OK, I’ll admit it, back in the day I read a lot of comics. Even then, though, I was skeptical — “Wait, how could Superman just pick up that building? It’d fall apart!”
But I was intrigued by one recurring character, Mr Mxyzptlk, a pixie-like “visitor from the 5th dimension.” His primary purpose in life (other than getting us to buy more comics) seemed to be to play tricks on or otherwise torment Our Hero.
Mxy wasn’t the only comics character coming in “from another dimension.” It seemed like the entire Marvel team (both sides) was continually flickering out of and into our universe that way. How often did Jane Grey die and then somehow get cloned or refreshed? (BTW, if the accompanying cartoon is a little obscure, show it to the friendly clerks at your local comics store — it may give them a chuckle.)
But my question was, where was that dimension Mxy came from? I got an answer, sort of, when our geometry teacher explained that a dimension is just a direction you could travel. Different dimensions are directions at right angles to each other. She was right (see my first post in this series), at least in the context of then-HS math, but that explanation opened an editorial issue that’s never been properly settled.
A dimension is a direction, not a location. You can’t be “from” a fifth or sixth or nth dimension any more than you can be from up. If there is a spatial fifth dimension, we’re already “in” it in the same sense that we’re already somewhere along east-to-west and somewhen along past-to-future.
What’s going on is that for the purpose of the story, the authors want the character to come from somewhere very else. We often associate a place with the direction to it — the sun rises in the east, Frodo departs to the west, Heaven is up, Hell is down — but those are all directions relative to our current location. We even associate future times as being in front of us and past times behind us (there’s that 4th dimension again).
But a place is more specific than a direction — to navigate to a certain there you need to know the direction and the distance (or another quantity that stands in for a distance). That matters. Jimmie Rodgers sang, “Twelve more miles to Tucumcari” as he kept track of the distance left to go along the road he was traveling. Or away from the town, as it turned out.
Physicists have lots of uses for the combination of a direction and a magnitude, so many that they gave the combination a name — a vector. The vector may represent a direction and a distance, a direction and the strength of a magnetic field, or a direction and any quantity that happens to be useful in the application at hand. A wind map uses vectors of direction and wind speed to show air flow. Here’s a very nice wind map of the US, and I love NOAA’s wind map of the world. Vectors will be real useful when we start talking about black holes.
OK, so Mr Mxyzpltk (the spelling seemed to vary from issue to issue of the comic) comes from somewhere along a fifth dimension, but they never tell us from how far away.
Next week –As Steve Martin said, “Let’s get small, really small.”
~~ Rich Olcott