: 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**.

# Information Theory

## All posts tagged Information Theory

# Why existing information theory EIT would fail to resolve the data deluge problem?

Published August 9, 2016 by anirbanbandyoInformation if considered as “bits” or “Qubits” contains no information, this is a reality.

10 reasons why Existing Information Theory, EIT though applied in Classical and Quantum can never solve the data deluge problem.

(1) **EIT discretizes nature**, losing most of its information; user sees what it wants to see, not what the system is, then imagine a theory, try to rebuild the natural system by adjusting that imagination and glorify the equation that fits the observation.

(2) **EIT rejects nature’s original information structure,** consolidates a faith that everything that happens in nature is an output of a series of events happening one after another. Nature is not sequential, not a circuit, adding many parallel lines do not mimic nature’s information structure.

(3) **EIT isolates the concept information and structure**, as if information is a property of a structure.

(4) **EIT endorses information as universal truth**. Though Quantum information theory explores the phase space, sensed information is always considered as real and factual truth. Note that phase is always unseen part in an information.

(5) **EIT practices intelligence as mysterious real function**: match output and input by any means, out-of-blue senseless functions are endorsed as key to nature (e.g. cancer cell growth = radioactivity).

(6) **EIT believes hierarchical processing means connection between logic-less mysterious functions**: “deep learning” means keeping several mysterious layers between input and output, none makes sense, but better fits observation.

(7) **EIT believes randomness leads to creativity**: creating something new does not mean making an unpredictable choice, use of randomness fools human sense.

(8) **EIT endorses imagination of every single outcome and encodes solution**: Self-taught software (STS) is a mere extrapolation of outcomes; extrapolation is not prediction.

(9) **EIT believes in making decision by reduction of choices**:

(10) **EIT believes speed and amount of resources can solve data deluge & everything**: The quest for better computing is faster speed and more memory/power.

# Incredible properties of AjoChhand computing: Why it would outperform all classical & quantum Turing computing

Published July 30, 2016 by anirbanbandyoWe have given a name to our geometric musical language based computing, AjoChhand computing. It uses Fractal tape instead of a Turing tape and uses Fractal Information Theory (FIT) instead of Quantum Information Theory (QIT). Why name is AjoChhand? Ajo word comes from Ajeya or Invincible, and Chhandam means Rhythm, so its an invincible rhythm computing.

Here are some of the incredible features of this class of computing.

(i) Search a massive database without searching (spontaneous reply).

(ii) Multiple nested clocks one inside another enable “a virtual instant decision making”

(iii) No programming is required as “cycles self-assemble/dis-assembly for better sync at all possible time scales simultaneously”.

(iv) “Phase space” keeps “volume intact” as required resources only increases phase density not a real space. Information = wiring geometry (hardware); Information = silence (not “bing” Philosophy); Information = Phase (geometric); Information = Perimeter or diameter (parametric).

(v) Perpetual spontaneous editing of slower time cycles (creation/destruction/defragmentation) “prepare for unknown” = higher-level learning.

(vi) We introduce “fractal resolution”, a complex signal’s lowest and fastest time scale signals are absorbed. simultaneously, & during expansion, the fractal seed delivers full output, from a seed of information (drastic shrinking of data).

(vii) The superposition of simultaneously operating million paths assembles into a sphere enables “extreme parallelism”. In quantum, only one Bloch sphere, here sphere inside a sphere inside a sphere…

(viii) Time cycle is memory, rotation along the cycle is processing, are same events, “no transport needed between memory and processing units”, no wiring, no communication, no communication channel.

(ix) No logic gate, no reduction of choices, which ensures that “speed” is irrelevant. No bits or Qubits. Object is not measured by an observer, object to be observed is not a separate thing, i.e. No measurement. Observer, Object and Environment integrates in the time cycle, (time cycle = unit of information = an event). A question is assimilated into the internal network of time cycles it affects the environment & observer in course of assimilation. That is how solution is derived, no computing is done to find an answer.

(x) All sensory information is converted to one geometric language that allows “perception”, a yellow color could have a taste. Perception is not a programming as wrongly perceived.

(xi) It never requires rebooting, only one computing runs for whole life, but of course it sleeps when it switches off certain interactive links with nature, yet even at that time all three internal rhythm networks run. Rebooting means temporary switching of the internal rhythm integrator. This is an equivalence of consciousness. The machine follows all ten criteria of a conscious machine set by us (see my consciousness post).

(xii) It always defragments internal structure, but self- editing is not so profound at the boundary clocks, there is a gaussian distribution of editing efficiency, clocks in the middle edits the maximum. There are various reasons why this is so essential. (i) Boundaries cannot be so vulnerable to changes, (ii) editing requires a high density of clock boundaries, (iii) Job description leaves only clocks in the middle to memorize environments, while faster clocks need to memorize hardware management, the slower clocks require to sync with the environment.

# 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.