Now see my response to MP's new system on 5/2/2011. I'll quote the entire thing here:
"I have some observations to make about the essay above, and I found one error. The observation is that your 1-2-6 triad corresponds to the Compliant personality, your 3-8-7 triad corresponds to the Aggressive personality, and your 5-4-9 triad corresponds to the Withdrawn personality. See pp 434-36 of Personality Types.
The error is your statement that the wing of each type is "the one you are second-most like." But that is not an accurate description of wing theory. The wing is the "second side of your overall personality" (PT, p.43). Riso then goes on to state that the traits of that wing may be a strong or very slight influence on your dominant type. The fact is that we humans possess traits from all 9 points on the Enneagram, but this does not disprove wing-theory.
Your essay then moves on to use your own definition of wings to replace traditional wing-theory (of whatever variant) with your own, and all I can say is that in doing so you no longer have wing-theory but something else. That doesn't mean your concluding theory is wrong, but it is based off of a false definition of wings and therefore isn't really about wings at all. So it's more like a straw-man version of wing-theory.
There is a questionable straw-man argument related to your primary axiom: 'The need for the wing type to be "adjacent" didn't make sense, since as my variable system indicates, the actual order of the numbers that the types were assigned is meaningless. There is no sensible reason that 7s should be next to 6s, for example.'
This one takes more explanation. While there is something rather arbitrary or "meaningless" in one sense, in another sense the 9 types are related in groups of threes by means of triads and centers. It is more practical to have 2-3-4 next to each other as they symbolize primary issues with emotions. The 2 projects emotion, the 3 represses or under-expresses emotion, and the 4 introjects emotion. The 5-6-7 center is related to the intellect, and the 8-9-1 is related to instinct according to the manner with which each type in the triad deals with instincts.
The 9 being on top has always held special significance as a symbol of unity for the entire structure of types.
So while there may be an arbitrary element here, there is indeed a purpose and a plan that goes back to original Enneagram theory given to us by P.D. Ouspensky (The Fourth Way), G.I Gurdjieff (who brought us the enneagram symbol), and Oscar Ichavo (particularly this latter who brought these ideas to the West). These are spiritual teachers who instructed students on the spiritual side of human nature. Any change to that original purpose and structure not only negates wing theory, it negates the Enneagram and leaves you with 9 types of a system by another arbitrary name of your own choosing. To treat the Enneagram itself as an arbitrary construct negates at least a century of teaching on the subject, even if you choose to retain the Enneagram symbol itself.
The origin of the Enneagram's construction, along with the ordering of the types, is found here (
http://www.endlesssearch.co.uk/philo_enneagramtalk.htm).
There you will find explanations of the Laws of 3 and 7, as well as the musical tones associated with 7 of them (the Octave). There is also a chemistry analogy presented here for the Law of 3, C+O+N > H, and a "cosmic octave."
So now you see that there is much more to the Enneagram than a typing system. And this is just the tip of the iceberg. It is a small part of a massive system of spiritual growth. But if all you see is a typing system, then there is indeed no basis for supporting the traditional system, and reconstructing it according to any design is highly possible."