While you're hoping, why not hope it never happens at all, which seems a pretty safe bet. I don't think I've ever seen it happen.

Yeah, but the jumping for a shot and dropping the ball does happen from time to time. ;)

"Discernible pause"? Really? Dude, now you're making sh!te up. (And: this isn't baseball.)

I think it's time for a poll :D

Yeah, kinda like calling a balk.:D Let me put it another way. A1 lifts the pivot and starts to step into the pass, but A2 has cut the other way and the pass is no longer available. Often you see A1 try to stop, but the ball comes out anyway. The decision to be made here is whether it was a pass or a fumble. But, if the motion obviously stops, A1 hesitates, then obviously, deliberately drops the ball straight to the floor, no way does this seem to me to be that he "threw, batted, or rolled the ball to another player."

And no way I call a travel without him touching the ball again.

Yep, nothing specifies that the thrower needs to know his recipient, nor throw it directly to a player. I just don't understand the reluctance to let this play out.

In reality, this is much ado about very little. In most travel/illegal dribble cases like this, the violator does touch the ball again immediately. The reason for the reluctance is that nothing in the rules states that a second touch is necessary to define a dribble.

A1 tries to save the ball under his own basket and tumbles into the bleachers. B gains control and goes the other way. As A1 returns to the court, A2 makes a steal and passes ahead to A1 at the free throw line. A1 turns to take it to the basket. He bounces the ball twice, but he uses both hands for both bounces. About this time he slips on a wet spot and crashes to the floor. He doesn't touch the ball after the second bounce. All other players are still on the other side of the division line. Is this a violation?

You're correct, it's not required in the rules (I reluctantly admit to liking the FIBA definition better here), but nothing requires it to be called, either. It's judgment, and frankly, as long as I can, within the rules, justify playing on, I'm going that route anyway. IOW, if I'm not absolutely positive it's a violation (dribble in this case), I'm not going to call it and the only way I can be absolutely positive it's a dribble is when A1 is the first to touch the ball in this scenario.

It depends, of course, on whether you judge that 2nd bounce to be a dribble. Personally, if he doesn't touch it, I'd be inclined to let it play out until the rules tell me I can't. :)

End of the play right there...my whistle is blowing.

Even though he doesn't touch the ball after the 2nd bounce?
Here's how I read his play:'
1. Bounce with two hands.
2. Catch with two hands.
3. Bounce.
4. Slip.
5. Ball flies away.

In this play he has already started his dribble and that 2nd bounce is part of the dribble. If however he attempted to catch the ball and fumbled it then no, I wouldn't have a violation.

Fair enough.