the (negative-3)-dimensional sphere

A 2-sphere ("2 dimensional sphere") is what you'd normally picture as a sphere, such as the surface of the earth. A 1-sphere is a circle. And a zero sphere is just a point. Higher dimensional spheres (hyperspheres) are also used a lot, both in math and physics (for instance, the large-scale structure of space in our universe most likely has the topology of a 3-sphere.) But today in Algebraic Topology he asked "do any of you know what a negative dimensional sphere looks like? say... a -3 dimensional sphere?" WTF?!

After a lot of blank stares, he asked the question again, followed by "c'mon, take a guess. be creative... anyone have any idea? Algebraic topology is so flexible, we can deal with negative dimensional objects very easily." Still a bunch of blank stares. One person then asked if it's the locus of points distance -1 from the origin. Clever, but obviously not right. "Nope, that's the empty set." He continued to ask us the same question... as if by asking us enough times, we'd suddenly go "aha! I can picture it now!" So he finally told us to go home and meditate on it. What a fun class! I'm still meditating, but I still don't have any ideas. Anyone know what he's talking about and want to give a subtle hint?

P.S. Got my colors done--haven't had a chance to take pictures yet.