As stated in the last blog entry, I see a comprehensive science as consisting of 3 distinct aspects, which for convenience can be named Type 1, Type 2 and Type 3.

Type 1 would correspond to the conventional scientific approach representing the analytic (quantitative) extreme to the interpretation of reality.

Its fundamental feature is that it is of a linear (1-dimensional) nature. This means that all relationships are rationally interpreted within single isolated polar reference frames.

In particular the (external) objective is abstracted from the (internal) subjective aspect; and the (individual) parts are abstracted from the (collective) whole.

Thus with Type 1 science, we have the reduction of subjective interpretation to objective explanation; equally we have the reduction of the whole (in any context) to parts.

By contrast Type 2 represents the holistic (qualitative) extreme to interpretation, which is all but unrecognised in our present world.

Whereas the Type 1 (analytic) approach corresponds with the linear use of reason, the Type 2 (holistic) approach is primarily based directly on intuitive insight, indirectly expressed in a circular rational manner. This implies that holistic type appreciation always appears paradoxical with respect to the conventional (i.e. linear) use of reason.

Linear reason is essentially geared to the quantitative analytic investigation of the parts of a system, where logical connections are made in a sequential manner. However intuitive awareness by contrast is directly geared to the qualitative awareness of the whole (where the relation as between parts are viewed simultaneously in a synchronous fashion). Indirectly, this awareness is then translated in a circular rational manner (that appears paradoxical in linear terms).

Though the importance of intuition might indeed be accepted by scientists, especially where creative work is involved, it is always in effect subsequently formally reduced in a merely rational manner.

So just as Type 1 science continually misrepresents the relation between analytic and holistic aspects in physical terms, equally from a psychological perspective, it fundamentally misrepresents the relationship as between (linear) reason and (circular) intuitive awareness.

Type 2 science starts where Type 1 science ends.

There are two fundamental polar sets that necessarily underlie all phenomena.

These are 1) the external/internal and 2) the whole/part aspects of experience.

The basic requirement with Type 1 science is that these poles be absolutely separated from each other, thereby eliminating consideration of the two-way interaction that necessarily takes place.

So for example as I am presently typing, I am aware externally of the computer screen (relative to my internal self). However through the dynamics of experience this keeps switching so that I also become aware of my internal self (in relation to the external screen). So a dynamic two-way relative interaction ceaselessly takes place (leading to transformation with respect to both external and internal aspects). However conventional science absolutely freezes this interaction, thereby creating the illusion that the external world has a coherent meaning (independent of the interpreting self).

Likewise there is a ceaseless two-way interaction in every context as between the whole (that provides a qualitative relationship for parts) and the constituent parts (that provide the quantitative data to be related).

However conventional science once more absolutely freezes this two-way relative interaction so that the (qualitative) whole aspect is inevitably reduced to its (quantitative) parts.

This is perhaps the most important and blatant form of reductionism in conventional science, that is so widespread that it is rarely ever even noticed!

The central concept in Type 2 (holistic) science is that of complementarity.

Thus what are understood in linear rational terms as direct opposites are now seen in Type 2 terms as constituting an essential unity.

To make this a little more accessible, I will deal firstly with a simple example that should resonate with everyone.

Imagine one is travelling along a straight road approaching a crossroads. Now once we define the direction from which it is approached in 1-dimensional terms (i.e. with respect to a single isolated pole of reference) Type 1 (linear) rational interpretation applies.

So if one is heading N and reaches the crossroads, then both left and right turns can be unambiguously defined. Then if having passed through, one then reverses direction heading S again both left and right turns can be unambiguously defined with respect to the crossroads.

However if we now simultaneously attempt to view the situation where the crossroads can be approached from both N and S directions, then an inevitable paradox applies to directions.

Thus what is defined as a left turn when approaching the crossroads in the N direction is a right turn when approaches from the opposite side heading S. And what is a right turn heading N is by the same token a left turn heading S.

Thus in this second context (where two reference frames are viewed simultaneously) both left and right have a contingent arbitrary meaning (depending on relative context).

Now the very ability to appreciate to the merely relative nature of the two turns at the crossroads requires holistic intuition (where two reference frames can be viewed simultaneously).

And as we have seen, this leads to a (circular) paradoxical outcome from the conventional rational perspective.

Now one might initially query why this example should have important implications for science. However the key here is the recognition that all actual experience is based on mutually switching polar reference frames. Thus on the one hand we have the necessary interaction of external and internal aspects of experience; likewise we have the mutual interaction of whole and part aspects.

Thus once we move to consideration of this dynamic interactive nature of experience, we must necessarily move on to a new holistic type of scientific appreciation (i.e. the Type 2 approach).

As we saw in our crossroads example, there is an inevitable complementarity as between left and right turns (when viewed simultaneously from 2 reference frames).

However, this complementarity universally applies to all experience (which is dynamically conditioned by interacting polar opposite reference frames).

Perhaps most critically, though it is not yet even been considered by the profession, it applies to all mathematical relationships.

My first realisation that there was something seriously wrong with accepted mathematical interpretation came at the age of 10, when I found myself in class carrying out empirical estimates of the area of various rectangular fields.

Thus if for example we have a field that is 80 yards long and 60 yards wide the area will be 4800 square (i.e. 2-dimensional) yards.

Thus as well as the quantitative change area with respect to the area there is an inescapable qualitative change also in that we move from linear (1-dimensional) to square (2-dimensional) units.

However in conventional multiplication, the qualitative aspect is simply ignored altogether.

Therefore 40 * 80 = 4800 (in a merely quantitative i.e. 1-dimensional manner).

Even at that tender age, I knew that there was something seriously wrong here! And this subsequently led me on a life-long quest to properly incorporate the neglected qualitative aspect into mathematical understanding.

This problem becomes acute, when we come to consider the relationship of the primes to the natural numbers (which is the most fundamental area of mathematical research).

The primes are considered as the "building blocks" of the natural numbers. So each composite number - say 6 - is uniquely expressed as the product of prime factors (i.e. 2 * 3).

However in conventional terms, only the quantitative aspect of the primes is considered.

So if we take the first prime i.e. 2 and attempt to break it into its constituents it would be given as

2 = 1 + 1. So each of the units here are interpreted in a homogeneous quantitative manner (i.e. without qualitative distinction).

This represents the cardinal notion of number.

However there is a corresponding ordinal approach (where the qualitative aspect is now emphasised).

So from this perspective 2 = 1st + 2nd. However 1st and 2nd only have meaning in the context of a circular type relationship. Thus their sum has no quantitative meaning.

I then realised that both the cardinal and ordinal approaches to number are themselves directly complementary.

In the cardinal approach, we deal with the quantitative collective aspect of number (where individual units have no qualitative distinction); in the ordinal approach by contrast, we deal with the individual qualitative aspect of number (where the collective sum has no quantitative distinction).

This then implies the crucial finding that the ordinal nature of number (which relates to the holistic notion of number interdependence) cannot be properly defined within the conventional (Type 1) mathematical approach.

And as both cardinal and ordinal recognition are necessarily intertwined in the very manner we understand numbers in experience, this means that we cannot properly define the cardinal notion either (in the absence of Type 2 understanding).

In other words, Mathematics is inherently of a dynamic interactive nature, where all relationships entail the interaction of complementary poles (in quantitative and qualitative terms).

However Conventional Mathematics is misleadingly represented in reduced absolute terms as the relationship between fixed static entities.

Thus the greatest revolution yet in our intellectual history will eventually begin to unfold when the inherent dynamic interactive nature of Mathematics is eventually embraced. And this will entail the recognition of both analytic (quantitative) and holistic (qualitative) aspects as equally important partners.

This of course equally applies to all the sciences (that are rooted in mathematical understanding).

Once again I find it striking how two developments with very opposite implications occurred at the same time in 1859. Darwin's theory of evolution really represents the last big application of the wholly reductionist approach to science. Riemann's findings regarding the prime numbers are however pointing directly to the severe cracks in the very foundations of that reductionist approach.

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