My firewall (the "Application Firewall" in OS X 10.8.2) detects that Mathematica (188.8.131.52) and "MathKernel" both request incoming connections. My configuration expects all incoming connections to be blocked, so I wonder what the consequences of denying these connections is.
Why do Mathematica and "MathKernel" request incoming connections? What are these connections used for and what, specifically, will be the consequences of denying them?
When I allow connections, and take a quick look at them, I see that both have opened several incoming/outgoing paris of connections to "localhost", which suggests that the connections are being used for local communication between each other, as suggested in Szabolcs's answer
but closer examination shows an additional connection for each that I'm not sure how to interpret
Blocking incoming connections seems to have no effect, and I wonder of that's really true (e.g., am I paying a performance price). Allowing would seem to be innocent, of all the connections are local; but I know of no way to guarantee that.