## Clifford rotations of planets

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.

### Clifford rotations of planets

In 3D, a planet rotates around one plane, but in 4d, there is this thing called a "Clifford rotation" where a 4D object can rotate around 2 planes at once, like XY and ZW at the same time. This would cause some wired effects. The sun's path through the sky would be chaotic. if the planet's rotation speed along the XY plane divided by the rotation speed on the ZW was somehow a fraction with relatively low numerator and denominator, then the sun may follow a shorter repeating path that could easily be tracked with a simple calendar and clock. But this is infinitely unlikely for a real planet. So civilizations that track time would have to probably design 2 calendars and 2 clocks for each plane of rotation of their planet. The other thing is about the sun's path is that it would be chaotic and would change regularly, the time the sun is up for would be extremely inconsistent. This would force life on said planet to not take advantage of the predicable cycles of seasons and days. It would also be hard to plan meetings with 2 clocks for each rotation. if you plan a meeting when it is 9:30AM on the first clock and 7:00PM on the second clock, you could be planing a meeting centuries away if that combination does not happen for a while. Planed times could vary to with this method depending on how close you think the time needs to be to these two values to count it time for this meeting because it will never be exactly perfect. So then you could just say 9:30AM for the time, but what if the 2 parties involved look at different clocks, this could also be during day or night depending on the planets exact rotation. Due to all of this, it would be very hard for life to cope with their planet having a Clifford rotation.
Frisk-256
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### Re: Clifford rotations of planets

We do know that orbits in any dimension other than 3D are inherently unstable, not because of Clifford rotation but because the inverse square law that keeps everything stable in 3D just doesn't work out to balance in any other dimension. (The other big practical problem with physics in any dimension other than 3D is that apparently waves are unstable too, but that's a whole other subject.)

Regardless, I do often like to think about what physics and life would be like in different dimensions, if we can handwave these dealbreakers away! So this fascinates me.

When it comes to timekeeping, in programming we often just a single "time elapsed since an epoch" value (like the Unix epoch), as opposed to using a pair of separate "date" and "time" values, as has been conventionally done throughout history due to the nature of the sun's perceived movement through the sky in a similar manner each day. I think, in this 4D world where the sun appears to have chaotic movement, civilisation would just learn to use epoch-based time much earlier on in its development, because they wouldn't be able to use "date and time" for the exact reasons you point out. However, this would rely on finding some time source other than the sun. The pendulum and chronometer would probably have been developed a lot sooner, for example.

Keiji

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### Re: Clifford rotations of planets

Suppose you are in a 4D Universe where orbit is impossible. There will still be stars and the planet will still rotate. So the concept of a day still makes sense.
PatrickPowers
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### Re: Clifford rotations of planets

I've written a book that has a whole chapter about this. The climate depends on the ratio between the two rotational periods, which I call the horological ratio or horatio for short. If the horatio is close to one you get a quite different sort of climate than otherwise. If the horatio is within a few percent of some other simple rational number then you get a repeating week-long pattern of sunrises and sets that changes slowly. It's not unlikely. Or maybe one of the rotations is very slow. If none of these cases apply then you get an absence of any simple pattern. Nevertheless it is not mathematically chaotic, rather entirely predictable. I "invented" a mechanical clock that would take care of all these cases.

The book was available for free on ResearchGate until ResearchGate decided to remove all such things. Anyone know a place that will host a free book for free?
PatrickPowers
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### Re: Clifford rotations of planets

PatrickPowers wrote:Suppose you are in a 4D Universe where orbit is impossible. There will still be stars and the planet will still rotate. So the concept of a day still makes sense.

The problem is far worse than that. The two orbits trade energy, so that no 4D orbit is stable, not even an atom around a centre of mass. Everything quite quickly either crashes together or flies apart. A star would part evaporate, part collapse.

The only way to stabilise a higher-dimensional universe is to compactify the extra dimensions (i.e. roll up into tiny "tubes") until there are only three big ones left. Enter string theory, stage left....
steelpillow
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### Re: Clifford rotations of planets

PatrickPowers wrote:I've written a book that has a whole chapter about this. The climate depends on the ratio between the two rotational periods, which I call the horological ratio or horatio for short. If the horatio is close to one you get a quite different sort of climate than otherwise. If the horatio is within a few percent of some other simple rational number then you get a repeating week-long pattern of sunrises and sets that changes slowly. It's not unlikely. Or maybe one of the rotations is very slow. If none of these cases apply then you get an absence of any simple pattern. Nevertheless it is not mathematically chaotic, rather entirely predictable. I "invented" a mechanical clock that would take care of all these cases.

The book was available for free on ResearchGate until ResearchGate decided to remove all such things. Anyone know a place that will host a free book for free?

Sounds interesting!

What format is your book in?

If it's e.g. a pdf then could you not just upload it on any standard file sharing site, like Dropbox?

Keiji

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Location: Torquay, England

### Re: Clifford rotations of planets

steelpillow wrote:
PatrickPowers wrote:Suppose you are in a 4D Universe where orbit is impossible. There will still be stars and the planet will still rotate. So the concept of a day still makes sense.

The problem is far worse than that. The two orbits trade energy, so that no 4D orbit is stable, not even an atom around a centre of mass. Everything quite quickly either crashes together or flies apart. A star would part evaporate, part collapse.

You could be right. I would be inclined that stars would tend to be held together by forces like magnetism in addition to gravity, but it's beyond me.
PatrickPowers
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### Re: Clifford rotations of planets

Keiji wrote:
PatrickPowers wrote:I've written a book that has a whole chapter about this. The climate depends on the ratio between the two rotational periods, which I call the horological ratio or horatio for short. If the horatio is close to one you get a quite different sort of climate than otherwise. If the horatio is within a few percent of some other simple rational number then you get a repeating week-long pattern of sunrises and sets that changes slowly. It's not unlikely. Or maybe one of the rotations is very slow. If none of these cases apply then you get an absence of any simple pattern. Nevertheless it is not mathematically chaotic, rather entirely predictable. I "invented" a mechanical clock that would take care of all these cases.

The book was available for free on ResearchGate until ResearchGate decided to remove all such things. Anyone know a place that will host a free book for free?

Sounds interesting!

What format is your book in?

If it's e.g. a pdf then could you not just upload it on any standard file sharing site, like Dropbox?

Dropbox wants money. I registered on a free site and they started loading advertising into my browser. To heck with this. The following will be available for 14 days.

PatrickPowers
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### Re: Clifford rotations of planets

Why not try a dedicated online book self-publishing site? There are several around. Some offer the choice of printed and/or ebook formats, and carry out useful quality checks.
I use lulu.com, which is totally free to publish (unless you want to sell print books through outlets like Amazon, in which case it is the price of the odd proof copy).
steelpillow
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### Re: Clifford rotations of planets

steelpillow wrote:Why not try a dedicated online book self-publishing site? There are several around. Some offer the choice of printed and/or ebook formats, and carry out useful quality checks.
I use lulu.com, which is totally free to publish (unless you want to sell print books through outlets like Amazon, in which case it is the price of the odd proof copy).

Aha. I'll give that a try. Maybe that will motivate me to finish the next revision.
PatrickPowers
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### Re: Clifford rotations of planets

PatrickPowers wrote:Dropbox wants money.

Dropbox gives you 2 GB of storage for free, AFAIK. (Not shilling, just legitimately confused by this statement. )

Either way, I've downloaded a copy for now - will enjoy reading through this

Keiji

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Location: Torquay, England

### Re: Clifford rotations of planets

Keiji wrote:
PatrickPowers wrote:Dropbox wants money.

Dropbox gives you 2 GB of storage for free, AFAIK. (Not shilling, just legitimately confused by this statement. )

Either way, I've downloaded a copy for now - will enjoy reading through this

The options Dropbox gave me were "try it for free" vs. "purchase now."
PatrickPowers
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