It's snowing in my consoles window!

No ports are open by default on iOS 6. This shouldn't be confused with the also true statement that iOS 6 will open network connections to several Apple servers so that APNS and iCloud push email and software updates work.

You will have to configure things like WiFi sync or run file sharing software or a web server to get the device listening on IPv4 ports.

I use an app called Netstat from the iTunes Store to inspect all network connections. That should help you determine which setting or app has opened port 1027 on your device. On all my iOS 5 and iOS 6 devices, the only default open port (LISTENING) is on localhost/loopback.

You can find it in Rudin, Principles of Mathematical Analysis, page 43, problem 2, the sum of the absolute values given there is called the height of an algebraic equation.