The thumb doesn’t normally cross over the index finger.  But it’s pretty much mandatory in playing scales single-string style.  At least if you’re trying to “lead” with the index. That was the assignment in this exercise: lead with the index.

I expect that sort of unorthodox cross-over would be just as necessary, however, if I were to lead with the thumb.  I’m new to this and just following instruction.

I played only the first five notes of the scale.  Three on the fourth string and two on the third string.  Index-thumb-index (crossover) followed by thumb-index.

I think you’ll agree, it sounds pretty tentative.   I’m still getting used to that cross-over.

When I’ve developed more confidence, I’ll add the remaining three notes of the scale.  I expect that’ll require more crossing over.  It’s just part of the single-string game.

The next assignment may pull the rug out from under me.   Like maybe now I have to lead with the thumb.  Or I have to extend beyond one scale and move into another.  Maybe just to the fifth note (a D on the G scale) or maybe clear through another entire scale.

Which you can bet will require a literal ballet of unorthodox finger work.  With who-knows-what sort of alternating action between the index and middle. Maybe the thumb will remain part of the act.

But new sounds demand new skills.  If you want to move past plain old Ionian and play in the Dorian or Mixolodian modes, you have to break a few eggs, right?

Maybe you don’t actually “have to.”  You could still play it melodic.  But you know what I’m saying.