: A new information theory.**Information Theory****FIT or Fractal Information Theory**. This is a new way of computing or decision-making by fractal logic gate, or fractal cavity resonator. For this purpose we proposed**Fractal tape**like Turing tape and Fractom machine. We often use nested cycle metric to generate fundamental geometric constants.: We have been developing a new generic version of quantum mechanics,**Mechanics****FM or Fractal Mechanics**, We conceptualized a new fractal harmonic oscillator alternative to QFT: We have been developing a new**Language****geometric musical language (GML)**and constructed**Continued Fraction Geometric Alzebra (CFGA)**and Geometric musical calculator (GMC).: We develop**Human brain model****fractal cavity resonator model of the human brain, (FCR-Brain)**and**Frequency Wheel of prime model**(FWPM) for any biological machine. We develop cavity math for protein design for life forms.**Nested Rhythm map of the Human brain (NRM-Brain)**. We discovered ferroelectric, piezoelectric & pyroelectric properties of microtubule and every protein, we have also discovered that**protein has electromagnetic resonance, Universal protein circuit model (UPCM)**.: We construct and information version for developing the theory of everything, and a theory of consciousness we call it**Geometric number system theory****Time cycle universe theory (TCU), this is not like GUT, ours is a set of integrated mathematical constructs and protocols that would help in the understanding the universe and or consciousness. For example relating e, pi, phi with all fundamental constants, frequency wheel of primes, ordered factor etc.**: We invent**Fourth circuit element****fourth circuit element, Hinductor**: We invent artificial life forms, kT driven thermal nanobots,**Thermal energy harvesting machines****Thermo Electro mechanical system (TEMS)**.We have developed**Musiceutical nanobots:****musiceuticals, vibration based medicines, Nano Brain**. Main focused diseases have been cancer and alzheimers.: We have developed a new kind of multi-kinetic synthesis, we invent a new class of condensation beyond Froelich condensation,**Fractal chemical kinetics and condensation****Fractal condensation**: We invented organic jelly that replicates**Brain jelly****biological rhythm like information processing, Brain jelly**. We invent**world’s smallest neural network**. Multilevel switch. Fractal beating like quantum beating for nested beating to be used to create**fractal cavity resonator for brain jelly**.

# Paradox

## All posts tagged Paradox

# Ten paradoxes of a new kind of Science that we explore

Published April 13, 2016 by anirbanbandyoInstead of equations, patterns would take over, replace equations and a new kind of science would be born. Feynman said it and there were plenty of followers, several greatest thinkers put thought into this matter, but none took this seriously. Latest in the frame was Wolfram. We learnt to investigate the origin of a new kind of science with these physicists. We worked very hard to experimentally implement the philosophy, over a decade. And then the time came when we realized that the dream of implementing pattern based computing would never succeed if we remain within the domain of Turing. We have to go beyond, and we also realized, all proposals of hypercomputing are nonsense. **Turing principle is so powerful that no one could hurt it in the last 100 years or so, and only way to go beyond is to enter into the world of singularity, an escape time fracta. However, the journey is not easy, because, we need to explore almost all area of science and re-build every single component we need newly**. This was around 2008. We started working on biological materials to learn if there is a fractal network how the information processing actually takes place, we started several projects together to learn the mystery of these systems. And at this point of time we learnt, that no science exists to support such a behavior.

We had to face severe problems one after another. In our entire research for over one decade we have made one little statement, “Every single cell of a Turing tape contains a Turing tape inside.” If we do just that we fall into a trap. We cannot do the science of Classical mechanics or Quantum mechanics. We needed a new mechanics. Not only that we had to find the true scientific construct of information in Nature. Developing a new scientific protocol for addressing the information integration such that natural events could be replaced was our first and foremost target. But, even if we integrate information, what would we do? Shall we recreate the natural phenomenon. Shall we take the whole information or would adopt reductionism? Then, came the question of representing a natural phenomenon in Nature, we built the concepts of (i) Fractal tape, (ii) three imaginary world’s construct of information, (iii) resonance chain, and (iv) frequency wheel then combined them to generate an information construct for a natural system, just like the one we created on a nano-surface with molecules.

The greatest problem that we have had is that “logic” and “argument” are to be replaced by time cycles and new mathematical and other constructs need to be built for the new kind of Science. We need a new language to process information, we have built one, this is called geometric musical language. Using this language we can convert any sensory information like visual, auditory, smell, taste and touch signals into nested time cycles or beautifully played music following strict grammar.

What would be haunting a general people is that if all the above jargons are true, how the philosophy of the new world of science be like? Unbelievable, remarkable like Quantum or something even funnier, shocking and amazing. Here we would like to address those issues. Note that all you need to know is that imagine a Turing tape and each cell has a Turing tape within, or “**a new typewriter inside every single key of a typewriter**“, that is sufficient to come to our world of science, but you need to have an attitude, “**We will not try to bridge the singularity using brute force, like re-normalization we will float and go deeper inside singularity and above to learn what are there, using specially designed tools and mathematical constructs for the new kind of science**“.

While discussing the philosophy of this new kind of Science, we will see that we need to include everything that Quantum information processing suggests and then we need to go beyond, far more exciting features need to be included. Our new kind of Science is absolutely not classical and far beyond Quantum.

**Why both classical and quantum mechanics fails and how should we work towards the development of a new kind of Science?**

**The trumpet-paint time-cycle paradox:**Using**The paint for us is the observer’s nested time cycle, it could penetrate above and below and much far away, it does not need to pass through as someone from far could “spontaneously reply”**.**The resolution of the solution is always ultimate,**therefore, just like Quantum we do not have any predictability, we also need contextuality, but**in Quantum the object that we are measuring, has got something, but for us, that object has got nothing**.**The paradox of infinite network of reality spheres:**Using the Banach-Tarski paradox and the “measurement” in a fractal information theory: In contextual measurement in Quantum mechanics observer has a Hilbert space and the measuring state also has a Hilbert space, they interact to create a common Hilbert space with an inner product. However, for us, we create a 3D projection of the observer, we have three Hilbert spaces, one for the world below, one above and one for the observer. However, we do not need to create**identical information replica is its greatness because the solution of a problem is an infinite space**.**the Hyper-webster dictionary and the generation of multiple spheres**: If there are large number of observers, of course there are infinitely large number of observers, therefore large number of “reality spheres” will be produced and those would merge just like the Hyper-websters dictionary. All these spheres are distinctly produce, yet they create a singular identity.**Imagine thousands of “reality spheres” being produced and all of them simultaneously hold the solution****Resonance Drive Paradox**: Density of resonance frequency R and frequency bandwidth B product RB determines**the degree of consciousness elements**, when environment remains constant. Ratio of RB of a device and its environment is essential index or the degree of consciousness (C=RB(M)/RB(U)). There is always a spontaneous drive of any fractal cavity resonator structure to to increase band-width ratio, this is perpetual, it is never ending, the machine senses more and adds more bandwidth then evolves to sync as much as possible. Resonance drive paradox leads to several other drives, for example drive to morphing etc.**Number system derived metric and its saturation: Ordered factor paradox**: Our number system study shows that only 12 primes are sufficient and number of solutions of fractal cavity resonators reaches 99.999% new by 10^12, therefore, we do not need more number of oscillators. Then how a large structure could form? The code to generate new structure must make a fractal repeating its entire process after each limit is reached. This is the reason, universe appears like a fractal, but actually it is not a fractal.**The observer-absolute paradox:**In a fractal tape there is no finite state for a particular cell, the observer syncs with the world below and the world above and creates a state for the measuring cell, then we never write information in this tape in any cell, we write only in the observer, only the observer exists and the rest everything, even the tape does not exist:**Twelve fundamentals of new information theory**: (i) Instead of modeling we will try to do morphing, The morphing of frequency wheels through the number system derived resonance chain is the route for information processing. (ii) The same information is complete at a moment, fraction at the other, linking at a particular time enables global link, this is a weakness of our system. (iii) The same information content gets different property at different environment, in the reality sphere, the same plane holding many nesting cycles behave differently. (iv) System spontaneously emerge information, even when no question is asked. (v) A mirror image is created without changing the source, though both source and the reader are coupled. (vi) The same information takes different form at different times thus creating wide ranges of information, also it looks very different from different directions. (vii) Information is alive, it senses, expands creates new life forms. (viii) Information is phase, frequency intensity of time cycles, these time cycles could self assemble in a single or multiple planes, they could make 11 planes holding 11 dimensions. (ix) Dimensions representing different planes inside the sphere rotates differently for different planes to accommodate higher dimensions. (x) Starting phase and direction of motion of system point are two parameters that higher dimensional planes process. (xi)The pot and the matrix are the same: the information that shapes an information content is the information itself. (xii) Identical information holds the same content yet different meaning, very different information holds the same appearance, duality is embedded.**The paradox of Infinity-mechanics: Quantum mechanics is a subset of fractal mechanics: Ten differences between Quantum Mechanics and Fractal Mechanics**(i) One imaginary world, and three imaginary worlds, (ii) Uncertainty principle is universal, uncertainty principle varies, depending on the observer and inner-outer world configuration. (iii) Contextuality is a side part in QM, contextuality is everything in FM, the observer is the only reality, “supplement” to complete a quantum state is essential, in FM, continued fraction geometric alzebra generates an infinite series to hold that. (iv) Entanglement is a property in QM, in FM, entanglement is the way time is connected. (v) Quantum deals with matter, FM only time-cycle. (vi) QM has its own version, of condensation, interference, oscillator FM also has its own versions for each of them. (vii) Psi is absolute in QM, Psi is deconstructed in FM. (viii) Like QM there is a Hilbert space but they do not take the tensor product of the inner space, its a phase-orientation calculation of time cycles in FM. Instead of normal tensor alzebra we need**continued fractal based geometric alzebra**to process. (ix) QED is based on a field theoretic concept, for FM, an universal unified field exists made of 12 nested time cycles and 12 dimensions. (x) Quadrupolar moment plays a vital role in determining complex time cycles in FM, but that is irrelevant in QM.**The paradox of quest**: Ten cultural practices that existing scientific practices follow and we do not need to make them blind religious: (i)**Survival of the fittest**, not just in biology, quantum to astrophysics to elementary particle physics, this is applied as universal physical principle, co-operation to survive is just opposite. (ii)**Something equals something**: Equations or inequalities is the only form to get an answer. (iii)**Step by step, not above and within**: Searching systems believing that they would work step by step is generating craps. (iv)**Universe is sum of two body system**: (v)**Do anything in the name of closed system:**Science considers close system to anything and whenever necessary makes it permeable, stops or vanishes anything (vi)**Decision making requires selection and rejection**: (vii)**Order and degree of differential equation captures all possible variations of a natural system:**:We say that nested time cycle could capture with the three imaginary time worlds operating simultaneously (viii)**Singularity has to be bridged**: Dancing in the singularity is all what we do in our new kind of science (ix)**Only one time, only one cell of a tape, only one clock, only one of everything:**In the existing science there are plenty of things, for us, there is only one thing, a single time cycle thats all (x)**Everything wants to be complete:**Every single system in the universe has different objectives in the current science, but for us, all systems have only one achieve 12 prime, 10^12 oscillator goal.**The cycle-non-reductionist paradox**: If there are many choices, then without reduction we cannot make a selection, what if there are not many, and we never would have to choose, in the information processing protocol we follow “spontaneous reply”, only the right one answers to the query. Therefore, the question of reduction does not appear. The next question is that when we model a system in nature, do we mimic the system as is? Do we take all information? No. Just like a single cell create a full grown human, a few delicate codes of natural system could regrow by morphing, the recreation could be limited by the number of resonators and its design. The information space gets filled up with matter, with a few code it is build up.**Ten principles of a Fractal tape**: (i) Every single cell in a tape has a tape inside, we get a Fractal tape. (ii) A tape has four tuples, convert to nested time cycles, match and expand, transform & reply back, restructure internal wiring or learning. (iii) Triplet of time cycles are unit of information, three imaginary worlds. (iv) Two kinds of fractals ET, and IFS work together to make the tape, (v) The tape does not exist in reality the observer does. (vi) Fractal tape leads to fractal machine just like Turing tape leads to Turing machine, an imaginary state processor, generalized complex number and the number system rule of 12 primes and 10^12 oscillators is key to the tapes structure formation. (vii) Fractal tape is good for QM, FM and CM all, it morphs to any information structure, the tape does not have a fix geometry. (viii) It operates through geometric-musical language. (ix) A tape finds the bandwidth of a system and draws a circle to connect it’s various time scale, just like spiders net, but the fractal tape has many many circles and it tries to touch all boundaries first and then it goes faster and faster time scales. (x) Fractal tape has no program, there is no search to find or transport communication among cells, the cells self-assemble to morph a system.**The equation-inequality-fractal paradox**: In the conventional practice of science, variables are correlated and equated to represent a system. The science of equations have been very successful. Now, if there is no equation, because of fractal tape then, we need to build up another language that runs in the undefined world. We replace equations by a new kind of alzebra called**continued fraction geometric alzebra**. Using this alzebra we solve several problems. This is the tool using which we plan to dance in the world of singularity, in this alzebra, we always have a circle and we draw several circles following certain set of rules, to do all kinds of mathematics Addition, subtraction, tensor operation. This is the route of**doing mathematics by drawing circles and always making a journey towards infinity**.**The paradox of illogical, nonsense decision making**: We are always advised to think logically. It means, we have to think that every event is sum of several sequential events. However, it could be possible that problems and solutions entangle in a single time cycle, and then we integrate them to construct entire information processing architecture, then, there would always be simultaneous robust response. There would be no logic like “if ** then **”, then there would be what?**Here are 10 ways of arguing differently (This is again copied from Hindu religious practices and we framed a scientific protocol by rejecting its religious essence):**(i) Always a question always has its answer in it, no question could be created without an answer. (ii) An argument is always sum of a set of new arguments, thus, its a fractal network. (iii) No answer is complete, there is always a question that invalidates the answer, fixing that to evolve answer is a journey to completeness (Godel hinted, never suggested a route to explore incompleteness). (iv) Logically circular or circular logic is the unit of a singular logic to enter inside and go above, always bring circular logic but follow the boundary limit of rule (ii). (v) Since question-answer couples always together, every possible solutions are connected to the question contextually. A question could have many answers in different contexts. All are mapped in a 3D nested time cycle geometry. (vi) Every single set of arguments form a geometric shape and a complex pattern of composition of basic geometries should form to compose a complete argument, the shape would be symmetric and follow the rules of geometries. (vii) No logical argument could stand alone, isolated, it needs a support, even though a fractal arrangement argues that at the top there should be one argument, but even that would require at least three perspectives, one from the arguments below that makes it, one from above or the argument it constructs with others, and one the perspective of an observer. (viii) A true argument does not have an idiom or universal truth, no assumption, all assumptions are environment and context dependent. There is never a truth or a false statement. (ix) Expansion of 12 tune Raga is the way to expand an argument. We cannot add them one after another, place simultaneously, considering all as truth like Quantum, then, we take always a circle of 12 argument cycles and then expand them, just like Indian classical Raga and our prime number theory. (x) Every natural event has a geometric arrangement of argument and the practice or game of argument is to morph with the nature’s geometrical arrangement of argument. (xi) An argument always have one less variable than the fixed truth and total number of variable and truth should compose like our number system metric, hence the network of argument could be constructed. If there is a little change in the most static argument all nested arguments would change simultaneously. (xii) One could enter inside an argument 12 times to generate 12 fundamentally different dimensions, however, if we enter more, then the relevance to the first argument becomes faint. We need to change the starting argument point regularly to sustain relevance in the nested fractal like argument practice. The rule (x) morphing comparison is the route to auto-correct an argument.**The paradox of an infinite field and limits of the universe: Infinity is everywhere in the Fractal tape universe and there are specific ten properties of this impossible universe**: (i) If nature is discretised once, it cannot be recreated, we follow, everything is connected to everything: Probability theory is not required (ii) Every point holds an infinitely large universe within. (iii) Every single point tries to reach 12 prime, 10^12 oscillator saturation to sense the environment with its maximum. (iv) There is no force only the time-cycles and time gaps, at the elementary scale only a time cycle. (v) Information is filled up in the all existing time cycles, total time cycle is infinity in number, they exists everywhere. (vi) There is no zero point, to have a zero point energy, also we cannot consider an external boundary if we simply consider universe is a frequency fractal, only thing it is made of is time cycle (of what? please note, nothing), there is no mass, no distance, all are perception of interaction between nested time cycles. (vii) nested time cycles self-assemble to generate all forces, and within 12 nested time cycle self-assembly, all structures are formed. (viii) All fundamental constants are nested time cycles made infinite network, they have dimensions as various powers of time only and those time series are symmetric in nature. This is beautiful to observe that fundamental constants do not appear random. (ix) There is no total energy of the universe to feed the fields, because energy could be created and transformed, what we see around us, and that is the truth, if we create an upper limit, we would surely need to tell whats outside, if we do not know what is outside then who gives you the right to draw a boundary. The energy could increase or decrease depends on the system, for the universe, we cannot make any rule. (x) There is no starting time and end time for the universe and for anything.**The paradox of time replacing everything: Universe is nothing but clocks**: We do not have mass, we do not have space, we have created a new Grand Unification Theory, our own, using only time cycles. The reason is that time cycles would interact and generate everything. This is how we have constructed the new information theory a new geometric language and this is what makes everything equal. Just imagine, only this consideration would resolve the matter-photon interaction. Even if you look at the Schrondinger equation just by looking at the mass you would laugh because it shows clearly, we do not know what to do with “mass”.When we see the foundation of our new information processing theory, often we ask ourselves, are all these new. When western scientists dig deeper into their thoughts they reach Greeks, even deeper into the realm of Sumerians. We find ourselves very much connected to the foundations of Hindu Philosophy, one could read here for details.

# Infinity paradoxes of 1=1+1, and our fractal information theory (FIT)

Published April 3, 2016 by anirbanbandyoOur information theory considers that “there is a Turing tape inside every single cell of a Turing tape”, this new tape now fails to become a Turing tape (popularly people would love to call it Fractal but there is no guaranteed self-similarity, it is Numtal!!!). To operate this tape now we need time cycles nested with each other. When we created this nested time cycles, we did not think about it much. Our only objective was to solve the immediate crisis. Since we have a singularity we need a tool to penetrate deep insight and harness an insight from within. So, the new Fractal tape uses a basic information processing unit, three-time cycles connected to each other, one that represents Turing tape inside a cell, one that represents the Turing tape above where the cell exists and third, the third unwanted Turing tape or the third time cycle is that of an observer. We initially did not want to bring the third Turing tape, but you might have already noticed that we do not have any representative tape for the cell under consideration, therefore we need a new tape to project the possible cells states of the cell under consideration, that task is performed by the observers tape. So, we get a projected hyperspace, namely “reality sphere” that sphere is the only real thing in the information units time loop architecture. Now, a time loop has frequencies at certain time gaps to write geometric shapes, that is information content and all the three loops are imaginary, does not come from infinity but imaginary space.

Now, above we described all that one needs to learn to understand the science behind our information processing unit, which eventually creates a resonance chain and morphs the events happening in nature. Mimicking the frequency space is amazing in the sense that suppose a protein is communicating with another protein, then if one images its shape its silent there is no movement. However, if we could somehow convert the information space into a shape changing material, then we could find a slowly shape changing material, and if we could enter inside the structure, then we would find some other structures are changing quite fast. If we could take one, and enter inside, we would find a large number of extremely fast shape changing materials. This journey would go on and on. Now, you learn all about the science of our information processing protocol.

Lets discuss the philosophy of infinity.

**Gabriel’s paradox**: Gabriel suggested a trumpet that looks like a cone but it goes thinner and thinner to infinity, it has infinite surface area, but when we try to paint it, we would require only a finite amount of paint, drop it from its mouth and it would pass through all the way.

**Hilbert’s infinite hotel**: Hilbert suggested a hotel with infinite number of rooms. Infinite number of guests could come in, yet there would always be a room available in the Hotel. The same event could be represented by a circle, we can take out infinite number of points from the perimeter of a circle, yet there would be no disjoint in a circle. A circle is finite only when we fix an area

**Dart on a dartboard**: Suppose we have a pin, we throw it on the wall wherein a circle is drawn. What is the probability of touching a particular point, given that there is infinite number of points in that area? If the probability is zero, then, the total probability of hitting the entire circle anywhere is zero, but that cannot happen. We need to consider a very small area, to get out of infinity paradox.

**How many numbers between 0 and infinity, Cantor diagonalization:** The answer is infinity, that so many numbers are there in between 0 and 1, even 0 and 0.00000000000000000000000001. Now, take any gap between any two rational numbers, we get infinite number of numbers between them. {n}={n^2}=….={n^n}

**Hyper-webster** is a hypothetical dictionary of infinite space of all possible letters. The idea is the same as numbers, it has 26 chapters of one letter each. Then each of these chapters have 23 paragraphs and so on. Now, if you go on dividing the possibilities are infinite. The exciting part begins now, suppose the first chapter of the dictionary has all possible words beginning with A, then if one removes A, the rest is same as all possible chapters with all possible words. In fact all 23 volumes are self-complete, i* f we print one of 23, we are done*.

**Banach-Tarski** This is very interesting now. We create the same dictionary on a sphere. One could write infinite words on the surface in the infinitely available paths on the spherical surface. Even if we start walking from any one point we could travel covering every single point on the spherical surface following , Up, Down, Right, Left, UR, RL, UL and DR. Now, if the lattice on the sphere could be a hexagonal or rectangular, with 6 and 8 neighbors respectively, we could have 3 and 4 equivalent roads respectively. * There would always be two poles and hence, two identical spheres could be created just from one sphere if we decide to walk on the routes following a given protocol*.

**Whenever there is a case of real number of points, by Banach-Tarski argument one could create 1=1+1, when the number of point is infinite**. This violates the proof of Bertrand Russell.

On the sphere we can start another journey. Either on the disc surface alone with 3 circles like the one below, or start with 4 spheres making a sphere Apollony fractal.

In 3D one starts with 4 spheres each at the vertices of a tetrahedron. An outer imaginary sphere is the boundary cavity that encloses the 4 spheres. The gaps are filled by subsequent Soddy spheres thus forming a solid object (at infinity). The result is often called an Apollonian sphere packing. The fractal dimension of the 3D Apollonian has been calculated as 2.473946 [M. Borkovec, W. De Paris, and R. Peikert].

Kravchenko Alexei and Mekhontsev Dmitriy have found an attractor that creates the Apollony fractal, the source code in C is provided here: apollony.c.

This is the union of three functions

f_{1}(z) = f(z)

f_{2}(z) = 0.5 (-1 + s i) / f(z)

f_{3}(z) = 0.5 (-1 – s i) / f(z)

where z is complex, s=sqrt(3), and f(z) = 3 / ( 1 + s – z) – (1 + s) / (2 + s)

Tetragonal space is the starting point. What about other starting packing?

The largest number of unit circles which can touch a given unit circle is six. For spheres, the maximum number is 12. Newton considered this question long before a proof was published in 1874. The maximum number of hyperspheres that can touch another in dimensions is the so-called kissing number. It is shown that optimality for sphere packing is n=4 The history of packing problem is here. One could have fun packing the area with circles here, how to draw these are sphere here.

* There are three imaginary worlds that constructs the fundamental unit of information for our structure. We see above that the three imaginary functions if they are different then they make an imaginary sphere. Though circle grows with three imaginary worlds, in the Appolony fractal, the sphere grows optimally with four spheres. For an external observer, a sphere always looks like as if it is made of three circles. This is how the apparent mismatch between the infinity spheres and circles are resolved*.

**Harnessing infinity in the sphere and modeling the human brain**:

Change in the brain’s physical structure is fatal to our brain modeling. However, there are plenty of brain models that simplify the brain structure to make it easy to process. For example, conformal mapping of the brain is done on a sphere (M.K. Hurdal, P.L. Bowers, K. Stephenson, D.W.L. Sumners, K. Rehm, K. Schaper, D.A. Rottenberg, *Quasi-conformally flat mapping the human cerebellum*, in C. Taylor and A. Colchester (eds), *Medical Image Computing and Computer-Assisted Intervention – MICCAI’99*, Vol. 1679 of **Lecture Notes in Computer Science**, Springer, Berlin, pp. 279-286, 1999). The idea is similar to those who want to map brain in a hypothetical structure, but we do not. Our fractal information processing theory suggest assembling the time cycles on the sphere. Compared to Hurdal suggested conformal flattening we do not change the physical shape of the any part of the brain, for our theory, any change in the structure means change in the information content. We are bound keep its purity intact, and then integrate tiny pieces of information in it.

**Are we driven by madness? How come we could even think of processing information of the entire brain?**

Above we have discussed that a single sphere holds an infinite number of paths and we could make a singular mathematical structure of sphere inside representing the entire human brain. Now, the time cycles would be on top of its surface as shown below.

Each of the circle with an independent center could represent the time cycle network representing various organs and their biological rhythms. Using such a sphere is beautiful because we get only one unified system to hold infinite possible time cycles. That is highly generous statement.

**One to one correspondance between the Gabriel’s paradox and renormalization**: One to one correspondence between Gabriel’s paradox and nested time cycle synchronization that is designed to replace renormalization, the surface area of the cone is infinity, however, when we put paint to color it, the paint passes through the tunnel and it blocks at the point depending on the density of the paint. The paint for us is the observer’s nested time cycle. **The resolution of the solution is always ultimate**.

**One to one correspondance between the Banach-Tarski paradox and the measurement in a fractal information theory**: Suppose we have a nested time cycle sphere, like the one shown here, the observer would also be a sphere, it would sync with the paths and generate the connected path and form a “reality sphere” just like the one here. Creation of an** identical information replica is its greatness because the solution of a problem is an infinite space**.

**One to one correspondance between the Hyper-webster dictionary and the generation of multiple spheres**: If there are large number of observers, of course there are infinitely large number of observers, therefore large number of “reality spheres” will be produced and those would merge just like the Hyper-websters dictionary. All these spheres are distinctly produce, yet they create a singular identity. Imagine thousands of “reality spheres” being produced and all of them simultaneously hold the solution.