However, perhaps the truly primary mode is that of volition (which expresses a fundamental purpose or orientation towards meaning, with respect to experience).
It serves therefore in effect as the key manner through which the attempt to achieve successful balance as between both the cognitive and affective modes is itself maintained.
When the personality is operating at the optimum level, substantial harmony therefore will be in evidence with respect to the complementary manner in which both cognitive and affective modes interact (without either attempting to dominate the functioning of the other). In such circumstances the will itself will tend to operate at the optimum level in enabling the further enhancement of the harmonious development as between the two other modes.
Indeed in such circumstances, the personality can operate with true freedom.
However when the initial relationship as between cognitive and affective is somewhat unbalanced, this sets limits to the freedom in turn in which the will can operate.
In other words, the will is likely to misinterpret the signals from the two other modes, thereby perpetuating a situation whereby just one mode maintains dominance.
However even here substantial readjustment is possible provided a person can keep tuning in with discernment to the quality of ultimate meaning being attained.
Therefore when this desire for true ultimate meaning is very marked - which is manifest for example in personalities with a strong spiritual orientation - the will can operate is such a way as to enable substantial transformation regarding any previous unsatisfactory relationship with respect to the cognitive and affective modes.
Thus the true nature of the volitional mode is rooted in the innate desire in the personality for ultimate meaning!
Therefore - though considerable overlap in practice necessarily takes place - the volitional, cognitive and affective modes are closely related to the spiritual domain of (ultimate) being, the rational world of (logical) thinking and the emotional world of (responsive) feeling respectively.
Though, again while stressing that every personality is unique, it is not really possible to attain true meaning without successfully balancing these three modes (without reduction of one domain to another).
In this context, the considerable problem of the scientific worldview, which dominates our present culture, is that it does in practice lead to the unbalanced - and therefore highly undesirable situation - where both the volitional and affective modes are substantially reduced in terms of the cognitive!
Though both cognitive and affective modes can indeed be given - as we have seen - a coherent holistic mathematical interpretation, this cannot be directly achieved in terms of the volitional.
However a fascinating indirect representation is indeed possible.
This entails adopting an 8-dimensional perspective.
Now in standard mathematical terms, the eight roots of 1 are,
+ 1 , – 1, + i, – i, k(1 + i), k(1 – i), k(– 1 + i) and k(– 1 – i) respectively, where k = 1/√2.
Now we have already dealt with the first four of these roots. The last four are all complex roots where the magnitude of both real and imaginary parts is the same.
In holistic mathematical terms, they enables us to provide an expression for the purest attainment of will where form = emptiness.
Thus from the perspective of form, at the highest level of personality, both real (conscious) and imaginary (unconscious) phenomena can be seamlessly integrated (without undue attachment to either aspect).
In this sense both real and imaginary are equalised with each other.
However using the Pythagorean Theorem, where both adjacent (real) and opposite (imaginary) sides are equal, the hypotenuse, which is the sum of the square of both = 0.
(For 12 + i2 = 1 – 1 = 0).
Now these diagonal lines, representing the hypotenuse of a right angled triangle are referred to in physics as null lines (literally without quantitative magnitude).
So the holistic mathematical interpretation is that when both real (conscious) and imaginary (unconscious) aspects of personality are brought into close equal balance with each other - entailing a highly dynamic seamless interaction of phenomena, experienced without undue attachment - a state of spiritual emptiness (i.e. nothingness in physical terms) results.
Thus we can see perhaps how beautifully the 2, 4 and 8 roots of 1 are related in holistic mathematical fashion to the dynamics of development.
The two roots (+ 1 and – 1) enable us to provide, relatively, positive (external) and negative (internal) directions for both cognitive and affective modes.
Then the four roots ( + 1 , – 1, + i, – i) then enable us to provide real (conscious) and imaginary (unconscious) aspects for both cognitive and affective modes, in both positive (external) and negative (internal) directions.
The eight roots then enable us to provide expressions of form (complex, with real and imaginary parts equal)) and emptiness (null lines = 0) for the relationship of will - in all four quadrants of the unit circle - with cognitive and affective modes relating to real (conscious) and imaginary (unconscious) aspects in both positive (external) and negative (internal) directions.
And this enables us, in holistic mathematical terms, to provide a complete model of Personality Types.
In fact, even for the most sophisticated models currently in vogue, we solely require a 4-dimensional (rather than 8-dimensional approach).