It’s not very often that someone invents a new sort, but I have certainly never seen that one before:

function f() {
    sleep "$1"
    echo "$1"
while [ -n "$1" ]
    f "$1" &

The idea is simple: you take the first element of the array, say n, you fork a new process which sleeps n seconds then displays that number. Repeat for the next element.

Calculation of the average complexity of this algorithm left as an exercise to the reader.

Related: Quantum bogosort.

For some reason, I feel like taking a nap.