If something was living in what for us is a 2d space

[Kyriakos]

If something was living in what for us is a 2d space, would that thing ever be able to be in contact with anything from our own perceived environment?

It seems to me that it would not. Most people may think that a 2d space is just a part of 3d space, but mathematically any 3d space has an infinite number of 2d spaces. For example you can't get a cube by adding any finite number of squares.

From that it seems to follow that the 2d space doesn't evolve to 3d, and likely a 3d space cannot devolve to 2d. They are not in the same 'space'.

Sometimes one can claim that for a theoretical observer from a 2d land, a vertically to his plane-world moving sphere would appear to him as expanding and then decreasing circular peripheries. I don't agree, cause i think he would not see anything at all. I think that the 3d object doesn't exist in the 2d space. It doesn't get translated to 2d for a 2d-capable observer, cause i think a 2d-capable observer is not in existence (by which i mean that i think his own world would also be in 3d, but in a different 3d level, one which is not the same space as our own).

*

Anyway, the topic is whether in your view the three spacial dimensions are just a chance system which humans are working with due to the senses, or if 3 dimensions of 'space' may be there for any other intelligent being with sensory input of space- including when the dimensions themselves are not our own and thus his world would never be part of our own or vice-versa.

 

[warpus]

Have you recently read Flatland perhaps?

It's a very good book! This is a somewhat interesting subject.

From that it seems to follow that the 2d space doesn't evolve to 3d, and likely a 3d space cannot devolve to 2d. They are not in the same 'space'.

They can be, mathematically speaking, if you define them to be. A 2D plane can easily exist in a 3D vector space. But I have a feeling you are trying to say something else here (I'm just not quite sure what)

 

[Gigaz]

Now if I had the task to communicate from my 3+1 spacetime with another being that lives in a surrounding 4+1 spacetime, the most robust approach would probably be by each of us changing the curvature of his universe.

 

[Borachio]

Flatland was good.

I think it's a lot more interesting to speculate what being a 4d object in 3d space is like. Since that might turn out to actually be our experience.

And wasn't that the point (!) of Flatland?

 

[Antilogic]

Link to video.

Okay, for the more serious response in an RD, I'm with Warpus. I don't quite understand the point you are trying to make, especially with the y=x^2 graphic.

 

[Kyriakos]

Have you recently read Flatland perhaps?

It's a very good book! This is a somewhat interesting subject.



They can be, mathematically speaking, if you define them to be. A 2D plane can easily exist in a 3D vector space. But I have a feeling you are trying to say something else here (I'm just not quite sure what)

Haven't read Flatland, but i heard of it in the forum many times

Yes, due to the 0-dimensional point axiomatically being able to intersect another (more dimensional) object in math (while in the world of the senses you cannot really pick up any 0dimensional object), and therefore also a 2d plane being able to intersect a 3d shape (eg a plane intersecting a cone, which is what the graphic alludes to, (Antilogic ) since it is about the reason an ellipsis/ellipse was named that by Apollonios of Perga ), you can in such an axiom-based system have less dimensional objects exist in more dimensional ones.
But, as known, the actual matter of the universe is not having to be tied to math. So it easily can follow that there a plane is not really at all part of a more dimensional object (eg a 3d one).

 

[Perfection]

Objects we interact with are made of atoms. Atoms are 3D objects in our universe, if we want to interact with a 2D object in our universe it can't be made of atoms. What it is made of would determine how we'd interact with it.

We can interact with objects like pentominos that appear 2D because of a uniform small width. It is also possible that we ourselves (along with everything else in our universe) are actually more then 3 dimensional objects with a uniform small width.

 

[peter grimes]

But, as known, the actual matter of the universe is not having to be tied to math. So it easily can follow that there a plane is not really at all part of a more dimensional object (eg a 3d one).

How do I communicate that my response to this is analogous to the feces of a bovine in an RD thread

 

[Cheezy the Wiz]

This topic reminded me of this, from the original Cosmos:


Link to video.

 

[Kyriakos]

How do I communicate that my response to this is analogous to the feces of a bovine in an RD thread

Uh... At least read what you wrote. Why would you pre-empt your own response being BS?

(and why do that in an RD thread as well).

As to what you likely wanted to post but confused your own self to not posting correctly: if you don't like the thread you are more than welcome to stay out of it

 

[peter grimes]

"the actual matter of the universe does not have to be tied to math, therefore [insert bizarre speculation here]"

I really don't understand what you're getting at. But it sure smells like bs.

 

[Kyriakos]

^Noted. Maybe we can now return to the RD status, mod?

 

[BenitoChavez]

If something was living in what for us is a 2d space, would that thing ever be able to be in contact with anything from our own perceived environment?

It seems to me that it would not

A 2D being could be in contact with a 3D object as long as that 3D object was in direct physical contact with the 2D plane of existence. For example, take a ball as the 3D object and a piece of paper as the 2D plane. Set the ball on the piece of paper and there is a point on that plane that nothing else could occupy. The 2D being would notice that there is a certain point that they cannot get to.

Objects we interact with are made of atoms. Atoms are 3D objects in our universe, if we want to interact with a 2D object in our universe it can't be made of atoms. What it is made of would determine how we'd interact with it.

Go further down the rabbit hole. Atoms are made of electrons, protons, and neutrons. Protons and Neutrons are made of quarks. Quarks and electrons (might be) made of 1-D strings. If a 1-D thing can exist, why not a 2-D thing?

 

[hobbsyoyo]

Are not very small animals effectively living in a 2D world already? From their perspective at least? I know it's not the same as mathematically defined 2D, but it should give some insight to the question i think.

 

[Perfection]

Go further down the rabbit hole. Atoms are made of electrons, protons, and neutrons. Protons and Neutrons are made of quarks. Quarks and electrons (might be) made of 1-D strings. If a 1-D thing can exist, why not a 2-D thing?

Absolutely could be the case, we just don't know what such a thing would be! So we can't say how it would work and how our electrons and quarks and photons etc would interact with it, it would depend on what it actually is.

Note that one thing that also bears mentioning is 3D space (or more accurately 4D spacetime) itself is a physical thing that atoms (and subatomic particles) interact with.

 

[Atlantic Pacf.]

Have you recently read Flatland perhaps?

It's a very good book! This is a somewhat interesting subject.

Thanks to this thread, I just finished spending half of my life watching the 2007 movie based on it. Between the terrible CGI and the pervasive misogyny (though the latter does stem from the attitudes found in the original Victorian-era book), it has gotten me thinking.

Our Flatlander not only has no conception of obvious things like "depth" or "the up direction," he does not understand reflection or even gravity! What esoteric fourth (spatial) dimension concepts would we not be able to envision? And perhaps religious experiences were all due to visits from beings from the fourth dimension!

 

[Kyriakos]

A 2D being could be in contact with a 3D object as long as that 3D object was in direct physical contact with the 2D plane of existence. For example, take a ball as the 3D object and a piece of paper as the 2D plane. Set the ball on the piece of paper and there is a point on that plane that nothing else could occupy. The 2D being would notice that there is a certain point that they cannot get to.



Go further down the rabbit hole. Atoms are made of electrons, protons, and neutrons. Protons and Neutrons are made of quarks. Quarks and electrons (might be) made of 1-D strings. If a 1-D thing can exist, why not a 2-D thing?

^While in math (ie in an axiom-created setting) indeed a 3d object will be in a 2d plane as a 2d translation of it there depending on the location of the plane in regards to the volume going through it, i doubt this can happen in the external world. The whole point of the thread is to note that maybe in the 'real' world of forms there is no 2d at all for anyone, including any entity which theoretically is living in what for us would appear to be a 2d environment. Maybe there would simply be no contact between the 3d and "2d" in the real space, much like there is no specific middle point in a progression of infinite numbers leading to a limit.

In essense the thread is about the question of whether math is inherently a tool of self-observation more, and secondarily of forming (eg in physics) human-centric theories of actual forms in space, cause those may be something completely outside of the realm of human thought.

(obviously this doesn't mean something against math as a hugely important bit of human logic; it refers to its own limits as a system, which likely are by and large also our own limits as human observers).

 

[Borachio]

Are not very small animals effectively living in a 2D world already? From their perspective at least? I know it's not the same as mathematically defined 2D, but it should give some insight to the question i think.

I've heard this posited before. It's interesting to speculate. Very small animals live in a world effectively without gravity as well, in the sense that it makes no difference whether they fall off stuff or not. I think domestic cats are at the limit. (Or something. I'm not sure.)

Then there's geckos, and things, who seem unaffected by stuff like walls and ceilings. If they think about it at all (which seems unlikely), their views must be pretty alien.

 

[filli_noctus]

Last week I was listening to a radio program discussing the origins of the universe (iPlayer link, the relevant discussion is about 15-20 minutes in but I don't have time to find it - sorry). One theory, which is apparently mathematically sound, that I found intriguing is that our three dimensional universe is a projection on the event horizon of a black hole equivalent situated in a four dimensional universe.

If (if) that theory is accurate it would follow that the event horizons of black holes in our universe would themselves have two dimensional universes projected upon them. I suppose potentially some form of contact could be possible depending on the exact characteristics of Hawking Radiation.

 

[Atticus]

The point of 2D fantasies, IMO, is not the idea that there could be a two dimensional world with inhabitants, but the idea that there could be a four dimensional world, to whose imhabitants we were like those 2D-creatures are to us.

The 2D world is there just for analogy's sake, to facilitate our understanding of what our world looks like from the perspective of higher dimensions.

To speculate whether it is possible or impossible for worlds of different dimensions to interact is IMO idle, as it is only about limiting thought. Perhaps they can't interact, but shouldn't we still be thinking about how they would if the can?

Furthermore, 2D-creatures wouldn't see the ball going through their world as circle, since their vision (analogously to ours') would be one dimensional. They see a straight line, composed of things different colour, some farther than the others. The ball would look to them as a line, whose ends seem to be farther away (given that they have some stereovision capabilities).