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Mumble tap dances while he walks on ice. Tap dancing while wearing tap shoes, when you're on smooth surfaces, prevents you from slipping.
Mumble's and Gloria's son being named Erik can be seen as some rather clever foreshadowing. We know Erik will find his talent sometime in the film, but we're never really given much hint as to what that talent is. It turns out he's really good at singing opera like another famous Erik.
From the first movie: Mumble came out of his egg feet first (as opposed to using his beak like birds normally do). Technically this means Mumble was born in the breech position. Breech babies tend to have a higher risk of having developmental problems.
The tendency of overenthusiastic suitors to drown out a particularly desirable female in their attempts to woo her leads to a sort of Fridge Heartwarming moment when Mumble finally embraces his dancing; not only does his "heartsong" match hers perfectly, but he will never drown her out. Rather than trying to convince her to accept a melody that isn't hers, Mumble provides an independent but perfect harmony that makes both of their songs more beautiful.
The elders are all composed of older, mateless males. They are also shown as staying for the duration of when the incubation. Two problems. One, female emperor penguins have a longer life expectancy. Two, if a penguin has no mate, they just go back to the sea.
Another problem is that there are more male emperor penguins in the movie. Due to the higher life expectancy, there is more competition between the females than the males for mates. Yet Gloria has a very large number of guys following her...
Gloria is supposedly a very desirable female because of her good singing voice.
The elders double as priests. They are celibate because they are married to their faith/people. The entirety of the flock are their chick/egg.
The elders are portrayed as a bunch of fascistic old religious fanatic stick in the muds. But their hostility toward dancing is rooted in both logic and survival. Mumbles was 'brain damaged' because Dad dropped the egg on the frozen ground long enough for him to freeze just a little. Dancing means moving feet. Moving feet are a threat to the survival of the egg for the same reason Mumbles almost died in, um, utero (eggero?). Eggs on ice lead to dead baby penguins. (IOW, they're 'prolifers' in a penguin kinda way).
Here's a doozy from the first film for all the Tropers to think about—why didn't Mumble just learn to rap?
Especially seeing as some other penguins from the first film such as Seymour rap instead of sing.
Even rapping requires you to hold a tune. Mumble can't even do that much.
Sven probably isn't the last puffin in the world; he may have been the last in the wild, although there are 3 species of puffin; the rest are most likely in captivity.
Mumble regularly swims while perpetually frozen in mid-molt. While molting, penguins are not waterproof, and thus unprotected from freezing water; swimming in that condition is deadly.