Jeopardy! category: A BRIEF HISTORY OF TIME (05-05-2014)

$1600 clue: Following Einstein, in 1908 Hermann Minkowski proposed the idea of 4-dimensional this hyphenated term

**The gist:** Yes, Minkowski followed Einstein with his theories, but Einstein also followed him – Minkowski had been Einstein’s professor at the ETH Zürich, an institute of technology in SwitzerlandAfter Einstein proposed his special theory of general relativity in 1905, Minkowski proposed a geometric understanding of *space-time* in which time becomes the imaginary (that is, the part multiplied by the square root of -1) fourth part of the spatial dimensions. In this new understanding of space-time, Lorentz geometry, which describes how the speed of light is constant regardless of reference frame, can be represented. Eventually, the imaginary bit of Minkowski’s theory was dropped, and he re-evaluated his fourth dimension as just another like the first three, expressed as *x*, *y*, *z* (the three dimensions we think of as “space” when we’re not doing advanced physics), and the new one, *t*. It’s in this four-dimensional milieu that physical events take place, and where each event’s light cone expands outwards as a four-dimensional cone. The light cone is the radius from the event that something travelling at the speed of light could reach, thereby defining the region of space-time in which the original event could plausibly cause another event. I hope you followed that, because I don’t think I did.

**The clue:** “The idea of 4-dimensional this hyphenated term” – a little awkwardly worded, don’t you think? Anyway, the really big clue in this one is the offhand mention of Einstein. When you see something added to a clue like that, when it the clue could easily stand without it, it’s a good bet that the writers put it in to make it easier, implying that it might be the key to the correct response. In this case, the term “space-time” (which isn’t really *always *hyphenated, but we’ll let that slide) is very strongly associated with Einstein, and particularly when dimensions are added to the mix.

**In Jeopardy!:** Well, at least the show is internally consistent, since “space-time” appears in 10 clues in the J!Archive, and “spacetime” appears none. There’s even one other clue that mentioned its hyphenated-ness. Einstein is mentioned in four of the clues, and four mention a “continuum” as well. There isn’t much in the way of patterns to look for, except that if the clue is about physics or relativity and mentions dimensions, continuums, or something like that, it’s likely going to be about space-time, with a hyphen.