A Spooky Refrigerator

Christina notices that food is disappearing from her refrigerator and yet her surveillance camera shows that no one is opening the door. Suppose our 3-D spatial world were really a 4-D spatial world, but we did not know anything about the existence of the fourth spatial dimension. There is still the single time dimension. Could a 4-D being remove food from her 3-D refrigerator without opening the refrigerator door?

Answer

Yes. Just as you could remove a dot from a piece of paper with an eraser brought in from the third spatial dimension, a 4-D being could enter the refrigerator without needing to open the door and remove a piece of food. That is, 3-D objects are open in the direction of the fourth dimension. Conceptually, visualizing a 4-D object is difficult in our 3-D world.

Some mathematicians suggest letting the fourth coordinate direction be represented by flashing color, such as the sequence of colors in the visible spectrum from red to indigo. Take any 3-D object a sphere, for example. As the sphere moves in the fourth coordinate direction its flashing color changes from red to orange to yellow, etc. A 2-D sheet of paper moving in the fourth dimension would be changing its flashing color also to indicate its fourth coordinate value. The inherent color of the object does not change, of course. Descriptions of 4-D objects intersecting our 3-D world are quite fascinating. For example, a 4-D sphere intersecting our 3-D world would first appear as a point, then an increasing 3-D sphere, then a decreasing 3-D sphere, then a point, then gone! The analog in fewer dimensions would be a 3-D sphere intersecting a 2-D sheet of paper, being first a dot, then a widening circle followed by a narrowing circle, then a dot again, and then gone.

Although most people would expect there to be more mathematical difficulty and complications in even higher dimensions than four, this expectation is false. The mathematics actually simplifies with five dimensions and more! Much geometry remains to be worked out in a 4-D space, whereas the mathematics is better understood in the higher dimensions.