I wonder if this thread might be a tad misleading because the "infinity move" isn't a move at all. It is an outcome--one that depends on a whole bunch of movements, timing, and equipment choices all coming together to produce high level skiing. I wouldn't say that one "gets" this as a breakthrough, rather it is more like the icing on the cake that comes along with some other breakthrough that finally brings things together. In my opinion, one doesn't try to do this specifically; the goal is to develop the kind of skiing where this shows up. In other words, the "infinity move" is nothing more than an apt description for very high level skiing.
Producing skiing that will show the "infinity move" requires using the bottom of the arc to ski the skis back up up underneath one's body; the sensation is that of sucking one's feet up and bringing the knees up while the chest sinks down to meet them. Doing this requires "working" the ski. At the top of the arc, once the skis are on new edges, they are allowed to track outward, across the fall line, which causes the stance leg to lengthen. The rate of tipping at the top of the arc is slow, the rate of tipping at the bottom of the arc is fast since the radius obviously has to tighten radically in order to ski the feet back in and underneath.
Making the skis do what is necessary to achieve the "infinity move" is completely counter-intuitive. You cannot, for example, ever push against the sole of the foot or straighten or even stiffen the outside leg--all of which most skiers will naturally tend to do when looking for grip. Instead, the outside leg has to keep softening through the bottom of the arc so that the outside foot can keep tipping the ski over at an increasing rate. The tipping of the outside foot is lead and controlled by the tipping of the inside foot, which, at extreme levels of flexing is accomplished by "pulling up" along the plane of the stance leg. Of course, this is a greatly simplified picture. There are other movements which must be mastered in order to support the necessary balance required to perform the lower body movements that would create the "infinity move."
Some (probably not all) things that will prevent the "infinity move" (in no particular order): First, only the very best athletes can (maybe) get away with a (micro) wedge in transition. For everyone else, rolling to big-toe edge as the first movement to start a turn will likely prevent the development of the level of precise footwork that is required to pull this off. Second, extension or even just stiffening of the legs kills tipping and will make skiing this way impossible. Third, finishing the turn with one's upper body facing the ski tips will also prevent the "infinity move" from developing. Fourth, dumping the hip in will lock the legs and stop the tipping necessary to tighten the arc and bring the feet back underneath. It should go without saying that parking on an angle at any point in the turn will also prevent the "infinity move." That is, angles have to keep increasing until the turn is released. Finally, (and by no means least) anything less than total balance on the outside ski will prevent the last bit of tipping needed to bring the skis back underfoot. If the inside ski is being weighted, it will block the turn from finishing properly.
The "infinity move" is really about learning to relax at the right times. Relaxation produces the most efficient skiing as well as the most performant. Skis grip better when they slice through the snow (as opposed to being "ground" when one tries to bend them by pushing against them). This is especially true at the bottom of the turn when proper movements will lock the tail-side edge of the ski into the snow so that the energy created by the turn is converted upon release and helps start the new turn. Additionally, the "infinity move" is about speed control. Recreational skiers can use the turn finish to ski with high energy but can choose whatever level of vertical velocity they desire; i.e., "ski the slow line fast." Racers can use the turn finish to make large lateral movements under the gate which accelerate them into the rise line for the next turn.
Note that the idea of "do nothing initiation" is necessary, but not sufficient with respect to the idea of the "infinity move." While the "infinity move" describes (among other things) the best possible turn finish, one does not need that in order to start a new turn without effort. While it certainly helps, the best skiers can start a turn from a stationary position without any effort. Certainly, most skiers will need to develop a parallel release to even have a chance at achieving the "infinity move", but having a release is just one step on a very long road. Which is to say that the only way to tell if you have the "infinity move" in your skiing is to see yourself on video. There are any number of less than desirable movement patterns which seem to produce positive feedback with respect to ski performance, but which are really dead-end approaches. Those on the chase would do well to avoid drawing conclusions based solely on how something feels. The path that will actually produce the desired skiing is extremely narrow and faint. Trust me when I say that it is very easy to follow the wrong path down to a dead end. The really hard part is recognizing a dead end when one encounters it. The best approach is to get coaching from someone who not only demonstrates the "infinity move" in their skiing, but can break down and teach the necessary movements to produce that type of skiing.
As I said though, the "infinity move" isn't something to be learned per se. It is the culmination of putting all the pieces together. Moreover, even with the requisite skills, equipment may still prevent this type of skiing. To start with, the "infinity move" is impossible without a very good boot setup. In order to "work" the skis through the bottom of the arc, the feet must be free to make extremely small and precise movements within the boot, which must activate the ankle and then propagate upward. This requires correct (for the specific movements of skiing) foot bed support, proper boot fit, proper cuff adjustment, proper under-boot canting, and (if necessary) adjustments to optimize for fore-aft balance. Undoubtedly, there is some very small percentage of humanity with perfect feet and alignment, such that they don't need any of this work. The rest of us, however, will live and die by our setup. Unfortunately, not only does the boot fitter have to understand all of the above, but so does the skier, because the latter has to be able to understand how the boot is supposed to behave at the micro-level in order to give the fitter the necessary feedback to make the necessary adjustments. Until a skier is close to being at the level required to achieve the "infinity move", they aren't likely going to be able to give a boot fitter enough information to set up the boot up as well as will be required. At this level, micro adjustments often make a huge difference.
The other piece of equipment that factors into this are skis. Not every ski will behave in a manner which will facilitate the "infinity move." In fact, I wouldn't be surprised if most skis won't behave well enough to ski this way. The key question, of course, is how does the ski respond to increasing the rate of tipping at the bottom of the arc? Ideally, the tip of the ski should bite and the arc should tighten in proportion to the rate of tipping. A good ski can be made to "snap" around extremely quickly. However, many skis won't respond well to this input. Undesirable behaviors include things like getting stuck on a radius and refusing to tighten further, losing grip and sliding, or my personal favorite, having the tip collapse and the entire ski just washes out. As with boot setup, one has to have a certain amount of experience and skill before being able to discern whether a ski has sufficient quality to produce the desired level of skiing.
I point this out because skiing is an equipment-intensive sport and anyone wishing to master the sport must learn to master their equipment. For anyone trying to achieve this level of skiing, but who doesn't yet have it, it is absolutely critical to continue to question boot setup and ski choice. If one reaches a point where the correct movements do not produce the expected results, circle back to equipment. The problem is chicken vs. egg. We need properly set up equipment to ski at our maximum ability, but we can't set up our equipment properly until we know what it means to ski at our maximum ability. So the solution is to pay attention to what the foot is doing in the boot and ask questions if something doesn't feel right. All set ups for non-expert skiers are by definition potentially sub-optimal. The same applies for skis. Pay attention to how they behave. If a ski doesn't reward good movements with the expected behavior, it is time for a new pair of skis. Incidentally, skis do wear out from skiing and resins break down over time. The best pair of skis in the world will not last forever. Learn when it is time to say goodbye.
Anyway, hopefully the above will be helpful to anyone who is out there chasing down the mobius strip. Keep making turns everyone...