OK, I still appreciate all the feedback, but this is my last response, partly because I'm getting a headache about people misunderstanding my terminology and partly because I'm sure I'm giving you all one too. My bad because I don't know the jargon and this is clearly a professional site. Letsee. Here goes:
1) Not knowing jargon does not mean I'm a closeted level 4. I have been skiing nearly a half century. My first lessons were at a new place in California called Mammoth; my parents knew Dave McCoy and we took lessons from some guy named Tony Millicent (sp?) who started their ski school. (He also was French, I think. Ironic.) I cannot ski more than 20-25 days a season because of my profession, so I depend on lessons to progress, albeit slowly, toward expert. I am generally sorted into the Level 8-9 classes.
I chose to talk about half circles partly because every ski instructor since creation at some point draws a little half circle in the snow to demonstrate a hypothetical turn. Then he/she draws another half circle at the end of the first, other direction. (Sort of like the little () you draw to represent bumps.) And as I said parenthetically, obviously few turns start or stop perfectly transverse across the slope unless you want them to. (I could add here that carves are seldom arcs of a circle either, but have decreasing radii.)
So yes, I do know about S's. You instructors always qualify the C's before or after you draw them by noting that what we're really after is S's. And yes, I have spent time creating clean lines across a slope, then letting my skis disengage/drift. I even do 360's on easy slopes and sunny days. Thank you all for the suggestions. They represent a lot of creativity and energy on your part. Not to mention confusion. Since all I wanted to know was about little toes and inside skis.
2) It wasn't so complicated, I thought, to visualize a half circle looking up a slope where 0 degrees is at the top, where you begin a turn, 180 is right where your instructor is standing at the finish, and 90 is at the maximum lateral bulge of your arc, out toward the woods. Call it an Platonic turn, if you like. Only exists in the mind. I was wrong. So here goes a more cinematic version:
Imagine you are edging in a straight line directly across this slope, idly wondering which snowboarder will cut you off. Simply transversing, bit more weight on what used to be called your downhill ski. No gates, no anticipation for the next turn, just waiting for divine guidance, or your instructor's whoop, on when to begin things. So you start to release your edges (remember you're still mostly transverse, tips pointed at that snow maker) to initiate your turn. But you are nowhere near flat yet, just getting those neurons to make your intentions about releasing into an actual movement.
That was the moment in the arc where I was interested in little toes and inside skis, because your soon-to-be-inside ski (downhill in the old parlance) is the one that has the little toe I'm talking about. It is the ski that some like my instructor say should be pressured a bit, by shifting your weight across the ball of your foot to outside the base of your little toe, with less consciousness about tipping the soon-to-be-outside (uphill) ski to start things. Realskiers says something like this also.
I deduce this is less about a sequence (obviously both should happen simultaneously) and more about how you visualize the initiation of a movement - do you think more about tipping the outside (uphill) ski, as most of my search results indicated, or about pressing your inside (downhill) ski toward release?
I also deduce that for a racer on a steep icy course, the problem is more about leg extension than it is for me. I also realize some of you assumed "ball" of foot meant pressuring the tongue from the toes, not a good habit. According to my instructor, it doesn't. In fact, he said he uses the location to get people away from feeling their boots and into feeling the snow under their feet. And obviously, the outcome is happening a LOT faster than it takes me to describe it.
In any case, a moment later, the carve is happening and we approach the fall line. That is by my apparently mistaken geometry when my tips are pointed straight down the fall line. Or as TheRusty suggested, all ten of my toes. I like that image too.
3) Now my instructor at Mt. St. Anne, teaching a mix of 7's to 9's, mentioned the necessity of letting skis run flat/neutral this instant, right down the fall line. No carving allowed. It lets modern shaped skis stabilize, he said in a thick accent ("become calm" was the exact phrase), and incidentally makes your carve rounder.
(I do not make a Z, and my carve marks stay pretty tight so no crypto-stemming and skidding. But my S's could be rounder. They look like they've been squashed down a bit. I hurry the "calm" part.)
So he actually made us count "one-thousand and one" on the fall line, skis running flat, before continuing the (long radius) turn to a stop pointed across the slope the other direction. He also noted that in short turns, the "pause" is just a blink, something instinctive. After practicing linking, with quicker flat segments, he then made us try it on an empty slope with our eyes closed, by the way. I've had others get me to try it on one ski. Which is kinda fun and great for learning about both edges. (I figure skate decently.)
But in any case, this 90 degree, fall line instant is what I understood to be the flat ski segment of the turn. And there I get lost vis-a-vis several of your comments.. I do not see how BOTH skis should be flat at any other aspect of a hypothetical 180 degree arc. In fact, for ANY arc radius, and however quickly you're moving edge to edge, the neutral/flat segment cannot BE initiation. It is the state AFTER you initiate some change in the edges and BEFORE both edges tip the other direction. That's not technique, it's physics.
In conclusion, one of you - Onyxji - actually understood my question about little toes and pressure enough to address it, said it was controversial. I'll try to follow that idea up on slope next lesson. And couple of others addressed the French/finesse conjecture. In any case, I've appreciated your effort, sorry I caused so much hassle, and I'll go back to the gear pages.
Over and out...