(See below at /time traveling tropes/ for comments thereupon)
: Don Kuenz <firstname.lastname@example.org> : Throw Complex Variables up against the wall. Does that stick? No. : The infinity used by Complex Variables is just the same old infinity : used everywhere else. Time to try, try again.
I don't know about stickiness (other than that it's the most underrated of the nesses), but "same old infinity" seems to be headed off in the wrong direction, since the various infinities (as cardinalities of sets, as in Cantor discussed upthread) are more than one.
: A story such as "The 4-D Doodler," that speculates about a fourth : spacial dimension, one dimension beyond our known world of three : dimensions, seemed promising to me, the dilettante, at first. Perhaps : 4-dimensional space uses an exotic infinity. Alas, as Wolfram notes, : it's the same old infinity. An infinity that's independent of spacial : dimensions.
It's c, or aleph-1 maybe, or whatnot. It is not the infinity of natural numbers; it's bigger. So there's at least two infinities, not the "same old infinity". Similarly, the cardinality of the set of paths in n>=2 d space (if I'm remembering a close enough description) is bigger still.
Of course that depends on what "uses an infinity" means in this context. "Cardinality of sets of points such that X" is what I took it to mean.
: In other words, the infinity that occurs at the ends of a line in : 1-dimensional space is the same old infinity that occurs along the : vertical axis when one takes the tangent of an angle in 2-dimensional : or 3-dimensional space. By induction, it is the same old infinity : that occurs with the taking of tangents in hypothetical 4-dimensional : space.
Well, you mostly lost me. Maybe you're talking about the hyperbolic asymptote, or the limit of tan(a) as the angle approcahces 90 degrees? Why would anybody expect the behavior be changed if you just change dimentions in which you are still drawing a line? Or is there some special n-dimentional tangent of which I've previously been unaware?
Now... if you're talking about the limit of the value of tangent as the angle approaches 90 degrees, I see no reason to expect that to change no matter how many superfluous dimentions it's done in. If you're talking about the cardinality of a set of points in n-dimentional space, I suppose that *is* a bit counterintuitive to be one of those things that doesn't change when you change the value of n, nor change even if matching subsets to the whole set. But... juxtaposing them as above in ":" is peculiar at the very least.
In any event, the "limit of the value of tangent as the angle approaches 90 degrees" isn't quite the cardinality of a set, so the two aren't the "same old" anythings. Or so I conclude.
So... most of ":" seems to me... forgive me, word salad. And what with the oily dressing, word salad never sticks. (Of course, doubtless much of what I've blathered above is likewise word salad, but so it goes.)
: There now. Does that help make everything as clear as mud? :)
Approximately, yes! Well, at least it seems to provide a clearer picture of the boundaries around the area of mud-clarity, so that's good.
"We demand rigidly defined areas of doubt and uncertainty!" --- philosophers' spokescritter in HGTTG
: At any rate, it's time for me to take a back seat to Butch Malahide : and others who specialize in SciFi's Cantorian tropes. (FWIW, SciFi's : time tropes captivate me.)
I keep saying I dislike SF's time traveling tropes, since most of them, as actually used in stories, make little sense, and/or have little self-consistency. But then, I keep ending up enjoying stories with time travel in 'em (oh, say, like Girl Genius, at least so far, but I'm a bit paranoid about where they're going with that), so clearly my dislike isn't as strong as I might like to make out.
 Examples: the meta-time that's quite rampant, as in BttF, where the protagonist is "fading away" as is his photo of his family. This requires that there be a time outside of time for time changes to change... things. It's not sensible at all, but it's a trope that occurs over and over and over and over and over. Ad infinite nauseum.
Or how about the digital chronometer in the Trekverse; not one that's been set up to track time travel changes, just the chronometer on the bridge. In "Amok Time" (iirc) when the Enterprise inadvertenty timetravels, it runs backwards... but nobody's body or metabolism nor nuttn runs backwards? How does the clock know better than any other physical process? An "ordinary clocks are magic" trope that gets used many many times in many many stories both trek and non-trek.
Or how about the dropping-into-a-tunnel-while-time-related-things- such-as-clocks-and-calendars-drift-by? I think one of the Teen Titan's episodes qualifies, but I've seen it in visual depictions all over the place, and I've seen other folks commenting on the peculiarity of it. (The New Who tunnels are better, but I digress) Why would things only symbolically connected to what you are doing suddenly show up? Magical thinking? I suppose it could be a halucination. But how about the "reset an enchanted (and/or nanotech) clock, and resetting the time it displays resets the universe" (or some subset thereof)? Where's the sense in that? OK, "it's magic" makes it make "sense" in a sense, so it doesn't need to make *proper* sense, but still, I sense bogosity there. A disturbance in the computronic field. (See: quantum bogodynamics)
(You may mean "trope" in a slightly different sense than I've taken it, in which case "never mind...")
ANYways... depiction of time travel in word and vid alike is more often wonky than not. Even Zelazny's "Roadmarks" is less wonky than most, and it's seriously wonky. That's my story, and I'm sticking to it like the sap of the maraca nut tree.
For at least somewhat less-wonky depictions of time travel, see "By His Bootstraps", possibly "The Door into Summer", possibly 'The Man Who Folded Himself", "Thrice Upon a Time" (to some extent), and singularista variants like "The Chronoliths" or "Iron Sunrise". The latter two proposing constructs of various kinds that occur along closed timelike loops, and basically end up quantum-interfering with anything that conficts with themselves, hence eliminating annoying metatime, and integrating predestination with free choice, in a sort of quantum sense. Interesting stuff, and less wonky than most. IMO; other folks' mileage may vary. Possibly even things like Swann's "Hostile Takeover" series, which is sort of nigh-singularista in nature (and I believe even has a slight connection to his Franks/Moreaus-iverse, so that's cool).
 Well, the Eschaton interferes with considerably more than quanta at one time or another, but I'm mostly refering to the "interference" between the Big-E, and the Space Nazis. 'Course, that's a bit different than the Chronoliths, since it exposes an intermediate state to observation, which the Chronoliths never do. OK, so maybe these weren't as similar as I was expecting, but there's a *vague* similarity still, despite the difference in detail of propogation of disturbances in the temporal flux. I suppose they'd be pretty much identical if the ending state contained the anomalous conflict preserved in temproal amber so to type. But sadly, we'll never know the outcome of the Big-E vs the Space Nazis, and whether it involved Alternate Time Lines (of which the final state is aware), ATL (which get wiped out and is just an authorial device), or It Was Always Like That. Tsk tsk.