Here she enters a world of chess pieces where everything is contrariwise, or not so much :)
If you take a deeper look, in this case read, it is not as contrariwise as it might look at first sight...
One of my favorite quotes of the book is the one where the red queen says:
"A slow sort of country!" said the Queen. "Now, here you see, it takes all the running you can do, to keep in the same place. If you want to get somewhere else, you must run at least twice as fast as that."In answer to Alice's statement that they'd been running like hell for a long time and still remained on the same exact place.
For me this makes sense... call me weird... but I think that we have to move fast or we will be left in the same place if not somewhere backwards... and then we'll have to go all way forward again, likewise in Moebius "Gardens of Aedena".