| Let's try to create the tesseract anyway. Using two fingers, stretch the cube out into a tesseract. In the event that you observe worrisome fractures opening up in the spacetime continuum in your vicinity, please turn off your iPhone at once. |
| There's no way to fit a cube into your two dimensional universe, but the shadow of a cube can fit. From the point of view of the 2D creature, the cube's shadow has popped into existence in the flat 2D space right in front of it, surrounded by a glowing circle. Spin the cube to see how the shadow of the cube changes as the cube spins in 3D. |
| Spin the tesseract some more, using both 3D and 4D rotations. Watch what happens to the orange cube. This is easiest to understand if you make only one very small 4D rotation at a time, following each with a series of 3D rotations to see how your 4D rotation affected the tesseract's shape in 3D. |
| Let's try to better understand how a cube's shadow changes as it rotates in 3D. We'll color one side of the cube orange so we can follow it easily. Notice how the orange side of the cube that is farthest away from the light appears in the shadow as the small square. |
| In the third dimension, we have no way of directly seeinga tesseract, because it exists outside our 3D universe. However, just like we cast a cube's shadow into 2D, perhaps we can cast a shadow of a tesseract into 3D. How would that work? |
| Earlier, we cast a shadow of a cube onto a flat surface, from 3D to 2D, making it visible to an occupant of the second dimension. In the same way, we can make a 4D tesseract visible in our dimension by casting its shadow through the fourth dimension onto a volume of 3D space. Read that last sentence over a few times until the screaming in your head stops. |
