The Mystery of Hyperdimensional Discus: Why a 4D Discus Won't Fly

[Hornbein]

If you have four spatial dimensions then a discus won't fly very well. A 4D discus or Frisbee has three large horizontal dimensions and one smaller vertical one. Spinning such a disc stabilizes only two horizontal dimensions. The disc is unstable in the other two dimensions so there is a tilt that can't be controlled. The disc will roll over and lose lift.

 

[Klystron]

If you have four spatial dimensions then a discus won't fly very well. A 4D discus or Frisbee has three large horizontal dimensions and one smaller vertical one. Spinning such a disc stabilizes only two horizontal dimensions. The disc is unstable in the other two dimensions so there is a tilt that can't be controlled. The disc will roll over and lose lift.

I threw my Wham-O Pro Classic Frisbee with my granddaughter this morning trying to visualize the 4th spatial dimension stability problem without notable success. We did notice the 3D fractal dimensions of the disc design between the bulging rim and the horizontal flat central section.

The Pro Frisbee includes 16 annular rings/grooves mounting from the curved rim to a single wider shallow groove where the flat interior top begins. We suppose these grooves provide some aerodynamic stability during (vertical?) flight in addition to the gyroscopic (horizontal) stability of the rotating disc. Note that the flexible disc deforms when thrown then flattens in flight, adding to the fractal nature of the disc geometry.

 

[Hornbein]

I threw my Wham-O Pro Classic Frisbee with my granddaughter this morning trying to visualize the 4th spatial dimension stability problem without notable success. We did notice the 3D fractal dimensions of the disc design between the bulging rim and the horizontal flat central section.

The Pro Frisbee includes 16 annular rings/grooves mounting from the curved rim to a single wider shallow groove where the flat interior top begins. We suppose these grooves provide some aerodynamic stability during (vertical?) flight in addition to the gyroscopic (horizontal) stability of the rotating disc. Note that the flexible disc deforms when thrown then flattens in flight, adding to the fractal nature of the disc geometry.

View attachment 324094

My first disc was embossed with

Flat flip flies straight. Tilted flip curves. Experiment!

 

[Klystron]

My first disc was embossed with

Flat flip flies straight. Tilted flip curves. Experiment!

Cool. I threw my first Wham-O Frisbee the Summer of 1958, made in California. The story goes that Southern Californians threw for distance, us Bay Area kids tried for maximum lift and hover time.

I have 'frisbeed' (verb) just about any object with a flat surface that I could throw and spin including aluminum pie plates, plastic dinner plates, playing cards, wooden boomerangs, knives and hatchets, even pieces of drywall. I store the disc in the above picture under the seat of my truck just in case.

When young and strong I would fling a disc at an angle from Santa Cruz beach out over the Pacific Ocean until it nearly disappeared then catch it when it boomeranged back to shore. Aerodynamic.

 

[Hornbein]

Cool. I threw my first Wham-O Frisbee the Summer of 1958, made in California. The story goes that Southern Californians threw for distance, us Bay Area kids tried for maximum lift and hover time.

I have 'frisbeed' (verb) just about any object with a flat surface that I could throw and spin including aluminum pie plates, plastic dinner plates, playing cards, wooden boomerangs, knives and hatchets, even pieces of drywall. I store the disc in the above picture under the seat of my truck just in case.

When young and strong I would fling a disc at an angle from Santa Cruz beach out over the Pacific Ocean until it nearly disappeared then catch it when it boomeranged back to shore. Aerodynamic.

I invented the world's farthest flying disc. Take a 150gr golf disk and fill it with foam plastic. 20% more distance.

 

[Algr]

If you have four spatial dimensions then a discus won't fly very well. A 4D discus or Frisbee has three large horizontal dimensions and one smaller vertical one. Spinning such a disc stabilizes only two horizontal dimensions. The disc is unstable in the other two dimensions so there is a tilt that can't be controlled. The disc will roll over and lose lift.

What you are describing is a sphere, with a small extrusion into the fourth dimension. That doesn't fly any better in three dimensions then four. What if it only had two large dimensions and two small ones.

 

[Hornbein]

What you are describing is a sphere, with a small extrusion into the fourth dimension. That doesn't fly any better in three dimensions then four.

To us it is a sphere, to them it is a disc. It is a flat object capable of pushing air downward, so it can fly.

What if it only had two large dimensions and two small ones.

Then it wouldn't have enough surface area to fly. In 4D, surfaces are 3D. An approximately 2D object doesn't have enough 3D surface area. And it would still flip over into the extra sideways dimension.

Taking things a step further, what to us is a hollow sphere is to them a ring. That would be the shape of their chain links.

As you can see, it takes a bit of getting used to. 3D intuition doesn't work in 4D. If it did then 4D would be a ho hum world.

 

[Algr]

To us it is a sphere, to them it is a disc. It is a flat object capable of pushing air downward, so it can fly.

I don't think that the names change in higher dimensions. A sphere is still a sphere, but they can see inside it. a 4d sphere is a hypersphere.

Then it wouldn't have enough surface area to fly. In 4D, surfaces are 3D. An approximately 2D object doesn't have enough 3D surface area. And it would still flip over into the extra sideways dimension.

Javelins are pseudo-one-dimensional, but they work in three dimensions. In order to tumble, you need to exchange one dimension with another. A spinning frisbee has three stabilized dimensions, so it is not clear to me that the fourth dimension would be able to exchange with one of the other three. Which one would it exchange with?

Taking things a step further, what to us is a hollow sphere is to them a ring. That would be the shape of their chain links.

Again the names don't change. Eight cubes make a tesseract. A tesseract has eight volumes, 48 sides, and one of something that needs a new name. (Hypervolume?). A hollow sphere might be LIKE a ring, in that they could put stuff inside it and move through it. But it would have a volume, whereas a ring only has an area.

 

[Algr]

I invented the world's farthest flying disc. Take a 150gr golf disk and fill it with foam plastic. 20% more distance.

Nope. This one is farther:

 

[Hornbein]

I don't think that the names change in higher dimensions. A sphere is still a sphere, but they can see inside it. a 4d sphere is a hypersphere.Javelins are pseudo-one-dimensional, but they work in three dimensions. In order to tumble, you need to exchange one dimension with another. A spinning frisbee has three stabilized dimensions, so it is not clear to me that the fourth dimension would be able to exchange with one of the other three. Which one would it exchange with?Again the names don't change. Eight cubes make a tesseract. A tesseract has eight volumes, 48 sides, and one of something that needs a new name. (Hypervolume?). A hollow sphere might be LIKE a ring, in that they could put stuff inside it and move through it. But it would have a volume, whereas a ring only has an area.

Volumes in 4D are 4D. Quartic centimeters of paint and so forth.

You are correct that rotations require exactly two dimensions. It is a little known fact (proved in 1890 or so by Clifford) that in 4D solid objects may have two perpendicular planes of rotation. Weird, eh?