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These observations correspond with my belief that physical reality is fundamentally spectral and random in origin. The traditional approach to this subject has been through analysis and therefore uniqueness. Notions of smoothness may be the wrong language to use here, with the Zeta function. For instance many phenomena in nature are fractal. As like the branches of a tree, they may exhibit glint, spikes or flash. Signals may be Analog or Digital, so signal processing provides a very general language and does not necessarily require a classical spatial continuum in its description. Indeed, Weierstrass, the father of modern day analysis postulated a continuous function that is no-where differentiable. A recent paper by S. C. Woon has indicated that Riemann Zeta function is a fractal and that through Voronin's Univerality encodes The Sum of All Theorems.

As a convolution of signals, everything maybe reduced to possible combinations of Signal + Noise in allowable configurations with effective Signal-to-Noise ratio – light, heat and sound are perceptions of waves and our brains are in fact wave-sensing devices. I suspect the total number of photons has to do with allowing the different features in scale to be seen from Quantum (very small) to Euclidean (in everyday experience) to Cosmological (very large). This includes the large-scale modulation (large wavelengths) that we simply don’t notice. It maybe that a critical amount of quanta is needed – Googol =10^100 say, to cause this as seen on the Dyson-Montgomery information curve. THERE IS NOTHING MAGICAL IN ALL OF THIS IN THAT IT IS ONLY THE AMOUNT OF POSSIBLE INFORMATION IN THE UNIVERSE THAT GIVES RISE TO ITS FEATURES OF SCALE - THAT IS ALL THAT THERE IS. The modulated Rice function is just an information curve – of all possible information. The primes represent unique ‘infon’ states albeit through a complicated relationship to the encoded Zeta function. The primes represent the minimal bit length of possible information that can be compressed19 as they can't be factored down into smaller integers (otherwise they would eventually be broken down to nothing). 

Zeta effectively simulates the ensemble of all physical reality, and the reality is itself quantal, although our brains are not consciously aware of this level of reality.

The RICE distribution contains a Modified I0 Bessel functions (of the 1st kind – zeroth order) multiplied by the Rayleigh density, and my modification is extended to be RICE distribution multiplied by a combinatorial sum which is the sum of all possible signals. 

Computation in Zeta may not have yet revealed the cosmological characteristics (viz. the Rice modulation of all combinations of signals) in the statistics of the Montgomery-Dyson curve, because of the current limits to bit capacity, and that bit itself is deterministic (quantum computing is still in its infancy).

The cosmological implication to all of this could be that the ‘Big Bang’ is still happening but only at larger scales; the spike could be that of dark energy – the missing 73% or so that pushed out  (area under the spike). The outgoing information 'shock wave' carries on for eternity. The dark matter are seen as ripples in the Montgomery-Dyson curve, and imprinted as the gravitational rotation curves (Reference Vera Rubin) associated within the space curvature across large scale galactic structures. Galaxies may have super massive black holes at their centers, such as 'The Great Annihilator' at the center of our Milky Way. They have the mass of millions of suns, and it has even been suggested are the gateways to other universes (via Rosen-Einstein bridge) by forming a neutral force ring between the central singularity and centrifugal rim. These lead to some important questions: Are black holes described by thermal phenomena limited to the left hand side of the curve? Could it be that black holes, as well as physically essential to stability, are demanded to logically exist?

What we see in our observable Universe is the small-scale debris left behind after a massive ‘shock wave’. If we increase our field of view looking out on the cosmos using some super telescope, SNR increases on the Dyson information curve (where the mean signal-to-noise ratio is normalised; <SNR>=¼). A constant position in scale in an expanding universe implies eventual thermodynamic ‘heat death’ as the noise-limited case is approached in time (increasing entropy), while the farthest reaches are seen to be accelerating away (negative tangent beyond the singularity at π/2). For 'Sum of all Possible Signals + Noise' , read as 'Sum of All Possible Universes'. This may help explain Hawking's 'No boundary' proposal, in that the universe is infinite.

This negative pressure field may represent the inflationary phase of the universe where matter and radiation were not yet separated, but the universe become transparent when crossover occurred to positive pressure, and gravity started to cluster mass objects. The Casimir Effect may affect the energy of the vacuum to be actually manifested in the resonances of the Riemann Zeta function in the far limits up the Critical Line.

Thus in effect:

The sum of all signals, where each signal is noise modulated with infinite detail, gives rise to physical reality.

Zero point energy is seen at these higher cosmological scales with some infinite bandwidth by Fourier transforming) from an unlimited information/energy tap from the ‘big bang’ spike in the ‘time' domain. This originates from the modulated tangent in the RICE probability density function and it may be the means why our Universe evolved from ‘Nothing’ (+d –d =0, where d® ¥), with a mirror image of an antimatter universe. It is therefore nilpotent at the zeros.

Renormalization makes the area under the spike finite. We'll discuss this next:


In recent months, I've had time to further reflect on some fundamental and probably unanswerable metaphysical questions within our present language. Partly based on my findings, I propose a possible programme for others to run with. I've put these in as bullets for discussion and allude to some of them:

"I am Alpha and Omega, the beginning and the ending,.." (Revelation 1:8)


Adrian Rifat


A special acknowledgement goes to my friend Ron Mantay who helped me construct this website. The pioneers of the internet have enabled an ordinary person like myself to disseminate my own findings and experience from a different subject perspective, that may be of interest to others. I am especially grateful to Matthew Watkins for including my paper to his site which is an audacious enterprise to connect Number Theory with Physics.

I have made 'clear blue water' between myself and the mathematical community for at least two years. I passionately believe that mathematical knowledge is for everybody and nobody owns it. There is a real hunger for understanding of the deep fundamental questions by people not necessarily associated with traditional academia, who work independently, but who have equally worthy contributions from their own professions and experiences especially in subject areas such as engineering and information science that may overlap. Often they can be easily dismissed and tarnished with the same brush as 'nutters' or 'cranks' . Individuals, hobbyists and amateur scientists & inventors are often self-driven, and may choose for whatever reason or be unable to be part of the other groups. They may feel excluded, they maybe ridiculed, yet the very exclusion may actually drive them. They may work in their garages or garden sheds and this country has a history of eccentric boffins. They may be highly creative, brilliantly successful or utterly bonkers, totally delusional and fail. However  they should never be underestimated and excluded from the discussion of how Science moves forward as they often play a crucial role.

Over-specialisation, professional stereotyping, commercial self-interest, financial constraints, regulated environments, cultural boundaries, differing motives  and a lack of understanding across groups have created knowledge 'tribes', between individuals and amateurs, academia and industry and within these organisations themselves , across departments and business units, between engineers and academics, applied and pure scientists . This calls into question how scientific progress is made and managed and about risk aversion in Science [15] - Smolin. Whether taking new directions within flexible career structures as opposed to going over the old, the safe and what is known . One thing is certain, the form mathematics is now taking is changing . Consequently the use of the internet is replacing traditional refereed journals .

Changes have always happened. It can be uncomfortable and disconcerting for some, but real shifts in Science are few and far between and in Physics has been a long time coming. It may start happening at an accelerated rate. We are not use to seeing this happen in our own lifetime especially with the complex structures, professional, and institutional, that have now been built in recent decades around existing paradigms. I believe we are standing at the cusp of new paradigm shifts in Information Science from Biological Systems to Cosmology. This presents a real crisis of credibility. 

The logical conclusion then is we need a representative body that encompasses all mathematicians – academics and practitioners, and represents their interests nationally and the interests of mathematical knowledge at large, that safeguards standards but also progresses the subject to take on the challenges of now and the future otherwise there will become widening gaps between academic and practitioners.

Indeed, I predict many new discoveries and opportunities will be made at the interface and in the gaps between specialities and disciplines, will need to become increasingly cross-disciplined, systems-engineering, especially in the rapidly developing fields of modern communications and signal processing, which are now flipping over into other areas including Theoretical Physics. 

More importantly, mathematics should be fun, and we should never be afraid to test new, unfamiliar ideas even if they turn out to be wrong. For a hundred duff ideas, one may hit the jackpot.  We should care about fundamental questions, but care less about what others may think, think for ourselves, be bold and challenge old assumptions otherwise we don't move on. Even experts can delude themselves that they are always right.  Whatever the outcome of such theorems, one thing that is certain is that if they are to be resolved, it will be in a manner that is both controversial and unexpected.

Also I would also like to thank Professor Sir Michael V. Berry and Professor E. B. Davies (Kings College London) for their advice and direction and for giving me the time to listen and push my ideas.

I would also like to thank my parents, particularly my Father, friends, my wife, Portia, and family for their patience and trying not to appear bored with my mutterings. Also a special acknowledgement goes to former colleagues Robert Brown and Brian Knapp who in many conversations, provided a useful sounding board as well as the necessary scepticism.

All material on this site is property of Adrian Rifat.