I have often stated that the current definition of "a string" is somewhat meaningless from any coherent physical perspective.

A string is viewed essentially as like a thin elastic band - extremely short in length - that is 1-dimensional (with no other spatial characteristic).

However this very definition requires the background existence of space. However it is then also admitted that the dimensions of space and time must in some way arise from strings (as the basic constituent ingredients of everything in the universe). So we clearly have an obvious problem.

Indeed there is a strong parallel here with a similar issue in mathematics relating to the prime numbers.

The prime numbers are conventionally viewed as the basic (independent) building blocks of the natural number system; however equally the general distribution of the primes intimately depends on the natural numbers.

Now I have explained that this issues of the primes in Mathematics ultimately relates to the fact that they can be given both a linear and circular interpretation which are relative.

So it is akin to the simple problem of defining left and right turns with respect to street directions. If for example one defines the direction of a road as either "up" or "down" (as independent) then left and right turns can be given an unambiguous meaning.

However when we treat them as interdependent with a relative meaning, then a turn on a road is both "left" and "right" (with the designation in any given circumstance purely arbitrary).

So with prime numbers when we try to treat the individual existence of prime numbers and the general distribution (overall) of prime numbers as independent, then both issues can be unambiguously studied through conventional mathematical methods.

However when we attempt to properly integrate these two areas, we require both a linear (quantitative) and circular (qualitative) treatment.

And indeed this is the very conclusion I reached with the Riemann Hypothesis which arises through attempting such integration in mere quantitative terms.

And of course it is exactly the same situation with respect to the world of strings.

So "a string" cannot be given an independent existence which already assumes a general background in space; likewise the dimensions of space and time cannot be given an independent existence as they only have meaning with respect to already existing phenomena.

So "a string" strictly has no phenomenal meaning as an independent physical constituent of matter; likewise "a string" has no phenomenal meaning with respect to the dimensions applicable to such reality.

It is only in relation to each other (where both the quantitative and qualitative aspects of matter dynamically interact) that phenomenal investigation of reality can begin.

And again the crucial point to realise is that this necessarily entails both quantitative and qualitative aspects of understanding (pertaining to both linear and circular interpretation of relationships).

Physical science as we know it is still based on a fundamentally false premise i.e. that phenomenal investigation of "specific objects" and corresponding investigation of the general dimensional background of such phenomena can both be interpreted in merely quantitative terms (using the standard rational linear approach).

However as we have seen object phenomena and the dimensions of space and time are in dynamic interactive terms quantitative and qualitative with respect to each other.

So therefore we must use a binary scientific approach combining both linear and circular type appreciation. Whereas the linear aspect corresponds to reason (as conventionally understood), the circular aspect corresponds directly to intuitive type appreciation.

However indirectly this intuitive aspect can be translated in a scientific rational fashion as "imaginary".

Thus a comprehensive scientific approach that can properly deal with the relationship of phenomena to space and time must be in qualitative terms of a complex rational nature (combining both real and imaginary aspects).

Properly speaking a string does not have an actual phenomenal existence (which would already imply space and time). Rather it represents the potential for manifest existence which has the two aspects of (differentiated) independence and (integral) interdependence.

So in a static sense, no distinction can be made as between the linear aspect of the string as (linear) differentiated form and the integral aspect as (circular) emptiness.

Thus in static binary terms therefore with respect to the string, the linear (1) cannot be properly distinguished from the circular aspect as nothingness (0).

However when these two aspects interact in dynamic manner (i.e. through the vibrations of the string) then we enter the world of actual manifest form. The most primitive excitations of the string would correspond in turn with the prime numbers (which in turn would represent the most fundamental particles).

And because at the lower energy levels very few particles become manifest which then serve as the basis for the natural phenomena we recognise, in like manner the majority of natural numbers arise as the composite expression of comparatively few early prime numbers!

So just as there are links in natural terms as between the original numbers (1 and 0), the primes and the natural numbers, there are similar links as between strings (defined in a binary fashion), the fundamental sub-atomic particles and natural phenomena.

However whereas both sub-atomic and natural phenomena enjoy a dynamic interactive actual existence in space and time, strings properly pertain to a mere potential for actual existence that underlies the manifest phenomena.

Thus irrespective of technological developments e.g. with respect to particle accelerators, it will never be possible to experimentally detect strings!

Once again from a more correct physical perspective, what are referred to as strings represent the inherent (linear) capacity of matter for differentiated form (as relatively distinct phenomena) and the equal inherent (circular) capacity for an overall qualitative integral relatedness (as holistic dimension).

Alternatively in more scientific language we can say that strings possess both a real and imaginary potential which in dynamic interaction generate both matter phenomena and the dimensions of space and time (which are inextricably linked).

## Thursday, September 16, 2010

## Monday, September 13, 2010

### Darwin and Riemann

When doing some research for my articles on the Riemann Hypothesis, I made the interesting discovery that both Darwin's Origin of Species and Riemann's famous article on prime numbers were both published in 1859 (just over 150 years ago).

Indeed the historic connection can be shown to be even closer with the publication date of Darwin's book in November of that year while the full text of Riemann's article also appeared in November (in the monthly reports of the Berlin Academy) though Riemann actually had delivered his address on the contents of that article to the Academy in August, 1859.

However recently I have come to see an even greater significance to this interesting coincidence of publication dates (of what constituted truly ground breaking initiatives in two different fields).

In earlier blogs I addressed the issue that any attempted reconciliation of science and religion would require two key developments.

1) the recognition of an alternative qualitative aspect to science, utterly distinct though of equal importance to the present recognised quantitative aspect.

2) the demythologisation of the manner in which universal spiritual truths are conveyed in the major religious traditions.

It is with respect to the latter of these requirements that Darwin's work is of such enormous significance.

Whereas Newton especially had paved the way early for this change with respect to the natural sciences, Darwin above all has helped to extend it to the biological sciences.

For example in the Christian tradition the evolution of life on Earth, especially with respect to the development of the human species had been shrouded in myth for which no proper scientific basis existed. So in providing a truly coherent scientific explanation for evolution of all life forms, Darwin effectively unmasked the nature of literal Christian beliefs in this regard.

Of course a proper scientific appreciation of the nature of evolution does not affect the legitimacy of spiritual beliefs per se (but rather the manner in which they may be presented in the religious traditions)!

As a child I had already embraced evolution (having dismissed in my own mind any literal basis to the Genesis account of Adam and Eve). However I never saw this as having any direct bearing on spiritual truth (which for me still possessed a powerful significance).

Perhaps because of this early clash with religious orthodoxy I have remained open to the manner in which so many Christian doctrines are still expressed in the form of mythical explanations.

So I do see unquestioning acceptance of the literal meaning of these myths as a major barrier to genuine discourse with the scientific community.

It is with relation to the first requirement above i.e. the need for a qualitative aspect to science, that I now see Riemann's article as being of immense potential significance.

As is well known, Riemann's article was to give rise to the famous Riemann Hypothesis (which still remains unproven from a conventional mathematical perspective).

As I had for many years suspected a hidden qualitative aspect to the Hypothesis in recent years I have given it considerable attention with a view to unravelling the barrier to its resolution.

To my amazement, I eventually was able to conclude that - when properly appreciated - the Riemann Hypothesis is really a statement regarding the basic requirement for maintaining consistency as between both the quantitative and qualitative aspects of mathematical understanding.

One obvious implication of this new understanding is that the Hypothesis has no proof from a conventional perspective (where only the quantitative aspect is recognised). Rather it serves as a more general axiom on which those axioms already used in conventional interpretation depend.

So, the Riemann Hypothesis in fact serves as a powerful expression of the need to incorporate a complementary qualitative with the recognised quantitative aspect of present science.

Thus from my newly adopted perspective, the very basis of the two great revolutions that are required (before science can be be properly reconciled with religion) have already been sown in two major contemporaneous developments in thinking some 150 years ago.

Indeed the historic connection can be shown to be even closer with the publication date of Darwin's book in November of that year while the full text of Riemann's article also appeared in November (in the monthly reports of the Berlin Academy) though Riemann actually had delivered his address on the contents of that article to the Academy in August, 1859.

However recently I have come to see an even greater significance to this interesting coincidence of publication dates (of what constituted truly ground breaking initiatives in two different fields).

In earlier blogs I addressed the issue that any attempted reconciliation of science and religion would require two key developments.

1) the recognition of an alternative qualitative aspect to science, utterly distinct though of equal importance to the present recognised quantitative aspect.

2) the demythologisation of the manner in which universal spiritual truths are conveyed in the major religious traditions.

It is with respect to the latter of these requirements that Darwin's work is of such enormous significance.

Whereas Newton especially had paved the way early for this change with respect to the natural sciences, Darwin above all has helped to extend it to the biological sciences.

For example in the Christian tradition the evolution of life on Earth, especially with respect to the development of the human species had been shrouded in myth for which no proper scientific basis existed. So in providing a truly coherent scientific explanation for evolution of all life forms, Darwin effectively unmasked the nature of literal Christian beliefs in this regard.

Of course a proper scientific appreciation of the nature of evolution does not affect the legitimacy of spiritual beliefs per se (but rather the manner in which they may be presented in the religious traditions)!

As a child I had already embraced evolution (having dismissed in my own mind any literal basis to the Genesis account of Adam and Eve). However I never saw this as having any direct bearing on spiritual truth (which for me still possessed a powerful significance).

Perhaps because of this early clash with religious orthodoxy I have remained open to the manner in which so many Christian doctrines are still expressed in the form of mythical explanations.

So I do see unquestioning acceptance of the literal meaning of these myths as a major barrier to genuine discourse with the scientific community.

It is with relation to the first requirement above i.e. the need for a qualitative aspect to science, that I now see Riemann's article as being of immense potential significance.

As is well known, Riemann's article was to give rise to the famous Riemann Hypothesis (which still remains unproven from a conventional mathematical perspective).

As I had for many years suspected a hidden qualitative aspect to the Hypothesis in recent years I have given it considerable attention with a view to unravelling the barrier to its resolution.

To my amazement, I eventually was able to conclude that - when properly appreciated - the Riemann Hypothesis is really a statement regarding the basic requirement for maintaining consistency as between both the quantitative and qualitative aspects of mathematical understanding.

One obvious implication of this new understanding is that the Hypothesis has no proof from a conventional perspective (where only the quantitative aspect is recognised). Rather it serves as a more general axiom on which those axioms already used in conventional interpretation depend.

So, the Riemann Hypothesis in fact serves as a powerful expression of the need to incorporate a complementary qualitative with the recognised quantitative aspect of present science.

Thus from my newly adopted perspective, the very basis of the two great revolutions that are required (before science can be be properly reconciled with religion) have already been sown in two major contemporaneous developments in thinking some 150 years ago.

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