I'd like to add, being a lifelong Okinawan Karate guy, that the idea of embusen comes from Kendo and other Japanese arts. I was taught that there is a difference between embusen and the sacred geometry inherent in the orthodox (Ryukyuan) kata. If you end up on the same spot, then you're lucky. Medulanet used the Nishime Kusanka video as an example of this positional coincidence. As a Mastumura Seito practitioner, I can say that you do often end up very close to the spot you started on. This is not any sort of rule though.
Delaney's bunkai description of Pinan Shodan is spot on, but he at once reinforces the opposing argument while invalidating his own. The idea he puts forth about the first movement in Pinan Shodan/Heian Nidan is the Okinawan way of looking at kata training. The student of good Okinawan Karate, and karate in general needs to understand the methodology behind solid kata training before application was an emphasis.
In its infancy the Okinawan style of training focuses on exactitudes: proper biomechanics, correct technique execution as your ryuha teaches it, blatant adjustment steps/foot movements, perfect alignment and getting the specifics down. Once this is a reflex and requires little to no thought, it is just a matter of repetitive and sound kata training before the analysis and applications start to come to you. There are always apparent bunkai, but the individual with a lot of experience and creativity will start to see the variety in the real world application of kata waza.
So thinking of that first gross movement in Pinan Shodan where you step to the left, right hand performing an upward "block" while at the same time the lower, left hand performs a middle outer "block", you can imagine at the later stages of training how just moving the feet or rotating the hips can lead to an application with the movements confronting a frontal attack versus a lateral one.
If the "embusen" was meant to be a true mirror image or to end up where you left off with every form, then the flexibility in kata training would be lost. You would be too concerned with preciseness beyond practicality, and most important of all, the intent of Okinawan kata training. This is of course to give a physical and mental mnemonic for solo practice, one which lends itself to a relaxed mind and body, resulting in efficiency and increased power generation. Partner sets are integral to karate training, as are jiyu kumite, iri kumi, hojo undo or the other aspects of karate training. Kata training enhances these adjuncts, but kata training is preeminent in the Okinawan MAs. It is the most important portion of ones training.
The important details are in the future unraveling of the so-called "hidden truths" which are revealed with diligent kata training. Whether or not you end up exactly where you started from is not one of these details. I'm speaking of most Okinawan systems. Maybe Nagamine's system is different and has been formulated to express his sensibilities and experience(s).
Good discussion. Don't ban the ones who keep these threads "hot". That Unyu guy is fun to read and he seems to know what he's talking about...