Direction names in 5+D

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Direction names in 5+D

Postby uky » Tue May 03, 2016 8:43 am

Hello everybody
I'm developing a trivial navigating system in any number of dimensions, so I'd like to know if there are used names for directions in the fifth and above dimensions (i.e. after left, right, up, down, ana, kata)
If not I guess I'd take the left and right words in ancient Greek (as ana and kata are up and down) for the 5th dimension
For 6 and above though I don't know, maybe up/down/left/right in other unused languages (maya, klingon, constructed languages...?)
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Re: Direction names in 5+D

Postby wendy » Wed May 04, 2016 6:14 am

I tend to disagree with the 'across' dimensions in 4D and higher. The trouble is that only parity exists and not direction.

Up/down is the result of gravity, and is felt by trees etc. Forward/backward is the result of motion, which animals have but trees don't.

When you look at a page representing a plan of a room, then the forward is up, and the bottom of the page is a line, on which we can impose parity. This is why we have left/right.

Imagine now you lay clocks on the floor. Forward is still up, so there is no alignment of the floor, so 'left/right/ana/kata is meaningless. What does it mean that this clock's 12 points north, while some other clock's 7 point's north? You still have parity, in that anticlockwise is pointing down (ie backwards), but there is nothing that demands every 3 oclock points east.
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Re: Direction names in 5+D

Postby uky » Wed May 04, 2016 8:51 am

To be honest I don't see where the problem is.
When you have a 3D space you can put an orthonormal basis on it. Then you can name the 3 axis as you like, like forward/backward, left/right and up/down.
Hinton coined the terms ana/kata for the 4th dimension. I just wonder if there are similar terms for 5+.
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Re: Direction names in 5+D

Postby wendy » Wed May 04, 2016 10:27 am

If you divide 4d space by 3d, along one of the directions up/down or backward/forward, you are still left with a 2d plane.

If you think in terms of say, star fighters from Starwars, what makes for them 'up'. They can come at any angle and still feel no gravity. You get shots from the space shuttle, and what makes for the astronauts up, is that they have bodies that are based on gravity. But the space shuttle has no roof, no floor, just walls. You can attach to any of the six walls, and what you see as 'roof' is not what the next chap is seeing as 'roof'.

So while up/down and left/right is meaningful, in that everyone will see them in the same way, the across-space can be rotated from one viewer to another, without causing any ill effect. It is this reason that i have not found words for these things. Yes, I see four dimensions, I see five and six too.

You can indeed put an orthogonal basis on it, but i don't really suppose it means anything.

By the way, Welcome to the forum!
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Re: Direction names in 5+D

Postby Hugh » Sat May 07, 2016 5:49 am

Hi uky, welcome to the forum.

You've raised a great question that I hadn't thought about. I've heard ana/kata for the 4th dimension spatial directions, as well and marp/garp that I think Jonathan Bowers coined, but I don't think I've ever read about the 5th and higher names... I'm sure they're out there somewhere though. I am constantly fascinated by the higher dimension renderings and mathematical formulas and codes that get posted on here, all way over my head.
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Re: Direction names in 5+D

Postby uky » Sat May 07, 2016 10:36 am

@wendy: I agree with you, one can't put universal directions through space. But 4D organisms will have senses able to locate them in 4D, so they will feel up, left and ana, even though these directions wouldn't be universal but relative to each organisms instead.
And in this case relative directions is exactly what I'm looking for.

@Hugh
I also saw marp/garp during my searches, this website even has a glossary that has different 4th D direction names (see Direction): http://hi.gher.space/classic/glossary.htm
For 5+, I think too that they must be somewhere on the internet but still no luck

I'm also fascinated by what I can find here, I have a maths/physics background but I never had the occasion to explore higher dimensions.
I started with the project I'm currently working on and I'll continue for sure.
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Re: Direction names in 5+D

Postby Keiji » Sat May 07, 2016 11:50 am

What Wendy is saying, is that humans only recognise the directions as different out of necessity.

We live in a world with 3 spatial dimensions and 1 time dimension. Having one time dimension means that things can move in one spatial dimension at a time. That dimension we call "forward" and "backward", and because of that, humans have a "front" and a "back". I call this dimension "frontal".

Next, we live on a planet which has gravity. Gravity also operates in one dimension, which we call "down" and "up". Because of that, humans have a "top" / head and a "bottom" / feet. I call this dimension "vertical".

This only leaves one dimension remaining, which we call "left" and "right". It is the easiest to confuse because there is nothing special left about it. Indeed people who have trouble with their directions (dyslexia for example) generally struggle specifically with left and right as opposed to other directions. You are far more likely to get 'b' and 'd' confused than 'b' and 'p'. Languages of the world are variously written left to right or right to left because at the end of the day it doesn't matter, and some are written top to bottom, but none are written from bottom to top. Indeed perhaps the fact that we are so bad at handling left and right explains why when we look in a mirror we think left and right are flipped (they aren't: it's actually forward and backward that are flipped, while our brains are thinking of an imaginary space that is rotated 180 degrees in the vertical axis). I call this dimension "lateral".

You may now think that, if humans were to go into space they would still be able to identify "down" and "up", and indeed they can, but only because they brought their bodies with them, which were still designed for a with-gravity environment. But if humans lived in space from the beginning, and noone had ever experienced gravity, there is no reason for the body to be shaped the way it is: it would make more sense for it to have a high degree of symmetry along the frontal (forward-backward) axis, looking for example roughly hexagonal or circular from the front. And then, these hypothetical humans would not have any concept of what "down" and "up" were, and would be more likely to think in polar coordinates, "how far out" and "how far around from a reference angle". In this case, there is only 1 frontal, and 2 lateral dimensions, and no vertical dimension at all.

So, let's now think of a 4D planet with gravity. In the absense of anything other than time and gravity, there is 1 frontal, 1 vertical and 2 lateral dimensions. Therefore, 4D beings in such an environment would recognise "forward", "backward", "up" and "down", but would not recognise "left" and "right". They too may work in polar coodinates for the two lateral dimensions, identifying a point in 4D space as "this far forward, this far up, this far out and this far around from a reference angle".

However, 4D beings may have reasons to design structures that identify dimensions as separate again. For example, my planar rail system creates an environment where all four dimensions have their own special properties, separating the 2 lateral dimensions into a "confined lateral" and a "navigable lateral". Thus one may use "left" and "right" to describe the navigable lateral, while using "ana" and "kata" to describe the confined lateral, or vice versa.
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Re: Direction names in 5+D

Postby Teragon » Sat May 07, 2016 8:58 pm

Well, if you don't use something like Keiji's rail system or if you leave the streets, left, right, ana and kata is of little to no use for your orientation. If you go forward and define some direction as left, you may be aligned in any angle to that direction, still facing the same direction. You can't just remember where the objects are relative to your body if you walk in a specific direction, because your direction of movement is not enough to define them. Maby it would be the best to declare lateral directions by their angle from some distinctive object. If you turn around, its not left and right that is changing (at least not necessairly), but clockwise and counterclockwise.
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Re: Direction names in 5+D

Postby Teragon » Thu Jun 09, 2016 12:13 pm

Left and right make sense in 4D if you define an additional reference direction. In 3D left and right are defined relative to what's in front and what's below. Most of the time you don't really notice it, but if you're facing someone and have to communicate you have agree on a reference point in order to define left and right.
In 4D it just needs another direction to define left and right. It turns out orientation is easier than it may seem. For example instead of turning left at the kiosk you will have to be turning to the right of the church at the kiosk.
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Re: Direction names in 5+D

Postby quickfur » Sun Jun 26, 2016 1:24 am

In 4D, it is possible to look at someone in front of you and rotate your body 360 degrees without breaking your forward gaze and without changing your vertical direction. This rotation swaps left/right with ana/kata, thus proving that there is no clear distinction between them. Of course, it can make a difference if you have limbs pointing a particular direction in the left/right/ana/kata plane to serve as a reference, but nobody will be able to agree on the assignments, because your particular orientation depends on which turns you made to get to where you're standing. Since it doesn't change your vertical direction nor your forward direction, there is no real preference for which orientation you arrive in, so a bunch of people congregating together will probably have completely random orientations in this plane, even when they are all facing the same direction and standing upright.
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Re: Direction names in 5+D

Postby Teragon » Fri Jul 01, 2016 9:07 pm

Yeah, that's a funny thing in 4D. In n dimensions you have the degrees of freedom of a (n-3)-sphere for turning around while facing the same direction (and staying vertical). Plus in 4D you can rotate your head in two directions instead of one without changing the direction you are facing.
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Re: Direction names in 5+D

Postby quickfur » Fri Jul 01, 2016 11:39 pm

Teragon wrote:[...] Plus in 4D you can rotate your head in two directions instead of one without changing the direction you are facing.

Another funny thing with 4D is the greatly increased possibilities for facial expressions. I mean, just in terms of the eyes alone, there are so many more ways you can roll your eyes, and so many more shapes you can contort your eyelids/brows into to make an incredulous look. You can totally make all sorts of funny faces impossible to imitate in 3D! :lol:
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Re: Direction names in 5+D

Postby joan » Thu Jul 07, 2016 7:31 am

Teragon wrote:Plus in 4D you can rotate your head in two directions instead of one without changing the direction you are facing.


Wouldn't it be more than that?

If you are looking down the W axis any rotation on a plane not containing it would let you rotate your head while still facing it. So immediately rotations on XY, XZ and YZ. But really any combination of these, so the entire space of rotations in 3D could be performed without you breaking your gaze… Not necessarily keeping upright though.
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Re: Direction names in 5+D

Postby quickfur » Fri Jul 08, 2016 6:01 pm

I think he's talking about keeping upright.
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