## ana & kata

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.

### ana & kata

Wikipedia: search=ana wrote: Hinton created several new words to describe elements in the fourth dimension. According to OED, he first used the word tesseract in 1888 in his book A New Era of Thought. He also invented the words "kata" (from the Greek "down") and "ana" (from the Greek "up") to describe the two opposing fourth-dimensional directions—the 4-D equivalents of left and right, forwards and backwards, and up and down.

When they say its ("ana" and "kata" the 4D equivalent to leftright forewards backwards up and down, they just mean its perpendicular to all of them right? are they just the extra dimension of the 4D? (if it is then i know what they're talking about and they worded it badly -_-)
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papernuke
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### Re: ana & kata

The idea is that the four axies are supposed to be

1. up / down = against gravity

2. forwards / backwards = against motion

3. left / right and 4 ana / kata are perpendicular to these.

In practice, left/right amd ana/kata are meaningless.

Consider this. You consider say, a room as the floor-plan of a 4d room. It's got six walls, one is the floor and one is the roof. You now arrange clocks on the floor, face up. These represent people, facing the room, like wall-flowers at a dance.

In three dimensions, the floor-plan is just, say a wall (the room rotated 90 degrees). The individuals are placed along the floor, with just the 3 and 9 counting. The 3 is the left-hand, and the 9 the right hand (if you are looking out a clock-face). ana and kata are supposed to represnt the 12 and 6 directions.

In four dimensions, the clocks can sit anywhere on the floor: the people are still standing up, and facing the middle of the room, but there is no reason that the 12's have to point the same way, and an individual can rotate in this direction while still standing up and facing the wall: there is no meaning to the four directions suggested here. You can't say 'turn left here', because the 3-direction is not fixed in 4d, like it is in 3d.
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wendy
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### Re: ana & kata

No left turns in 4D. Got it. That's really weird, but it makes logical sense.

Here's another way to approach it: In 3D, a plane divides space into two halves, which may be arbitrarily assigned as "left" and "right." In 4D, however, a plane does not divide hyperspace into sections (no more than a line can divide space). I knew this, but never before thought of it in terms of trying to distinguish right from left. Thanks!
zero
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### Re: ana & kata

zero wrote:No left turns in 4D. Got it. That's really weird, but it makes logical sense.

Here's another way to approach it: In 3D, a plane divides space into two halves, which may be arbitrarily assigned as "left" and "right." In 4D, however, a plane does not divide hyperspace into sections (no more than a line can divide space). I knew this, but never before thought of it in terms of trying to distinguish right from left. Thanks!

Well, it is always arbitrary to perspective, no? Let’s say you are floating in space half way between the Earth and the Sun, at ≈74 1/2 million km from the Sun, Venus and Mercury are on the opposite side of the Sun. Is down towards the Earth, or is it now toward the Sun? What if you are facing perpendicular the two, so that the Sun is closer to your left hand and the Earth is to your right; are you on your side with the Sun or Earth down? Similarly, up-down, left-right, forward-back, ana-kata, will be relative to a viewing perspective. Considering we have to adjust for perspective in 3d it’s not surprising the 4d would a little “lefthand side/stage right” treatment.

I think we need to keep in mind this Euclidean 4d not Spacetime 4d.
Olorin
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