As well as the Myers-Briggs (based on Jungian insights), I have also found special merit in the Enneagram system, once again attempting to view it from a holistic mathematical rationale.

Whereas the Myers Briggs is based on "4" with all possible profiles (16) representing the square of this number, The Enneagram is based on "3" with again all possible profiles (9) based on the square of this number.

Indeed "9" seems especially suitable from an integral perspective, and indeed in several respects I have found the Enneagram system better suited to deal with the dynamics through which successful integration of personality may take place.

Indeed it is easy to demonstrate some special holistic mathematical attributes of "9". In the denary (base 10) number system we employ, 9 represents – 1 (with respect to 10). And – 1 in turn represents the unconscious direction of development (which is directly relevant for personality integration).

Here is another interesting feature of 9! Take any number and then write its mirror version (reverse number)!

For example based on today's date, we can construct the number 200116. The reverse of this is then 611002. Now subtract these two numbers (with the smaller subtracted from the larger, we get 611002 – 200116 = 410886. Now divide by 9 and we obtain 45654. And this number is a palindrome (i.e. where the number and its reverse are identical).

Now a perfect palindrome will not always emerge from this procedure. However very frequently, one will arise. In most other cases the number will be very close to a palindrome, where with a small adjustment (e.g. changing the last digit by 1) a perfect palindrome emerges.

The holistic mathematical significance of this is that personality itself is based on the integration of complementary opposite directions. Thus when one successfully balances one polar tendency with its opposite, integration thereby results (with both opposite directions now identical with each other).

And as we have seen, just as "9" is especially useful in analytic terms for generating palindromes (from the combination of numbers with opposite sequences), equally "9" can play a special holistic role in terms of the successful integration of opposite tendencies in the personality.

Indeed the number 11 (which is + 1 with respect to 10) is also very interesting in this regard. It is holistically consistent with the positive (i.e.) conscious direction of personality!

Fascinatingly, when we attempt to generate palindromes in the same manner for 11, a polar split is in evidence.

When the number has an even number of digits, we must add the number and its reverse before dividing by 11. However when the numbers have an odd number of digits, we must subtract before dividing by 11.

So in this case (with 6 digits) we must add i.e. 200116 + 611002 = 811118. (Now in fact we already have a perfect palindrome, which will arise when the total contains the same number of digits. However such numbers will always be divisible by 11 (with again strong palindromic tendencies in evidence).

There are further fascinating number aspects.

With respect to the Enneagram, two distinct number groups (for integration purposes) are singled out.

The first is built around the unique sequence of digits for the reciprocal of 7!

Now 7 is especially interesting in this regard as it is the first - and best known - example of a full cyclic prime (in the denary system). For a full cyclic prime, the unique sequence of digits occurring in the decimal expansion of its reciprocal is just 1 less than the number in question!

And with 7, the unique sequence of recurring digits is 142857.

What is remarkable from a holistic mathematical perspective is that the primes represent the most independent of linear numbers (with no factors other than 1 and the prime number itself).

However when you then obtain the reciprocal of a prime, a complementary opposite picture emerges with its unique sequence of digits exhibiting amazing circular properties.

So for example if you multiply 142857 by 2, 3, 2, 5 or 6, the same circular sequence of digits will appear. For example when we multiply by 2 we get 285714 (which is the same number sequence with the circular position simply switched).

Therefore in holistic terms, this unique sequence of digits (for the reciprocal of 7) serves as a complementary model of interdependence (i.e. integration) in personality terms.

And remarkably with respect to the Enneagram, this circular sequence of digits (of the reciprocal of 7) plays a unique role.

For one attempts to achieve integration strictly with respect to an ordered movement through this circular number sequence. So for example a 4 (the Individualist) in Enneagram attempts to achieve integration by moving in the opposite direction (with respect to the circular sequence of digits).

Therefore the 4 would move to 1 (the Reformer) and then to 7 (the Enthusiast), 5 (the Investigator), 8 (the Challenger) and 2 (the Helper) respectively to achieve integration. The opposite direction then defines the process of disintegration. So the unhealthy direction for a 4 would be to move to 2 (and then to 8, 5, 7 and 1).

The other number (made up of the remaining digits) is 396.

This is already a very composite number with 5 factors (2.* 2* 3 * 3 * 11) again serving well for holistic integrative purposes. So for a "3" (the Achiever) to achieve integration movement would be in the opposite circular direction, to 6 (the Loyalist) and then 9 (the Peacemaker) with the opposite direction leading to disintegration.

Interestingly, in view of my earlier discussion on the holistic significance of palindromes, both 142857 and 396 are divisible by 9 and 11 respectively!

In fact Don Riso, who is perhaps the most authoritative writer on the Enneagram, provides an excellent blueprint of 9 different versions (from the healthiest to the most unhealthy) for all the 9 Enneagram types.

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