Speaking of keeping the hands firmly grounded on the mat, here's a video of Maria Villella talking about keeping the hands firmly grounded on the mat in jumpthroughs and jumpbacks. I don't know much about Villella, but if this video is any indication, she definitely knows her stuff. Check this out:
I really agree with her remarks at around 0:50 that "fingers are more for steadiness and balance." I think the fingers are often overlooked in jumping through and back; many people I have observed over the years tend to think that it is the palms that are doing all the work, and are not aware that the fingers can serve as invaluable "brakes" and "steering pads" to control the direction and momentum of the jump. In this way, an action which seems so static on the outside (keeping the hands grounded on the mat) is actually a dynamic process of continually negotiating the weight distribution between the palms and fingers on a mini-second-by-mini-second basis. Pretty interesting, don't you think?
I also really like her remark (somewhere around 1:10) that being able to balance on the hands is the result, not the focus of a dedicated practice. A very nice reminder of the importance of Vairagyabhyam (nonattachment) to the practice.
Well, and here's another impressive demonstration of balancing on the hands from Briohny Smyth of the Equinox videos fame. This one will probably raise a few eyebrows, and send more than a few panties into a wad (pun very, very intended) in the yoga blogosphere, but I always believe that we can learn something useful from anything. So, may I humbly suggest that you put aside your preconceptions, and check out the following video:
If you remember that blogstorm about the Equinox video that flared up in the yoga blogosphere some few millions years ago, you will remember that a lot of cyber-fire was directed at the close-ups of Briohny's body during that storm. But if you watch the above video in a certain way, you will see that these close-ups can actually serve a pedagogical purpose, from an asana intructional point of view. Specifically, the close-ups of her belly (at 0:28--0:30, and at 1:20--1:22) serve as a great illustration of the engagement of Uddiyana Bandha that is really key to maintaining the integrity of the postures. In addition, even the infamous butt shots serve a couple of pegogical purposes here: (1) They do actually give a pretty good picture of good alignment in updog, and (2) also give a good picture of the extent of lumbar flexion needed in order to go from Bakasana up into handstand.
As with many other things in life, a lot of what is actually going on is very much a matter of how we perceive things, don't you think? Beauty (or the lack thereof) is very much in the eyes of the beholder, no?