Richard nodded his agreement. "Of course you can do the separate parts, lacking only the smoothness that comes from practice of an unfamiliar maneuver. A beginning flier points the stick of his broom in the direction he wants to go. An advanced one, such as yourself, knows that a good broom will go in any direction no matter which way it might be pointing. When you did those slow rolls, you vectored your lift - which is really just a vertical thrust - around your broom so you held altitude instead of falling out of the sky when you were upside down. And I must say, after just a little practice, you did it most smartly, no bobble at all. When you did that inverted quaffle grab demonstration, I knew it would be easy for you once you mastered the principle of a rolling vector. In the same way, you can vector forward thrust so as you do a flat spin you will continue smoothly in your direction of travel."
He pitched his broom forward until the stick was pointing straight at the ground, holding a steady hover. "I'm a Seeker, and I think the Snitch is below me, so I prepare to dive down on it when I spot it, but I hold my altitude with reverse thrust, just in case. And here it comes, rising quickly, I will have to climb to match speeds." He began reversing upwards. "I want to move in the right direction as soon as possible, even though my broom is pointing the wrong way. And I want to keep my eye on the Snitch as it goes by." He pitched more, until he was fully inverted, still climbing, even upside down. "As it goes past, I continue the tumble, still climbing, until my broom is pointing in the proper direction for least wind resistance." He continued the tumble until he was upright on the broom and mimed a two-handed grab at the imaginary Snitch, then let his broom drift straight down until he was beside Arcturus again.
"Most fliers do a Tumbling Pigeon in a downward direction because they don't need to pay much attention to vectoring lift properly when it is done that way. Also less strain on less capable brooms. One of the reasons I had you practice that reversed-control stop was to help you realize that what you knew, as an experienced flier of the brooms of your day, did not necessarily apply to a high-performance broom from my time. So, start with enough altitude to do a recovery if something goes awry with your initial practice, and try your Tumbles in a vertical climb first. That was how I was taught, actually. As you gain confidence, flatten out the climb until you can do them on the horizontal, or descending, or traveling any which way you might prefer."