When one properly recognises how the qualitative aspect of understanding (pertaining to interdependent relationships) is necessarily involved in all mathematical understanding and that furthermore this aspect cannot be appropriately understood from a quantitative perspective (which entails gross reductionism) then the very nature of Mathematics is transformed in a radically different manner.

For from this new perspective, Mathematics is understood inherently in a dynamic manner (through the interaction of both quantitative and qualitative aspects).

Now every mathematical symbol, theorem, relationship etc with an established quantitative interpretation can equally be given a distinctive qualitative interpretation (of a holistic nature).

Though I have made this point repeatedly over the years, I have the strong impression that very few have grasped the significance of what it means.

For we are not talking here at all about an extension of existing Mathematics (as it is currently understood) but rather an entirely new type of Mathematics which will have many important applications that cannot yet be even imagined.

Conventional Mathematics is based on a very strong specialisation in the linear rational approach.

Though intuitive capacities may informally be recognised as also necessary for such Mathematics (especially where creative work is involved) it is given no formal role in interpretation. Quite simply therefore the very nature of intuitive understanding is grossly reduced in a misleading rational manner (which ultimately distorts its true nature).

So the qualitative aspect of Mathematics is based directly on specialisation of the intuitive nature of understanding (which indirectly can then be interpreted in a circular logical fashion).

Thus with respect to Mathematics we have two extremes 1) the specialised quantitative approach based on linear reason and 2) the specialised qualitative (contemplative) approach based directly on intuition (that indirectly can be given rational expression in a circular logical fashion).

And in between these two extremes we have the inevitable interaction of both quantitative and qualitative aspects in a dynamic manner. And this is where mathematical activity properly takes place.

Most of my own work has been with respect to the qualitative interpretation of number and I spent many years in attempting to precisely clarify the holistic qualitative meaning of all the major number types i.e. the original numbers (1 and 0), the primes, natural numbers and integers, the rational and the irrational numbers (algebraic and transcendental) the transfinite and most of all imaginary and complex numbers.

For example it strikes me as amazing that mathematicians make widespread use of imaginary numbers (without having any clear philosophical notion of what this entails).

The understanding of the deepest problems in Mathematics and elsewhere ultimately requires a strong philosophical dimension and this is especially true with respect to the fundamental nature of prime numbers. No amount of mathematical techniques, regardless of how sophisticated, can substitute for example for a proper philosophical understanding of the true nature of the Riemann Hypothesis.

Indeed I would maintain that such understanding would quickly lead one to the realisation that this proposition cannot be proven (or disproven) in conventional mathematical terms! In fact in the best sense of the word it transcends the very nature of current mathematical interpretation!

A dynamic approach to Mathematics immediately establishes a direct relationship with the physical world where - by definition - it is necessarily seen as an encoding of what in some sense already phenomenally exists (in a physical manner).

Once again the Riemann zeros lead inevitably to the view that the prime numbers do not in fact abstractly exist (which itself arises from the merely quantitative perspective) but in fact are already inherent in physical matter - literally - at its most primordial (i.e. prime) level.

When one follows this to its logical conclusion, as we probe ever closer to the original nature of matter that Physics and Mathematics become inseparable. So in this sense the ultimate nature of the physical universe is inseparable from the ultimate nature of the prime numbers.

Now admittedly there is some growing recognition of this fact with the Riemann zeros being likened to the vibration of some physical system. I would put this more emphatically. The prime numbers (in their relation to the natural numbers) in fact correspond to the vibration of an original physical system that subsequently governs the nature of physical evolution!

However Mathematics, from the dynamic perspective, not alone has a direct relationship to physical phenomena (through which they are encoded) but also psychological reality.

Just as external (objective) and internal (subjective) dynamically interact with respect to experience, this means that Mathematics - when seen from this dynamic perspective directly relates to all psychological life.

Now again speaking in the context of the Riemann zeros, this is an aspect that has been totally missed with respect to their nature.

For not alone do these zeros have immense significance in physical terms, they equally have immense importance from a psychological perspective.

The prime numbers in qualitative terms bear a close relationship with primitive instincts where basically conscious is directly confused with unconscious interpretation. Indeed in this sense we could refer accurately to the beginning of physical creation as a totally primitive state! Now attaining the highest contemplative state requires a profound mastery of such instincts!

I have little doubt that some future stage in our evolution, qualitative mastery of the nature of the Riemann zeros will enable many to reach extraordinary levels of spiritual realisation.

So the quantitative problem of understanding the nature of the primes (lying at the beginning of physical evolution) ultimately coincides with the complementary qualitative problem of fully mastering the nature of primitive instinctive behaviour (lying at the end of spiritual evolution).

Indeed both these tasks are identical as appreciation of the ultimate nature of the prime numbers in pure mystery (from a quantitative perspective) can only be fully achieved through the corresponding realisation of an ineffable spiritual state (from a qualitative perspective).

Thanks for sharing the information and I am here to discuss about a simple topic in mathematics that is rational expression,Rational expressions is known as an expression that is the ratio of two polynomials.It is called as rational because one number is divided by the other that is like a ratio.

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