Dimensions - Sixty Symbols

What would life be like with just two (or four) dimensions?

Flatland: A Romance of Many Dimensions by Edwin Abbott.
The Planiverse by A. K. Dewdney

This project features scientists from The University of Nottingham

Sixty Symbols videos by Brady Haran

[TheMilwaukeeProtocol]

The sphere versus a circle that changes sizes is very insightful but got glossed over pretty quickly. XD

[sixtysymbols]

thanks - you can show Pete (the artist) some love by checking the link in the video description!

[Archlyche]

So in 4 spacial dimensions, escape velocity would be easier to achieve than it is in 3?

[lpfplus]

Rudy Rucker’s book “The fourth dimension and how to get there” is great for these thought experiments. I first read it 30 years ago and it still comes to mind whenever trying to picture other dimensions.

[mistycremo]

Escape velocity would be achievable! It would just be nearly impossible to reach it. Also, by the logic that in two dimensions, Gravity is one over distance, then gravity does not dissipate in one dimension.

[MathAndComputers]

To give half an example, one point in a 4D cube can be viewed as 4 points on a line segment, where the single coordinate of each of the 4 points corresponds with one coordinate in the 4D space. If the 4 dimensions aren't the same size/shape, you can use 4 separate line segments, and if one dimension depends on the location in another (e.g. surface of a cone; height on it affects radius of circle around other direction), you can vary even the size/topology of each as necessary.

[fakjbf]

Two questions, it would be great of someone could explain them to me

1) For the escape velocity example, wouldn't that be working on the assumption that the mass of the 2D object is the same as that of the 3D object? In 2D it would have far less mass, so while the rate of gravitation drop-off would be less, the actual amount of gravity you are having to overcome is also less.

2) Is graphene REALLY only 2D? Yes it's only 1 layer of atoms thick, but atoms are 3D. The electron orbitals don't all line up in one 2D plane, they go out in all directions. So while the distance across would be extremely small, it is not zero.

[nathanokun]

Higher dimensions has problems too. Knots that cannot be untied by themselves (need somebody to unravel them so that they can hold things together solidly by themselves) cannot be made, from what I saw in a video once, which greatly removes many things we can do in 3 dimensions. (Turns out things like knots are important in many, many things!)

[Xaio]

"...eleven spacial dimensions."
*spits out drink*

[sixtysymbols]

See link in video description for a chance to get some of Pete's original artwork in this video!

[bobkilla]

Great vid but I wish they would have explained a 4th dimension more.

[whotookmybadjas]

It is very good of you to question these things, this makes a good scientist. You kinda have to get into these mathematics and suprisingly you'll start getting a feeling for certain problems and know from the start what the answer will look like. Experience mixed with talent/intuition is key.

[PhelanVelvel]

I loved Flatland.  :D  It was cute and funny enough that I think kids would like it, but it also brings up a lot of interesting ideas about perspective and reality.  Very cool book.

[naotak]

This video was fascinating. You should consider having Mike do a video explaining what the problems with the Kepler spacecraft were/are. Maybe something about what that this might mean for its future and for the engineering of other spacecraft.

[ianremsen]

I don't understand what one means when they say a dimension is 'small' or 'bunched up'.

[Veon]

It's not just for gravity, the power law applies to anything that radiates from a point (so, for instance, electromagnetism also decreases like 1/r^2 in 3d and 1/r in 2d, same thing for sound, circular water waves, etc). Like AlanKey said, what matters is that you are spreading out over the area of the surface of a sphere, which grows likes r^2 in 3d. In 4d it would go like r^3 because that's the area of a "3-Sphere", etc. If you want to know the maths just google "Gauss Law".

[alektad]

Graphene still has probability to has its electrons outside the 2D plane. And if you break it, you will definitely be convinced it is 3D. One thing that is always 2D is shadow, but the problem with shadows is that they don't really exist. The concept of a shadow only exist in our heads, because we are capable of perceiving lower dimensional spaces, even though they do not exist. 

[werdnativ]

Those animated segments are a marvelous addition to these videos!

[gpd]

You could use the same orifice for eating and.... exiting out what's left after digestion.

[BKBrunelle]

I would love to see this conversation cover more dimensions and go on longer than 7 and a half minute. I could listen to a 45 minute talk about the subject and I would rather enjoy it very