
Planets in the Fourth Dimension - diego898
https://johncarlosbaez.wordpress.com/2015/03/17/planets_in_the_4th_dimension/
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Rumford
You could also think of this time like dimension as _acceleration_. When above
the plane, the planet is accelerating, and it is decelerating when below the
plane.

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tokai
Awesome!

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mattxxx
Cool. Physics is about modeling. If you create a model, and it's consistent
with the real world, then it's inscrutable. Cool.

The only time you can contradict a model in Physics, is if the model conflicts
with something observable. Isn't that why we have so many coexisting
cosmological theories?

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stevebmark
This is fundamentally wrong and very poorly described. All this unusual
article amounts to is "you can rotate things." A planet is not a 3d projection
of a 4d object. Space itself contains at least four spatial dimensions but it
is not shaped like a hypersphere around every star that a planet revolves
around.

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impostervt
I'm not adding a fourth dimension to my code.

[http://www.aretheplanetsaligned.com](http://www.aretheplanetsaligned.com)

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superobserver
Cool find. Added spatial dimensions always intrigue when presented visually
(rather than logically or symbolically).

Edit: this makes me wonder what other eliptical orbits might look like. Would
the 4-sphere have to rotate about the barycenter to give the effect of this:
[http://www.polaris.iastate.edu/EveningStar/Unit4/Graphics/Pi...](http://www.polaris.iastate.edu/EveningStar/Unit4/Graphics/PicES4_8.jpg)

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danneu
I noticed sci-fi author Greg Egan in the comments.

Looks like he's still battling against Google using the wrong image for him
when you google his name:
[http://gregegan.customer.netspace.net.au/ESSAYS/GOOGLE/Googl...](http://gregegan.customer.netspace.net.au/ESSAYS/GOOGLE/Google.html)

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mjcohen
Google is sometimes doing the same to me, but the picture is of a younger,
better looking guy, so I'm not complaining.

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madaxe_again
This is a topic I like to muse on day-to-day - I find visualising hyperspace
interesting.

Extending the same notion of there being a time dimension that is less dense
the further it is from a gravity well - well, it changes certain aspects of
how one might look at the universe, such as, say, why distant galaxies are
redshifted, why galaxies rotate evenly throughout their volumes, and why the
speed of light is a thing.

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peter303
I've seen a similar trick in numerical analysis. You add an fourth dimension
to a computation grid and it reduces numerical problems with the 3D
computation. I dont know if there is a name for this trick.

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DarkUranium
There is also a trick (read: algorithm) in computational geometry that
computes (2D) Delaunay triangulation by mapping the points onto a (3D)
paraboloid, and then computing the convex hull of _that_. E.g.:
[http://i.stack.imgur.com/OuWmZ.png](http://i.stack.imgur.com/OuWmZ.png)

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Xeoncross
> In fact, they’re moving in circles in 4 dimensions. But when these circles
> are projected down to 3-dimensional space, they become ellipses!

Um, no. They are moving in 3 dimensions and when they are projected down to
2-dimensional space they become ellipses.

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drcube
I think you missed the point. Planets orbit in ellipses in the regular, 3D
world.

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Xeoncross
Are we talking about "orbiting in elliptical paths" or "planets are ellipses"?
In regular Height-Width-Depth (3D) space (excluding time) the plants are
circling in ellipses. In only Height-Width (2D) space plants are flat circles
and when projected onto a plane produce an elliptical path. So why the
downvote?

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jwcacces
It's true, I do that planets go around the sun in elliptical orbits...

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dashoffset
probably

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ebbv
I'm no physics major but I'm pretty sure this is a bunch of horse shit and the
elliptical orbits are explained perfectly by General Relativity.

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subnaught
General Relativity is not needed to explain elliptical orbits. This is a very
clever reformulation of classical mechanics, and certainly not horseshit.

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ebbv
I could "very clever"-ly reformulate Newtonian physics as a series of
invisible frogs who push things around by jumping into them. It's still horse
shit.

This article about a "weird fourth dimension" that's "like time but not time"
certainly seems like horse shit to me.

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mbrubeck
The author could instead have used only abstract mathematical language (like
"a configuration space with a basis of cardinality 4" and "parameter _s_
defined by _s_ = ..."), but this would be accessible to fewer readers. If you
prefer dryer language, read the second half of the article, or the other
resources it links to.

Using a configuration space that is a good fit for a specific system is not
unusual in math or physics. It's the same thing that astrophysicists do when
they work in orbital elements, or that engineers and programmers do when they
make calculations in Fourier space. It's worth understanding these concepts
even if you're not a physicist.

Configuration spaces are so fundamental and useful that they are introduced in
the _very first lecture_ on classical mechanics in Leornard Susskind's
excellent series of Stanford physics courses:
[http://theoreticalminimum.com/courses](http://theoreticalminimum.com/courses)

(Neal Stephenson's novel _Anathem_ also has a simple introduction to
configuration spaces in an appendix, because that's the sort of thing that
ends up in a Neal Stephenson novel.)

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claar
I've been playing the Kerbal Space Program (KSP) game lately; it's funny how
when you actively use orbital mechanics, thinking about them is easier.

This fourth dimension observation is cool and likely very useful
mathematically, but it's also kinda obvious (at least after playing KSP) that
if you subtract the time/gravity element from an orbit, it becomes circular.
It's equivalent to saying that if you subtract out the gravity effects of the
planet you're orbiting, your orbital speed is constant, which just makes sense
intuitively.

Calling this observation a fourth dimension is useful, but perhaps
unnecessarily complicated for the simple concept.

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fixermark
I was a little sad to learn that because KSP's orbital model uses conic
sections, it's not physically accurate enough to model things like Lagrange
points.

Then I remembered that it's still accurate enough to be awesome and stopped
worrying about it. :)

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valarauca1
Actually Newtonian Conic Sections is how we (humans) calculated orbital, and
interplanetary trajectories up until the 1980's.

There weren't powerful enough computers to model full Eisenstein N-Bodies
Systems until actually very recently (also its complete over kill for inner-
solar system travel). Relativity is really complex math, and even modern
computer clusters struggle to model very complex systems.

Yes we sent astronauts to the moon using KSP math.

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theothermkn
> Yes we sent astronauts to the moon using KSP math.

I'm almost positive that we did not.

While patched conics would have been used very early on for rough mission
analysis and design, we had a very good understanding of perturbation theory
at the time. Wikipedia tells me that the restricted 3-body problem was also
essentially solved in 1917. I've seen very detailed plots of the free return
trajectories that the Apollo missions followed, too.

Using patched conics for the earth moon system would have resulted in an error
on the scale of lunar escape velocity upon entering the sphere of influence of
the Moon.

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valarauca1
>I've seen very detailed plots of the free return trajectories that the Apollo
missions followed, too.

Free return trajectories can be calculated with patched conics. 3 Body problem
was solved, but actually doing all the math involved dynamically was far to
complex for mission computers.

You forget that at the time NASA was using IBM System/360's which were
struggling to maintain 5 megaFLOPs

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theothermkn
I get that the idea that we "went to the moon with a slide rule" and similar
ideas are appealing, but I'm not convinced that your statements are resting on
a basis of fact.

For one thing, I'm not convinced that your mental models of what a "mission
computer" is and what a "mission computer" would be doing, or when, make sense
from an engineering perspective. I'm also not convinced that you know what an
orbital perturbation is, nor how they would be used to plan and fly a mission.

To take an example from aviation, we didn't have practical simulations of
general viscous fluid flow in the 1960s, but it would be meaningless to say
that we "used Bernoulli's principle" to fly across the Pacific.

The Apollo vehicles had an on-board IMU. A trajectory could thus be pre-
planned and flown to using feedback control. That trajectory would certainly
have been calculated ahead of time. Thus, while there would be no need to have
"[done] the math involved dynamically," that by no means implies that patched
conics were used while in flight, nor does it imply that they were in any
meaningful way used for the final design of the missions' flight paths.

Further, on any deviation from the planned flight path, numerical integration
methods would yield results that would be good enough for later correction,
again, by using feedback control.

If you still need to believe that "KSP math" is how we got to the Moon, go
ahead. You've certainly done nothing to convince anyone else, though.

