We may not be able to step into the fourth dimension of space, but a new formulation of the physics of objects in many dimensions can help us understand what it would be like.
While it is fairly easy to picture a one-dimensional or two-dimensional object, and we interact with three-dimensional objects every day, making the leap into four dimensions is difficult. The 19th century novella Flatland imagined how beings on a 2D plane might perceive 3D objects, but scaling that up into more dimensions isn鈥檛 particularly intuitive.
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Here in the 21st century, we have virtual reality to help. A few years ago, Marc ten Bosch, a game designer in California, made a video game called 4D Toys in which you can move 4D shapes such as hypercubes and hyperspheres around a 3D slice of a 4D space. A slider lets you move your slice across the fourth dimension.
To make the game, ten Bosch first had to figure out how these objects would move and interact with one another. 鈥淏efore, people were thinking about the abstract concept of a 4D shape, but not actually the world around it or the idea that it can be solid and collide with other shapes,鈥� he says.
He devised a using geometric algebra and fluid dynamics to describe how objects move around a space in any given number of dimensions, and used this formula as the basis for the physics in his game. He will be presenting the work at the virtual SIGGRAPH conference this year.
鈥淚t felt like a toy would be a good showcase of this weird physics so you could get a feel for it by playing with shapes and not really worry too much about all the complexities,鈥� says ten Bosch. 鈥淚t could help you build an intuition for these concepts that are pretty inaccessible now.鈥�
He says he hopes that his work will help researchers envision higher-dimensional spaces, like the 11 dimensions that are predicted by string theorists.
