Can an n-dimensional being hurt an (n+x)-dimensional being?

Question

Can a N dimensional being physically interact with a N+X dimensional being "sliding" a part of itself in said N dimensional world?

Giving it some thought I came up with three options:

1. Yes, the interaction is possible and the physics stays the same as if it were two N-dimensional objects interacting.
2. The physics that affects the lower-dimensional entity is constrained to the realm of that lower dimension, meaning that the lower-dimensional entity would not be able to affect anything higher-dimensional.
3. The lower dimension could (physically speaking) not be an infinitesimally but finitely thin slice of the higher dimension, so that the lower-dimensional entity can negligibly affect the higher-dimensional entity.

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• Assume N+X where N and X are strictly positive, and, unless strictly necessary, assume both are natural numbers. I would constrain it more, but again, maybe an irrational number of dimensions is a thing and I don't know it.

• In option 3, I did not look lower than the atomic level as I greatly lack knowledge to do so. I can't (and don't want to) deal with elementary particles, Plank's length, black holes, etc...

  If going lower is required, that is not a problem.

  I also don't have the knowledge to go to the atomic level, but at least I have a slightly better understanding of my own incompetence, and I have to start somewhere.

• For any required details that are not specified, you may use a realistic setting of your choice.

• If an unproven but credible theory would permit it, then I would gladly hear about it. (By "credible", I mean loop quantum gravity or string theory, for example, are OK. But stuff like flat earth or me-not-getting-my-midnight-snack theory are not.)

• You may handwave anything that is not about the physical interaction.

Answer 1

Yes. Depends on X and N, and on the cut.

More specifically depends mainly on N (and on the the ratio between X and N+X). The lower the value of N, the worse the damage.

Of course, the size and location of the cut in respect to the whole being also play a part, if N allows it.

In principle, a large enough M-1 dimensional cut may cleave a M-dimensional polytope (or sentient being, the cut does not care which) in two. The fact that the cut would be infinitely thin in the extra dimension is immaterial: the object doing the cut is interfering with chemical bonds on its two sides (if it didn't, there would be no cut).

The simplest case we can directly experiment is X+N = 3. A three-space-dimensional being could be us.

Should a two-dimensional being (N=1) hit us, that would be a very precise, microtomic cut, and it would be potentially painful and even lethal. To be precise: the cut itself would be painless, but an instant later, the broken chemical bonds on at least one side still connected to the brain would start sending pain signals.

But a one-dimensional (N=2) hit would be a zero-width stab and we would not even feel it. It could pierce us through, and it would do no damage whatsoever. Not having width or breadth, the stab would leave no hole. Even a moving one-dimensional wire, describing a 2-dimensional arc (so, impossible for a one-dimensional being) would do little damage, the chemical bonds interrupted for too short a span to be really massively disrupted.

Answer 2

Probably Not

For this answer, I'll specifically be using 2D and 3D as example, but it should still give you some insight into how this would work with other dimensions.

So you are a 3D person, now lets say in front of you, there was a 2D plane, like, perfectly 2D.

A 2D plane would be invisible to any 3D person, because a 2D plane is infinitely thin, so no photon/light of any wavelength will be able to reflect off of the plane, they just pass right through it, because they would need a wavelength infinitely small.

But it is not just photons, any massive(has mass) particle has a wavelength, determined by the equation: wavelength = h/mv where h is Planck's constant, m is mass, and v is velocity. Therefore, any thing with mass will also pass through the plane, since no massive particle has an infinitely small wavelength.

So basically a 2D plane would be completely undetectable to any 3D or higher dimensional being. Since no light would be interacting with the 2D plane, no 2D person would see anything 3D passing through the 2D plane either (think: if you were invisible you wouldn't see anything since no light can hit your eyes).

So no, neither the 2D people nor 3D people would be able to interact or even detect each other.

Answer 3

Avatars.

I agree with KaffeeByte's answer as being the "most likely scientific explanation as we understand it". There are ideas of a real higher dimension that has real meaning but so far as I know there is no concept that we could interact with it, or vice versa.

But that's no fun. H.P. Lovecraft is famous for his extra-dimensional monsters, and numerous sci-fi/fantasy stories have flirted with ideas of extra-dimensional entities and one of the more common ways they resolve it is simply having "avatars".

Humans do not have the ability to project into a 2-dimensional universe in order to interact with it. But what can 4-dimensional entities do? Who's to say, other than you, dear author. It wouldn't raise many eyebrows to simply claim that a 4th dimensional being has the power to project an avatar -- a representation of itself -- into our world in order to interact with it.

If you follow the Lovecraft model, these projections are distorted horrors liable to drive you insane simply from looking at them, since they clearly aren't bothering with the laws of physics. If you follow more of the traditional fantasy model, then they can look human, or however you please (devils, angels, fairies), but it's important to realize that in all cases, the "avatar" is not the main body of the entity.

Typically, to make it interesting, avatars are necessarily physically here and can be damaged or destroyed, but it's the equivalent of a gnat biting your thumb. You might go "ouch" and pull your finger back but it's not going to seriously harm you.

In some world concepts, these avatars require some effort by the higher level entity, so getting them to retreat makes the characters safe for some time -- the entity needs a minute to recover (which, to humans, could be 5 minutes or a billion years). So, typically, these entities can be "harmed" but as their main body is outside of our dimension and likely subject to laws of physics we can't comprehend, the ability to do them any real harm is likely zero. The ability to do them temporary harm is up to your imagination.

Answer 4

The more I thought about this, the more I want to answer...

This is a proposal for the rules of your world

Because in the Real World, creatures of dimensions X<3<Y don't exist. Well, maybe they do, but here's the problem: there has never been any evidence of any effect in the Real World that can only be explained by the presence of such creatures (or even passive objects).¹

But that's no fun at all!

Can an N=1 creature hurt anything?

No — but it could be yes!

The most complex N=1 creature is a straight line. A very rigid worm, you might say, but because it has no other dimension it's infinitely thin in every direction other than the direction of the line. Being infinitely thin, it has no mass. Therefore, it passes cleanly through any dimension N>1 without damage. At worst, more massive objects deflect it or they just move imperceptibly out of the way to allow it to pass. No molecular cohesion is ever lost.

Unless you want it to. That's the fun of creating rules for your world. If you want N=1 creatures to cause damage, then we need to ask ourselves, "what would molecular disruption look like if a 1D object passed through something?" Let's stay away from atomic cohesion. Disrupting atomic cohesion is called fission and it's nasty. But molecular cohesion... A sheet of metal might be very cleanly cut by such a creature. A living being, where cells have the ability to re-establish cohesion, might not be damaged at all.

Can an N=2 creature hurt anything?

No — but it could be yes!

But remember the N=1 problem. When you look at a 2D creature edge-on, what you're seeing is the 1D edge of the 2D object. It's infinitely thin. We can model that process by hanging a 3 meter x 3 meter sheet of aluminum foil. When you face it, it's opaque. But when you look at the edge (on a very calm day with a very flat sheet), you can't see it. If you walked directly into the edge (and perfectly...), you'd have the same damage properties of a 1D object... kinda.

What happens when that infinitely thin sheet has entirely separated you into two halves? That's a good question! It's infinitely thin, but does that mean it's not there? If the material is impermeable, meaning nothing can pass through it, then you just cut our poor test subject in half. Maybe.

The problem is that "impermeable" is an interesting word. Maybe fluid can't pass through it, but can magnetism? How about the atomic forces? In other words, our test subject may continue walking, and they'd better hurry before the lack of blood, which has stopped flowing, leads to their death. Could the electrical charges in the brain continue to flow in such a condition? The electrons can't pierce the sheet — but would the charge couple to the other side of the synapse?

Ah, the joy of creating rules for your imaginary world!

Even if we consider the other direction, the sheet-on direction, where the 2D object can be very clearly seen by the 3D person because it's blocking sunlight (in your world, an infinitely thin object can be opaque!), but would it hurt to run into it? A 2D object still has no mass because it's infinitely thin. It would cause less notice than running through air! But it's impermeable! So you suffocate because this opaque, weightless object you just ran into is... wait. You didn't suffocate, because the sheet can't be bent. That would require a third dimension. Which means when you hit it, it bounced harmlessly away and you only noticed it visually because you didn't feel a thing.

But how does gravity affect a 2D object? From our Real World perspective, it has no mass, and so isn't subject to gravity. Once tossed in the direction of the sky it would keep on going forever until the face of the sheet struck something else. Hopefully something soft so it stopped rather than bouncing off and continuing its journey. But as we discussed, it could cause harm. If anchored, it would stop a runner. If used to slice into a 3D object and held there, that object would eventually die due to necessary 3D things not having the ability to happen any more — so long as your rules allowed an infinitely thin object to be, for example, impermeable.

To quote Captain Jack Sparrow (second time in two days, imagine that...), "Ah-ha! So, we've established my proposal as sound in principle. Now, we're just haggling over price."

If you're asking about Real Life, the answer is simply "No." If asking about your imaginary world, the answer is, "absolutely yes!" We just need to set the rules.

This Stack often focuses too much on the Real World. There's a lot of cool stuff in the Real World! It's also boring, which is why we read novels, go to movies, and play video games. What makes those flights of fantasy fun is that they invoke rules that aren't identical to the rules here. They let us play the "What If?" game.

I like your world! Cool things happen there! It'd be a scary place because things I can't see can hurt me!

The question is, how do you want them to hurt people?

If my answer has provided you with sufficient inspiration to answer that question, then have at it and consider posting your final story on the Worldbuilding blog, Universe Factory. Some amazing fiction has been written there!

If you're still in need of inspiration and guidance, you'll need to ask a new question. Remember, you need to be specific and you need to describe a problem to solve. Help us understand what you're trying to do and why you're trying to do it. Then explain what's stopping you from solving the problem. We're really good at taking it from there.

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_{¹ This is a generalization. There are plenty of people who may jump on this and start talking about Quantum Strings and such things. But that's just arguing for the sake of arguing. No one has ever been garrotted by a quantum string. A lot of physicists would probably be happy if it had happened just once, though.}

Answer 5

Making physics work between 3 and 4 dimensional beings is weird

If your higher being is only 1 dimension more complex, the cut could be like a cut constrained along a single axis. It does not matter that you cut someone in half flatly or at an angle, the outcome is still the same.

The problem you are running into with your energy equation is that you are using the wrong unit of measurement. Mass is a property of a given volume of matter. Just like you can not use volume and area interchangeably, you can't use 3d mass (Mass₃) and 4d "mass" (Mass₄) interchangeably.

If Mass₃ = Volume * Density, then Mass₃ = X * Y * Z * Density and in 4 dimensions Mass₄ = W * X * Y * Z * Density. So your sword has zero Mass₄ just like a plane has zero volume, but it still has Mass₃ just like a plane still has area, even when represented in 3d space.

The sword is not stopped by the 4d body because along with having no Mass₄, it also has no resistance in 4d space because the area of intersection is zero. Normally X/0 is undefined because it makes an infinite set of different possible outcomes, but 0/X is always 0; so, 0/0 produces an infinite set of numbers that all equal 0 meaning that 0/0 is equivalent to 0. So in 4 dimensions, your sword has neither mass₄ nor resistance₄; so, it is not stopped by the body of the 4 dimensional being, but can cut through it normally in 3 dimensional space.

If your higher being were 2 dimensions more complex instead of 1, then things might be different. The result would be like getting acupuncture from an infinitely thin needle; so, it would not really effect the higher being at all, but at 1 dimension different, you can still cut the higher being in half... which is probably fatal, just depending on how this higher beings biology works.

One final consideration is that it might be easier for a 4d being to bleed out than to be cut in half. If you break a line on a square, then any fluid inside can flow out. If you break square on a cube, then 3 fluids can flow out, so if your break a 3-dimentional aspect of a 4d being, then 4d blood can be spilled; so 3d trauma should kill a 4d being regardless of if you can cut it in half or not.

The easier solution is to simply treat humans as 4 dimensional.

Just because we only perceive and interact in 3 dimensions does not mean we are not 4 dimensional beings... heck, we could very well be 11 dimensional beings, and simply have no way of knowing it. So if we assume we actually exist in 4 dimensions, then to the higher being, we would also be 4 dimensional beings, but we would behave like trains stuck on a track, unable to deviate from the paths that we can understand. We could will our selves in some directions, but not others.

So in this manner of thinking, having a 4 dimensional being enter our 3 dimensional awareness would be like the higher being steeping out onto the train tracks. Sure she could stand next to us all day and night and we would never notice her, but once she is on our track, we can see her, hear her, and most importantly for the sake of this question, plunge our 4 dimensional sword right into her.

Either way, I believe the sword could be fatal, but I think treating every being as existing in, but not necessarily aware of the other dimensions will make understanding your world a lot easier.

Answer 6

It will hurt as much as striking at your shadow.

This answer may not be 100% scientific, but maybe it's more approachable for non-sciency people. Humans have different ways to project themselves into a 2-dimensional space. They take pictures of themselves in their 3-dimensional world and display them on a 2-dimensional surface. They also cast shadows which reduces their 3-dimensional body to a 2-dimensional projection. Striking at any such projection doesn't hurt the actual human.

As you said yourself, humans cannot interact with or even see a 4-dimensional space, so the Goddess must project her image into 3 dimensions, like a hologram. You can play with this idea like you play with video filters on your phone: add or reduce contrast, color or sharpness, distort the image or make things suddenly appear that were previously hidden behind another object.

But that still doesn't allow humans to interact with the actual Goddess. Depending on the technology or magic used to create the hologram, they could interact with that (like cracking a screen), but the actual 4-dimensional being isn't affected by any of that.

Answer 7

(I will be grossly approximating things below, but this is to give an idea more than a physics lecture I cannot do anymore)

You can use gravity as an example of a field in a higher dimension interacting with our 3D.

In 3D (the world around as as we see it), an object attracted by another object (say, the Earth by the Sun) sees it as a force.

There is a complete topic of physics devoted to that explains apples falling on the head of people, and the ability to predict the next eclipse.

When looking at that in a higher dimension, there are no more forces, but shortest paths of movement. And again, complete physics was devoted to that that explains everything.

So it is not really that physics changes between the dimensions, it is just interpreted differently, with the tools of that dimension. The hypothetical entity in a higher dimension could interact with the 3DS one, by changing something with their physics tools - and that would be seen by the lower-dimension entity as something happening with their measurements, based on their physics.

In other words, the high-D entity does something (modifies the curvature for instance), and the low-D entity interprets it as a mass having changed.

Answer 8

The answer depends on the physics you choose, but the closest real life physics we have says "yes, it can interact."

The best models of how things interact today use fields, such as electrostatic fields, where the "mover" of particles are distributed throughout the space. This means that, in any N-subspace of a (N+X)-space there is the ability to impart motion.

The physics we understand today are all built on calculus and the idea of limits. We can think of a thin slab of the (N+X) space and look at what the interactions are like. This slab can be any shape in N dimensions, but must be "thin" in the remaining X dimensions. We can then make the slab thinner and thinner until we approach the limit of "a slab with 0 thickness." With current mathematics, this limit descries a N dimensional shape, so whatever behavior your chosen equations yield, that's what you get. The mathematics of this decrease in dimension from N+X to N is pretty robustly backed by current mathematics. Since current mathematics is what we're invoking when we say "N dimensions, I think this shapes your answer.

As we are not used to thinking of higher dimensions, it may be useful to think of our reality as the N+X and look at how a lower dimension works upon it (instead of the other way around). In particular, consider N=2 and X=1. This situation does a very good job of capturing how an Obsidian blade works. Obsidian blades are used in surgery (particularly cosmetic surgery) because they can be made with a blade edge that is a single molecule thick. As such, they can cleave a cell in half, cutting the cell wall apart. Now a molecule is theoretically a 3d object, but it is not hard to think of what would happen if we slimmed that down to something infinitely thin (such as a plane of electrons).

Now the question to ask is "what happens while the 2-d blade is inside the cell wall of the 3-d cell?" A full 3d Obsidian blade will indeed push the halves of the cell apart, but a 2d one would not. A 2d one, however, would react with the cell wall. For example, this would decidedly shift the surface tension. This might cause the lipids in the cell wall to pull away from the knife, allowing water to rush in. When the 2d knife was removed (pulled out or passing through), the movement in the cell wall will have occurred, and there will be a hole to heal. Conversely, if the physics of the cell wall caused the lipids to push towards the blade, one would see something similar to the decorative marbling on chocolate:

The physics of a 3-d surface tension causing something to be drug along a 2-d surface are intuitive.

Now what about the other interaction? The trickiest aspect of this is that most of the forces we understand are central forces. This means that if something in the 3d surface is not in-plane with the 2d surface, the forces it applies are "out of plane." This is a huge problem for Obsidian knives. If a torque is applied to the knife, it is brittle and the edge snaps. It's 2d nature is brittle and weak in the 3rd dimension. You would have to have a physics which deals with this.

One interesting solution to this might be to have the surface curve in response to out of plane forces, curving until the sum of all forces is in plane (at which point the physics would behave sanely again)

Another interesting question would be what if your N dimensional space was not a subspace of the N+X dimensional space. If the N dimensional space is a subspace of the N+X space, you have a N+X dimensional manifold, which is easy. But this doesn't have to be true. Consider a funny space which consists of the surface of a sphere (2 dimensional space), where each point on the sphere has a "hair" attached to it (a 1 dimensional line). This is not a manifold, and the physics of what happens are harder to define with calculus. A 2 dimensional object would be confined to the sphere because it's too high of dimension to fit into any of the threads. There would be some interaction at the surface where the surface and the hairs meet, but it requires some special effort to define how they should interact there.

Answer 9

Well i want to give my 2 cents as well xD

So, as others such as Starfish Prime have pointed out the answer depends on what you want it to be. And i dont agree with anyone saying Yes or No. I consider those dishonest answers. We dont know how such interactions would work and accordingly anything said is pure speculation with no evidence. No matter how much some want to use "Science", the fact of the matter is that we dont know.

With that disclaimer, i would approach the answer to this question with an example our brains can imagine. Flatlanders. I.e 2D beings.

We know that it is Mathematically impossible for us to interact with a proper 2D world because dimensions really dont work that way. There isnt some huge XY Plane dividing the universe into Positive and negative coordinates. So the notion of a 2D world is fairly ambigues as it is. But, if we assume for the sake of argument that this 2D world lives on the surface of a magical sphere we can make some predictions. The Sphere is a 3D entity, so we can interact with it. Even though the Surface is 2D.

So how might Flatland look to us ? Well honestly, it would probably be pretty empty because we comprese an entire Universe into a finitly sized sphere. So chances are anything interesting happens at scales approaching the Planck lenght.

If we again just assume the scales are large enough that we can make observations, we would almost certainly be able to directly interact with the Flat Landers. Because as a higher entity we could for example move somthing through the 3D Sphere. Though the question here is if the Sphere is solid or in what way interactions obey the laws of physics. For example, in Flat Land (so on the Surface of the sphere) Gravity would be an inverse law, not inverse square. So Gravity would be significantly stronger. Same with all other Forces, such as the Strong, Weak and Electromagnetic interactions. Chances are, the moment we for example send a small sphere to pass through Flat land it will almost instantly collapse into the equivilant of a Neutron Star or Black Hole as there is SO MUCH mass so close together.

Meaning for the Flat landers, any interaction we have with them would be very destructive. But again, this depends on the scales envolved. If what we send through is, from their POV, the size of a Galaxy the consequences will be more significant.

Another thing to point out is that by definition, the Constants of the Universe in Flat land are drastically differnt, so it could be that the Energy we send into Flat Land is way more or way less destructive.

Now, during all of this we have not talked about them ain question, can the Flatlanders interact with us ? The answer is, yes and no. They cant send anything out because they exsist on the Surface of a sphere. They are 2D and 2D objects cannot exsist on their own in our universe. Hence why the only way for us to interact with them is if Flatland is a 3D sphere. If Flat land was not closed we couldnt interact with it.

The Flat landers migth be able to interact with objects we send in assuming those objects stay in the right shape. We could for example establish a very simple Morse code since we can just look at them and see what they are doing. But this is very one sided since one party sees everything while the other cannot imagine what we look like.

It is a resonable assumption to make that these principles also apply to n+ Dimensions for us. If there is some 5D entity, it could prosumably only interact with us if the Universe is a Hypersphere or some other closed shape. If that is the case they can make the same attempts at communication. And the same differences apply.

In a 5D world, Gravity is a inverse cube law so it is SIGNIFICANTLY weaker. Same with the other forces. But the difference is not as bad as with the jump from 2+1 to 3+1 Dimensions. (Remember, Flat Land still has a time dimension).

Weather or not they could slide into us is also answered, Yes prosumably. We could push a rod or whatever through a Flatlander so higher entities prosumably could do the same.

But remember, to us that wouldnt be "sliding in", rather a n-1 shape would appear. As in, we push a 3+1 object into Flatland and they see a 2+1 object. Same with higher dimensions. If a 4+1 entity pushes a 4+1 Rod into us, we see whatever that shape is in 3+1 dimensions. Which mathematically is the crosssection but for higher dimensional shapes that is a bit hard to imagine.