Transistor radios are receivers only. Cell phones are transmitters that move between various fixed receiver cells. At the very least the phone company knows what cell any given phone is currently connected to. In practice they know the locations and signal strengths of all the cells in range of the phone, which allows triangulation to within a few dozen meters, at worst.
It's a cellular telephone -- they need to know all the cell towers near you and direct your phone between them. It's a rough area but my phone provider definitely knows I'm at work right now.
Your assumption is that GPS is required to know where you are. But each cell tower has a well known physical address and your phone connects to multiple towers making it trivial to triangulate your location. Much less exact than GPS and highly dependent on cell density, etc.
They registered with the nearest cell towers, and ask them to watch signal strength so they can make handover work. This is coarse location information (since the company that runs the cell towers knows where their own cell towers, and uses your current tower registration to figure out which cell tower to send a call to), and can be made a little more fine-grained if you use signal strength from the various towers and triangulate. This does not involve the Global Positioning System or other satellite-based positioning systems at all.
If it does not do this, it is not a cellular phone. There are other types of portable phones that don't work this way, like cordless landline phones (the base doesn't know where it is, just that it's plugged into a phone jack) or satellite phones. But the "cellular" part refers specifically to dividing up the terrain into cells, finding which cell the phone is in, and assigning it to a tower based on that determination.
(This is all pretty irrelevant to the point I was making above that cellular network operators can easily choose not to use the location information or signal strength information for anything other than routing calls, and that deciding that they can just use the information however they want would be creepy.)
GPS tracking is a complete red herring; you're focusing on the wrong thing. No one ever claimed that GPS was necessary. Here's the statement that was made: "Your cell phone cannot function without actually knowing where you are (to some approximation)".
That "approximation" is: "Which cell towers can hear your phone transmit, and how strong is the signal?" Your cell phone would work just as well as a phone if you disabled the GPS chip, but your location can be estimated by triangulating from signal strength. It's not nearly as precise, or as accurate, as a GPS-provided location would be, of course.
Not GPS tracking. Simply tracking the fact that you transmitted a signal to a particular cell tower (the one nearby in radio terms) is sufficient to narrow your location considerably.
> That's like saying a transistor radio needs to know where broadcast antennas are, which is obviously absurd.
Cellphones are called cell phones because they divide the world into location-based cells which determine which antenna your phone talks to. At the very least, the telephone company knows which cell you are located in to communicate with you.
That's like saying a transistor radio needs to know where broadcast antennas are, which is obviously absurd.