Does anything exist in only 1 or 2 dimensions?

Aside from the fictional 2-D beings in one of the episodes of Star Trek: TNG, what observable things exist in less than 3-D? Photons? Sound waves?

Rainbows. Or is it that they can only be seen from one side?

I’m not a physicist, but I was under the impression that electrons are thought to be zero dimensional.

A shadow.

Electrons are physical objects with mass and size.

The concept of single or two dimensional space is miseleading. Describing space in three dimensions (with time as a fourth) is just so we can visualize things in orthogonal measurements.

Those are not things, just optical effects. A kind of thing that exists in only one dimension (length) is a string singularity. I can’t find any cites for that, just some memories from things I read on quantum physics.

The only thing I can come up w/ is a black hole if all mass does compress to a single point, then again that would be 0d

The electron is known as a point mass and has a radius of less than 10[sup]-18[/sup]cm. It hasn’t been proven yet, (and may never be) but the electron is certainly as close to a true one dimensional object one can get.

I read this in High School, and have a copy of it somewhere. I actually FOUND the complete text of this book on the Internet, and was about to paste in a link.

But… copywrighted materials are sacrosanct here. So, all I can do is recommend the novel called “Flatland”, by Edward Abbott. It’s an incredibly revealing look at dimensional math. For once, providing a link here would have crossed some lines. Go, find the book, it’s astonishing.


Anything you draw on a piece of paper is 2 dimensional (unless you draw a dot, in which case it is one dimensional).


What about Al Gore?

Bwahahahahahahahahahahaha. I kill me.

Actually, it’s not, because both the paper and the ink/graphite lines used to draw the object have height, even if it’s only measured in nanometers.

We call flat art two-dimensional, but that’s just an informal term, not used as a mathematician or physicist would use it.

What about the image currently displayed on your monitor. The glass may not be two-dimensional but the image seems to me like it may qualify.

Basically in a 3 dimensional place like our universe, nothing in 1 dimensional. Even though an electron is extremely small,we can always talk about half an electron. Basically whether something exists as 2 dimensional depends on how you look things. You can say a height of ‘1’, the smallest measurement, is 10^-32 cm or 10^-64. People thought protons and electrons were as simple as things got, but they discovered quarks. I also believe we know of particles that make quarks up, but i don’t remembered naything about them.

I love Flatland, a Romance in Many Dimensions by A Square (Edwin A. Abbot). I agree with *Cartooniverse, it’s astonishing. It is an amusing fantasy that takes place in a plane. There have been several sequels. I have a copy of it together with SphereLand, A Fantasy about Curved Spaces and an Expanding Universe by Dionys Burger, IMHO, the best sequel. It takes off where Flatland ended and tells how the inhabitants of Flatland come to realize that their universe is curved and expanding. Flatland and Sphereland are both classics.

Isaac Amimov says the following in the introduction:

I thought posting a link to copyrighted material was OK, you just can only post short excerpts.

In answer to the OP: The number of dimensions is just how many coordinates we need to specify where (or where and when) something is. There are definitely things have fewer (or more) than three dimensions. If you are at sea, your location is two dimensional. Is your location observable? I’d say yes. You want something one dimensional, how about time? Time sure is observable.

An invisible collumn between an object and the shadow it casts makes it 3 dimensional.

I don’t have a link to it, but just FYI, because Flatland was published before 1923 (in the 1880s IIRC), it is no longer under copyright and is under the public domain. Therefore, any discussion about whether or not it is acceptible to post copyrighted material is moot in this situation.

Hmm. Not really, I’d think. It just means the two dimensional thing is curved in three dimensions. I think there’s a difference between that, and saying that it actually IS three dimensional. But I could be wrong. …but isn’t that sort of the current thinking behind what gravity is? Four-dimensional curves affecting the three dimensions we percieve in our universe?

Anyway, along those lines, I’d say a reflection on a mirror is also two-dimensional.

In case you’re wondering why I care, discussion in other threads about the properties of our universe refer to a 4-D hypersphere. I couldn’t find a definition for that term on Merriam-Webster’s site and I can’t imagine a 4-D hypersphere since I’m in 3-D. It got me thinking about 1-D and 2-D planes of existence.

Flatland sounds like an interesting read. I’ll check it out.

I shouldn’t have limited my OP to “observable things.” Are there any theories about “sub-3-D” existence?

Some people are talking about superstring theory. This is where you get these two dimensional ‘string’ thingies, but it only works if there are 9 dimensions (I dont know why, and any sites about it would probably be too dificult to understand anyway unless you had a degree in quantum physics. RyanD004, you cant have half an electron. Black holes dont condense to a point, they are just very condensed material, and they are 3 dimensional. just think of them as a very small sphere. Sci-fi tv programmes etc. give people the impression a ‘black hole’ is like a hole in a piece of paper (ie a circle) when it is a sphere.