And why does Kara's ship spontaneously appear in a lake on Earth (while the Omegahedron fell from the sky)? I generally like the movie but the Innerspace stuff always bugged me. They could have at least explained how Argo City got there and what it's relation to Krypton was.
In the Comics, Argo City is a City on Krypton that somehow survived the planets destruction as it was blown out into space.
The movie has Innerspace kind of like a different dimension within our own. Not sure how that worked really, and how Argo City got there I don't think the movie says.
Innerspace is what at least Kara's community of Kryptonian refugees called interdimensional space.
I'm sure you heard Zolton chastizing Kara for not doing nearly so well in Sixth Dimension Geometry....
Well, the first three dimensions are up/down, left/right, forward/backward, or what we call space. The fourth dimension is time, which really can be argued as being a two-directional dimension, not just the one-direction way of looking at things on a timeline. The first four dimensions are pretty scientifically and mathematically sound.
The fifth dimension is at this point still pretty much entirely a theory, but is the basis for every sci-fi story's faster-than-light travel of getting to very far away places in much less than the multiple lifetimes that current technology would actually require for interstellar travel.
Some sci fi stories (A Wrinkle in Time) call it a tesseract, where space and time are found to fold and allow a traveller to step from the peak of one fold onto the peak of a formerly distant fold, in one single step, going from one planet to another to another in quite literally a matter of steps, no extra technology involved.
Some sci fi stores (Stargate) call it a wormhole, where the folds are already always there, but the peaks are never where you would want them to be, so, instead, they have a piece of technology that allows you to bring the fabric of multiple folds together in one place, and very temporarily bore a hole all the way from the first one to the final one, getting you wherever you want to go, so long as the technology already exists at both ends.
Some Stories (Star Trek) don't even try to explain it, but simply call it 'hyperspace'.
What the above stories all share in common, however, is that Fifth Dimensional travel is exactly that: travel. Point A to Point B, go in, come out, go into warp, come out of warp, etc. There is nothing inside the Fifth Dimension to allow anybody to actually stay there.
That's where the sixth dimension comes in.
The much more theoretical, much less scientifically conceievable Sixth Dimension, is in some way a fold within a fold or a warp within a warp, or something, which allows not just interdimensional travel, but, allows for some sort of interdimensional residence.... taking space... ergo in..er..space, or innerspace.
Superman's father, Jor-El, was one of Krypton's most noted leaders, politicians, and scientists, with the rather annoying habit of predicting Krypton's doom and total destruction, which most of the folk on Krypton not only wanted to ignore, but to censor.
Jor El, therefore, was not allowed to use any of the many ways he and his teams of scientists ever thought up for saving as many of the folk of Krypton that they could.... but he did send his relatives, as many as would, into as many of those tests as he could, in an effort to save them.
Superman was always meeting up with extraterrestrials who knew someone who knew someone who knew someone who was related to the great Jor-El, and therefore, related to him, playing on the six degrees of separation between everybody in the universe.
Argo City is just one of the MANY small communities of Krypton refugees that got saved by Jor-El and his scientists.
My take on that is that Argo city never did actually leave Krypton like Kal-El's spaceship did, but they used the super-power-sources dreamt up by Jor-El and his scientits to simply put the entire city into interdimensional travel, without a destination, and keep it there, until after their star went supernova, when they no longer had a place to go back to....
and that the entire reason that their community was so keen on teaching their children to think sixth dimensionally is so that perhaps one of them might find a way to find a destination for their entire community, not just the one little one-man ship which allowed them to keep in touch with Krypton until the supernova event.
Argo City appears to me to be a place where it took some great minds to get them into innerspace, but unfortunately, none of those great minds stayed with them when their star went supernova, so it became up to the children to learn enough to some day get everybody out of innerspace and back into the real universe.
This also explains why Kara, whose whole community survived Krypton's destruction when she was a young teen is still a young teen when she reaches earth, while Kal-El, who left Krypton on the eve of that same disaster still wearing diapers has become an adult.
It also explains how Kara and everybody in Argo City know of Kal-El and his destination being Earth, which also never got explained in this movie.
It required the audience to do a bit of reading between the lines.
Wait a minute. Argo City is in trans-dimensional space. The barrier between Innerspace and Outer Space, which Kara gains her superpowers and becomes Supergirl, is a doorway between universes. Instead of the doorway opening up in outer space, the doorway opened up in a lake on Earth. I don't know much about trans-dimensional space. But I do know it's about trans-dimensional wormholes.
About the lake...water is often said to be a porthole, or wormhole for time travel/space travel etc. Remember the film "Kate and Leopold". In order to get back in time, Leopold has to jump into the Hudson River at just the right time and distance to get back to the 16 or 1700s.