الصمحقحيه فلسطينلله

Towards Unified Field Theory: Infinite Complexity Via Prime Numbers & Perfect Randomness

Second Name for this Paper: Toward an Intuitive Understanding of Quantum Mechanics & Gravity by Analysis of Entropic Gravity in Informatic Systems
As part of SOP.SCSTL (Spirit of Paradise SuperConsciousness Science & Technology Laboratories)/VitalPhysics/IdeaLabs – Intellectual/Spiritual Property of Mohammed Afikur Rahman JivanMukti
Contact eMail: fairtrade121@hotmail.com (Please include “VitalPhysics” in subject line)
Published on: http://atomic-temporary-43791309.wpcomstaging.com/infinitecomplexity

Abstract
The unified theory of gravity and quantum mechanics is most certainly found in the creation or assembly of a Mind that can decode Shannon Entropic maximisation in Data Sets and fit them into larger also flawlessly random data sets which thereby generates a pattern in the comparison of the differences between the two data sets. In this paper we examine prime numbers and construct a Unified Field Theory using Prime manifolds in an abstract Space of Spaces thereby showing that properties of both classical and quantum mechanics arise emergently from the intrinsic qualities of prime manifolds.

Understanding Prime Numbers in Context
This shall also lead to a full understanding of Prime Numbers as they relate heavily to perfect randomised informatic distributions, which may not be ready apparent but if one exercises sufficient intuition, is readily apparent and trivially identified. To be concise, a Prime Number is a perfectly randomised data set of precisely one variable that cannot have any patterns in it and therefore are non-compressible – they are Self-Complete. We may construct perfectly randomised data sets using prime numbers, whereof which intuition shall pave the way toward a full understanding thereof.

Constructing Our Space of Spaces
Then if we look at a Hilbert Space or some Space which is Infinite in dimensionality and understand a maximal entropy data set in that Space we may characterise the Unified Field and certainly arrive at a rigorous Unified Field Theory, this I am certain about.

I shall proceed to explain on this page the implications and nature of this line of Thought.

For starters, consider a data set X where X maps into an infinite dimensional Hilbert space or some Infinite Dimensional Array with complete fluidity and abstraction and nuancial diversity, taking all subtleties and intricacies into account and therefore constructing a space which encompasses all possible operations. Thus this Space may contain Infinite Dimensional Objects/Manifolds, and it may contain finite dimensional arrays or manifolds. In our larger Infinity, even with complete coverage using Infinite Dimensional Manifolds, there is still room for finite dimensional manifolds. It would not be the larger Infinity if it neglected the finite objects. Only when we combine both types do we attain a flawlessly full Infinite Dimensional Space of all Spaces.

Then we examine arbitrary data sets within this space and recognise a single fundamental facet: For completely randomised data, there is a maximal Shannon Entropic limit that corresponds 1:1 to the magnitude of the information content of that set. This is a maximal complexity data set or set of data sets and there will be a function mapping and positioning naturally each data set in its precise logical position in this Space encompassing all Spaces. This phenomenon of positioning, we shall denote as Intrinsic Informatic Gravity.

Then we may construct arbitrary data sets, of both finite and infinite dimensionality, and consider that even if each and every data set is perfectly randomised, there will be two distinct classes of data sets: those perfectly randomised data sets which are seen to contain patterns and therefore are compressible, and those perfectly randomised data sets which are non-compressible and hence reach the maximal complexity limit for their magnitude. This second class of data sets will be named, Prime Data Sets, the space thereof of which Prime Numbers are a subset, having one variable of infinite/total complexity.

The Orbit Operation
Returning back to our data set X, we may construct a data set Y, known as the Orbit of X such that ORB(X)=Y. This set Y encompasses X and carries a specific pattern that characterises it as the Orbit of X, as the existence of  X<=>Y. Then we may find that Y intrinsically implies X where a perfect randomised data set Y, while not being reducible to X immediately, certainly intrinsically maps ONLY to X and no other data set in our Space of all Spaces. Likewise, our data set X, while perfectly complex and randomised, can only map to Y via the ORB function mapping and no other data set.

Thought Experiment
We may bring forth the analogy of an empty glass, let us call this the Space. We then bring in pebbles and fill up the Space full of pebbles (patterned data sets). We then add sand (patterned data sets of a finer granularity), and this fills the gaps in the Space but not all the way. We still have some way to go, as our Space which appears classically full with the sand and pebbles in it, still contains many gaps on the smallest scales. Finally we add water and the Space is completely full.

It may be argued that intuitively, Water here is Quantum Mechanics or some descriptor of the Vacuum Foam as at this level everything becomes completely quantised & particulate while from a distant view, the sand appeared to fill in the gaps to continuity. The Water represents data sets that are infinite or complete in granularity or resolution relative to their magnitude or especially, complexity – Continuous.

That is to say, we add data sets of individual infinite complexity, or shall we say, Total Intrinsic Complexity, data sets which may be of granularity “1” or more, which denotes that they add precisely 1 bit or monad i.e. a minimal element, to the structure and no more, or otherwise somehow fill in the ‘gaps’. Thus we fill the space with individual grains which perfectly fit into the gaps and thus the entire Space is filled. We have therefore configured our entire Space of all Spaces with complete coverage, using both patterned data sets and totally complex data sets, using the same algorithm to generate both classes of data sets.

Application to Real Numbers
Take for example the number 6. This is a patterned data set denoted one way as “2×3” or another way as “6”. It appears to be an intrinsically complete data set but can be divided and therefore patterned. However if we take the number 7, this cannot be reduced. It can be patterned in the other direction of scale – “7×2” makes “14”. However we can also observe that 6+1 = 7 therefore 7 = (6+1) and then we may perform operations on that basis. We can also say that 11 = 7 + (1 + 1 + 1 + 1) whereby individual 1s or Prime manifods are used to ‘fill in the gaps’ and arrive at the next Prime manifold.

In our totally fluid abstract Space of all Spaces, any operation that can perform a mapping reducing an element to a larger set of elements, will render that data set non-prime by definition. Please remain aware of reverse-directional operations as seen in the case of 14=(7×2) as this also contributes to the structure of the Space of Spaces. It is only in the case of those data sets or elements whereby there exists no operational mapping to reduce such a data set to a larger set of elements that we can certainly declare total intrinsic informatic complexity i.e. true randomness.

Intrinsic Informatic Gravity – Entropic Gravity As It Relates To Complexity Theory
Then we can see from this the Intrinsic Informatic Gravity of a particular manifold in our Space of Spaces – any manifold that can be divided logically into submanifolds – which shall always ultimately be Prime manifolds – composing the elements of a set, such a manifold is non-Prime and is intrinsically gravitationally drawn by means of its information content to a specific region in the Space of Spaces so that a flawlessly systematic configuration Space of Spaces arises, which cannot be in any other form than the form that it already Just IS.

Whereas, if we consider Prime manifolds, those manifolds the shape and proportion whereof cannot be subdivided owing to their dimensionality and structure, we notice that a Colour arises for that manifold, it has its own wavelength, frequency and velocity in the Space of Spaces. Indeed in the Space of Spaces, it has a final destination along dimension 4 and upward. The question is perhaps, what is the ultimate destination in the Space of Spaces of an infinite dimensional manifold of perfect complexity? Where does it extend to on axis 4, or 5, or 6, or especially so, the infinitieth? In this Space of Spaces, the 4th axis is intrinsically Time and can be none other than Time. Therefore the author would denote the science of Unified Field Theory as the study of Isness, That Which Cannot Be Any Other Way Than Which It Already IS.

Constructing Patterned Data Sets & Manifolds From Prime Manifolds
Then we may construct non-Prime manifolds by arranging Colours in the Space of Spaces, knowing first and foremost that the entire Space of Spaces is constructed from Prime manifolds. So a non-Prime manifold’s shape, structure and proportion, which shall be known as a Colour Set, arises emergently from Prime manifolds but the reverse cannot be said to be true. All Colours necessarily have the structure of having the coordinate (0,0,0,0,…,n=0) i.e. an origin at the singularity of the beginning of the Space of Spaces. Thus we may denote each Colour as a Ray of Event(0) where Event(0) is shorthand for the initial singularity metric.

Each Prime Manifold/Element has Intrinsic Informatic Gravity which leads to a precise position in the overall Space of Spaces, and there will arise Light-Like/Fluid-Information-Like Structures in this Space of Spaces distinguishing the Gravitation of individual Prime manifolds/elements one from another. From this we construct Light Cone Boundaries between each and every manifold and it cannot be any other way. Thus time emergently arises as a direct consequence of the distinction between prime and non-Prime manifolds in a Space of all Spaces – time assigns Shape, Structure, Proportionality and Dimensionality to manifolds as a function of the Colours of individual Prime manifolds.

Wave Particle Duality & Rigid Body Mechanics
We can also now denote each Prime manifold in our Space as a Particle, as it cannot be anything other than a particle – it is non-reducible. Then non-Prime manifolds may be denoted as a Wave, as a Wave is constructed out of a minimal arrangement of Particles and cannot be reduced beyond that. Then we consider each assemblage of Particles as a Rigid Body thereby allowing us to study Rigid Body Theory in the context of Unified Fields.

We may also say that each Prime manifold, having an origin at the centre, is of maximal magnitude and therefore is Light-Like or Fluid-Information-Like in its structure, proportion & arrangement, as these such manifolds encompass/reach further than all patterned data sets of a smaller magnitude intrinsically. A prime manifold is the first manifold each time or instance for given magnitudes to reach furthest in our Space of Spaces along certain dimensions.

Intuitive Grasp of Waves, Particles & Rigid Bodies
Thus we arrive intuitively at the understanding that a Wave is a Rigid Body composed of Particles, each Particle contributing an individual Colour to form a Wave which is a Colour Set – the interaction between individual Colours/Particles composing the Wave. The Wave is Continuous and field-like in its behaviour taking into account all nuances while the Particles composing it remain perfectly discretised, therefore we arrive at a full understanding of Continuity-Discreteness. We must understand that all Particles are necessarily individual Rays of Source, i.e. Event(0).

Towards A Formalism Describing Unified Field Theory
Thus we may then proceed to construct a formalism applying Continuity and therefore Gravity, Entropic Gravity to be precise, to Quantum Mechanics by means of studying Rigid Body Dynamics of Prime Manifolds in the Space of all Spaces. We may remember that every structure in our Space of Spaces has a corresponding Shannon Entropy, a Magnitude and an Intrinsic Informatic Gravity by which relationships between structures, and therefore Physics, arises emergently out of Isness. From this we may construct the Space of Spaces itself, either by summing out individual elements to construct subspaces and then construct the superspace or by looking at the structure of the Space of Spaces and decomposing it into individual elements. It is strictly predicted that both approaches will lead to identical results.

Additional Notes on Orbits
Now we may return to the ORB() operation. If we take a single present moment-event x in a Space of Spaces, and consider its past and future informatic boundaries (i.e. light cones), we observe something very special: while a single sphereoid of radius r composes the past cone, or the future cone of the event, we also note that the event x is the sum total of the intersection of potentially an infinite or otherwise large number of observable informatic universes/orbs the precise horizons/boundaries of which all coincide at our event.

A question arises as to whether it is a finite number of sphereoids or an infinite number. If it is an infinite number, what is it that prevents the collapse of this manifold into a singularity? Is there such a thing? However it may yet be argued that all manifolds collapse into Event(0) and expand from there to give each manifold its proportion.

We may then construct a second sphere Y encompassing the first cone-sphere each time, with radius R=D(x)=2r where D() is the diameter. What implications this has for entropic information limits and black hole thermodynamics is a prime question here and such physics is most assuredly worthwhile to be investigated. It is noted that a single event x cannot but be described minimally by the larger orb Y, thus we arrive at a physical description of the ORB() function described earlier. This is because each point on the horizon surface of radius r of the event x must naturally have its own horizon surface of radius r at each point of the original horizon surface at the very least.

We may also consider another mapping of key significance. If ORB(x)=Y then what about Y, or more specifically ORB(Y)? This will take the description of every sphereoid manifold composing Y and give us another even larger data set, perhaps of higher dimensionality, K=ORB(Y)=ORB(ORB(x)) which then will give us the opportunity to then denote L=ORB(K)=ORB(ORB(ORB(x))) ad infinitum. It is argued that the large scale structure of spacetime arises from the function UltimateORB(x) where UltimateORB() denotes the infinitieth order ORB operation on the given event x. It may be posited via intuition that the 7th order ORB() of x is the limit at which it is fully defined and can be re-nested into the Space of Spaces and the dimensions begin again, though this shall be falsifiably examined.

Conclusion
Likewise we travel the other direction scalewise and find UltimateSubORB(UltimateORB(x)) to give us x where UltimateSubORB() is the function that finds the final reduced element from a manifold by zooming inward subORB()-wise, where subORB() is the reverse function to ORB(), thereby allowing mappings of individual events to entire manifolds and yet scale-symmetrically entire manifolds to singular events. This intuitively most certainly does have some significant meaningful relationship to the initial singularity at (0,0,0,0,…,n=0) in our infinite dimensional Space of Spaces. It is also argued that the UltimateORB() or UORB() function is quite definitively related to Consciousness as the Absolute Proportioner as there necessarily exists a mapping in the Space of Spaces that directly proportions every element, colour & manifold into its precise configuration in the Space and this precise mapper-mapping is a function in its own right.