The compressor will hum when it is operating. I am assuming you are implying it also hums when it is supposed to be on an off cycle. In that case, the relay is probably stuck. Are you sure it is the compressor you hear humming? I've heard some loud humming contactor relays when they are loose. If it's a heat pump, the reversing valve relay could be humming.

Yes it hums when its on the off cycle. It changes in frequency from pretty loud to almost unnoticeable. It always hums, all day. I have two identical units in the house, and the other is totally quiet when its off.

Are they heat pumps?

The first answer I had is the old joke... it's humming because it doesn't know the words to the song...

Anyway, What I suspect is that the relay coil or some other part is humming. You can't really know what it is unless you open it up. Since we are at the end of the cooling season, have a service person look at it when you have the furnace checked.

Someone told me to try starting a heating cycle, and I found that the compressor does not cycle into heat. It have a reversable heat pump. I am in FL so I will require my AC for a couple of more months. I will be honest I know enought about AC systems to set the temp, and expect it all to simply work. The humming continues.

My guess is that it's a relay or a transformer coil. Have it checked when you have your regular maintenance done to avoid a trip charge.

Find the breaker that is for the inside air handler,
turn it off, if the humming stops it has to do with something in the 24v controls.
It is probably the reversing valve solenoid being energized in the cooling mode. Turn the thermostat to heat lower the temp so it does not come on. Does it still hum?
Most the time you may hear a loud hum if there is no 220v power to the outside condenser or if the contactor is not making full contact to run the condenser and the thermostat is calling for cooling/heating. That is the Contractor coil energized humming.