xoxos, who's created some of the nicest algorithmic music generators out there, asks us in a post [1] to imagine a future where creators of algorithms are considered in the same way as today's musicians, and their algorithms are considered much like today's recorded music. The audience/performers, instead of playing an audio file, could "play" an algorithm.
I think we're still a few generations away from such a thing becoming mainstream, but I'd love to be proven wrong!
When you said "play an algorithm", it reminded me of this idea I had where I wanted to play back the execution of a running program and map the assembly or IL to notes/frequencies/instruments/sound. Literally, "playing the code as if it were music".
Then I had this strange thought - what if you could monitor the cacophony of your running systems, and detect a problem, or a certain event, just by the presence of a particular audio theme or tune. I bet an infinite loop would be pretty annoying and obvious. Just as long as the server getting overloaded doesn't sound like getting rick-rolled ("Never Gonna Give You Up" by Rick Astley).
People did this with old computers that emitted lots of radio interference like the PDP-1. It was possible to debug in exactly the way you're describing by listening to a radio held up to the CPU.
I think we're still a few generations away from such a thing becoming mainstream, but I'd love to be proven wrong!
[1]: http://www.kvraudio.com/forum/viewtopic.php?p=5210459#p52104...