Edit: thank you!

Man I get gestures have been embraced by the community, but this is emphatically not what I meant. The only gesture that makes sense to me is pinch-to-zoom and maybe swiping on cards that appear to be floating.

There's no way to discover this functionality outside of googling documentation and it often doesn't work with one hand.

There is another that is fairly intuitive for a Mac person: tap-and-hold to get a contextual menu. Shame they have hidden it under some kind of "haptic feedback" thingamagig.

The ipad also has an icon above its keyboard. Whatever lack of obvious interaction is available on the phone seems intentional.

Cynically, I think you'd just look like even more of a fool shaking an ipad and this is the only reason they approved such a button.