I think you mean the digital pin to the base? (Edit: I see you fixed that already. It's good practice when you edit, to show what you changed... else others will think I'm imagining things....)
The npn requires the load on the high side, so from the top down, you have:
Ground (same as power -ve)
Then on the "side" so to speak you have:
Controller digital pin to base (through a resistor)
Controller ground to same ground as the transistor, which is the same as the Emitter.
But I don't really understand your question.....
The grounds need to be common so that all voltage measurements have the same reference. If the controller ground isn't the same as the equipment ground, then the transistor has no 0 for the controller io signal, and it's a bit like imagining one hand clapping.
Edit: I guess it's easiest to say that the Arduino ground, the power supply -ve, and the emitter are the same point.
Yes sorry I did edit it, you are not imagining things lol.
Basically what I'm asking is why can u just have 1 wire coming from the arduino into the base or the transistor? The current will flow from the base to the emitter , base being the "positive" side of the circuit and the emitter being the "ground".
If I can put it in another way, say u have 2 1.5v batteries, or two power supplies. You take one battery/power supply and connect a wire from the positive terminal to the load, then you take the second battery/power supply and connects the ground wire to the negative side of the load. You see the two batteries/power supplies
Are separate from one another but the load still see's a positive and a negative? Why can't this work?
I just wana know why I can't ONLY put 1 arduino digital pin on the base of the transistor and not connect the arduino ground. Why can't the arduino use the higher power circuits ground? Why can't the electrons flow from the arduino to the ground of say, a battery?