## 4D compass

Ideas about how a world with more than three spatial dimensions would work - what laws of physics would be needed, how things would be built, how people would do things and so on.

### 4D compass

Ordinary 3D compasses are needles that point NS but it doesn't have to be that way. The compass could be magnetized differently and point EW, or any angle in between. Let's call EW magnetization transverse magnetization.

On a 4D planet there would be no needle magnets. Instead you could have a disc with transverse magnetization. That would align itself with the strongest magnetic plane.

There would be infinitely many remaining planes dual to the first. Find them like this. The disc has a spherindrical axis. Once the major plane has been found, rotate the axis into the major plane. The disc will then align itself with the minor magnetic plane.

Is that right? EDIT: No. The second plane has no degree of freedom.

It won't work if all directions have the same magnetic strength, but I don't think that would happen. Geodynamos are too complicated and chaotic to have such a neat solution, IMO.
Last edited by PatrickPowers on Thu Feb 25, 2016 5:12 pm, edited 1 time in total.
PatrickPowers
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### Re: 4D compass

I really can't imagine a planetary dipole too much off the rotation axis. I fear that it would cause the planet to undergo some kind of realignment.

It is hard to imagine what the 4d magnatism would look like under a clifford rotation. Not enough is understood here though for me to feel it. If the sun somehow gets involved, it is possible that the earth's magnetic field would align with something like climata, which would really be a north-south alignment. But the zodiac is at an angle to climata, so the vector could build if it was driven by some process that integrates past a year. Then the north and south hedricies of the magnetic field would align with the climata lattitudes, and the magnetic field would be orthogonal to this, would in the main point to the nearest N S points.
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wendy
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### Re: 4D compass

Geodynamos are complicated and somewhat chaotic. I don't claim to understand them. It isn't a mature discipline and there is no consensus. But I'll tell you what I've gathered so far.

What drives a geodynamo is convection. Heat comes out of the center of the heavenly body. It heats up material and this moves upward. Due to Coriolis force this material tends to rotate. You have a vortex of electrically conductive material.

If there is a magnetic field in the vicinity this induces a current in the vortex. This current increases the magnetic field. This induces more current. So the field builds on itself. The polarity of the field is the same as the initial field, whatever that happened to be.

The magnetic field is the sum of the fields of these vorticies, all inducing magnetic fields in one another. The vorticies are deep in the interior of the Earth, so the complexity is almost entirely smoothed out by the time it reaches the surface.

The vorticies interact in a complicated way that is unstable. In the case of the Sun the instabilities are cyclic. The polarity of the Sun's magnetic field changes every eleven years. In the case of the Earth the instabilities are chaotic. Reversals of the magnetic field polarity have no period, and are not long-term predictable.

In the case of the Sun the heat comes mostly from nuclear fusion. In the Earth it is mostly from the "heat of fusion" of magma freezing into a solid, and some from nuclear fission.

Some heavenly bodies have magnetic fields, others like Venus or the Moon have none. It depends. The main thing in planets and true stars is that you have to have convection. You have to have a heavenly body where conduction/radiation isn't enough to carry the heat outward, so convection starts. Material carrying heat outward and moving around more or less freely. Rotation is necessary, but it doesn't take much.

In the Sun this is all massively complex and ever-changing. In the Earth there are two main plumes of rising heat, one in the center of the Pacific and a smaller under southern Africa. The heat sinks in a large region centered in the South China Sea. It is all very similar to the celebrated Lava Lamp, except that the plumes braid into vorticies.

There is no particular reason the magnetic pole should be aligned with the rotational pole. The Sun doesn't really have a magnetic pole at all, or only in a statistical sense. The Earth's magnetic pole is about 15 degrees away from the rotational pole and moves around constantly. The Earth's magnetic field strength has dropped 30% since 1820 or so. Like I said, it is an unstable system. Maybe this is unusual, maybe not.

We can't predict what the magnetic field of the Earth will do, so predicting the magnetic field of a 4D planet is far out of reach. I think it is safe to assume if such exists it would be equally complicated. Given that, a 4D compass could reveal a good deal of useful information.

A 4D compass could be chiral or not depending on how it was magnetized, or at least so I think today. If chiral, it could be either of the same chirality as the planetary field or opposite. Which of the three types would be most useful?

I think the compass would be planar or biplanar. A planar compass could be made here on Earth without much trouble. It would give more information than the standard needle compass too, like a combination of a trad needle and a dipping needle. Less practical, though.
PatrickPowers
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### Re: 4D compass

PatrickPowers wrote:If there is a magnetic field in the vicinity this induces a current in the vortex. This current increases the magnetic field. This induces more current. So the field builds on itself. The polarity of the field is the same as the initial field, whatever that happened to be.

That's not true. Induced magnetic fields always counteract the currents that induce it.

PatrickPowers wrote:In the Earth it is mostly from the "heat of fusion" of magma freezing into a solid, and some from nuclear fission.

It's radioactive decay and primoridal heat.

Most of the time the sun does have magnetic poles, but the field lines do not run straight between north and south pole and the magnetic field reverts about every 11 years.

Essentially the drawback of compasses in 4D is that they can't show you unique directions, but circles with constant angles to the field planes. Only the direction normal to the field planes is uniquely defined (supposing you know where above and below is).
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Teragon
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### Re: 4D compass

Teragon wrote:
That's not true. Induced magnetic fields always counteract the currents that induce it.

I'm no expert, but that's the basic idea. In the 21st century a geodynamo containing liquid sodium has been constructed in a laboratory. If you can explain to me better what is going on I would appreciate it. It's called magnetohydrodynamics.

Teragon wrote:It's radioactive decay and primoridal heat.

I'm going with the guy now at Cal Tech whose name I forget. The experts don't agree on this issue, so we may believe as we please.

Teragon wrote:Essentially the drawback of compasses in 4D is that they can't show you unique directions, but circles with constant angles to the field planes. Only the direction normal to the field planes is uniquely defined (supposing you know where above and below is).

In 4D a properly designed compass can show you the two magnetic planes. That would narrow things down quite a bit.

With N odd the compass could show the pole as well.
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### Re: 4D compass

PatrickPowers wrote:I'm no expert, but that's the basic idea. In the 21st century a geodynamo containing liquid sodium has been constructed in a laboratory. If you can explain to me better what is going on I would appreciate it. It's called magnetohydrodynamics.

I'm no expert on MHD too. Still I can say you've got the basic idea right, but as far as the currents are stationairy also the magnetic field is static. If that's the case the magnetic field doesn't act back on the currents. If there is a change in the currents, the corresponding change in the magnetic field induces an electric field that counteracts that change (this is classical electromagnetism).

PatrickPowers wrote:
Teragon wrote:It's radioactive decay and primoridal heat.

I'm going with the guy now at Cal Tech whose name I forget. The experts don't agree on this issue, so we may believe as we please.

Might be, not sure what the role of the different heat sources is. It's just what some geophysicists have told me.

PatrickPowers wrote:In 4D a properly designed compass can show you the two magnetic planes. That would narrow things down quite a bit.

Yes, and therefore you can determine circles of directions with constant angle to the polecircle.

PatrickPowers wrote:With N odd the compass could show the pole as well.

What to you mean by that? The magnetic pole (or what defines the origin of the local magnetic field) is N-2-dimensional.
What is deep in our world is superficial in higher dimensions.
Teragon
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### Re: 4D compass

Teragon wrote:
PatrickPowers wrote:With N odd the compass could show the pole as well.

What to you mean by that? The magnetic pole (or what defines the origin of the local magnetic field) is N-2-dimensional.

With the definitions I am using, in 4D it is possible to have two magnetic planes so that there are no magnetic poles. In 5D there may be two planes and a pole. In 6D three planes, and so on.
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### Re: 4D compass

PatrickPowers wrote:With the definitions I am using, in 4D it is possible to have two magnetic planes so that there are no magnetic poles. In 5D there may be two planes and a pole. In 6D three planes, and so on.

What you call the pole direction is not distinguishable in any way from the plane or any linear combination of both, that's why I prefer the term 3-pole/polevolume. I guess you mean "two planes" in 6D.
What is deep in our world is superficial in higher dimensions.
Teragon
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### Re: 4D compass

"motions of a conductive fluid in the presence of a magnetic field give rise to induced currents that in turn generate magnetic fields that reinforce the original field (Larmor 1919; see also, e.g., Rüdiger and Hollerbach 2004)" https://progearthplanetsci.springeropen.com/articles/10.1186/s40645-015-0058-1

Unfortunately for me the R-H book costs \$502 used. They want \$53 for a review of this book!

"helical motions can deform initially straight magnetic field lines into loops which are associated with induced currents parallel to the applied field" https://www.researchgate.net/publication/225524936_Laboratory_Dynamo_Experiments

The root of it all is turbulent motion of conductive material in a magnetic field. The Coriolis force organizes some of this turbulence into coils. Now the objection was that a geodynamo would violate Lentz's law. If motion induces a current then that current tends to generate an opposite magnetic field. So wouldn't it cancel itself out? I couldn't find an explanation clear enough for me to understand, but my best guess is that that the magnetic field of each turn of a coin weakens the field in itself but strengthens it in neighboring turns, which in turn builds up the field generated by that turn.

It is said that "realistic numerical simulation is impossible," though approximation has been done which seems to confirm the model. While liquid dynamos have been produced, https://progearthplanetsci.springeropen.com/articles/10.1186/s40645-015-0058-1 attempts to create a geodynamo in the laboratory have failed so far.
Last edited by PatrickPowers on Sun Jun 06, 2021 2:02 am, edited 1 time in total.
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### Re: 4D compass

Deleted.
Last edited by PatrickPowers on Fri Jun 04, 2021 7:13 am, edited 1 time in total.
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### Re: 4D compass

Teragon wrote:
PatrickPowers wrote:With the definitions I am using, in 4D it is possible to have two magnetic planes so that there are no magnetic poles. In 5D there may be two planes and a pole. In 6D three planes, and so on.

What you call the pole direction is not distinguishable in any way from the plane or any linear combination of both, that's why I prefer the term 3-pole/polevolume. I guess you mean "two planes" in 6D.

In even dimensions there can be magnetic fields such that a charged particle in motion relative to the field always feels a magnetic force, no matter the direction in which it is headed. In odd dimensions there is always at least one direction of motion in which no force is felt. It can be one dimensional, in which case I call it a magnetic pole. In such a case it is possible to have an Earth-like compass that points in a specific direction.
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### Re: 4D compass

The magnetic field of a 4D planet is too difficult to know, but as usual I'm going to speculate anyway. Let's simply assume that a geodynamo like ours exists on HyperEarth. There is an outer core of iron about as viscous as water. It is full of chaotic currents that generate the field. There is a solid inner core of iron that resists change. There is a thick mantle which smooths out the chaos so on the surface of HyperEarth the field appears relatively steady. This is all very dubious but what the heck.

The outer core currents are chaotic but the Coriolis force and the nature of magnets tends to get them to line up to some degree. If the planet has two different rotational periods then most of the field will tend to align with the faster plane of rotation while the rest will align with the slower plane, giving a 4D field. This would tend to be Earthlike as there would be occasional unpredictable magnetic field reversals in which one or both of the fields reverses polarity. These reversals take about 5000 years to overcome the resistance of the inner core.

If the rotation is isoclinic then there are an infinite number of pairs of planes of rotation, none of which is preferred. The orientation of the magnetic field drifts slowly without any "normal" direction. There would still be periods of weakness of the magnetic field but there would be no reason to prefer any particular direction when the field grows strong again.

There would be no magnetic poles, but I bet the two magnetic fields would be at an angle other than 90 degrees. This makes for preferred horizontal direction, though possibly vague.

If the radius of HyperEarth is much less than Earth then the rotation must be much faster to generate a geodynamo. You could have a day a few seconds or even milliseconds long with ensuing huge Coriolis and Eötvös forces. Bodies on ice or floating in water would tend to move in 3D Lissajous curves. (I think. Haven't checked it out.) If the planet's rotation is not isoclinic then the curves vary depending on latitude, making it even more complicated. It would give ball sport teams a major home field advantage. :-)
Last edited by PatrickPowers on Wed Jun 09, 2021 3:23 am, edited 1 time in total.
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### Re: 4D compass

Wendy, do you have the power to actually delete those "Deleted" posts?

We ordinary users can only delete the most recent post, I think.

[answer] I can do anything to your posts that you can do. Since the set of `your` is somewhat larger for me, you get the idea. But I normally use it to do things to delete evident spam or the like, not because i disagree with someone's legit post.[/answer] Wendy
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mr_e_man
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### Re: 4D compass

mr_e_man wrote:Wendy, do you have the power to actually delete those "Deleted" posts?

We ordinary users can only delete the most recent post, I think.

Oh yes, she does. We had fun hunting down a lot of new bot traffic once, didn't we, Wendy?
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### Re: 4D compass

mr_e_man wrote:Wendy, do you have the power to actually delete those "Deleted" posts?

We ordinary users can only delete the most recent post, I think.

[answer] I can do anything to your posts that you can do. Since the set of `your` is somewhat larger for me, you get the idea. But I normally use it to do things to delete evident spam or the like, not because i disagree with someone's legit post.[/answer] Wendy

I didn't even notice that anything was added, until now, as I'm looking through all my old posts.

There was no question of deleting over disagreement.
I was referring to posts like this or this (I'm pretty sure there were others), which are evidently useless and unwanted by anyone.

PatrickPowers wrote:Deleted.
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