4d arms and hands

[alkaline]

Here's an interesting question: how many hands would a tetronian (4d being) need to hold a box? (let's say it's a box that is equivalent to a 2 feet cubed box to us)

[Keiji]

4.

Fred needs 1 hand to hold it, Bob needs two hands to hold it, so Emily would need 4 hands.

The number of hands an n-dimensional person would need is 2 ^ (n-2)

[alkaline]

with fred using just one hand, a box wouldn't be completely stable. But, he could balance one edge on his hand, and the other on his arm. If you consider this cheating, that means he would have to use two hands/arms.

For Bob, he can technically carry a box with one hand like Fred can, but it's less stable. When Bob adds a hand (for a total of two), one dimension is stablized (left/right), but the second dimension(forward/backward) still isn't quite as stable. However, but it isn't completely unstable - the contact area of hands with the box isn't a point, it's linear. This stabilizes the motion somewhat. To make it the most stable, bob can rest the side of the box facing him against his body.

For Emily, she can also carry a box with one hand if she's really talented at balancing. Two hands would be more stable, and i argue that it wouldn't be hard for her to do it. The left/right motion is already taken care of by holding the left & right edges of the box. The area of contact of her hands with the box takes a two dimensional shape, so her hands would stablize the other two dimensions. One of these two, the forward/back dimension, could be further stablized against the body. The second of these two would be less stable (lambda/rho) because she wouldn't be able to use her body to balance it, but if the box wasn't too heavy unbalanced she could carry it without much trouble (just as we can hold boxes away from our body). If she added two more hands to hold the lambda & rho sides, then the only semi-unstable dimension that is left could be held against the body.

[Oren]

To my way of thinking, it's really just a matter of tension or compression. One hand provides one fixed point. The box can move away from that point, but not beyond it. A second hand on the opposite side provides a second barrier, and thus the box is contained along one dimension. Friction keeps the box from moving along a perpendicular dimension. I would say, therefore, that no matter how many dimensions are involved, the answer is two hands.
...Unless you are using gravity as the second hand, in which case you can balance it on one.

[alkaline]

yeah, i would agree that you could use two hands no matter the dimension. Depending on the dimension though, there is a limit on how many hands you can use - in the third dimension you can use two, in the fourth you can use four, for the fifth you can use eight, etc.

[Polyhedron Dude]

Tetronians would most likely have between 3 to 6 arms arranged like the vertices of various polygons. Pentonians could have 4, 6, 8, 12, or 20 arms - arranged like vertices of various polyhedra. The hands of a tetronian would not be chiral (in left and right handed forms) - a tetronian could wear his left glove on his right, wint, or zant hand (using a 4 armed tetronian in example) - this is because his left hand would have a mirror symmetry between the wint and zant side of it. Each hand would likely have 14 fingers and a double thumb (fingers could be arranged like this - 3 index fingers, 4 middle fingers, 4 ring fingers, and 3 pinkies) I put this description in a book I started writing a couple years ago titled "Welcome to the Fourth Dimension"

Polyhedron Dude

[alkaline]

Speaking of left-handed/right handed, i was thinking about the directions and non-reversible orientation in tetraspace. The area where arms could be attached to a tetronian forms a circle around the body. If the tetronian has four arms, they each point in one of the directions left, right, lambda (zant), and rho (wint). Since you define wint as 90[sup]o[/sup] clockwise from left, then the order would be left, wint (rho), right, zant (lambda). Would this orientation be reversible? What kinds of orientations wouldn't be reversible?

btw what is the definition of "chiral"? What would be the arrangment in a 3d surface of these fingers (if they intersected a realm)? And how's your book coming along?

[nestheking]

Think about a basketball. I can not hold it with just one hand. I need 2 hands to hold it. But any NBA player can hold the ball with just one hand. And think about spiders, or ants or such bugs. They have lots of hands but they can not hold a basketball. Why should tetronians be like humanbeings? Maybe they are giants or ant-like creatures. If they are giants, one hand (with enough fingers) is enough to hold the box. If they are ant-like creatures then probably thousands of tetronians are necessary to move the box.

Think about chimpanzees. They use their feet and tails like hands. I mean you can call chimpanzees five-handed creature. They also live in our 3d world.

Think about some space-guys (which we have not seen yet). Maybe they have 4 or 6 or 8 hands. We do not know. But they live in our 3d universe (if they exist)

That's why we can not answer this question.

[Geosphere]

You sure can hold a basketball with 1 hand - palm up.

Assumption here is lack of 'gecko hair' or similar gripping feature.

[pat]

Maybe an easier question is... how many legs would one require on a stool. That answer, if I'm not mistaken, is 'n'. The same number of points that determine an n-dimensional hyperplane.

[RQ]

Yes, I do believe the answer would for the least possible balancing number of legs would be n (chair). But what if it was a really thick leg?

[elpenmaster]

a really thick leg is not any different in holding up a stool than a really thin one. the difference is probability. the thicker that a leg is, the more likely it is to hold up the stool. three legs on a normal stool are the same thing as a triangle that has each leg for a vertex. when you talk about how many legs can hold up a stool, in order to need more than one the legs must have less dimensions than the stool, and for conciseness would be one dimensional

[RQ]

Yes, you are right, I was just saying that for simplicity's sake.

[PWrong]

A stool will not fall over as long as its centre of gravity is directly above part of the base. The base is the shape drawn by all the points of contact with the ground. So a stool with three legs has the same base as a stool with a thick, triangular leg. But a stool with two legs has a long skinny base, so it will probably fall over.