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Note: I'm talking about a fourth spatial dimension.

As far as I can tell, a 2 dimensional creature has one possible digestive system structure; have a cavity inside its body connected to the outside by one point (a mouth). Food and waste would enter and exit through the same mouth. (I suppose they could have more orifices, but not without a hooking mechanism.)

Three dimensional creatures could do the same thing, but they can also have a tube structure, where food enters at one orifice, progresses through the tube, and then exits at another orifice. They could also have additional openings throughout the tube, as long as they can stay as one connected body.

I assume that a four dimensional creature could have a third 'structure'. How could one describe it, and would it be more useful?

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    $\begingroup$ A digestive track is a line and is 1D in nature and it's then wound around into a structure in w/e dimensions there exist for that creature. $\endgroup$ – A. C. A. C. Jul 19 '17 at 19:50
  • $\begingroup$ According to my best knowledge, the fourth dimension is time. $\endgroup$ – Mephistopheles Jul 19 '17 at 21:27
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    $\begingroup$ @RedactedRedacted In our universe of the 4 dimensions available to us, one is indeed time. It's sort of incorrect to call it the 4th though as there is no way attribute a number to a dimension that isn't arbitrary. In this question however, they're refering to a world with an additional spatial dimension. Which would of course mean time is one of 5 dimensions in their universe. $\endgroup$ – AngelPray Jul 19 '17 at 21:30
  • $\begingroup$ @AngelPray Idk, I always imagined it like having a certain point with N amounts of values ordered to it in the Nth dimension. $\endgroup$ – Mephistopheles Jul 19 '17 at 21:38
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Not really. But I understand why you'd think so.

You're making the point that a 2 dimensional creature would be completely cut in two if it had a digestive track with two openings like we do in 3 dimensions. You're then extrapolating this fact and wondering that if we 3 dimensional creatures can have 2 holes wouldn't 4 dimensional beings be able to have even more holes:

2 dimensions = 1 hole -> 3 dimensions = 2 holes -> 4 dimensions = +2 holes?

However, a digestive tract is by very function 1 dimensional. It consists of getting stuff from one point to another point (a line). This means that while the exact dimensions and topology of a digestive track would change you can't simply assume more holes could be added: a line segment only has 2 extremities regardless of how many dimensions are available to you.


We can however correct your initial deduction if we take into account structures beyond digestive tracks:

A 2 dimensional creature is cut in two by a line (1 dimensional).

A 3 dimensional creature is cut in two by a plane (2 dimensional).

A 4 dimensional creature is cut in two by a 3 dimensional hyperplane.

The general rule is this: any structure can be cut in two by a hyperplane of dimension n - 1 of that of the structure.

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    $\begingroup$ So to expand on this answer, a 4 dimensional creature could have a digestive tract shaped like an unbounded plane, unbounded in that it extends completely to the creature's surface, without cutting it in half $\endgroup$ – Phoenix Jul 19 '17 at 23:43
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    $\begingroup$ ...but it probably wouldn't be any more useful than a simple tube. $\endgroup$ – Draco18s Jul 20 '17 at 14:45
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If the digestive system is approximately 1-dimensional, as with a digestive tract, or even a network of tubes connected together in some way, then a 3-dimensional body will be able to house it. This is because any graph (aka the network of tubes) can be embedded in three dimensions, with the graph complement connected (ensuring that the body housing the tube network is connected and doesn't fall apart).

However a 4-dimensional body does allow for more possibilities of higher dimensional digestive systems. For example you may want your digestive system to be the shape of a 2-dimensional plane.

Picture your animal as a 3-dimensional solid sphere with a slice cut right the way through it, which I will call its stomach, splitting its body into an upper and lower hemisphere. It could insert food in the shape of a large 2-dimensional plane (e.g. a large leaf) into its stomach without the need to cut the food up, and it could digest the food simultaneously in all parts of its stomach. Perhaps only some substances in the food can be digested, so in the stomach these substances are broken down and absorbed into either the upper or lower hemisphere of its body, and the rest of the food passes out the other side of the animal still as a solid plane. If the animal were 3-dimensional you would need to connect the upper and lower hemispheres by tendrons of some sort, which would then have to cut through the food as it passes through - which might be difficult if it ate really tough leaves. But with a fourth dimension these tendrils could loop round by perturbations in the fourth coordinate and avoid cutting through the food. In fact they needn't be tendrils, they could be continuous gluings of the two hemispheres that loop round using the extra dimension.

I see this creature as a bug that clamps itself onto a large leaf and crawls along it, digesting as it goes. Of course this assumes that there are still 2-dimensional leaves in our new 4-dimensional world.

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