gonegahgah wrote:[...]I'm thinking that a 4D person won't think of sideways as having two directions. I'm thinking they will see it as a continuity of the full 360deg.
I'm also thinking that 4D space and physics won't tend to treat them as two separate directions of sideways either.
So, whereas the cubinder takes the forward rolling 2D circle, extends it one sideways, then extends it the other sideways,
I'm tending to think that what 4D will do is take the forward rolling 2D circle and extrude it all sideways directions (360deg) equally at once.
This will create a circle into sideways centred on the original rolling 2D circle.
Our 3D tyres do the same thing. They extend into all available directions of sideways equally (but there is only 1 sideways).
In 4D there is a whole 360deg of sideways so I'm guessing that 4D nature won't differentiate.
You'd most likely get even more bizarre shapes of crystals for example as you do even in our 3D world that completely ignore our ideas of things shaping in 3 directions only. [...]
gonegahgah wrote:You're right, I was starting to realise that perhaps the shape could be arbitrary too but I am trying to consider if one shape is more desirable than another for any reason.
Our 3D tyres needn't be perfect cylinders either. They could have wave like shapes. ie.:
This wheel is always flat to the ground as it turns but it is probably not practical to make wheels like this.
So perhaps there are other practical considerations such as having too many right angles that would perhaps weaken the tyre?
I also imagine in a 4D world that you will want rotation as well as direction.
When we shoot upwards into space we may rotate however we like as we go.
Obviously the more spin you get the greater the sideways forces but it may allow our 4D race cars to slip around those corners just that degree tighter to the corner.
In general we tend to make our rockets round as well as they have no preferential side direction. The shuttles aren't cylinders as they have to land.
I do think that there needs to be a mechanism to add and remove rotation. I don't think the car would spin of itself like this though corners may somehow add some spin.
I think the steering wheel could be designed to handle both turning as well as rotation in a 4D world.
Why would a cubinder prevent spin? You could spin a boxy shaped rocket just as well as a cylindrical one.
I'm not sure if a duocylinder is the shape I'm describing or not yet???
As mentioned in the other threads I'm tending to believe that 4D creatures will have three of things. Three legs, three arms, two claw-posable thumbs.
So their thinking would perhaps be more tri-side direction than quad-directional. I'm suspecting they would also have to have three eyes to determine distances along two axis.
gonegahgah wrote:It's just a suspicion at this stage but I do have an initial reason why I think that 4Ders might have an extra leg than us.
In 4D you could really have any number of legs side by side without any of them getting in the way; though there is probably a limit due to available space :/
But I think minimalisation would tend to be the trend for higher order land based vertebrates hence we have two legs (though not one because hopping is not a good look).
I guess less legs means that we can dedicate less brain power to co-ordinating our walking I guess; maybe.
The other aspect of our having two legs (and another reason for the lack of one legged hoppers) is to allow us to move forward freely while maintaining a steady sideways balance. We can fall gracefully foward to walk without having to worry about falling sideways. Having two legs not only provides us with another leg to walk to but also provides us with stabilisation hence why they are side by side and not one in front and one behind (and also so that the strides can be longer).
However, a 4Der can fall sideways in 360deg of direction rather than just left or right.
And a tripod as you also mentioned is certainly the minimum that you need to prevent falling in 360deg of direction.
So as a minimum I suspect that we need at least three legs, to allow the sort of stable walking that we take for granted, to occur in 4D.
[...]If it is so then whereas we tend to have a sidewards pendulum gait they would tend to have a more triangular/circular gait as they walk.
quickfur wrote:Yeah, at least 3 legs are necessary for balance. For walking, I postulate 4 as the next smallest even number, so pairs of legs can alternate in the walking gait.
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