4d fingers and toes.

Ideas about how a world with more than three spatial dimensions would work - what laws of physics would be needed, how things would be built, how people would do things and so on.

4d fingers and toes.

Postby anderscolingustafson » Wed Jun 09, 2010 1:29 am

In 3d most animals have their fingers and toes arranged across a line. In 4d because of the extra dimension organisms would need to have their fingers and toes arranged along a plane. 4d toes would still need to be linear however because if they were planar they would be stuck together and unable to spread out to support the organisms weight. Just as in 3d the line that toes are arranged along is curved in 4d the plane that toes would be arranged along would also be curved as that would make it easier for the toes to spread out to support the organisms weight. For the plane the toes would be arranged along the more sides the better as the more sides it would have the easier it would be for the toes to spread out to support the organisms weight. Many 4d organisms might have 19 toes all arranged into a hexagon with three layers of toes. The 1st layer would be the central toe the 2d layer would have 6 toes and the 3d layer would have 12 toes.

4d hands would probably still only need 2 sets of fingers to get a good grip. The main set would probably have the same number of fingers as the number of toes a 4d foot would have with the same basic arrangement as that would allow the fingers on it to spread out and surround things better. The other set would just be the thumb that would be able to move independently of the main set so that it could move under the main set to allow the hand to get a better grip on a 4d object just as our 3d thumb allows us to get a better grip on 3d objects.
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Re: 4d fingers and toes.

Postby A_Square » Thu Jun 17, 2010 12:37 pm

You need 2 legs to stand up in 2D, and you need a tripod to stand up in 3D (that, or 2 legs + balance, but let us consider 'balance' to be a single leg for simplicity). It's correct to extrapolate that you need 4 legs to stand up in 4D because the number of parameters (legs) needed to define the orientation of a(n) (hyper)plane in n dimensions is n.
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Re: 4d fingers and toes.

Postby Halfbaker » Wed Aug 11, 2010 11:39 pm

In 3d most animals have their fingers and toes arranged across a line.


You mean most vertebrates?

Assuming the 4D animals had toes organized in a human-like fashion, yes, they would be arranged in a plane. Imagine what a human footprint would look like to a dionien: a wall of toes and a ball. If weight was applied to the foot the toes would appear repulsed from the center by some force and the "wall" they connect to would seem to spread out. Same thing for 4D-to-3D footprints.

The main set would probably have the same number of fingers as the number of toes a 4d foot would have


Why? I think you *may* not realize that the human/vertebrate configuration isn't the only one that works.

Bye the way, what's the story behind the red and blue A's? :D
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Re: 4d fingers and toes.

Postby Mrrl » Mon Jun 06, 2011 7:01 am

May be, it's enough to have 7 fingers: six are covering half-sphere (S2) as vertices of half-icosahedron, and one is opposite to them. I assume that palm has form close to thin spherical cylinder, and fingers are on it's side (like our palm is similar to circular cylinder, and four fingers cover half of circle)
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Re: 4d fingers and toes.

Postby Keiji » Fri Jun 17, 2011 10:31 am

That sounds plausible. Could there be a reason for having more than one thumb per hand?
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Re: 4d fingers and toes.

Postby anderscolingustafson » Sun Jun 19, 2011 3:56 am

That sounds plausible. Could there be a reason for having more than one thumb per hand?


As it was a year after I typed this topic it was kind of tough to remember exactly what I wrote although I did read back over what I said and I noticed that I did not say that a 4d hand would have more than one thumb just more than one finger as indicated by what I said here.

4d hands would probably still only need 2 sets of fingers to get a good grip.


Bye the way, what's the story behind the red and blue A's?


Oh yea the red and blue A's in my signature are there to represent a mathematical pattern that is similar to the pattern of prime numbers in the sense that there is no (known) natural process that can specifically produce that pattern of numbers. The blue A's are to represent the numbers that can be rooted by another other than one whole number to get a whole number. The pattern includes the numbers 1, 4, 8, 9, 16, 25, 27, 32, and so on. Basically if you take a number and try rooting it by some of the lesser whole numbers and when one or more of it's whole number roots equals another whole number it will be represented by one of the blue A's in my signature so long as it's lesser than the total number of A's in my signature. So because any root of one is one the first A of my signature is blue, because the square root of four is two the fourth A of my signature is blue, because the third root of eight is two the eighth A in my signature is blue, because the square root of nine is three the ninth A in my signature is blue, because the square root of sixteen equals four and the fourth root of sixteen equals two the sixteenth A in my signature is blue, because the square root of twenty five equals five the twenty fifth A in my signature is blue, and so on. The A's in my signature also extend beyond what you can see of them on the screen and using this information you can figure out were the next blue A's of my signature are.
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Re: 4d fingers and toes.

Postby Keiji » Mon Jun 20, 2011 6:38 pm

anderscolingustafson wrote:As it was a year after I typed this topic it was kind of tough to remember exactly what I wrote although I did read back over what I said and I noticed that I did not say that a 4d hand would have more than one thumb just more than one finger as indicated by what I said here.


My post was in reply to Mrrl...
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