N-D anatomy

[Oren]

Some thoughts on 2-D and 4-D anatomy

I believe a 2-D person would first be bilaterally symetric, able to go forward or backward with equal efficiency. He'd have two stalked eyes, able to see forward or backward with equal acuteness. His digestive system would be similar to that of a colenterate, with mouth and anus being the same orafice. Anything else would split him in two.
His body would be dome shaped, allowing the plane-space people to easily climb over one another without harming each other. They would have four arms, two on each side, and two legs.
Instead of a circulatory system, nutrients would pass directly through cells via phagocytosis and reverse phagocytosis.
The brain would be very different, probably unlike anything we have ever seen. In order for neural pathways to form circuits which don't obstruct one another, they would have to be in constant motion.

4-D people, on the other hand, would probably be a great deal like us, just in 4-D. They'd have 2 eyes set in front of the head (I've heard it said that they would need 3 eyes, but since one eye would see a 3-D image, only 2 would be needed for 4-D vision.) They would have 2 arms and 2 legs. Their nervous systems and cirulatory systems would be similar to ours, but far more efficient, not having to snake around quite so much.

Anyone have any additional or contrary thoughts?

(suddenly notices his icon) hey! I'm one-dimensional! I've evolved! Let's celebrate! spaghetti and eels for everyone!

And on an interesting side note, I got a taste of life in planespace the other day when the horizontal dimension on my TV gave out last night. What fun watching a linear version of Wayne Brady!

[Keiji]

4D people would need 4 legs - if they had 2, they would have to hop around, like if we only had 1 leg.

They would probably be very flat through the gravitational (usually y) dimension. This wouldn't let them sit down.

[alkaline]

I believe a 2-D person would first be bilaterally symetric, able to go forward or backward with equal efficiency. He'd have two stalked eyes, able to see forward or backward with equal acuteness.

Ever read Planiverse? this book describes a 2d universe in detail, it's really fascinating. In that book, the beings are indeed symetric, and they have stalked eyes.

His digestive system would be similar to that of a colenterate, with mouth and anus being the same orafice. Anything else would split him in two.
...
Instead of a circulatory system, nutrients would pass directly through cells via phagocytosis and reverse phagocytosis.

The solution that Planiverse used was to have "zipper" systems where one side would open when something went in, then that side would close, and when something needed to go out, the zipper on the other side opened. Thus, the being was never completely split in two. I think the author mentioned your method in an appendix, but i'm not sure.

His body would be dome shaped, allowing the plane-space people to easily climb over one another without harming each other.

In Planiverse, the beings had these hole things with covers. When two met up, one would have to go into the hole, the other would close it then walk over, then the other would exit the hole and continue on its way. This would probably have to be the method used if they were carrying anything. If they weren't, having a dome shaped body might be the easiest and simplest solution. Most likely, both would be used.

In order for neural pathways to form circuits which don't obstruct one another, they would have to be in constant motion.

In Planiverse, the neural pathways had some kind of cross-curcuit that allowed signals to cross from one side to its opposite side without affecting the path that it crossed. I don't remember the details, though.

4-D people, on the other hand, would probably be a great deal like us, just in 4-D. They'd have 2 eyes set in front of the head (I've heard it said that they would need 3 eyes, but since one eye would see a 3-D image, only 2 would be needed for 4-D vision.)

I agree - the eye of any dimension sees an image of one dimension less, so the second eye gives the depth of the extra dimension.

Their nervous systems and cirulatory systems would be similar to ours, but far more efficient, not having to snake around quite so much.

Also, systems would be much more compact so paths could be shorter. Neural systems and electronics could be faster and thus smarter.

They would have 2 arms and 2 legs.

4D people would need 4 legs - if they had 2, they would have to hop around, like if we only had 1 leg.

Actually they wouldn't have to hop around. It doesn't matter what dimension you are in, you need to hop if you have only one leg. Having two legs lets you shift your weight back and forth between the legs, so at least one leg is supporting the weight at once. Thus, no matter one the dimension, if you have two legs you don't need to hop. But, the problem with only two legs in tetraspace is that it would stabilize the left and right directions, but not wint and zant. forward and backward is stabilized by movement and by shape of the feet. Thus, four legs would be most beneficial in tetraspace.

They would probably be very flat through the gravitational (usually y) dimension. This wouldn't let them sit down.

I'm not quite i understand what you're claiming here.

(suddenly notices his icon) hey! I'm one-dimensional! I've evolved! Let's celebrate! spaghetti and eels for everyone!

Here are the icon ranks for reference:
4 = linespace
16 = planespace
64 = realmspace
256 = tetraspace (visitor only)
1024 = tetraspace (citizen)

you can tell i'm a computer scientist...

[Keiji]

His digestive system would be similar to that of a colenterate, with mouth and anus being the same orafice. Anything else would split him in two.
...
Instead of a circulatory system, nutrients would pass directly through cells via phagocytosis and reverse phagocytosis.

The solution that Planiverse used was to have "zipper" systems where one side would open when something went in, then that side would close, and when something needed to go out, the zipper on the other side opened. Thus, the being was never completely split in two. I think the author mentioned your method in an appendix, but i'm not sure.

"You might imagine a kind of flat creature, like an amoeba, that could eat by opening a hole in its side and swallowing things, then opening another hole to excrete (it couldn't open both holes at once, or it would fall apart)."
- Space

His body would be dome shaped, allowing the plane-space people to easily climb over one another without harming each other.

In Planiverse, the beings had these hole things with covers. When two met up, one would have to go into the hole, the other would close it then walk over, then the other would exit the hole and continue on its way. This would probably have to be the method used if they were carrying anything. If they weren't, having a dome shaped body might be the easiest and simplest solution. Most likely, both would be used.

The best shape would probably be something like this:

Code: Select all

  /----\
/      \
/        \

In order for neural pathways to form circuits which don't obstruct one another, they would have to be in constant motion.

In Planiverse, the neural pathways had some kind of cross-curcuit that allowed signals to cross from one side to its opposite side without affecting the path that it crossed. I don't remember the details, though.

I think it's called cross-filtering.

4D people would need 4 legs - if they had 2, they would have to hop around, like if we only had 1 leg.

Actually they wouldn't have to hop around. It doesn't matter what dimension you are in, you need to hop if you have only one leg. Having two legs lets you shift your weight back and forth between the legs, so at least one leg is supporting the weight at once. Thus, no matter one the dimension, if you have two legs you don't need to hop. But, the problem with only two legs in tetraspace is that it would stabilize the left and right directions, but not wint and zant. forward and backward is stabilized by movement and by shape of the feet. Thus, four legs would be most beneficial in tetraspace.

... which is what I said. Sigh.

They would probably be very flat through the gravitational (usually y) dimension. This wouldn't let them sit down.

I'm not quite i understand what you're claiming here.

::realizes that I can't describe what I actually mean for lack of the ability to imagine a fourth spacial dimension in this way::

(suddenly notices his icon) hey! I'm one-dimensional! I've evolved! Let's celebrate! spaghetti and eels for everyone!

Here are the icon ranks for reference:
4 = linespace
16 = planespace
64 = realmspace
256 = tetraspace (visitor only)
1024 = tetraspace (citizen)

you can tell i'm a computer scientist...

2^2 = 4
2^4 = 16
2^6 = 64
2^8 = 256
2 ^ 10 = 1024

Me too.

[Aale de Winkel]

Already thought that it would be some binary system and gathered that I would reach the next level at 32, I now see that the rule is

n-spacian at 2[sup]2n[/sup] contributions

steep ascend though, I doubt that I'ld become a 4-spacian, or as you call it a visitor in tetraspace.
a 5-spacian (a tetraspace citizen) is very unlikely to be reached by us mere mortals.

(being a computerprogrammer by profession, and mathematical physicist by education)

[Aale de Winkel]

Under the assumption that tetra-gravity emerges from a single tetra-point, the construction of a tetra-foot ought to be thus that in conjucture with the tetra-musculature tetronians can stand erect on a single foot, balancing the rest of the tetra-body aganst the tetra-gravity.
Just when searching for an other place to stand a second foot is needed to find another equilibrium of forces at that point.

Further extremities are needed if the above balancing act fails, as a trionian I also need my fore-legs (we regularly call arms) if I fail to balance myself against our tri-gravity. For the sole purpose of this one other extremity would suffice, so I have one too many.

So one foot a tri- or tetronian needs to keep standing, one further to get moving and one as a fail-safe device.

[alkaline]

sometimes your writing is really obfuscated. You don't need to use phrases like "ought to be thus that in conjucture with" and "For the sole purpose of this" because they are really confusing to most people. i will try to reword what you said here:

"If we assume that tetra-gravity comes from a single tetra-point, then a tetronian could stand on a single foot by using their tetra-musculature to balance their body against gravity. If the tetronian wants to move somewhere, they would need a second foot in order to shift their balance forward to their destination. If their balancing act fails, they would need more limbs - for example, as a trionian, sometimes i need my arms to balance myself. "

Note: in order for arms to help in balancing, they need to come in pairs. If you raise just one arm, it shifts your balance away from that arm when you raise it, and you become less stable. If you raise two arms at the same time on opposite sides of your body, your balance doesn't change. The reason arms are helpful is that when they are extended, you have more angular momentum and you won't tip over as easily.

If you're talking about using that arm as a third leg, then that's a different matter. Tetronians could have three legs equi-distant from each other located in a triangular pattern around the body. In this pattern all three legs would be used in movement, and all the directions except forward and back would be balanced by the positions of the legs.

[Aale de Winkel]

sometimes your writing is really obfuscated. You don't need to use phrases like "ought to be thus that in conjucture with" and "For the sole purpose of this" because they are really confusing to most people. i will try to reword what you said here:

Excuse me for having my own style for phrasing things, I often get headaches to reftase thing for simpeltonians (don't take offense to this term)

Wheter the third leg is also useable as an arm perhaps make the subspecies I only stated that the third paw might be needed if the balance fails, one might do without! (again obfuscating (will look this word up!) perhaps?)

[alkaline]

sorry, i didn't mean any offense by what i said. i know how hard it is to rephrase things sometimes - i'm taking advanced english composition right now, and sometimes it can take half an hour or an hour just to get one paragraph right. I'm still not done with my tetraspace pages - i've completely redone them once, and i intend to rewrite them yet again.

if you're writing for other people to read, then you can't write something that they can't understand. It all depends on your audience. If you're fine with only dedicated people with advanced education understanding what you've said, then you've accomplished your goal. If you're writing for a wider audience, then you haven't. I write for a wider audience, so i strive for ease of understanding. That means i have to put a lot more time into my writing, and it takes a lot more time. In the end, i find this effort worth it.

[Jay]

Energy dissapates quicker in higher dimensions because it has more directions to travel in, right? Does this apply to heat energy too?

If so, would most 2-d beings be a lot larger than us, since body-heat would dissapate less rapidly from their core? And would 4-d beings have to be much smaller?

[alkaline]

yes it's true that heat would dissipate faster with distance from the source in higher dimensions, same as with all other types of energy. However, heat dissipation is actually more of a problem in higher dimensions than in lower dimensions, even though beings of lower dimensions are bigger. This is because the ratio of volume to surface area is higher, so more heat is produced per surface area. This would force beings of higher dimensions do be even smaller so that the heat produced could reach the surface faster and dissipate more easily.

[Jay]

I don't think a 1-d creature would need eyes, b/c if they were between any two objects, everything would be dark, as no light could get to them.

How would a 1-d world function? If the inhabitants were either confined to left-right or forward-back motions, they would have nothing to push off of but each other. But if the only motion was up-down, then there would only be one being, unless they were stacked on top of each other.

[Aale de Winkel]

sorry, i didn't mean any offense by what i said. i know how hard it is to rephrase things sometimes - i'm taking advanced english composition right now, and sometimes it can take half an hour or an hour just to get one paragraph right. I'm still not done with my tetraspace pages - i've completely redone them once, and i intend to rewrite them yet again. .

no offence taken. If I have time I rewrite my texts also, as a frisian proverb says "skriuwen is skrassen" (to write is to delete).
problem with these kind of text I write here is that they are spontaneous thoughts and thus rough drafts. People who take the time to know what "trength" means, ought to be able to understand (If not I'm just an email away)

if you're writing for other people to read, then you can't write something that they can't understand. It all depends on your audience. If you're fine with only dedicated people with advanced education understanding what you've said, then you've accomplished your goal. If you're writing for a wider audience, then you haven't. I write for a wider audience, so i strive for ease of understanding. That means i have to put a lot more time into my writing, and it takes a lot more time. In the end, i find this effort worth it.

I agree with all this, however as you are an alpha-IT-specialist, I'm a beta-IT-specialist. Time you spent in simplifying the only language you know to please the masses, I spent in learning a language more to be able to read the written stuff
Though I have trouble reading shakespeare I concider myself fluent in english, which might turn out somewhat technical sometimes since I simply don't know what the regular John/Jane Doe knows, and as said I'm just an email away to clarify things.

[alkaline]

Though I have trouble reading shakespeare I concider myself fluent in english, which might turn out somewhat technical sometimes since I simply don't know what the regular John/Jane Doe knows, and as said I'm just an email away to clarify things.

I can't read shakespeare either, and i really don't like his plays - they're rubbish. Anywho, i don't exactly know what a regular J Doe knows either, so i have these J Doe's read it, and they can tell me what they don't understand, so i can fix it for everyone else who reads it.

[alkaline]

I don't think a 1-d creature would need eyes, b/c if they were between any two objects, everything would be dark, as no light could get to them.

I agree. If there were "air" in 1-d between objects, the objects would never touch each other because the air molecules would always buffer them.

How would a 1-d world function? If the inhabitants were either confined to left-right or forward-back motions, they would have nothing to push off of but each other. But if the only motion was up-down, then there would only be one being, unless they were stacked on top of each other.

1-d worlds are too simple to get very excited about I don't know that self-movement is even possible. The molecules are at the whim of random forces, i suppose - but could forces even pass each other?

[Jay]

I don't know about forces passing each other, but I know that certain forms of energy, like sound and electromagnetism, wouldn't be able to exist in 1-d, because they are waves. Waves would require at least 2 dimensions to function.

[alkaline]

actually, sound is a longitudinal wave, so it only needs one dimension. I believe electro-magnetism needs three dimensions since the "electrical" part of the wave is perpendicular to the "magnetic" part, and each part is two dimensional since they are transverse waves.

[gonegahgah]

4-D people, on the other hand, would probably be a great deal like us, just in 4-D. They'd have 2 eyes set in front of the head (I've heard it said that they would need 3 eyes, but since one eye would see a 3-D image, only 2 would be needed for 4-D vision.)

We see 2-D images yet we need 2 eyes! I don't believe extra retinal dimensions are suitable compensation to the greater arena of space in higher dimensions.
Even with our 2 eyes in 3D we still rely on the horizon to feed additional clues to our brain.
It is my view that lining up objects in 4D will be much harder (than it is in 3D) if we to have just two eyes.
I very much pity the people in 4D who, via whatever cause, have only one eye!
I guess it may still offer more options than complete blindness?
When I get my 4D model up and running someday I'm hoping that this sort of thing will be much more discernable.
It is harder to use lower dimensional levels (or slices) to discern this sort of thing because they automatically line things up for us.

They would have 2 arms and 2 legs.

Balancing would be so hard with just 2 legs in 4D.

[gonegahgah]

Perhaps the toes of the 4D n-ped (> bi-ped) would follow a similar evolutionary process as ours.
So in that case the 4D creature would have a circle of legs for their upright posture with the minimum being a triangle.
We have big toes inside between our legs so perhaps they would also have big toes between each adjacent leg.
This would mean that they would have to have two big twos per feet.
But the 4D being also has a centre to their circle (or triangle of legs).
So they may also evolve to have a major toe that lies at the edge of their foot closest to the common centre of the circle (or triangle) of legs.
Then from those and between these they would have increasingly minor toes to the outer edge; like ours.
So, one major toe, two big toes, and lots of increasingly minor toes?

[DonSoreno]

Perhaps the toes of the 4D n-ped (> bi-ped) would follow a similar evolutionary process as ours.
So in that case the 4D creature would have a circle of legs for their upright posture with the minimum being a triangle.
We have big toes inside between our legs so perhaps they would also have big toes between each adjacent leg.
This would mean that they would have to have two big twos per feet.
But the 4D being also has a centre to their circle (or triangle of legs).
So they may also evolve to have a major toe that lies at the edge of their foot closest to the common centre of the circle (or triangle) of legs.
Then from those and between these they would have increasingly minor toes to the outer edge; like ours.
So, one major toe, two big toes, and lots of increasingly minor toes?

In Humans tows evolved as a relic from monkeys that use foots to hold onto trees. There is no need for toes in Humans. And 4d creatures would probably need different hands. Human hands are able to hold long thin cylindrical shapes; sticks; branches and so on.

A 4d creature would probably need to grab SPHERINDRICAL shapes.
So they would probably have a row of fingers, like we have; and perhaps 2 opposing thumbs. The 2 opposing thumbs combined with their index finger can then form a sphere. Like we can form a circle with our thumb and index finger. And they can stop small amounts of torque in their 3 axis. The row of fingers, that extends orthogonally to the opposing thumbs, into the 4th axis, would stop the torque that lies parallel to it.
If you hold any type of cylindrical grip in your hand, then the row of fingers is long enough to resist the torque that top-heavy swords or clubs produce.
Similarly, a 4d creature would need hands that can withstand a certain amount of torque that their swords/clubs/stick produce.
If tetronians want them to use items that are elongated in 2 (!) directions, then they would need 2 orthogonal rows of fingers.

[PatrickPowers]

Perhaps the toes of the 4D n-ped (> bi-ped) would follow a similar evolutionary process as ours.
So in that case the 4D creature would have a circle of legs for their upright posture with the minimum being a triangle.
We have big toes inside between our legs so perhaps they would also have big toes between each adjacent leg.
This would mean that they would have to have two big twos per feet.
But the 4D being also has a centre to their circle (or triangle of legs).
So they may also evolve to have a major toe that lies at the edge of their foot closest to the common centre of the circle (or triangle) of legs.
Then from those and between these they would have increasingly minor toes to the outer edge; like ours.
So, one major toe, two big toes, and lots of increasingly minor toes?

In Humans tows evolved as a relic from monkeys that use foots to hold onto trees. There is no need for toes in Humans. And 4d creatures would probably need different hands. Human hands are able to hold long thin cylindrical shapes; sticks; branches and so on.

A 4d creature would probably need to grab SPHERINDRICAL shapes.
So they would probably have a row of fingers, like we have; and perhaps 2 opposing thumbs. The 2 opposing thumbs combined with their index finger can then form a sphere. Like we can form a circle with our thumb and index finger. And they can stop small amounts of torque in their 3 axis. The row of fingers, that extends orthogonally to the opposing thumbs, into the 4th axis, would stop the torque that lies parallel to it.
If you hold any type of cylindrical grip in your hand, then the row of fingers is long enough to resist the torque that top-heavy swords or clubs produce.
Similarly, a 4d creature would need hands that can withstand a certain amount of torque that their swords/clubs/stick produce.
If tetronians want them to use items that are elongated in 2 (!) directions, then they would need 2 orthogonal rows of fingers.

Hands that are essentially 2D work surprisingly well in N dimensions. A 2D hand can grab any object with N-2 dimensions or less. In 11D, a 2D hand can grab a flat 9D object no matter how large it is.

Tree branches are for the purpose of getting things from one place to another. So they essentially 1D in any number of dimensions.

Toes are useful for balancing. They would be arranged in an N-2 sphere. It seems to me that there is no need for toe that is larger than the others even in 3D, but it is hard to be certain about that.

[PatrickPowers]

Perhaps the toes of the 4D n-ped (> bi-ped) would follow a similar evolutionary process as ours.
So in that case the 4D creature would have a circle of legs for their upright posture with the minimum being a triangle.
We have big toes inside between our legs so perhaps they would also have big toes between each adjacent leg.
This would mean that they would have to have two big twos per feet.
But the 4D being also has a centre to their circle (or triangle of legs).
So they may also evolve to have a major toe that lies at the edge of their foot closest to the common centre of the circle (or triangle) of legs.
Then from those and between these they would have increasingly minor toes to the outer edge; like ours.
So, one major toe, two big toes, and lots of increasingly minor toes?

In 3D, two legs are not stable. So I say that such stability is proved to be not a requirement.

So why don't we have one leg? It's because walking is more efficient than hopping. Two legs are better than one.

It would be harder to balance in N dimensions as N increases, but it seems to me that beings that evolved in such a Universe would (ahem) take this in stride. I say that two legs are enough no matter how great is N. This is particularly true for birds, for whom low weight is a high priority. That being said, there are advantages to having 2^(N-1) legs for creatures such as cattle or vehicles such as trucks, where high volume per limb/wheel is a priority.

Arms are different. There might be a use for more pairs of arms. I kind of like N-2 pairs of arms, but can't make much of a case for this.