Fourth Dimension
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What is the fourth dimension?

It depends on who you talk to-some people think it's the dimension of time, like in Donnie Darko. Others think it's another dimension of space, like the designer of the game Miegakure.

No one's quite sure - the fourth dimension mystifies even scientists like Michio Kaku, who said he felt like Alice in Wonderland after reading up on it. However, two new studies published in Nature have started to give a better picture of the fourth dimension.

Two teams of physicists created two separate experiments that simulated what the quantum Hall effect would look like in four dimensions by using only 3-D (and some nearly 2-D) materials. Essentially, the scientists figured out how to visualize fourth-dimensional phenomena in our lower, simpler third dimension.

The applications of this are still incredibly abstract, but there may be some sci-fi levels of payoff once we wrap our heads around the fourth dimension, according to Mikael Rechtsman, one the authors of the new papers: "Maybe we can come up with new physics in the higher dimension and then design devices that take advantage the higher-dimensional physics in lower dimensions."

If you're wondering what the quantum Hall effect is, you can watch this short video explaining it:

It's understandable if all this gets a little confusing-as we mentioned, even Michio Kaku was mystified by the fourth dimension.

Even the abstract of one of the new studies is nearly impenetrable to anyone without a degree in advanced physics:
When a two-dimensional (2D) electron gas is placed in a perpendicular magnetic field, its in-plane transverse conductance becomes quantized; this is known as the quantum Hall effect1. It arises from the non-trivial topology of the electronic band structure of the system, where an integer topological invariant (the first Chern number) leads to quantized Hall conductance.
Sometimes it's helpful to take a step back and try to think of the fourth dimension in terms that don't involve 2-D planes of electron gas. Here's Carl Sagan describing it: