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You see, while the mathematicians have been studying their manifolds, the beekeepers have been baffled by a mystery of their own. For millennia, they’ve been puzzled by an odd little routine that bee scouts perform when they return to the hive. Known as the waggle dance, this strange performance sees the scout moving through series of loops and figures of eight, while vibrating the back half of its body at various points in the process. This seems to provide the other bees with strikingly accurate directions to the best sources of pollen, though how on earth the scout bee is able to transmit such complex data through such a simple little dance has always been a mystery. A mystery, that is, until Barbara Shipman looked at the shadow of her flag manifold and saw in it not the complex geometry of a theoretical six-dimensional shape, but the familiar waggle dance of her father’s bees.

It’s easy to forget in the midst of day-to-day life, but logical conclusions needn’t always be boring, pedestrian things. Sometimes, a logical conclusion is so wild, so wonderfully bizarre, that only the fact that it is a logical conclusion allows any sane person to imagine it in the first place. The logical conclusion to be drawn from Barbara Shipman’s observations is this: though we as human beings live our lives entirely in the familiar three dimensions, bees do not. Bees are fully aware of, and see and communicate in, six-dimensional space. What does that mean, practically speaking? What does the world look like to a bee? What do we look like, going about our three-dimensional business? It’s impossible to say because the human mind is completely incapable of comprehending the answers to these questions. There are some things out there that we simply cannot understand.

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