In
particular I singled out his song “Tapestry” in this regard. This provides both
a wonderfully poetic description of the holistic interdependence of creation
and the grave threat that is now posed to our environment through economic
mismanagement of the planet’s resources.

Now you
might think that this has nothing whatsoever to do with Mathematics, but
certainly from my perspective you would be fundamentally wrong in this regard.

The current
mindset that dominates economic thinking (with its emphasis on the exploitation
of natural resources) is firmly rooted in our limited view of science (that
attempts to view the environment in a detached objective manner).

And this
view of science in turn is rooted in an ultimately distorted appreciation of
Mathematics that misleadingly attempts to divorce quantitative from qualitative
reality.

And this likewise leads to the attempted separation of the arts and the sciences
(which again from an overall holistic perspective is most unhealthy).

Though I would maintain that the arts and sciences represent separate domains corresponding
to distinctive methods of understanding, they do so in a merely relative sense.
So ultimately from an overall human perspective they represent complementary
pursuits (that are necessary for each other's integrated development).

Thus when
we adopt an experiential perspective that is truly holistic, we no longer
attempt to compartmentalise disciplines in a rigid manner.

Therefore in
this spirit, I am suggesting to you that obtaining the fundamental insight
to appreciate what the Riemann Hypothesis is truly about, can perhaps more easily come directly from
artistic rather than scientific - or indeed direct mathematical - appreciation.

Indeed in
this regard I suggest that you listen with a fresh mind to a song like “Tapestry”.

In
connection with the Riemann Hypothesis, mathematicians often use the analogy
of the music of the primes. However because of their compartmentalised
training, they never seem to make the connection that music
represents essentially a qualitative - rather than quantitative - mode of appreciation.

Put another
way, it represent a holistic appreciation of the qualitative interdependence of
various constituent notes, chords, instruments etc. rather than the strict analytic interpretation
of each individual item in a quantitative manner.

However as it stands, Conventional Mathematics is totally lacking a qualitative dimension (in
formal terms). Alternatively it is totally lacking a genuine holistic means
of appreciating its relationships.

And as the
mystery of the Riemann Hypothesis essentially relates to the marvellous interdependent
aspect of the number system, Conventional Mathematics remains simply
incapable of recognising its true nature.

So it is like in a detective story where all the evidence is available to solve the crime, but no one can make the obvious inferences.

Now,
though admittedly written in an artistic – rather than scientific – context,
the opening lines of “Tapestry” are very revealing.

“every
thread of creation is held in position

By still other
strands of things living."

So in the
context of our holistic appreciation of the number system, the threads here
refer to the prime numbers.

Now these
prime numbers are held in position by the (non-trivial) zeta zeros. And I have
been continually making the point that there are in fact two complementary sets
of zeta zeros (Zeta 1 and Zeta 2).

So these
zeta zeros play a true holistic function in perfectly shadowing the prime
numbers (which - relatively - are of an independent analytic nature).

In other words
they ensure that the primes are locally distributed in just one optimally
possible manner, so that their (relatively) independent nature at this local
level, is yet fully compatible with their overall holistic interdependence in collective terms.

So in this
way we have individual unique notes (the primes) comprising a cosmic number
symphony (with not one note out of place). And this is because the precise
positioning of the primes is holistically determined by the zeta zeros.

We could equally maintain from the reverse perspective that there is a holistic
nature to the primes (as a collective whole) which ensures that not one of the non-trivial zeros (as
relatively separate) is out of place!

As I have
continually emphasised in my blogs, the holistic nature of the primes comes from
their dimensional nature (which indirectly is expressed in a circular manner).

So, for example, we can
view the prime number 3 in two ways:

1) in a
linear cardinal manner. Here 3 = 3

^{1}(where the quantitative number 3 is raised with respect to 1 as representing its default qualitative dimension).
2) in a
circular ordinal manner. Here 3 = 1

So the primes (which must always be considered in two-way relationship to the natural numbers) keep dynamically switching as between cardinal (quantitative) and ordinal (qualitative) meanings.

^{3 }(where the default quantitative value 1 is raised to 3 as representing its varying qualitative dimension). Indirectly this qualitative dimensional notion of 3 is expressed in a circular quantitative fashion through the 3 roots of 1).So the primes (which must always be considered in two-way relationship to the natural numbers) keep dynamically switching as between cardinal (quantitative) and ordinal (qualitative) meanings.

Now the
lyrics of Tapestry refers to “other strands of things living”.

This leads
to the greatest surprise of all regarding the number system i.e. that from an
authentic dynamic perspective, it is indeed living!

The reason
for this remarkable property is that properly understood, numbers do not exist in some abstract
world, but rather as the fundamental inherent encoding of all living phenomena.

So through
incorporating the qualitative with the quantitative aspect of number, one’s
whole appreciation of the nature of number radically switches to viewing it as
the intrinsic encoded nature of all living systems. And from this perspective, everything
in nature - from the most minute sub-atomic particle up - is understood as necessarily comprising part of a living
process!

So perhaps we
can now appreciate a little better the tapestry of the number system (as
a dynamic living system with twin analytic and holistic manifestations which can switch
depending on context).

This of
course also implies that the number system is an intelligent system.

Again the
very reason why we find this so difficult - even abhorrent - to appreciate is because
we have become so used to looking at number in a distorted (merely quantitative)
fashion.

So again
the mystery of how the primes can be so perfectly distributed throughout the
number system, points directly to its holistic intelligence (manifested through
the zeta zeros) which ensures such synchronicity. Thus in a very important sense, the fundamental nature of the holistic intelligence that pervades all creation is thereby enshrined in the zeta zeros.

I will
quote part of another verse from “Tapestry” which may be instructive.

“Where
the birth and the death of unseen generations

are interdependent in vast orchestration

and painted in colors of tapestry thread.

When the dying are born and the living are dead."

are interdependent in vast orchestration

and painted in colors of tapestry thread.

When the dying are born and the living are dead."

Now again
in the context of the number system, the unseen generations here can be taken to
refer to the unlimited nature of the zeta zeros.

Though
many billions of these have now been detected (and inevitably will keep
increasing), this represents but a very small set of all zeros.

So the interdependence
of the primes with the number system is in fact dependent on all these unseen generations
of zeta zeros which act to ensure perfect synchronicity.

So again this
is how we can locate the “tapestry threads” i.e. the individual primes (through the background holistic activity of the zeta
zeros).

Now the
last line is very instructive here:

“when the
dying are born and the living are dead”

This essentially
points to the ultimate paradoxical nature of the relationship of the primes to
the natural numbers.

The very appreciation of interdependence implies paradox (from a dualistic
perspective). If the primes and natural numbers are truly interdependent - which
indeed ultimately they are - this implies that the primes in a sense are contained in the
natural numbers and the natural numbers in turn contained in the primes. So from the cardinal perspective each natural number represents a combination of prime factors; however equally in reverse from the ordinal perspective each prime represents a combination of natural number members!

So in
this sense the primes (ultimately) are seen as perfect mirrors of the natural
numbers and the natural numbers as perfect mirrors of the primes.

And the only
way of truly seeing this relationship is through avoiding any rigid
identification in understanding with either perspective (in isolation).

So in this highly dynamic appreciation,
the primes, as mirrors of the natural numbers, only can live briefly in experience
through letting the alternative complementary perspective (of the natural numbers as mirrors of the primes) momentarily die.

Then the
corresponding dynamic appreciation of the natural numbers as mirrors of the primes can in
turn only live briefly through again letting the alternative perspective
(of the primes as mirrors of the natural numbers) momentarily die.

Thus
ultimately the pure experience of this mutually interdependent relationship is ineffable!

I will
finish up by quoting the last verse of “Tapestry”

“Every
fish that swims silent, every bird that flies freely,

every doe that steps softly.

Every crisp leaf that falls, all the flowers that grow

on this colourful tapestry, somehow they know.

That if man is allowed to destroy all we need.

He will soon have to pay with his life, for his greed.”

every doe that steps softly.

Every crisp leaf that falls, all the flowers that grow

on this colourful tapestry, somehow they know.

That if man is allowed to destroy all we need.

He will soon have to pay with his life, for his greed.”

This
clearly is pointing to the holistic nature of intelligence that pervades, in a
fully natural manner, all plant and animal life on the planet.

The
remarkable assertion here is that human beings uniquely possess the capacity to
behave in an unnatural manner, thereby having the potential to destroy all that
is in nature.

Now the
intellectual roots of this unnatural behaviour lie deep in the nature of our distorted
mathematical appreciation. And it is such appreciation that directly informs in turn
our scientific and economic thinking!

And as we
have seen, though again most readers again might find this abhorrent to accept, the ultimate
reason for our capacity for such unnatural behaviour lies
in this deeply confused interpretation of the nature of the number system (and by
extension all mathematical understanding) where we have attempted - wrongly - to completely
divorce qualitative from quantitative type appreciation.

So we
have lost any concept of the global holistic nature of intelligence (as the collective
unconscious of all life forms).

And again
this is because we have attempted to portray Mathematics and the sciences - misleadingly - as representing merely
conscious activity.

We are
thereby reaching a true crisis now on our planet where due to this great imbalance, we are in increasing danger of
being swamped through ever more frequent economic and environmental
disasters.

Much as
we might hate to admit it, the key intellectual cause of all this problem lies in our extremely limited interpretation of the nature of the number system (and by extension all mathematical relationships).

Many
continue to look on Mathematics as the one area of truth that can remain
safely insulated from the contamination of global change.

In fact, properly seen,
Mathematics (or rather our false understanding of Mathematics) is the root intellectual cause
of this growing contamination!

## No comments:

## Post a Comment