L293d and ground

Hi everyone! I have a question about L293D but probably it's something about "ground" in general.

Why in this circuit (please look at the attached picture) the ground of the battery is connected to the ground of Arduino? The circuit of battery/motor should work without being connected to the ground of Arduino, shouldn't it? And viceversa of course...

And the other (linked) question is: L293 needs to be connected to ground to work, doesn't it? I mean, it must be connected to ground to make internal circuit (e.g. AND circuits etc.) work, right?

Your attachments failed.

I don't know why, I used the specific button...

Please read and follow the instructions in the "How to use this forum" post.

Image posting guide