## 4D Hands and Fingers

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 Hands and Fingers

I've imagined this quite a few times, what it would be like to be picked up by a four dimensional being. Most notably, what the finger arrangements could be, when protruded into our 3-plane. I suppose that the minimum requirement could be two fingers, in all dimensions, but more is better in this case. And for opposable thumb-like appendages, more dimensions could mean a requirement for more axially opposed digits. Take something like a three-fingered hand, in 3D. It's 2D trace would be three skin-circles in a triangle. A tetronian's equivalent in 3D would be four skin-spheres at the vertices of a tetrahedron, which would then collapse around you, and lift you out. Then, we could have a 4D hand with eight skin-spheres at the vertices of a cube. Or, even a pyramid-shaped digit array, mimicking our hands in a 4D way. The square array of skin spheres would be opposed by the single thumb skin-sphere, above and opposite. And of course, any other geometric or nongeometric shapes.

But, that's all assuming the 4D fingers are in the shape of a spherinder. They very well could be duocylindric, or even cubindric shaped fingers. I feel it would have to be some open toratope in its basic form. A spherinder seems most likely in an intuitive way.
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### Re: 4D Hands and Fingers

I imagine that a 4-D hand may look something like this. It has two thumbs, three index fingers, 4 middle fingers, 3 ring fingers, and two pinkies. Just rendered this .

Added a new render of a horizontal cross section of a trigonal human at arms level . . . . . hmmmm, almost looks like a 4-D Lara Croft .

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### Re: 4D Hands and Fingers

I usually figure some form of hedrid form, like a finger*line prism.
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### Re: 4D Hands and Fingers

Polyhedron Dude, that's a cool render! The bottom one is close to the 4D monsters I imagine. I picture a cluster of morphing skin-blobs, popping in and out of our 3D plane. It would be frightening, and cool as heck to play against one in a computer game. Maybe some Deadspace -centered theme, but with 4D beings attacking you left and right. And, I suppose up and down, and ana/kata! Or, it could manifest as a heard of animal-like appendage protrusions, that gallop together, and recombine, like some biological transformer.

wendy wrote:I usually figure some form of hedrid form, like a finger*line prism.

That sounds like a cubinder-shaped finger. If a 3D finger is generally cylindrical, then a prism of such would be appropriately cubindric. If that's the case, then I suppose the attachments to a 4D palm could be in two locations, with two knuckles, given the additional flat sides to anchor in place. Hmm.....
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### Re: 4D Hands and Fingers

Realistically speaking, in a battle between a 3D player and a 4D enemy, the 4D enemy is totally in an unfairly advantageous position. He can stand 0.01 inches away from the 3D hyperplane, and the player would not be able to touch him, and he just sticks his finger through the 3D player's brain in the 4th direction, and that's the end of the fight. Only a stupid 4D creature would remain intersecting with the 3D hyperplane where he can get hit by the 3D player.

Now with regards to hands, we've had this discussion a few times before. In the case of a 3D hand, one way to think of it is that the fingers + opposable thumb allows grasping of objects by restricting motion in 1 dimension. The 4 fingers then, curling around the object being held, confers an additional degree of restriction. Say you're picking up a long stick: the opposable thumb lets you maintain grip on the stick, and the 4 fingers restrict its rotational motion around the grasping point. This leaves an additional degree of freedom (e.g., sliding your hand up/down the stick) which is held in place primarily by friction.

Generalizing this to 4D, then, it would appear that to grasp a 4D stick, you would need at least two opposable digits, in at least two independent 2D planes, so that you can hold the stick in place. Then some number of fingers would be required to restrict rotational motion in another plane. Now the trouble is that in 4D there are six principal planes of rotation, so this may not be enough to fix the stick's orientation. So you potentially need two sets of fingers in different 2D planes (probably two orthogonal planes). That makes for a lot of fingers! So Jonathan's image seems a likely candidate for a 4D hand.
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### Re: 4D Hands and Fingers

Hands and fingers were originally used for walking and later evolved for grasping so 4d hands and fingers being used for grasping would likely have evolved from the front feet and toes that were originally used for walking. So 4d hands and fingers would be modified feet and toes so when figuring out what 4d hands and fingers would look like something to think about is what would 4d feet and toes look like and how could the shape of 4d feet and toes be modified to produce 4d hands and fingers.
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### Re: 4D Hands and Fingers

quickfur wrote:So you potentially need two sets of fingers in different 2D planes (probably two orthogonal planes). That makes for a lot of fingers! So Jonathan's image seems a likely candidate for a 4D hand.

Whoa, .... man! Crazy stuff. So, you need two independent grasping directions to properly hold something in 4D. Two orthogonal clamping abilities combined into one appendage. I suppose that's the only way to hold on to a board of infinite L x W, which is analogous to a 1-D pole in 3D. Or, properly grasp a spherinder pole. And yes, it's true that a 4D being need only mess with us from 4D, to be invincible from our attacks. But, that wouldn't make for a good selling franchise. Once you start the game, you get killed out of nowhere, and you're like "What the heck happened? " and the game is like " You got attacked from the 4th dimension!!! Respawn? " . Which would be boring and lame

anders wrote:Hands and fingers were originally used for walking and later evolved for grasping so 4d hands and fingers being used for grasping would likely have evolved from the front feet and toes that were originally used for walking. So 4d hands and fingers would be modified feet and toes so when figuring out what 4d hands and fingers would look like something to think about is what would 4d feet and toes look like and how could the shape of 4d feet and toes be modified to produce 4d hands and fingers.

That goes back to one of your older threads about walking gaits in 4D. It was more specific in the legs, but not so much the toes ( at least I don't think..). One interesting thought experiment would be to explore how a 4D foot makes contact and provides traction on a 3D realmic surface. Maybe also what the heel to toe strike analogies would be, or how one could corner while running on a 3D surface.
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### Re: 4D Hands and Fingers

ICN5D wrote:[...] And yes, it's true that a 4D being need only mess with us from 4D, to be invincible from our attacks. But, that wouldn't make for a good selling franchise. Once you start the game, you get killed out of nowhere, and you're like "What the heck happened? " and the game is like " You got attacked from the 4th dimension!!! Respawn? " . Which would be boring and lame

Until you realize that the point of the game is to acquire the ability to navigate (and see) in 4D before you get killed, in which case it suddenly becomes a lot more interesting...
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### Re: 4D Hands and Fingers

There you go. Now you're thinking.... Spaceship shooter or first person? Strategic dismemberment, wasteland survival, etc...?
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### Re: 4D Hands and Fingers

Then the game would just continue with five or six dimensional monsters attacking us
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### Re: 4D Hands and Fingers

quickfur wrote:Until you realize that the point of the game is to acquire the ability to navigate (and see) in 4D before you get killed, in which case it suddenly becomes a lot more interesting...

If the arena were 4D, and our 3D viewpoint was able to freely move around within it, we'd be able to see at least a 3D slice of the 4D being wherever he was within it.

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### Re: 4D Hands and Fingers

Hugh wrote:
quickfur wrote:Until you realize that the point of the game is to acquire the ability to navigate (and see) in 4D before you get killed, in which case it suddenly becomes a lot more interesting...

If the arena were 4D, and our 3D viewpoint was able to freely move around within it, we'd be able to see at least a 3D slice of the 4D being wherever he was within it.

That's like trying to survive an Unreal Tournament deathmatch with a 1 pixel wide display.
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### Re: 4D Hands and Fingers

Or we could design an engine to show something like the following but with better algorithms and production. This would still give us an idea of where the creatures are even when they aren't in the current slice.

This is a simple tesseract lying on the ground shown as multiple rotated slices with the current slice depicted solid.
It would be better as continuous rather than slices, without the black outlines and with ana areas of objects behind the object and kata areas in front of those objects.
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### Re: 4D Hands and Fingers

quickfur wrote:
Hugh wrote:
quickfur wrote:Until you realize that the point of the game is to acquire the ability to navigate (and see) in 4D before you get killed, in which case it suddenly becomes a lot more interesting...

If the arena were 4D, and our 3D viewpoint was able to freely move around within it, we'd be able to see at least a 3D slice of the 4D being wherever he was within it.

That's like trying to survive an Unreal Tournament deathmatch with a 1 pixel wide display.

I'd suspect we'd have a larger size view of it. We'd see the surface of the 4D creature that is facing us, consisting of a macroscopic conglomeration of all of the particles that make it up that are nearest to us.

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### Re: 4D Hands and Fingers

That isn't gonna help; instead of getting a 1-pixel-wide slice of the view, you'd get a 3-pixel-wide slice of the view squished into a 1-pixel-wide display, which makes it even more incomprehensible.
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### Re: 4D Hands and Fingers

quickfur wrote:That isn't gonna help; instead of getting a 1-pixel-wide slice of the view, you'd get a 3-pixel-wide slice of the view squished into a 1-pixel-wide display, which makes it even more incomprehensible.

I think it would be much more than that.

Picture one particle of 4D matter in front of your 3D viewpoint. Can't see it because it is so small, but 3 axes of its 4D existence are within your 3D viewpoint to see.

Add more and more 4D particles to the first one until you get about a golf ball size.

You'd see a golf ball size slice of the 4D object in front of you.

Even as you add more, you'd still see 3 axes of its existence in front of you.

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### Re: 4D Hands and Fingers

Well yes, that is the point... 3 axes of existence from a 4D point-of-view amounts to nothing but a 1-pixel slice across the world. Trying to out-maneuver a 4D being with such a crippled view is analogous to trying to win Unreal Tournament deathmatch on a 1-pixel-wide screen. (Or a 2D slice of the 3D world.)
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### Re: 4D Hands and Fingers

quickfur wrote:Well yes, that is the point... 3 axes of existence from a 4D point-of-view amounts to nothing but a 1-pixel slice across the world. Trying to out-maneuver a 4D being with such a crippled view is analogous to trying to win Unreal Tournament deathmatch on a 1-pixel-wide screen. (Or a 2D slice of the 3D world.)

The 3D renders of 4D figures that are shown in other threads seem to be much more than this...

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### Re: 4D Hands and Fingers

Yes, because they are dealing not with 3D slices of the 4D world, but projecting the entire 4D scene into a 3D volume. As long as you only deal with 3D slices, you're effectively only working with a 1-pixel-wide display (analogously speaking). You need to work directly with the 4D aspects of the scene in order to get a non-crippled representation of it.

Actually, even with the images made from 4D->3D projection, we're still handicapped, because we can't display a 3D dot-matrix on the 2D computer screen, so we have to make a further projection from 3D to 2D. This imposes a limitation on scene complexity, because past a certain point, the projected 3D image is just too complex to represent on a 2D computer screen, and you'll either get an incomprehensible jumble of elements, or you'll have to sacrifice accuracy for clarity by omitting some subset of the visible elements. There is no way to have both unless we can somehow feed 3D data directly into our brains without going through the 2D visual apparatus.
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### Re: 4D Hands and Fingers

quickfur wrote:Yes, because they are dealing not with 3D slices of the 4D world, but projecting the entire 4D scene into a 3D volume.

Well, if a 3D viewpoint was able to move around its 3 axes within that 4D world, the entire 4D scene would be revealed.

Just like if a 2D viewpoint was able to move around its 2 axes within a 3D world, it could reveal everything as well.

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### Re: 4D Hands and Fingers

Playing Unreal Tournament on a 1-pixel-wide screen can also reveal everything if you just turn around 360° standing still.
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### Re: 4D Hands and Fingers

Yeah, it works exactly like this:

Canceling out one dimension to represent a shape takes away a lot of information about it. We have to move around to see how the rest of it fits together. Cross sections are all we will actually see. A projection of a real 4D object would require some sort of advanced 4D sensing technology, that could display it back to you, in 3D pieces. So, we really do have to explore the darn things, if you want to see the rest of it. But, we won't have any sense of motion in this higher space. It would only seem as if the slices could transform magically, right before our eyes. The sense of motion is a trained thing, something you acquire later on, after getting the hang of it. Other than piling together slices in a cut array, one could also combine cross sections with 4D projection, as probably the ultimate way to sense the higher dimensional structure. But, no matter where you go in 3D space, you can never escape the vision or accessibility of a 4D creature. It'll always be there, watching you from ana/kata.
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### Re: 4D Hands and Fingers

ICN5D wrote:We have to move around to see how the rest of it fits together. Cross sections are all we will actually see. A projection of a real 4D object would require some sort of advanced 4D sensing technology, that could display it back to you, in 3D pieces. So, we really do have to explore the darn things, if you want to see the rest of it. But, we won't have any sense of motion in this higher space. It would only seem as if the slices could transform magically, right before our eyes.

You mention having to move around to explore it to see the rest of it. If one could move around the line of sight and interchange axes, that would reveal more.

Just like a 1D line could sweep an entire square, or a 2D plane could sweep an entire cube, or a 3D cube could sweep an entire tetracube.

What about thinking of the movement going on not with the observer but with the matter itself?

When you think about matter on it's smallest levels, it's very tiny, and it's in constant motion.

Hypothetically thinking, let's say the smallest particle of 4D matter is in front of a 3D viewpoint, and it is like our matter, in constant motion.

I don't think there would be visible "edges" to it, it would just be like a moving cloud.

The 4 axes of its existence would be constantly spinning around, exposing all of itself to the 3D viewpoint, as in "a 3D sphere could sweep an entire tetrasphere."

A 3D viewpoint wouldn't have to move around it to be exposed to all of it, it would get exposed to all of it due to the movement of the particle itself.

Now, let's add in more 4D matter particles around the first one, each one in constant motion on the tiniest of scales.

So a 3D viewpoint would be exposed to all of the particles nearest to it, due to the movement of the particles themselves.

A 3D viewpoint would be looking at a conglomeration of a cloud of those 4D particles, as they spin around all the different ways.

Also, what about thinking about how tiny particles of matter can be piled on top of each other to make something that sticks out on a larger, more observable scale?

From what I understand, it's easier for things to fall over and apart in 4D, because of the extra room for movement.

When I think about stacking a pile of blocks here on Earth, there is a limit to how high I can stack them because the power of gravity is strong enough eventually to overcome any other forces holding the blocks together.

It's impossible to stack loose soccer balls to a hundred feet high for example.

In a similar way, there is a limit to stacking the tiniest particles of matter because the forces between the particles cause them to fall over to make a less pointy surface.

In 4D, there would be even more of a constraint to stacking due to the extra room to fall in.

So what I'm thinking, is that a real 4D large object, would be less "pointy" than a 3D one, thus, less chance of something being "out of viewpoint" to begin with.

In addition to this, what fascinates me is the idea that there are actual higher dimensions to ourselves and the universe, making this discussion even more interesting.

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### Re: 4D Hands and Fingers

I'm trying to imagine what the 4D hand is actually trying to do?
That would tend to shape the hand more than anything...
I'll have a think about it...

Just generally the fingers would probably tend to be evenly spaced like ours are.

Our fingers have one axis of movement. Maybe a 4D finger will have two axis of movement?
That might even be necessary if the fingers are somewhat circularly positioned?

Hands in 4D might not tend to have an inside and outside seeing there is no preferential left or right.
So is it possible that 4D hands might actually have a circle of thumbs opposing the fingers?

This begs the question on what would be the pointer finger?
What do we name all those fingers especially seeing many are similarly placed?

I will try to explore the idea of what is necessary to hold a spear in 4D first?
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### Re: 4D Hands and Fingers

Considering that hands probably evolved from feet - similar to our world - it might be worthwhile to consider them first.

The most consistent circular space tends to be hexagonal and sub-triangles.
Also the tendency is for the longer digit to be towards the middle of the hand and approximately the foot.
The thumb evolved out of the big toe for us.

4Der's don't have an inside toe because there is circularity to their side-by-side being.
As a consequence they more likely have a middle toe/finger, like we do, emanating outwards to outside toes/fingers.
This middle toe/finger is likely to be the longest and most protruding; in approximate fashion to ours.

A possible pattern for the foot (and approximately the hand) is:
(base 19x3 = 57)

As mentioned our hands evolved from feet.
it is most likely that the outmost digits become the thumbs.
So that would be either of the following possibilities where the thumbs are shown as black:

Or possibly the following possibilities:

Or maybe even the following possibility:
(base 25x3 = 75; can you imagine the multiplication tables?)

Or perhaps the other way:
(base 13x3 = 39)

Our thumbs dropped further up the arm and moved to being opposable to the fingers.
So 4D thumbs would probably do something similar I would think.
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### Re: 4D Hands and Fingers

I've been now thinking about musculature for the 4Der to support movement and stability.

Our toes tend to claw down slightly and I would venture this to be the same for the 4Der.
Whereas our toes have a single top line which claws down the 4Der, I'm thinking, would have a whole top circle of lines that claw down.

So whereas our toes use a single muscle to claw pull a toe down (and opposite muscle to pull up) I think a 4Der's toe needs to pull down a whole circle of claw action.
So I certainly think that a single linear clawing muscle may be insufficient to stably claw a 4D toe.
I suspect that even two oppositely directed linear clawing muscles may struggle with the full 360° of clawing directions present in each toe (as compared to our single available clawing direction).

So I would either expect that there would need to be a continuous 360° of claw muscle for each toe or that perhaps this can be simplified to a minimal 3 claw muscles per toe.
There would also be then an equivalent 3 unclaw muscles per toe too.

My suspicion is that would be a common theme throughout the 4Der's body with each joint requiring a circle of 3 bi-paired muscles to stably control their movement.
So whereas we have one bicep and one tricep per arm; I suspect a 4Der would have 3 biceps and 3 triceps per arm as a minimum.
Does that sound reasonable?
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