- L. Agrawal, K. Ray, D. Fujita, A. Bandyopadhyay, Fractal Information Theory (FIT) derived Geometric Musical Language (GML) for brain inspired hypercomputing; Advanced Intelligence System and Computing AISC, Procedings of Soft computing conference SocPros 2016, Springer.
- L. Agrawal, S. Ghosh, B. Ghosh, K. Ray, S. Sahu, D. Fujita, A Bandyopadhyay; Replacing Turing tape with a Fractal tape: a new information theory, associated mechanics and decision making without computing, Consciousness: Integrating Indian and Western perspective. Chapter 6, 87-159 (2016). Delhi, India.
Last 100 years we have seen that engineers used to cut tools into pieces and then connect them together to make a nice products. It was subtractive engineering. Making a hole, cutting it into a geometric shape, pasting, what a culture it was for the manufacturing. Now, we are having additive manufacturing in terms of 3D printing. This kind of additive manufacturing will change the world, we will be making things that would initiate adding liquids, jelly, and create just everything.
There are several limitations of subtractive engineering. We often make the machines bigger, we need smaller tools to make a smaller products. Often it was energy consuming and waste of materials was enormous. Now with the additive engineering, we create machines taking exactly what we need. We do not need to cut things. Of course we will see 3D printing to take over and destroy entire system, economy and everything in the world. A new world order will be set and we will have to face loss of jobs in a huge number.
Then there were two more classes of manufacturing waiting in the lab desk, self-assembly and fractal condensation. Self-assembly was proposed in 1988 and fractal reaction kinetics and related condensation was proposed by us in 2016. Self-assembly is found to be limited because it requires materials in a particular form and elementary structure to proceed. While fractal condensation is a brilliant way of putting it, whenever “fractal” word includes in the formation of any structure, self-assembly from a nucleus by core shell growth and then self-assembly of several such nucleus run simultaneously.
Until now the grammar of fractal manufacturing noted above is not established, but, one could use number system and the pattern of primes to regulate the growth process. If a manufacturing follows the pattern of primes, it will never be left alone, no need to program and self-healing would be fundamental to it. For self-healing “fractal” is always the best choice.
“I am fumbled to an interest in maps among rings, and products of rings….the ring idea constitutes the skeleton, the bare bones….. only one variable the phase, only one observable, the phase…….singularities happen only in models not in the real world”. A Winfree 1977
“Singularity is almost invariably a clue”. Sherlock Holmes
“Information of the universe is not written in the “bing” but in the silence between the “bings””.
We all know about the crystal of matter, however, we all got excited to hear that matter could also form a crystal. Frank took the term “time crystal” in his 2012 PRL paper, used by A Winfree way back in 1977 (The geometry of biological time, Second edition 2003, just after his death in 2002). He even used the same phrase “ring device” taken from Winfree, and used the concept of “tick” (page 79, GBT) to edit this “ring device” to generate spontaneously a new “ring device” or a new clock. When we read the book by Winfree, it appears as if Frank was largely inspired by that book and copied everything therein. Winfree argued that (p 79) if a neuron is kept under a constant bias or kept in a calcium deficient solution, it fires spontaneously and rhythmically (Guttman et al 1979). Thus, spontaneous rhythms are born with a “tick”.
Winfree talked about material crystals that make life, like virus. To him, life is a time cycle and crystals of time cycles or rhythms is a life, every single event of life, like birth and death of a living cell, ovulation, everything is like a ring, it returns to the initial state. Mitosis cycle is considered to be a simple clock (Campbell 1964, GBT) Surprisingly we also believe in that. Nature makes time crystals and the materials take the form so that it can sing the music properly in the most feasible way. Frank wanted to provide a more concrete physical presentation of the Winfree’s work, but failed miserably. Nesting of clocks are more important and Frank did not get it at all from Winfree’s work, because nesting was largely missing. A vivid copy of Winfree’s work is found in Brain Rhythm book by G. Buzsaki, but, he merely tried to establish the very old Winfree’s concept with more examples. Nested rhythms came many times, but, a proper mathematical structure of nesting was never born. Our contribution is exactly there. We took “phase singularity” suggested by Winfree and used that as a generic tool to integrate information and proposed a new information theory which rejects the existing Integrated Information Theory (IIT) proposed by Coch and others.
Say, a pendulum is oscillating periodically, Frank Wilczek will call it a time crystal, because time is fixed like atoms are fixed in a crystal, of course it can have a classical and a quantum version. The similarity between Winfree’s proposal and Frank’s argument is enormous. Winfree talked rigorously about the dynamics in the ring, so did Frank, but Winfree said explicitly that this ring may not be a real ring and he emphasized that repeatedly, while Frank wanted to see it in real system as a pendulum. If the diameter of its time cycle changes i.e. pendulum moves a shorter distance, then, they will call it a spontaneous time symmetry breaking. Now, why the pendulum will change its oscillation diameter, if there is no friction. Spontaneous property of the system, so they call it, spontaneous symmetry breaking (SSB). The point is that changing the diameter of a circle is fine, but when the proposal comes that all materials making the ring or the time cycle need to be frozen in the ground state and at the same time moving, this is utter nonsense. This is like considering that a particle is moving and stopping at the same time. Frank suggested that in superconducting ring put a thrust to the ionic motions and they will rotate in a circular path, then, in the ground state (even after thrust they remain in the ground state, nonsense!) they will change the rotation speed characteristically. So, we can say, that time symmetry is breaking!
If we consider the ring as a cavity resonator, then what happens in a cavity resonator we all know, we will get a fundamental frequency and then its harmonics, obviously, shall we say that in every single cavity resonator in the universe time symmetry is spontaneously broken? No, we cannot say that kind of nonsense, because spontaneous birth of a clock or spontaneous symmetry breaking is driven by a human choice, or free will. We are externally applying a force or an energy, then use of the word “spontaneous” is a crime. This is “induced”. Monroe et al has claimed (ArXiv first experimental evidence of time crystal) that they have experimentally realized time crystal in a superconducting ring, however, by that logic every single guitar string is a time crystal. Because the time profile would look similar and “melting of the crystal”, is a mere imagination
The mistake made by Frank was that he did not consider “phase singularity” suggested by A Winfree. He have gone into extensive details to prove that there truly exists a “phase singularity”, his list is rich in examples, and he himself did several experiments to establish that. Actually, phase singularity concept was introduced by Brady 1975 (p81) Moreover, he came up with several observations which could change the way we topologically represent the rhythms. Phase reset, amplitude reset are two examples that one must take into consideration. He never put these parameters into a mathematical perspective. However, he did suggest that there is a self-similarity in phase integration. Phi = Phi + 1. Change in the amplitude of a rhythm changes the phase of other interconnected rhythms. The grammar of topological treatment of rhythms or time cycles or clocks were never established. Though Winfree suggested the birth of a singularity due to the change in higher phase (page 52, Geometry of biological time), and every point of singularity is a screw axis. Whenever there is a decomposition of “bing” a expansion of the information sphere generates a spiral or helical motion radially outward. Because there is a full rotation of the circle as all system points reset their clock. So, clock reset with external motion is the origin of movement in the time cycle network. This is the origin of helix in nature, if we include Winfree findings (WinFree 1973a) with ours philosophically. This is beautiful to see that every time environment changes something, the effect builds a singularity and that singularity causes all associated clocks to reset and thus, allowing a helical growth. This should be the construction route of a time crystal. It’s mathematics and conceptual provisions are much more profound than Frank’s time crystal.
And we did develop the grammar very extensively, we told that there will be a “bing” at the point of “phase singularity” and these bings, hold geometric information. Winfree’s phase reset study showed that after reset if we plot phase 0 points we get Archimedes spiral. Thus, the development of e, pi and phi with i was inherently evident in Winfree’s analysis. The time crystals if we really want to build, it will be a vortex jelly (page 69, The geometry of time). One could find that this rotation is quantized, thus, quantization is a classical process, as it should be, however, continuously, the new singularities are born and resetting the clocks would happen all over the information network or 3D phase sphere. Of course clock reset is localized, but the domain of localization is redefined every time. Thus, uncertainty and superposition of several ways of resetting the amplitude or clock remain there, giving birth to quantum jelly of time, a true analogue of time
The Winfree’s journey into the concept of black hole and astrophysics leads us to a point (page 69-71, The geometry of time) where we could discuss the correlation between CTC (close time cycle loop and the time crystal). CTC is much closer to what Frank has been arguing (https://www.its.caltech.edu/~kip/scripts/ClosedTimelikeCurves-II121.pdf). CTC has a history of nearly a century (1927 van Stockum first made the solution of Einstein’s field equation, which represents a infinitely long cylinder made of rigidly and rapidly rotating dust). It would really have been wonderful of Frank could adopt his time crystal from CTC not from Winfree’s time ring. Because time ring and time crystal of Winfree survives only when we enter inside the singularity and find another world, so it will become a fractal crystal of time neither classical nor quantum as such.
Franck took everything from Winfree but “singularity”, had he taken that, he would not have to get into a blunder of adventures.
- Background, purpose
Making an artificial brain is a supreme goal, and this global effort is going on in the full swing. Not only this has become a prime goal for several countries across the globe, all major multinational companies are doing the same with the largest investment of the world. Brain has machines from atomic scale to the meter scale. Therefore, one has to master the technologies that spread from molecular electronics, photonics, design and synthesis of organic materials, computer science, mathematics, physics etc. For example, nano scale machines would carry out important tasks in the future. However, they should have brains providing intelligence to these nano-machines at the atomic scale. We are the first to develop a brain for the nanobots and continuously we are building more and more life-like nano-machines. World’s smallest artificial life was our target.
The fundamental building block of a life form is protein and human brain expresses almost all of the 30000 proteins. For this purpose we need to unravel the mystery of information processing in the biomaterials. Until now, people were considering that protein is like a conventional electronic component found in an electronic shop. But is that true? If not, then what is protein? Now, if protein follows an unprecedented electronics, what is the basic information in biology, in life, and in the brain? If brain is not a circuit, not a machine, not a processor like the conventional computer, then, every single research being done in the world.
- Results of research: inventing ten research fields
In the five-year period, 2011-2015, we have completed the background research for a new science for bioinformatics and associated electronics and materials science research, both experimentally and theoretically. There are ten research fields that we have created, which did not exist earlier, not even proposed. We have explained the fields in the form of a chart to our right.
By doing research on proteins we found that a new kind of fourth circuit element (we call it Hinductor ) that mankind was searching for over 150 years, we have found that device. This is research field number one. This device is used to build fractal cavity resonator which is the fundamental device used by nature for its information processing.
Information in nature is not “bits” or “qubits” its time cycle. So we have developed a new Fractal Information theory (FIT), this is our second research field. For the last 115 years we have been using only one information theory, this is the second [2, 3, 10].
No one writes a software program for nature, it does everything by itself, so an information theory was not enough we had to build a language of nature, using which the biomaterials processes information and there is no need to do programming. We call this third field as geometric musical language (GML) [3,10].
The fundamental physical process that regulates GML is fractal beating, this is a new kind of beating, an advanced form of quantum beating. There are plenty of associated features followed when we discovered this unique process. We introduced Fractal mechanics research field that also delivers all the prerequisites for the FIT and GML combo. A generic form of Quantum mechanics is therefore the fourth research field that we introduced [4, 10].
There are three research fields, which generated from this fourth research field of Fractal mechanics. First, the fractal beating we could encode in the molecular nano brain using which we could build non-chemical physical drugs, we call it musiceuticals. This is the fifth field and we have tested on cancer and Alzheimers .
Second, a new kind of chemistry we introduce for fractal reaction kinetics and fractal condensation. Thus, Fractal chemistry is the sixth research field .
Third, using GML, Fractal chemistry, FIT, and musiceuticals we have been successful to design brain jelly an organic jelly like solution that mimics the brain rhythms. Brain jelly an advancement of nano brain is our seventh research field .
Using the fourth circuit element and the fractal mechanics, we have created a genre of thermal motors. These motors harvest thermal energy and a basic element in the nano brain and brain jelly, we built thermo-electro-mechanical systems (TEMS), this is our eighth research field .
Based on FIT, GML and fractal mechanics we have created a fractal cavity resonator model of an entire human brain considering every single component of a human brain. We are building a global platform for the nested rhythms found in the brain. Modeling the vibrations and the rhythms of a human brain is our nineth research field .
This brain model shows that a fundamental prime number theory and the mathematics of e, pi, phi and i, regulates evolution of every single new features that we observe in the biomaterials and biophysics research. Therefore in the tenth field we have fused number system and geometry for finding the key evolution of symmetries that nature follows while designing and synthesizing materials .
- The prospects: the follow up commercial products
All the ten research fields that we have introduced have direct connection to industry.
First, fourth circuit element is good for ultra-low power electronics.
Second, fractal information theory is directly related to the data deluge problem that we face.
Third, geometric musical language is to avoid massive programming and the development of natural language; it is for the instantaneous solutions in an unknown situations like outer space missions.
Fourth, fractal mechanics gives us a new kind of piezoelectric, ferroelectric and pyroelectric properties.
Fifth, musiceuticals are drugs that will have no side effects.
Six, fractal chemistry enables 100% conversion in synthesis, minimal side products and natural product synthesis.
Seven, brain jelly as the neural jelly for the futuristic robots.
Eight, TEMS, thermal energy harvesting.
Nine, human brain model for vibrational frequencies and rhythms will help treating various neurodiseases.
Ten, the prime number theory and fusion of basic geometry is formulated to predict unprecedented materials with unique properties.
1) Helical symmetries observed in proteins: An inductor made of arrayed capacitors (2010) Japanese patent has been issued on 20th August 2015 JP-511630 (world patent filed, this is the invention of fourth circuit element), Satyajit Sahu, Daisuke Fujita, Anirban Bandyopadhyay, US patent has been issued 9019685B2, 28th April 2015.
2) S. Ghosh, D. Fujita & A. Bandyopadhyay; An organic jelly made fractal logic gate with an infinite truth table; Scientific Reports 5, 11265 (2015)
3) S. Ghosh, S. Sahu, D. Fujita, A. Bandyopadhyay; Design and operation of a brain like computer: a new class of frequency-fractal computing using wireless communication in a supramolecular organic, inorganic systems. Information, (2014), 5, 28-99;
4) L. Agrawal, et al, Replacing “bits” by “time cycle”: Fractal Information Theory (FIT) and Geometrical musical language (GML) for brain inspired hypercomputing; SocPros 2016, Springer conference proceedings.
5) (a) S. Ghosh, S. Chatterjee, A. Roy, K. Ray, S. Swarnakar, D. Fujita and A. Bandyopadhyay, Resonant Oscillation Language of a Futuristic Nano-Machine-Module: Eliminating Cancer Cells & Alzheimer Aβ Plaques, Curr. Topic. Med. Chem. 15, 534-541 (2015), (b) S. Sahu, H. Oono, S. Ghosh, A. Bandyopadhyay, D. Fujita, F. Peper, T. Isokawa, R. Pati: On Cellular Automata rules of molecular arrays. Natural Computing 11(2): 311-321 (2012).
6) (a) S. Ghosh, M. Dutta, K. Ray, D. Fujita and A. Bandyopadhyay, A simultaneous one pot synthesis of two fractal structures via swapping two fractal reaction kinetic states, Phys. Chem. Chem. Phys. 18, 14772-14775(2016) [cover highlight]; (b) A supramolecular archtecture creation by successive phase transitions and radiations, Subrata Ghosh/Satyajit Sahu/Anirban Bandyopadhyay/Daisuke Fujita, 2014/10/29, JP2014-219958 (this is creation of nano brain)
7) (a) S. Ghosh, M. Dutta, S. Sahu, D. Fujita, A. Bandyopadhyay Nano Molecular-platform: A protocol to write energy transmission program inside a molecule for bio-inspired supramolecular engineering. Adv. Func. Mater. (2014), 24, 1364-1371; [Cover page] (b) Continuously self-assembling material, Subrata Ghosh/Anirban Bandyopadhyay/Daisuke Fujita, 2014/8/7, JP2014-161746, (this is creation of nano brain)
8) Thermal Noise Driven Molecular Rotor, Subrata Ghosh/Satyajit Sahu/Daisuke Fujita/Anirban Bandyopadhyay, 2014/4/25, JP2014-091141; (this is creation of a motor for nano brain)
9) (a) S. Sahu, S. Ghosh, D. Fujita, A. Bandyopadhyay Live visualizations of single isolated tubulin protein self-assembly via tunneling current: effect of electromagnetic pumping during spontaneous growth of microtubule. Scientific Reports, 4, 7303 (2014); (b) Ghosh, S. Sahu, and A. Bandyopadhyay Evidence of massive global synchronization and the consciousness. Comment on “Consciousness in the Universe: A Review of the ‘Orch OR’ Theory”. Phys. Life Rev. (2014), 11, 83-84; (c) S. Sahu, S. Ghosh, K. Hirata, D. Fujita, A. Bandyopadhyay Multi-level memory-switching properties of a single brain microtubule. Applied Physics Letters 102, 123701 (2013); (d) S. Sahu, S. Ghosh, B. Ghosh, K. Aswani, K. Hirata, D. Fujita, A. Bandyopadhyay Atomic water channel controlling remarkable properties of a single brain microtubule: Correlating single protein to its supramolecular assembly Biosensors and Bioelectronics 47(2013)141–148, (e) S. Sahu, S. Ghosh, D. Fujita, A. Bandyopadhyay Computational myths and mysteries that have grown around microtubule in the last half a century and their possible verification; Journal of Computational and Theoretical Nanoscience 8, 1-7 (2011), (cover page)
10) Book chapter related to this article: L. Agrawal, et al; Replacing Turing tape with a Fractal tape: a new information theory, associated mechanics and decision making without computing, Matter and consciousness in Indian epistemology. Chapter 6, 87-159 (2016). Delhi, India.
Vibrations holds the key, for everything. Until now, we were considering that the vibrations and rhythms are only key to some enzyme cycles. But our proposal is that deep down below even to the molecular scale there are rhythms. And there are 12 types of memories that works at the 12 scales of operations in the brain.
All memories are geometric in nature
1. Periodic memory: Chain of guiter string we see mostly in DNA, proteins, period of periods in the nodes of the string. Edit the memory by changing the periodic length of elementary point oscillators.
2. Spiral of spiral memory, in DNA and proteins, also in microtubules. Edit the memory by changing the twists and the number of hierarchical periods by inducing more and more twists.
3. Vector memory, orientation of helices to make cavities inside protein. 3D orientation makes it a multipolar complex 3D vibrational element. Edit the memory by changing the orientation of column oscillators.
4. Lattice memory, microtubule, actin-beta spectrin network, protein complex. Change the lattice parameters to edit the memory.
5. Chemico-electric memory, chemical transmission cycles. There are nested time cycles highly interconnected, to edit the memory, change the diameter, phase, delay or starting points.
6. Leak density of Cavity memory, ion diffusion holes in the cellular membrane. To edit the memory change the leak density on the cavity surface.
7. Spiral geometric memory, assembly of neurons etc. To edit the memory, change the pitch-diameter-length of the spiral.
8. Vortex or fractal memory, memory stored in the geometric parameters of vortex. A vortex has divergence parameters and scale repeat unit, these two parameters are changed to edit memory.
9.Nodal & polar memory: Nodes in the spinal cord brain network (nodes in a tear drop). Geometry of the shapes are changed among 8 different choices from teardrop to ellipsoid to edit nodes and polarity memory.
10. Electromechanical phase memory: organs sync and desync like a giant molecule. This memory is edited by changing the bond length or wiring length and distribution.
11. Multipolar loop in Phase space loop memory: Hyperspace memory. This memory is non-physical and hence not editable.
12. Phase of phase duality generator memory: hierarchical assembly of reality sphere. This memory is non-physical and hence not editable.
Sound is a mechanical rhythm and we have 12 different rhythms in the brain, like
1. Electromagnetic rhythm, [carrier is photon or electromagnetic wave is trapped in a cavity to generate beating or rhythm].
2. Magnetic rhythm, [spiral flow of electrons or ions, they are the carriers editing the magnetic flux, geometry of path forms the periodicity].
3. Electrical potential rhythm, [change in the arrangement of dipoles editing the electric field, fractal distribution of local resonators generate a time function of potential]
4. Solitonic & quasi particle rhythm, [carriers are solitons, defect in the order flows in a ordered structure, the ordered structure is edited to make a loop].
5. Ionic diffusion rhythm, [ions are carriers, tube like cavities are formed in a circular shape or continuous path to generate a loop]
6. Molecular chemical rhythm, [molecules like proteins, enzymes etc are carriers, tube like cavities are formed and sensory systems make sure a circular signalling pathway]
7. Quantum beating, [spin is the carrier, wavefunctions interfere in a squeezed excited photonic, electromagnetic or spin state]
8. Density of states rhythm, [orbitals coupling, wave function modulation, virtual carrier, a virtual continuous loop is made]
9. van-der Waal rhythm, [atomic thermal vibration is looped in a spiral pathway].
10. electro-mechanical rhythm [classical beating with a mechanical beating like tuning fork]
11. Quasi-charge rhythm polaron, polariton [topological fractured band based continuous loops]
12. mechanical rhythm, sound wave [similarly elastic pathways to make a circuit of sound waves].
Just imagine, such beautiful patterns are one of 12 different formations. Their physics is different, application domain and range are different.
- Information Theory: A new 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.
- Mechanics: We have been developing a new generic version of quantum mechanics, FM or Fractal Mechanics, We conceptualized a new fractal harmonic oscillator alternative to QFT
- Language: We have been developing a new geometric musical language (GML) and constructed Continued Fraction Geometric Alzebra (CFGA) and Geometric musical calculator (GMC).
- Human brain model: We develop 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).
- Geometric number system theory: We construct and information version for developing the theory of everything, and a theory of consciousness we call it 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.
- Fourth circuit element: We invent fourth circuit element, Hinductor
- Thermal energy harvesting machines: We invent artificial life forms, kT driven thermal nanobots, Thermo Electro mechanical system (TEMS).
- Musiceutical nanobots: We have developed musiceuticals, vibration based medicines, Nano Brain. Main focused diseases have been cancer and alzheimers.
- Fractal chemical kinetics and condensation: We have developed a new kind of multi-kinetic synthesis, we invent a new class of condensation beyond Froelich condensation, Fractal condensation
- Brain jelly: We invented organic jelly that replicates 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.