As stated before in this holistic mathematical model, I outline 7 major bands on the overall spectrum of development (with three main levels in each band).
We have already looked briefly at the three main levels of the lower band.
So we are now ready to look at the next band (referred to as the middle band).
Again this comprises three main levels.
Though again each level entails spiritual, affective and cognitive aspects of development, as I am mainly concerned in the present context with the scientific implications of such development, I will concentrate therefore mainly on cognitive and spiritual aspects.
Up to the middle levels, the holistic nature of the unconscious remains confused to a degree with the specific conscious recognition of phenomena.
So the initial task of development is largely concerned with the gradual differentiation of conscious from (confused) unconscious type recognition.
As this successfully unfolds through the lower lowels, consciousness becomes more linear in nature with a child increasingly able to abstract the fundamental poles - which fundamentally underlie all experience – from each other.
For example, all experience is governed by external (objective) and internal (subjective) poles. So linear understanding in this context thereby entails the ability to consider the external as independent of the corresponding internal pole.
Likewise all experience is governed by whole (collective) and part (individual) aspects.
Again linear understanding in this context entails the analytical ability to view parts in abstraction from their overall whole context.
Now, linear implies 1- dimensional. So linear interpretation is literally 1-dimensional in nature whereby - in any relevant context - understanding is based on just one isolated pole of reference
Now the great benefit of such differentiated conscious understanding is that detailed knowledge of an unambiguous rational nature is made possible which can be applied to a wide range of fields.
However the corresponding disadvantage, which unfortunately becomes quickly overlooked, is that it leads to a reductionism and fragmentation with respect to overall experience.
In other words the analytical process of differentiating overall experience (which is of a conscious nature) is quite distinct from the corresponding holistic process of achieving integration with respect to such experience (which is directly of an unconscious nature).
Thus the specialisation of conscious experience (which is the appropriate task of the middle stages) should be seen as just one important step with respect to the much greater task of overall development.
Unfortunately in our culture it is largely seen as an end in itself!
So our current notions of Mathematics and Science are built - almost - exclusively on the linear rational modes of consciousness that characterise the three levels of the second band.
So rightly understood, though we have indeed made great progress with respect to the specialised development of differentiated notions of science, we have neglected almost entirely the task of developing corresponding integral notions.
Therefore from this perspective, present science can be seen as highly unbalanced.
Thus rather than just one type of science (including Mathematics) as at present, properly understood we should have at least three!
1. Analytic science - based on specialisation with respect to differentiated (conscious) interpretation of a rational nature.
2. Holistic science - based on specialisation with respect to integrated (unconscious) interpretation of an intuitive nature.
3. Comprehensive science - based on the balanced dynamic integration of both analytic and holistic aspects.
Thus once again, the 2nd band is only directly of relevance to analytic notions of science. Successful specialisation with respect to holistic and - ultimately - comprehensive notions of science, require ongoing development with respect to all the major bands on the full spectrum.
The first level of this band (Middle 1) relates to the more superficial perceptual experience of the senses where a growing specialisation with respect to its specific concrete data occurs. Piaget refers to this level as Conop (i.e. Concrete Operational Thinking). More simply I generally refer to it as the concrete level.
The second level of the band (Middle 2) is relating now to rational specialisation with respect to the deeper more general concepts of experience as exemplified by abstract theoretical expressions of a universal nature. Piaget refers to this level as Formop (formal Operational Thinking) which in simpler terms can be referred to as the formal level.
The thirds level of the band (Middle 3) is related to the more creative expression of the previous two levels.
Though implicitly it is dependent on a rich deposit of intuitive type appreciation (of an unconscious nature) it is expressed formally though accepted linear rational modes.
So a great scientist like Einstein would have operated very much from this level. However having obtained his key insights from intuitive type recognition, he then sought to formally express his theories in the traditional linear rational mode. So Einstein stuck rigidly to the objectivist fallacy right through his life i.e. the idea that external (objective) phenomena somehow remain unchanged through our internal (mental) interaction with them.
So this is precisely linear in the manner that I define the term.
Even though Quantum Mechanics raises severe questions regarding this approach, there is as yet no acceptance of the need for an alternative scientific paradigm.
Thus to conclude this entry we can briefly see how all these three levels of the middle band are very much to the fore with respect to conventional scientific practice.
The 1st (concrete) level is especially important for scientific research; the 2nd (formal) is then to the fore with respect to formulating (and proving) abstract hypotheses and theories; the 3rd level, is then evident where especially creative new scientific discoveries are concerned.
However even within accepted notions of science there are obvious dangers with respect to over-specialisation with respect to each of these levels.
For example .with too much focus on concrete data a scientific researcher we lose the ability to recognise key general patterns with respect to such data; equally too much attention to abstract theory can gradually erode the ability to meaningfully apply such theory in a concrete situation; finally too much attention on the “big” insights can lessen the ability to rationally apply such insights in a scientific acceptable manner.
The huge danger - that is again largely unrecognised in conventional scientific terms - is that extreme specialisation with respect to (linear) rational modes of analytic enquiry creates an enormous shadow with respect to corresponding holistic unconscious modes.
Properly understood, what we exclusively identify in our culture as acceptable science represents an extreme narrowing with respect to its full potential expression.
And unfortunately the very process of specialising so much in this analytic type of science greatly erodes the very (unconscious) base from which the alternative holistic type can emerge.
In my next entry, I will use a fascinating holistic mathematical explanation to demonstrate the precise nature of this problem.