4+1D Flight

[Hornbein]

Suppose you have space with time and four perpendicular Euclidian dimensions. Assume that atoms exist and the laws of physics are the same. This doesn't seem likely, it's just intellectual exercise. Then assume things on Earth have the same number of atoms they have in 4D. The main result which surprised me is that things of the same mass have much smaller dimensions but a much greater surface area. We measure surface area by the number of atoms exposed on the surface, which is 3D. People of 100kg mass would be about three millimeters tall but have maybe a thousand times more surface area than do we. With the surface-to-mass ratio a thousand times greater than ours the world would be in some ways similar to that experienced by our insects. The terminal velocity of falling would be about 7 mph.

So...could winged elephants fly? No. It might be possible to get enough lift from wings but flight would take too much energy. But today I ran into a spider web and had an idea. What about the "ballooning" that spiders do? They spin a web into space then are carried away by the wind. Some bigger animal doesn't have to spin anything, just securely attach enough thread to its body. That might work.

Looking at it from another angle, gnats would have maybe a hundred times the surface area they have in 3D. I think that would make holding on to moisture such a problem that gnats couldn't exist. East Asia has biting gnats. Tokyo has few gnats but their bite is amazingly obnoxious. I wouldn't miss them.

Under these assumptions Earth gravity is a million times stronger. But let's ignore that for now, shall we?

 

[DaveC426913]

I kind of see where you're going with this by reducing it a dimension.

The occupants of flatland will have a much more difficult time inventing flying machines because their "wings" only have one degree of freedom: length. Double the weight of the contraption and you need to square the length of the wing.

But now that I think of it, I'm not so sure. For a 3D aircraft, if you double the weight you need to square the area of the wing - which you can do because you have two degrees of freedom.

This leads me to speculate that a four dimsnesional craft, in doubling its weight, will need to merely square its wing "volume", which it can do since it has three degrees of freedom.

So now I'm not sure of your conjecture that 4D elephants could fly is not solid ground.

 

[Hornbein]

Suppose you have space with time and four perpendicular Euclidian dimensions. Assume that atoms exist and the laws of physics are the same. This doesn't seem likely, it's just intellectual exercise. Then assume things on Earth have the same number of atoms they have in 4D. The main result which surprised me is that things of the same mass have much smaller dimensions but a much greater surface area. We measure surface area by the number of atoms exposed on the surface, which is 3D. People of 100kg mass would be about three millimeters tall but have maybe a thousand times more surface area than do we. With the surface-to-mass ratio a thousand times greater than ours the world would be in some ways similar to that experienced by our insects. The terminal velocity of falling would be about 7 mph.

So...could winged elephants fly? No. It might be possible to get enough lift from wings but flight would take too much energy. But today I ran into a spider web and had an idea. What about the "ballooning" that spiders do? They spin a web into space then are carried away by the wind. Some bigger animal doesn't have to spin anything, just securely attach enough thread to its body. That might work.

Looking at it from another angle, gnats would have maybe a hundred times the surface area they have in 3D. I think that would make holding on to moisture such a problem that gnats couldn't exist. East Asia has biting gnats. Tokyo has few gnats but their bite is amazingly obnoxious. I wouldn't miss them.

Under these assumptions Earth gravity is a million times stronger. But let's ignore that for now, shall we?

Now I realize that I don't know why or how 3D spiders ballooning works. So no chance of understanding the 4D case.

A friend of mine has a vid he took of a rotating leaf blowing around above his yard for eight minutes. I don't understand that either.