No, the phone didn't ring but there it was - a voice message waiting for me. I must have missed a call. I made sure it wasn't in the vibrate mode, checked the ring volume, sighed and contemplated the latest fashions in hearing aids.
Now it turns out the problem could simply have been I was on the 'net. Like the dial-up modems of old, if I happen to be transferring data via the EDGE network, no phone calls can get through. Ouch
According to the iPhone Atlas:
... stems from the fact that there are two types of EDGE network types, NOM1 and NOM2. When your iPhone is connected to a NOM1 network, the data transmission will generally be interrupted, and the incoming call allowed to come through. When your iPhone is connected to a NOM2 network, however, the EDGE data transfer process cannot be interrupted, and the call will generally go to voicemail.
To see which network type your iPhone is in, go into the iPhone Field Test mode by entering *3001#12345#* with the phone keypad and press Call. Under the GPRS you will see either 1 or a 2 assigned to the nom field. Don't get your hopes up too high. Apparently the ATT network is primarily NOM2 and it is not a certainty that the iPhone can even handle NOM1.
The solution? Use the Wi-Fi mode whenever you can.
I checked the voice message. It was a telemarketer. I wonder if they sell smart phones?