ours (even if still analogous in some
> ways). One of the major problems being that the atom is unstable in
> 4D, and would quickly disintegrate. I don't know exactly why, but it
> has something to do with the stability of 4D standing waves which are
> required for stable electron orbitals around the atomic nucleus.
Actually, this is part of a larger phenomenon, which is that forces
weaker than inverse-square do not have stable orbits.  Both gravity
and EM would be inverse-cube in 4D, so there would be no stable
planetary orbits.  (Actually, EM as we know it wouldn't exist, due to
lack of cross-products, but could be replaced by something even more
bizarre.)
However, this gives you opportunities of (e.g.) Universes with
Aristotelian laws of motion (I'm fiddling around with this for the
Ferrochromon (home of Ebisedian)), so beings could navigate in proper
4D, not the 3-sphere (note: manifolds are named by dimensionality of
surface, not of insides) they would be restricted to by sticking to
the surface of a 4D-planet.

> > Mind you, just imagining the possible body-plans for a 4D lifeform
> > breaks my brain!
> [...]
>
> This is actually a very fascinating, though difficult, topic. So far,
> I've tried to stick with essentially a 3D anatomy suitably generalized
> to 4D. However, that probably wouldn't quite capture the aesthetics a
> natively 4D creature would have. Designing a truly 4D creature that is
> crafted specifically for 4D (as opposed to generalized from 3D) is a
> truly mind-bending task, but extremely interesting. For example, in
> Garrett Jones' 4D discussion forum, we came up with the conclusion
> that although bipedal creatures such as humanoids are certainly
> possible, it would probably be much more common to find quadrupeds or
> hexapeds, especially the latter, since the additional dimensions imply
> that 6 legs are a lot more stable than 2. There are a LOT more ways to
> fall over in 4D. :-)
>
> We've also decided that 4D creatures probably need more fingers per
> hand, in order to be able to grasp 4D objects adequately. Or, at the
> very least, 2 orthogonal groups of fingers opposite an opposable
> thumb. Basically, a 4D hand needs a way to adequately grasp a 3D
> volume in order to get a sufficient hold on objects.
>
> Also, like you said, I've pondered about the need for more joints per
> limb, just so you can bend your limbs adequately to reach all 4
> dimensions. Although you can probably get by with only a shoulder and
> an elbow per arm, I suspect it would be much more convenient to have a
> shoulder and two elbows, just so you have 3 degrees of freedom for
> positioning your arm.
4D-joints are hard to imagine, but I think you can have a
sphere'sworth of freedom even with a simple knee-analogous joint.  I
am having a little trouble extending a hip-joint type of joint, but I
think it would have full rotational freedom.  There would, of course,
be the "stacked" 3D joints (a bit like polygon->prism) which would
just rotate about an angle.

Anyway, though 4D sound is still just vibrations and we would be able
to hear it, we would have great difficulty pronouncing it.  (Now
*that's* a niche market, mouth simulators for simulating sounds of
phonemes, especially in 4D!)

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