A Mistake In Everyday Life on a Hypergeometric Earth:Surfing

[PatrickPowers]

I've realized that the surfboard section of Everyday Life on a Hypergeometric Earth is wrong.

Start with mundane surfboards in 3D. Usually there is a fin in the back on the center line. I used that concept in 4D. Well, that's wrong. There would be no center line on the surface of a 4D surf board. There might be a center line, but it would be internal to the board so you can't mount a fin there.

Going into more detail, let's say that a 4D surf board is long in the forward-back dimension, small in the up-down dimension, and of equal width everywhere in the sideways plane. That is for any point [w,x,y,z] on the surface of the board, z is wide-ranging, y is of narrow range, while w^2+x^2 = r^2 with r a constant. No w or x value is preferred as the center.

You could however arbitrarily make one of the fins larger than the others, thus artificially making a prefered orientation. I'd guess some would like one way, others would prefer the other way. But whatever they may do, the diagram I have assumes a center line for this sideways symmetrical board so it makes no sense.

[quickfur]

I don't see why not. A 3D surfboard is essentially a 2D object with a slight 3D thickness in the vertical dimention. It's long in the forwards/backwards dimension, and narrow in the sideways (left/right) dimension. The center line runs down the middle of the 2D surface, and the fin is attached to the back end of this line, and extends upwards in the 3rd dimension.

In 4D, a surfboard would be essentially a 3D object with a slight 4D thickness. Assuming analogous proportions, it'd be long in the forwards/backwards dimension, and narrow in both lateral dimensions. In other words, it'd be something like a 3D cylindrical spindle, plus a little 4D thickness. The center line runs down the middle of this spindle, which is internal in the 3D sense but nevertheless external in the 4D sense. A fin could certainly be attached to the rear section of this line, protruding upwards in the 4th dimension.

I don't see the problem here.

[PatrickPowers]

I don't see why not. A 3D surfboard is essentially a 2D object with a slight 3D thickness in the vertical dimention. It's long in the forwards/backwards dimension, and narrow in the sideways (left/right) dimension. The center line runs down the middle of the 2D surface, and the fin is attached to the back end of this line, and extends upwards in the 3rd dimension.

In 4D, a surfboard would be essentially a 3D object with a slight 4D thickness. Assuming analogous proportions, it'd be long in the forwards/backwards dimension, and narrow in both lateral dimensions. In other words, it'd be something like a 3D cylindrical spindle, plus a little 4D thickness. The center line runs down the middle of this spindle, which is internal in the 3D sense but nevertheless external in the 4D sense. A fin could certainly be attached to the rear section of this line, protruding upwards in the 4th dimension.

I don't see the problem here.

Aha you are right. Nevertheless I didn't fully understand the situation. Here in 3D a surfboard has two sides called "rails." If the dimension is greater than 3 then there is only one hypercylindrical rail. I didn't get that, so the diagram is wrong.

[quickfur]

It depends on what the function of the rails are. Is it necessary for them to cover the entire span of the lateral extremities? Is it possible in 4D to have, for example, some n-polygonal arrangement of rails the stretch from tip to tip along the lateral boundary of the surfboard's cylindrical surface, for example?

[PatrickPowers]

The rails are just the sideways extremities or edges of the flattish board. Here in 3D one tilts the board so that one rail or the other digs into the water so it will turn without skidding. In 4D a portion of the single rail would dig into the water.

It's the same as the metal "edges" of a ski. So in 4D skis would have a single cylindricalish edge.

The fin on a surfboard is to resist sideways skidding. It's possible to surf on a finless board, though too difficult for almost everybody. There are all sorts of fin arrangements on surfboards to get the right amount of skid with from 1 to 5 fins. The single fin in the center works in any number of dimensions. The most popular arrangement is a center fin with two left-right side fins called "thrusters" that are angled slightly toward the center line. If you used that in 4D then turning wouldn't be sideways symmetrical. Turning to the left or right would be somewhat different from turning ana or kata. Knowing surfers, they might take advantage of this in some way. Knowing surfers they would try all sorts of things.

[quickfur]

Gotcha. If the purpose is to dig into the water, then I'd imagine the 4D surfboard should just have its entire cylindrical-ish edge curve downwards in the 4th dimension so that the surfer can dig into the water from any of the lateral angles symmetrically.

About fins, a crazy idea that occurred to me is to tilted fins arranged in a circle around the surface of the 4D surfboard, such that it will rotate in a spiral fashion as it travels through the water. It will probably be disorienting for the surfer, but in theory, the angular momentum ought to stabilize the direction of travel as the surfboard moves through the water.

[PatrickPowers]

Well you know how it is in sport. People make things more difficult on purpose, golf being the prime example. There could be a place in 4D for the autospinning surfboard.