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 dimensional 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 on 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.

 

[pbuk]

Assume that ... the laws of physics are the same.

You cant: the three dimensional laws of physics are not consistent if applied to four dimensions. For instance if you say "Gauss's theorem is still true" then you no longer have inverse square laws for electromagnetism or Newtonian gravity, and this breaks pretty much everything from chemistry to star formation. If you think "that's OK, we'll do without Gauss's theorem" then you no longer have conservation of energy.

 

[Hornbein]

This is fiction. I can assume anything I like. It doesn't have to be realistic or true.

 

[DaveC426913]

This is fiction. I can assume anything I like. It doesn't have to be realistic or true.

Oh. I thought it was a thought experiment- where you'd make one change and see what consequences fall out. With that, I'd assume pbuk's concerns would be valid.

 

[pbuk]

It doesn't have to be realistic or true.

No, but if you want to ask questions like

So...could winged elephants fly?

then you need to make some consistent rules otherwise the answer to any question becomes 'yes'.

 

[Hornbein]

No, but if you want to ask questions like

then you need to make some consistent rules otherwise the answer to any question becomes 'yes'.

The rules are that atoms exist, have the same mass and diameter as on Earth, chemistry is the same, gravity on Earth's surface is the same, the Earth orbits the Sun, life on Earth is the basically the same, real estate agents exist, etc. None of this is realistic. Things have the same mass as here, engineering and evolution minimizes cost and maximizes usability and utility. It's all an excuse for developing intuition in 4D. Otherwise all you can discuss is imaginary geometric objects like 4D cubes. Too limiting say I. Not that much to say about them. I'm more interested in the steering of a 4D automobile.

There are only three or so people really interested in this but we all reach similar conclusions more or less independently.

 

[DaveC426913]

The rules are that atoms exist, have the same mass and diameter as on Earth, chemistry is the same, gravity on Earth's surface is the same, the Earth orbits the Sun, life on Earth is the basically the same, real estate agents exist, etc. None of this is realistic. Things have the same mass as here, engineering and evolution minimizes cost and maximizes usability and utility. It's all an excuse for developing intuition in 4D.

How can you develop an intuition in 4D if you throw away the rules willy nilly.

Knots fall apart in 4D; inverse square laws fall apart in 4D, etc.

I mean, it's OK if you want to premise a story on it, but it's more than fiction, it's fantasy. Larry Niven (author of Ringworld and Known Space) asserted that you can break rules for your story if you want to, but at least the rules have to be self-consistent within your own story, or it's just bad fantasy.

And that's fine too, but I for one, don't know how we might be able to help you, since any consequence we're going to come up with you'll just arbitarily say either "I'll allow it" or "I'll ignore that one." - and we won't know which one until after-the-fact. No?