How A’, A, and 2A in Linguistics Create Nano Potency in Multiple Nano Quantum Therapies, Braids, Strings, Knots, Topological Quantum Computing, Logic Gates, TGD, TQC, DNA, and 4 Quantum Operators : Gurmukhi, Schwa and Be Happy Philselfologically 168

In this part of the series, we discuss how the Vowel of A, which is very popular as the Schwa Vowel plays one of the most important role of the Knots, Braids, Braided Group, Quantum Strings, Quantum Computing Operators, Essentials of DNA and Quantum Computing, which is based on the Topology and Homology of A as the A’-A’ giving us A as from A’+A’=A, and that A+A=A-A=2A, which seem to well constitute the Nano Potency in not only Homeopathy, Tissue and Cell Remedies, Electra-homeopathy, Electron-Homeopathy, Electrohomeopathy, Bach Flower, Herbal and Nutritional Extraction Based Therapies, Ayurveda, Herbalism, Food and Diet Supplement Systems, and thus what we can also term say as the Ancient Quantum Nano Multiple Therapies, which are also popular as the Sacred Multiple Therapies in the world embracing the Holistic, Whole-holistic, Integrated and Para Therapies, and thus the Nano Quantum Potency based Therapies, which are say about 500 kinds of therapies we discuss the bases, basics and Nano Potency Systems in these sacred, ancient and even most modern systems of say Homeopathy here say as Nano Homeopathy for the given reasons.

Now, first all when we can consider that the Vowel of A, the Schwa is made of the A’-A’, which is the Topology of Two Circles when its as A’-A’ and when it adds as A’+A’=A, we have our first knot. It’s as if to say that A’-A-A’, the Parameters of Cobordism of M, W, N in which we have the M=A’, W=A and N=A’, and it creates the Circle(A’)-Knot(A)-Circle(A’), which we deal as the Linguistics String in all world languages, linguistics and the grammatical systems.

In this regard, we have the A’-A’-A’ as the A-A’, which is the 3 Circles with possibility of 1 Knot while the A’-A’-A’-A’ can create the 2 Knots in the 4 Circles, which follow the Topology and Homotopy with homogeneity almost simultaneously. Its the Primal Linguists Dipole that has 4 Circles with 2 Knots. We can create as many Quantum Circles, Braids, Strings, Braided Groups, Knots, Topological Quantum Computing Operators, and the Quantum Logic Gates, and lot more as it can play a very significant role in the DNA and RNA Structure based DNA Quantum Computing and the Computers with its Quantum Qubit Programming as the A’-A-A’ is the Cobordism and the Qubit say simultaneously.

The A’, 2A’, 3A’, 4A’ as the A, E, O, AE act as the Topological Quantum Logic Gates:

“Quantum logic gates are represented by unitary matrices. The most common quantum gates operate on spaces of one or two qubits, just like the common classical logic gates operate on one or two bits. This means that as matrices, quantum gates can be described by 2 × 2 or 4 × 4 unitary matrices.” (With thanks from the source: https://en.wikipedia.org/wiki/Quantum_gate )

We can easily notice that as we have the following basic points in the A’, A and 2A, we can see the role of √2:

1. The 2A=A+A

2. The A=A’+A’

3. The A=√2A’ if we use the A’, A and 2A in the Cartesian or Qubit, the Bloch Spheres as while following the Pythagoras Theorems

A^2=A+A, A=(A+A)^1/2=4A’^1/2=2*A’^1/2=2*√2A’

A=1/2*2*√2A’=√2A’

Thus, in the Philosophy of Qubit’s, we can very easily notice the Role of √2A’.

If we use this Philselfological Model and Theory for the Topological Quantum Computing, we can notice that when we have the 3A’+A’, we can create the Quantum Circuit of Two Qubits say as follows:

1. The A=1/2A’

2. The AA=1/2A=1/4A’

So, when we create the Quantum Qubit Circuits from the Two Sets of 4A’s, we notice the following:

(A’-A’-A’)-A’-A’-(A’-A’-A’)

(Qubit1)-A’-A’-(Qubit2)

And what we get from it is the Quantum Qubit Bus Circuits as we see the Two Qubits joined say as (A’-A’-A’)-A’-A’-(A’-A’-A’)=(A’-A’-A’)-(1,0)-(A’-A’-A’) . The Magic of A’ and A with and say as Pi/2 and Pi Plays a Big Role as we see in the images below:

Figure 1 (high res version): The chip used to observe Berry’s phase consists of a micron-size superconducting electronic circuit functioning as a quantum mechanical bit (qubit) (blue structure in lower middle image). The qubit is integrated into a centimeter long one-dimensional superconducting microwave resonator (upper image) essential for controlling and measuring the qubit using coherent microwave radiation. Injecting an appropriately modulated microwave signal into the resonator controls the qubit geometrically. This is analogous to a vector being parallel transported on the surface of a sphere around a closed path (lower right). The Berry’s phase is just like the angle that the vector is rotated by after it has completed the path. (With thanks from the source: http://www.its.caltech.edu/~jfink/research.html )

So, we notice that the (A’-A’-A’)-A’-A’-(A’-A’-A’)=(A’-A’-A’)-(1,0)-(A’-A’-A’) , which is the most essential part of the Two Qubits Joined to get the (Qubit1)-A’-A’-(Qubit2)=(Qubit1)-A’-A-A’-(Qubit2)=(Qubi t1)-(1,0)-(Qubit2) gives us the A’-0-A’, A’-1-A’, A’-A-A’ as the Berry’s Phase, which as a token of respect to the Schwa Quantum Systems of A, we can also write say as the Schwa Quantum Phase for the students, scholars and researchers of Languages, Linguistics, Grammars and of course the International Phonetic Alphabets and the SAMPA, X-SAMPA, SAMPROSA and the similar quantum systems as they all are the First Quantum and the Classical Human, AI, Computer and Machine Programmers of the Humanity:

Quantum Computing using Berry Phase:

Berry phase, so called because it was discovered by Michael Berry in 1984, is a concept crucial to our understanding of many quantum mechanical effects. For example it affects the way in which chemical reactions occur, it modifies the motion of vortices in superconductors, and the motion of electrons in nanoscale electronic devices. It has recently been suggested that it could be used to make a quantum computer. Phase is a basic property of all waves, for example the difference in phase between two waves determines whether they interfere constructively or destructively. All quantum particles have wavelike properties, such as phase, because of wave-particle duality. Berry phase is a special phase that the particle acquires if it is forced to slowly rotate. It appearsn that one way of controlling a qubit is to control its Berry phase. However to do this we require a quantum computer with qubits made from robust quantum systems with Berry phases. These qubits must be coupled to each other and yet be isolated from everything else.” (With thanks from the source: http://r.whitney.free.fr/recent-work/BP+quant-comp… )

Please read more about the (A’-A’-A’)-A’-A’-(A’-A’-A’)=(A’-A’-A’)-(1,0)-(A’-A’-A’) , which is the most essential part of the Two Qubits Joined to get the (Qubit1)-A’-A’-(Qubit2)=(Qubit1)-A’-A-A’-(Qubit2)=(Qubi t1)-(1,0)-(Qubit2) gives us the A’-0-A’, A’-1-A’, A’-A-A’ as the Berry’s Phase:

“In classical and quantum mechanics, the geometric phase, Pancharatnam–Berry phase (named after S. Pancharatnam and Sir Michael Berry), Pancharatnam phase or most commonly Berry phase, is a phase difference acquired over the course of a cycle, when a system is subjected to cyclic adiabatic processes, which results from the geometrical properties of the parameter space of the Hamiltonian.” (With thanks from the sources: https://en.wikipedia.org/wiki/Geometric_phase , https://en.wikipedia.org/wiki/Berry_connection_and… , http://www.princeton.edu/~npo/SurveyTopics/Berry_e… )

The Berry Phase and the Adiabatic Theorem keep the affinity that when we have the (A’-A’-A’)-A’-A’-(A’-A’-A’)=(A’-A’-A’)-(1,0)-(A’-A’-A’) (Qubit1)-A’-A’-(Qubit2)=(Qubit1)-A’-A-A’-(Qubit2)=(Qubi t1)-(1,0)-(Qubit2), we have the A’-A’-A expressed say as the (E-)-E0-(E+), and thus we get the Adiabatic Theorem verified as well described at the Physics StakeExchange:

“The adiabatic theorem is required to derive the Berry phase equation in quantum mechanics. Therefore the adiabatic theorem and the Berry phase must be compatible with one another. (Though geometric derivations are possible, they usually don’t employ quantum mechanics. And while illuminating what is going on mathematically, they obscure what is going on physically.)

The question of degeneracy points is a little more subtle, but let me make one thing clear: if one crosses a degeneracy point, the adiabatic theorem is no longer valid and one cannot use the Berry phase equation that you have written in the question (the denominator will become zero at the degeneracy point).

Now, let us take the spin in magnetic field example as an illustration of the Berry phase. Suppose we have a spin-1/2 particle in a magnetic field. The spin will align itself to the magnetic field and be in the low energy state E=E−. Now, we decide to adiabatically change the direction of the magnetic field, keeping the magnitude fixed. Adiabatically means that the probability of the spin-1/2 particle transitioning to the E=E+ state is vanishingly small, i.e. Δt/ℏ<<E+−E−. Suppose now that the magnetic field traces out the loop below, starting and ending at the red point:berry phaseIn this case, one will pick up a Berry phase equal to:Berry Phase=γ=−12Ωwhere Ω is the solid angle subtended. This formula is proven in Griffiths QM section 10.2. However, it is not that important to understand the overall picture.” (Please read more from the source with our thanks: http://physics.stackexchange.com/questions/70707/a… )<br/>

It well leads to most of the Quantum Brain Theories as well:

“Yasue thinks that several layers of the brain can host quantum processes, whose quantum properties explain consciousness and cognition. Yasue presents the brain as a macroscopic quantum system. He focuses on water megamolecules in the space between neurons, which can combine to form extended quantum systems, interacting with the neural networks.He focuses on the sensory system, whose quantum field causes some special molecules in the membrane of the neuron to undergo Froehlich condensation and cause, in turn, macroscopic coherence.

He focuses on structures such as microtubules which lie inside the neuron, and which contain quasi-crystalline water molecules that again lend themselves to quantum effects. The function of this quantum field could be cognitive: some particular quantum states could record memory.

He focuses on a bioplasma of charged particles which interact with the electromagnetic field, an ideal vehicle for a merge of the sensory quantum field with the memory quantum field, an ideal vehicle for the creation of classical reality. Thus, classical order can continually unfold in this bioplasma.” (With thanks from the source: http://www.scaruffi.com/science/qc.html )

As we have said that the A’ is also the Quantum Spin as well as the UP and DOWN Spins in the Spintronics, and thus if we take A’-A’, its the UP and DOWN Spins of the “Same Electrons that constitute the Spintronics and the Quantum Bits as the Qu-bits or the Qubit’s”. So, we can assign the A’-A’ a set of two bits which creates Qubit due to its UP and DOWN Spins, and thus we have it say as A’-A-A’, and its same as A’-(0,1)-A’ or A’-(1,0)-A’, in which we have the 1 or 0 as the UP and DOWN of the Resulting Spin with the Berry’s Phase:

“Quantum-based technologies exploit the physical rules that govern very small particles — such as atoms and electrons — rather than the classical physics evident in everyday life. New technologies based on “spintronics” rather than electron charge, as is currently used, would be much more powerful than current technologies.

In quantum-based systems, the direction of the spin (either up or down) serves as the basic unit of information, which is analogous to the 0 or 1 bit in a classical computing system. Unlike our classical world, an electron spin can assume both a 0 and 1 at the same time, a feat called entanglement, which greatly enhances the ability to do computations.

(Please read more from the source with our thanks: Quantum Computing Moves Forward with Spintronics Progress)

When we consider the (A’-A’)-(A’-A’), we can notice it as the Molecular Spintronics in which one Quantum Bit, the Qubit is inside the Molecule, which can be say any food, herbal, nutraceuticals; the food and diet supplements, and thus we can the Bio Qubit, the DNA Based Qubit:

“Molecules can be considered as physical Quantum Objects. The use of molecular materials represents the advantage that the active quantum processing elements consist of an atomic core of one-to-few open spin ions surrounded by a shell of organic material.

At low temperature such molecular spin objects behave as simple, few-level systems and their spin degree of freedom can be sufficiently decoupled from the environment to achieve long decoherence times and making them to ideal candidates for the implementation of qubits.” (With thanks from the source: https://www.int.kit.edu/1709.php )

So, one may ask what is (A’-A’)-(A’-A’), well, it’s the Quantum Gate:

With A=1/4A’, we have it all of the Quantum Gate Systems:

“The Hadamard gate acts on a single qubit. It maps the basis state 

 to 

 and 

 to 

 and represents a rotation of 

 about the axis 

. It is represented by the Hadamard matrix:

.

Since 

 where I is the identity matrix, H is indeed a unitary matrix.” (With thanks from the source: https://en.wikipedia.org/wiki/Quantum_gate )

If we thus use the (A’-A’)-(A’-A’) as the Molecular, Bio or DNA Based Qubit, we can have many good and great results from it that can help humanity:

“Quantum computing will lead the future revolution of information technology.

Quantum information processing proposes to exploit the laws of quantum mechanics for the realization of logic operations and implementation of algorithms. The realization of Quantum Computing will outperform current classic information technology by dramatically increasing speed and providing the capacity to handle intractable problems, like the simulation of quantum systems.

Hot topics to be covered by the symposium (but is not limited)

Chemical design of qubits using lanthanide and transition metal complexes

Organic radicals for quantum computing

Design and control of quantum coherence through chemistry

Physical methods to unveil and study quantum entanglement within molecules

Realization of multi-qubit quantum gates

Pulsed and HF-EPR for the detection and characterization of quantum coherence

Simulation of magnetic anisotropy and quantum coherence through theoretical methods

Quantum simulation of quantum systems

Quantum Manipulation of small molecular or atomic ensembles

Surface nanostructuration of molecular qubits and qugates” (With thanks from the source: http://www.emrs-strasbourg.com/index.php?option=co… )

The Quantum A, the Schwa as the Quantum Matrix Systems: The still greater wonders include about how we use the A’-A’-A’-A’ in the Quantum Matrix Systems, and it can be Quantum Matrix of Orders of say A’-A’-2A’-4A’, 4A’-2A’-5A’-2A’, A’-A’-A’-2A’-A’-3A’, and other rows and columns with say (A’-A’)-(A’-A’) as A’-(A’-A’)-A’ as defined in the matrices or the matrix systems in Math, Computing and or Otherwise:

“Matrices are commonly written in box brackets or an alternative notation uses large parentheses instead of box brackets:

The specifics of symbolic matrix notation varies widely, with some prevailing trends. Matrices are usually symbolized using upper-case letters (such as A in the examples above), while the corresponding lower-case letters, with two subscript indices (e.g., a11, or a1,1), represent the entries.

In addition to using upper-case letters to symbolize matrices, many authors use a special typographical style, commonly boldface upright (non-italic), to further distinguish matrices from other mathematical objects.” (With thanks from the source: https://en.wikipedia.org/wiki/Matrix_%28mathematic… )

We can very easily use the A=1, A’=i, 2=A=A and thus say something that we use in the Conjugate Systems of Matrix as shown in the image below:

If

Then

The notations of say a+ib say as A+A’A should not surprise us:

(Please read more from the source with our thanks: https://en.wikipedia.org/wiki/Conjugate_transpose )

We need to take care that if we use the A’-A’-A’ or the A’-A’-A’-A’ as the Identity Matrix Systems, it can be a great fun in the Quantum Maths:

“In linear algebra, the identity matrix or unit matrix of size n is the n × n square matrix with ones on the main diagonal and zeros elsewhere. It is denoted by In, or simply by I if the size is immaterial or can be trivially determined by the context. (In some fields, such as quantum mechanics, the identity matrix is denoted by a boldface one, 1; otherwise it is identical to I.) Less frequently, some mathematics books use U or E to represent the identity matrix, meaning “unit matrix”<1> and the German word “Einheitsmatrix”,<2> respectively.” (With thanks from the source: https://en.wikipedia.org/wiki/Identity_matrix )

Now, when we consider the A’-A’, and what it creates as say sound energy is written say as the A’-0-A’ and A’-A-A’, and when we write it as A’-A-A’, it’s called the Cobordism of A’ and the A, and similarly if we use the A’-A’-A’, its used to denote what we read say as IE or EE say when we A-A’-A’ as the IE, and when A’-A’-A as EE, and here to keep the count of A’s upright, we can write the same say as A-A’-A’-A’=IE and A’-A’-A’-A=EE or EI for the reason that A’-A’-A’=E as A’=O and that A’-A’=A with A’-A’-A’-A’=AE is something that international phonetic systems describe and the Indian Sacred Systems also use it all in the Sacred Languages, Linguistics and the Grammatical Systems.

The Hypothesis of Philselfology assumes that when we write the A’-A’-A’-A’, it creates the Columns and when we combine it say as A’A’-A’A’ or even AA-AA, it creates the Rows, and if we expand the AA-AA-AA-AA, it goes down in the Matrix, and thus A-A and AA-AA are two members each in the Columns and the 2 Rows of 2*2 Matrix, and in the Indian Sacred Systems, the A-A-A-A is considered the Power and the AA-AA-AA-AA is the Energy Systems, and the A-A-A-A creates the Series, the Linear Systems while the AA-AA-AA-AA creates the Layer Systems in any given system of Math, Computing and Linguistics (Languages). So, the following addition can occur if we add say A’ and A’ or A and A:

A+A=2A (Power Addition, the case in Exponential)

A+A=AA (Energy Addition, the case in the Linear Functions where the Power is 1)

We can thus notice its, the Power Functions and Energy Functions and Addition, Multiplication, Division, and the other mathematical and the quantum operations related to it all, which has a great use in our daily educational and mental health math and for fun:

Exponential Expression – an expression or term with a power or exponent that is not one:

For example, x2 is an exponential expression while x is not an exponential expression. Similarly, x1/2 (called the square root of x) is an exponential expression while 2x is not an exponential expression.

Exponential Equation – an equation with a term that has an exponent greater than one:

For example, x3/2 + 2x + 1 is an exponential expression while 2x + 3 is not an exponential expression. Similarly, x3 = 27 is an exponential equation while x + 2 = 29 is not an exponential equation.” (With thanks from the source: http://www.platinumgmat.com/gmat_study_guide/expon… )

We can very easily notice that A’ is odd number say as even 1, and if it combines with the other A’, it can give either 0 or 1, and in its Quantum Algorithm, we can have always A’, 2A’ say as A’-A, which can create the infinite series of this nature that is A’-A-A’, and the chain goes say as A’-A-A’-A’-A-A’-A’-A-A’-… N Times, and in every case when we have A’-A’, it can generate the Qubit and when we need Quantum Logic and Algorithm in which A’+A’=A is the Part of the Prime Numbers as its always exactly 1 and if we consider the spin, it can be either 0 or 1, but all goes how rapidly we notice the A’-A’ changing into A and next pairing up with either A or A’, and that is A’-A-A’, A’-A-A’-A’ or A’-A-A, A’-A-A-A’, and its the Basics of the Shor’s Algorithm for Quantum Computing:

“The problem we are trying to solve is: given an odd composite number N, find an integer d, strictly between 1 and N, that divides N. We are interested in odd values of N because any even value of N trivially has the number 2 as a prime factor. We can use a primality testing algorithm to make sure that N is indeed composite.

The algorithm is composed of two parts. The first part of the algorithm turns the factoring problem into the problem of finding the period of a function, and may be implemented classically. The second part finds the period using the quantum Fourier transform, and is responsible for the quantum speedup.” (With thanks from the source: https://en.wikipedia.org/wiki/Shor%27s_algorithm )

Now, as we notice that A’-A-A’ and A’-0-A’ can give us A=1 or 0, and it can be thus the qubit j is in state xj, with xj either 0 or 1, and thus Quantum Fourier Transformations for say the A’-A’ as the Xj, and no wonder Xj as (X’-X’)j as the (A’-A’)j is the Sacred Structure of the Qubit as in the Qu-bits of A’ and A’ as the A’-A’ as the Two Bits that function and work as the Qubits:

“The quantum Fourier transform can be approximately implemented for any N; however, the implementation for the case where N is a power of 2 is much simpler. Suppose N = 2n. We have the orthonormal basis consisting of the vectors

.

The basis states enumerate all the possible states of the qubits:

| x \rangle = | x_1 x_2 \ldots x_n \rangle = | x_1 \rangle \otimes | x_2 \rangle \otimes \cdots \otimes | x_n \rangle

where, with tensor product notation \otimes, |x_j\rangle indicates that qubit j is in state x_j, with x_j either 0 or 1. By convention, the basis state index x orders the possible states of the qubits lexicographically, i.e., by converting from binary to decimal in this way:

x = x_1 2^{n-1} + x_2 2^{n-2} +\cdots + x_n 2^0.\quad

In other words, the discrete Fourier transform, an operation on n-qubits, can be factored into the tensor product of n single-qubit operations, suggesting it is easily represented as a quantum circuit. In fact, each of those single-qubit operations can be implemented efficiently using a Hadamard gate and controlled phase gates. The first term requires one Hadamard gate, the next one requires a Hadamard gate and a controlled phase gate, and each following term requires an additional controlled phase gate. Summing up the number of gates gives 1 + 2 + \cdots + n = n(n+1)/2 = O(n^2) gates, which is polynomial in the number of qubits.

(With thanks from the source: https://en.wikipedia.org/wiki/Quantum_Fourier_tran… )

Now, we may wonder about how 1 and 0 can give everything that we know as the Quantum and the Qubit, and here here 1 is the Root of Unity System:

“An nth root of unity, where n is a positive integer (i.e. n = 1, 2, 3, …), is a number z satisfying the equation<1><2>

.

And it goes say as:

Setting x = 2π/n gives a primitive nth root of unity:

When we use the Euler Formula for 1 and 0 of Qubit of A’ and A’, we have all the way Quantum and the Qubit going on:

(Please read more from the source: https://en.wikipedia.org/wiki/Root_of_unity )

So, we can say that 0 and 1 find the Quantum Playground of Qubit with the 

(Please read more from the source: https://en.wikipedia.org/wiki/Quantum_Fourier_tran… )

For the above reasons, I have put it all say the A’, 2A’ and the 3A’ Systems say as:

E=O+A, which is same as saying the 3A’=A’+2A’

Here the 3A’=A’+2A’ Spins of say Electrons create the 2:1 Qubit, which we may call the E-Qubit is very interesting phenomenon in nature as we can see below in which we see the E’-E’ say the 3 Spins to 3 Spins:




Please read more about it: “The finding, by a team led by Princeton physicist Jason Petta, could eventually allow engineers to build quantum computers consisting of millions of quantum bits, or qubits. So far, quantum researchers have only been able to manipulate small numbers of qubits.” (With thanks from the source: http://www.kurzweilai.net/breakthrough-may-lead-to… )

When we use the Linguistics, Languages and the Grammars say as for the Math and Computing, we can very easily notice the role of Solid State of Matter say as the AA-AA, the Conductive Band say as A-A, and thus the A’-A’ as the Nano Scale Works as according to pressures we have on the AA, A, and A’ Systems can be assumed to go as shown below:




If we thus use the simple concept of AA-AA, AA-A, A-A, A-A’, A’-A’, which is comprised of 5 Basic Steps in the Differential Centrifugation as we can correlate in the images below:








With the use of Qubits with 8, 6, 4, 3 and 2 Spins, we can have it AA-AA, AA-A, A-A, A-A’, A’-A’, we can create the Berry Phase, which seem to hypothetically create the Consonants, the Vowels, the Vowel Quantum Bits to create what we see, hear and touch as say light, sound and solids from the Berry’s Phase Glow, which is same as the Bindu, the Quantum Dot in our Hypothesis of Philselfology.

Thus, the Quantum Dot is with the 8, 6, 4, 3 and the 2 Spins say as the AA-AA, AA-A, A-A, A-A’, and the A’-A’.

Now as the Quantum Dot seem to create the Quantum Noise, the Consonant Part in the World Languages say as the Quantum Sounds in the Universe, we can notice that the Quantum Dot with the Berry Phase can have the Levels of Phase which give us the 5 Phases of AA-AA, AA-A, A-A, A-A’, A’-A’ relatively say as the Solid, Fire, Water, Air and Space, and that too in say the Sacred Sequence of AA-AA, AA-A, A-A, A-A’, A’-A’, the Results of Differential Centrifugation, and that can be very easily understood say as the 5 Rows of Consonants in the Indian Alphabets say the Gurmukhi, while the Hindi and the Sanskrit also keep it all in the same manner.

This is the Story of Differential Centrifugation giving 5 Rows of Consonants with Quantum Sounds, popular as the Quantum Noise, and that is say the Quantum Spins of 8, 6, 4, 3 and 2 as AA-AA, AA-A, A-A, A-A’, A’-A’. If we expand it say 8 Spins of AA-AA as in the Space Element, the Berry’s Phase of Space Element say the Close to Vacuum Systems, we have the K functioning say as the KA, and all of this process seem quantize the AA-K-AA, which is same as the 4-4 Spins in the Space, and if we create say the Nano Products, the Nano Crystals, the Nano Carbon Tubes, and the Semi-Solids and the Solids, its denoted by the Second Row of the Indian Vowels which are say YA, RA, LA, VA, RHA, and its all the Quantized Products from the AA-K-AA, and is written say as the AA-K-AA-RA, the AAKAARA, which means the Visible Virtual, the Nano, the Chara, the Quantum World, and if we change the count of spins, we can have say the A-KAARA world, which is the Semi-solid Virtual Quantum World, and the Third is the A’-KAARA, the Nano Quantum World, andd this is how all Indian Terms say in the Sanskrit, Hindi and Gurmukhi have been created, constructed, composed and written to explain the Classical (AA) and the Quantum Universes (A’) with the Intermediate Universe of AA-A’ as the A-Universe in which we all live. This is based on the Hypothesis of Philselfology and the Indian Languages, World Languages, Linguistics, Phonetic Systems, etc., and we can very easily understand it with a little home work to grasp the Indian and World Theories and the Models of Elements, Dimensions, Light, Consciousness and Sound in the Universe.

When we consider the A-A’ or the A’-A, we notice say as the 3-Dimensional Manifold in which the Direction seems to work say as the Direction Dimension as its the most unstable state where the A’-A or A-A’ wants to go either to A-A or to the A’-A’, the more stable levels of the systems, and it can be the Universe as the Quantum System:




We can call it the Self-braiding Quantum Systems:

“In more than two dimensions, the spin–statistics theorem states that any multiparticle state of indistinguishable particles has to obey either Bose–Einstein or Fermi–Dirac statistics. For any d > 2, the Lie groups SO(d,1) (which generalizes the Lorentz group) and Poincaré(d,1) have Z2 as their first homotopy group. Because the cyclic group Z2 is composed of two elements, only two possibilities remain (The details are more involved than that, but this is the crucial point).” (With thanks from the source: https://en.wikipedia.org/wiki/Anyon )


We can consider the Quantum Spins of 8, 6, 4, 3 and 2 as AA-AA, AA-A, A-A, A-A’, A’-A’ as the Topological Order for the States of Solid, Liquid, Gases, Air and Space that also includes the Superfluids and the Plasma in which we can also consider the A’ as the Chiral Spin:

“In an attempt to explain high temperature superconductivity<13> the chiral spin state was introduced.<4><5> At first, physicists still wanted to use Landau symmetry-breaking theory to describe the chiral spin state. They identified the chiral spin state as a state that breaks the time reversal and parity symmetries, but not the spin rotation symmetry. This should be the end of story according to Landau’s symmetry breaking description of orders. However, it was quickly realized that there are many different chiral spin states that have exactly the same symmetry, so symmetry alone was not enough to characterize different chiral spin states. This means that the chiral spin states contain a new kind of order that is beyond the usual symmetry description.<14> The proposed, new kind of order was named “topological order”.<1> (The name “topological order” is motivated by the low energy effective theory of the chiral spin states which is a topological quantum field theory (TQFT)<15><16><17>).” (With thanks from the source: https://en.wikipedia.org/wiki/Topological_order )

So, when we think of the Topological Quantum Field Theory, the TQFT, we can think of Quantum Spins of 8, 6, 4, 3 and 2 as AA-AA, AA-A, A-A, A-A’, A’-A’ as the Dimensions equal to 0, 1, 2 and 3 Topological Manifolds as proposed by Atiyah and Others with say d=0 (0, the Light), d=1 (A’, the Point Particle), d=3 (A-A’, the Qubit and a Point Particle) and d=4 (A-A, the Two Qubits), and here we may fully use the Cobordism as say d= has the A-A’, the 3 Dimensional A as A-A’, which we can arrange with 1 Dimension of A’ to make and keep it say the d=2 as if we put A-A, it goes say d=4 with 2-D of A with 2-D of A say as A-A or the 2A, and thus the 0, A’, A, A-A’ and AA Summaries the Topological Quantum Field Theory, the TQFT with the point that with the 3-Dimensions, we have the A by itself as the Consciousness, the Self-assembling and Reassembling of Matter that we know say as the 4th Dimension:

“A cobordism between two manifolds represents some kind of evolution from one state space to another state space. In quantum mechanics we have an evolution in a continuous time parameter. In order to get a TQFT that describes this, choose:

0-dim topological manifolds, i.e. points, as objects (or “the point” as the only object)

1-dim cobordisms of the points as arrows,

Add a Riemannian structure to the 1-dim cobordisms, which equips them with a length.

Now a TQFT on this category will be a functor that

Associates a (finite or infinite dimensional) vector space H to the point,

Associates a linear operator U(t):H→H to every (or the) interval of length t such that

U(ts)=U(t)U(s) (functoriality).

For infinite dimensional vector spaces we would need to assume that they are (complex) Hilbert spaces. And we would in addition have to assume that the linear operators that are associated to cobordisms are unitary operators. Then the TQFT is identical to the Schrödinger picture of quantum mechanics. Rays in the vector space H represent the state of a physical system and the operators U(t) represent the evolution of the system from one state at the time 0 to the time t. (Please read the full article as the Questions and Answers: Atiyah’s definitions of Topological Quantum Field Theory)

Now, when we go for the Cobordism with the M, M’ and M”, its same say as the 2A, A and A’ or A’, A, 2A, and that too say as 4A’, 3A’, 2A’ and A’, which we easily summarize and use to explain the following:


“There are various important operations one can perform on cobordisms, but I will only describe two. First, we may `compose’ two cobordisms M: S -> S’ and M: S’ -> S”, obtaining a cobordism M’M: S -> S” , as illustrated in Figure 2. The idea here is that the passage of time corresponding to M followed by the passage of time corresponding to M’ equals the passage of time corresponding to M’M. This is analogous to the familiar idea that waiting t seconds followed by waiting t’ seconds is the same as waiting t+t’ seconds. The big difference is that in topological quantum field theory we cannot measure time in seconds, because there is no background metric available to let us count the passage of time! We can only keep track of topology change. Just as ordinary addition is associative, composition of cobordisms satisfies the associative law:







A’ as the Identity Cobordism:





(With thanks from the source: http://math.ucr.edu/home/baez/planck/node3.html )

One may ask what is A’, A, A-A’, A-A, and the Higher Dimensions say the A-A-A’, A-A-A, etc., and we can say its the most charming way to study what we know as the Differential Topology as one needs to study it to understand and comprehend the Topological Quantum Field Theory as well as the Quantum Field Theory say as the TQFT and QFT:

“To put it succinctly, differential topology studies structures on manifolds which, in a sense, have no interesting local structure. Differential geometry studies structures on manifolds which do have an interesting local (or sometimes even infinitesimal) structure.” (With thanks from the source: https://en.wikipedia.org/wiki/Differential_topolog… )

Thus, the Quantum Spins of 8, 6, 4, 3 and 2 as AA-AA, AA-A, A-A, A-A’, A’-A’ seem to be the easiest solution and summary to the Stokes Theorem as when we differentiate the AA, we get AA’, A’A’ and the A’, and if we integrate we get the A’, A, AA’, AA, and the higher dimensions:

“In vector calculus, and more generally differential geometry, Stokes’ theorem (also called the generalized Stokes’ theorem) is a statement about the integration of differential forms on manifolds, which both simplifies and generalizes several theorems from vector calculus. Stokes’ theorem says that the integral of a differential form ω over the boundary of some orientable manifold Ω is equal to the integral of its exterior derivative dω over the whole of Ω, i.e.,




(Please read more from the source with our thanks: https://en.wikipedia.org/wiki/Stokes%27_theorem#Ke… and https://en.wikipedia.org/wiki/Navier%E2%80%93Stoke… )

When we consider the Pauli’s Exclusion Principle for the Pair of Spins A’-A’ or even the A-A or the 2A-2A, we can easily notice that it goes well for most of the Symmetries and the Asymmetries, which we claim by A’+iA’ or the A+iA, and thus for the Quantum Spins of 8, 6, 4, 3 and 2 as AA-AA, AA-A, A-A, A-A’, A’-A’, and what the Wikipedia of Symmetry (Physics) explains say as the C, P, and T symmetries, and all that otherwise mentioned in the Wikipedia embraces all of the topics, which we discuss with the Quantum Spins of 8, 6, 4, 3 and 2 as AA-AA, AA-A, A-A, A-A’, A’-A’ or even the 0-A’ as the 1-Spin:

“Physics: Continuous and discrete transformations give rise to corresponding types of symmetries. Continuous symmetries can be described by Lie groups while discrete symmetries are described by finite groups (see Symmetry group).

These two concepts, Lie and finite groups, are the foundation for the fundamental theories of modern physics.

Mathematics: Continuous symmetries in physics preserve transformations. One can specify a symmetry by showing how a very small transformation affects various particle fields. The commutator of two of these infinitessimal transformations are equivalent to a third infinitessimal transformation of the same kind hence they form a Lie algebra. (Please read more from the source: https://en.wikipedia.org/wiki/Symmetry_%28physics%… )

So, when we consider the A’, 2A’, 3A’, 4A’ say as the A’, A, A-A’ and A-A, we come to discuss the “Particle in Box” that gives us the “Initial Wavefunction’s of initial 4 States of the Particle say as in the 1-Dimensional Setup that we can express say as A’, 2A’, 3A’, 4A’, and here all 4A’s are the 1-Dimensional, and thus we have the hypothesis seems to be well following the image below:




At the same time, we also notice that A’, 2A’, 3A’ and 4A’ goes with the following primal quantum points:

When we have the A’ going to 2A’, we naturally have the Time, Space and Direction involved and thus all of it also goes say as the Wave Vector, and please read more from the source: https://en.wikipedia.org/wiki/Wave_vector

One of the idea that I want to patent is as follows:

A’-A-A’ gives us something that is same as A’-mc2-A’ or the A’-mc^2-A’, and we can write it say A’-mcv-A’, the reason is that the Qubit Formation and the Photon Formation involves that we have mass, charge and spin (velocity) active on the light (c), and in it the mass is directly proportional to A’-A’ System as is the velocity of light and momentum and the natural velocity that we can denote by v, and thus the “mcv”. I have been expressing it in this way:

A’-A’ can become A when we have the S, H and A acting in the Quantum Systems simultaneously as S is the velocity of light, H is the general velocity and A as the Mass, and I have been able to put it all say as:

S+H+A=C+V+M, and it’s also say as E+A+O, which is the Integrated Cobordism of 3, 2 and 1 Dimensions, and this creates the following system that shows the hypothetical mass and general velocity (low) and the highest velocity of light at the center with A’-(S-H-A)-A’, which is same as A’-(M-C-V=E=MC2)-A’, but it’s a big claim that I would seem to make:



As we have already discussed that in general, we have the E=O+A, and that for the Imaginary and Complex Number Systems, it’s the Sinusoidal Wave Function as the E=O+iA, where E=SinA+iCosA generates the Wavefunctions of the E, and we have the O in the Y-Axis as A’, the Hypothetical A’ in Y and thus “O”, and in the X-Axis and the Direction, it’s the A’-A’=A.

When we consider the A’ to be Spin, which can be UP or DOWN, we can also notice that A’-A’ constitutes the Wavelength λ (Lambda), and it goes to qualify the Eisenstein and De Broglie’s Equations:

“In 1905 Einstein postulated the proportionality between the frequency of a photon and its energy, E = hf,<9> and in 1916 the corresponding relation between photon momentum and wavelength, λ = h/p.<10> In 1923, De Broglie was the first to suggest that the relation λ = h/p, now called the De Broglie relation, holds for massive particles, the chief clue being Lorentz invariance,<11> and this can be viewed as the starting point for the modern development of quantum mechanics. The equations represent wave–particle duality for both massless and massive particles.” (With thanks from the source: https://en.wikipedia.org/wiki/Wave_function )

When the A’ forms waves, these start as A’-A’-A’-A’…, but as A’+A’=A, it also goes as A’-A-A’-A-A’, which appear as the Longitudinal Waves, the very waves, which constitute the sound we can hear:


“Matter waves were first experimentally confirmed to occur in the Davisson-Germer experiment for electrons, and the de Broglie hypothesis has been confirmed for other elementary particles. Furthermore, neutral atoms and even molecules have been shown to be wave-like.” (With thanks from the source: https://en.wikipedia.org/wiki/Matter_wave )

One may wonder that if A’-A-A’-A-A’, these can also create what we know as the A’-(A-A’)-A-(A-A’)-A’ and also the A’-(A-A’)-A-A, and so on, and all of it too is very right as the Longitudinal Waves of A’-A-A’ nature slowly change into these patterns with passing of time, that is, in the longer time periods as we can see in the image below using the Double Slit Experiment:



“In most modern interpretations this description is reversed – the quantum state, i.e. wave, is the only genuine physical reality, and under the appropriate conditions it can show features of particle-like behavior.

Two-slit diffraction is a famous example of the strange behaviors that waves regularly display, that are not intuitively associated with particles. The overlapping waves from the two slits cancel each other out in some locations, and reinforce each other in other locations, causing a complex pattern to emerge. Intuitively, one would not expect this pattern from firing a single particle at the slits, because the particle should pass through one slit or the other, not a complex overlap of both.

However, since the Schrödinger equation is a wave equation, a single particle fired through a double-slit does show this same pattern (figure shown above).” (With thanks from the source: https://en.wikipedia.org/wiki/Schr%C3%B6dinger_equ… )

The A’, A, A-A’, and A-A are the amplitudes, the phases () that differ by Pi/2 say as , and thus we have the A’ say as the y(t) and A’-A’ as the x(t) and in other words A’+90 Degrees (Pi/2)=A, and we can put that A’=SinA’ and that A’+90 Degrees (Pi/2)=CosA’, and if we rearrange and arrange these factors, we get the Waves and the Phases with say the Wave Functions, and all as the phase of an oscillation or wave refers to a sinusoidal function such as we have in the following phase expressions:


where A, f,  are constant parameters called the amplitude, frequency, and phase of the sinusoid. (Please read more from the source with our thanks: https://en.wikipedia.org/wiki/Phase_%28waves%29 )

If we consider the A’ creating the Circular Systems of Waves for the , we get the following from the Bohr Model and the De Broglie with Quantization of Angular Momentum:

“These quantized orbits correspond to discrete energy levels, and de Broglie reproduced the Bohr model formula for the energy levels. The Bohr model was based on the assumed quantization of angular momentum L according to:



According to de Broglie the electron is described by a wave and a whole number of wavelengths must fit along the circumference of the electron’s orbit:


This approach essentially confined the electron wave in one dimension, along a circular orbit of radius r.” (With thanks from the source: https://en.wikipedia.org/wiki/Schr%C3%B6dinger_equ… )

In the ideal cases of A’ as A’-A’=A, we have the Radius of the Circle also as equal to A’ or A.

We notice as the Density Operators, the A’, A, A-A’ and A-A all say as A’, 2A’, 3A’ and 4A’ not only create the Bloch Sphere of Quantum Qubit Philosophy, Science and Math, but also the Basics of Qubit and the Quantum Systems with the C*-algebraic formulation of density states say as the Self-adjoints of A’, 2A’, 3A’, 4A’ that create the Density Operators say as the A’, A, A-A’ and A-A:

“In quantum mechanics, the Bloch sphere (also known as the Poincaré sphere in optics) is a geometrical representation of the pure state space of a 2-level quantum system. Alternatively, it is the pure state space of a 1 qubit quantum register. The Bloch sphere is actually geometrically a sphere and the correspondence between elements of the Bloch sphere and pure states can be explicitly given.

Formulations of quantum mechanics in terms of pure states are adequate for isolated systems; in general quantum mechanical systems need to be described in terms of density operators. The topological description is complicated by the fact that the unitary group does not act transitively on density operators.

A density matrix, or density operator, is used in quantum theory to describe the statistical state of a quantum system. The formalism was introduced by John von Neumann (according to other sources independently by Lev Landau and Felix Bloch) in 1927. It is the quantum-mechanical analogue to a phase-space density (probability distribution of position and momentum) in classical statistical mechanics. The need for a statistical description via density matrices arises because it is not possible to describe a quantum mechanical system that undergoes general quantum operations such as measurement, using exclusively states represented by ket vectors.

It is now generally accepted that the description of quantum mechanics in which all self-adjoint operators represent observables is untenable.” (With thanks from the sources: http://www.quantiki.org/wiki/Density_matrix , http://www.quantiki.org/wiki/Self-adjoint_operator , http://www.quantiki.org/wiki/Bloch_sphere , http://www.quantiki.org/wiki/Pure_state , http://www.quantiki.org/wiki/Hilbert_space )


The format of A’-(M-C-V=E=MC2)-A’ is the Nano Format, and for Semi-solid state its say as A-(M-C-V=E=MC2)-A, and for the solids, it’s AA-(M-C-V=E=MC2)-A, and thus its for the Point Particle (A’), Atomic Particles (A) and the Molecular Particles (AA), and thus the AA (A-A), AA’ (A-A’), A’A’ (A’-A’), and A’ can be classified and put say as:

Macroscopic object (A-A)> Molecule (A-A’) > Atom (A’-A’)> Subatomic particle (Composite particle Elementary particle) (A’); please read more from the source: https://en.wikipedia.org/wiki/Subatomic_particle

If we consider the Macroscopic (A-A), Molecular (A-A’) and the Atomic (A’-A’) Systems, we can notice that it forms the Classical Universe of 3-Dimensions, and its almost same as Quantum Qubit with the Bloch Sphere, and if we use the AA, AA-AA, AA-AA-AA, we can think of the parallel universes as these go to huge bosonic solids like stars and the galaxies. When we deal with A’, A, A-A’, A-A, we have it say as the “Consciousness, the Quantum Universe Level” and when we deal with say the AA, AA-A, AA-AA and the Higher Dimensions, we mostly deal with the Classical, the 3-Dimensional Universe. So, we need Two Qubit Systems to understand both the quantum and the classical universes and or the systems. The A’, A, A-A’, A-A, AA-A with AA, AA-A, AA-AA, AA-AA-A, etc. are the Braided Groups that thread the Classical and Quantum Universe Systems together, and we access the DNA with this approach:

“Hybrid architectures, consisting of conventional and topological qubits, have recently attracted much attention due to their capability in consolidating robustness of topological qubits and universality of conventional qubits. However, these two kinds of qubits are normally constructed in significantly different energy scales, and thus the energy mismatch is a major obstacle for their coupling, which can support the exchange of quantum information between them. Here we propose a microwave photonic quantum bus for a strong direct coupling between the topological and conventional qubits, where the energy mismatch is compensated by an external driving field.” (Please read more about it from the relevant source with our thanks: http://www.nature.com/srep/2015/150728/srep12233/f… )

We can understand the DNA Strand as if say A’-A’ and A-A, which has a twist to left and or right based on the A-A’ or A’-A Position in its 4 Basic Points of Conscious A’, A, A-A’ and the A-A Systems no matter how we interpret it:





We can notice for n=1, 2, 3 and 4, we have the A’, A, A-A’ and A-A, which we can expand to the higher manifolds and the dimensions, while going closer to the solutions of, to and for the Poincare Conjectures.

“The n=4 case is the only outstanding case. Mike Freedman has proven that a 4 -manifold which is homotopy-equivalent to S^4 is homeomorphic to S^4, so the smooth 4-dimensional Poincare conjecture is the only outstanding problem among the generalized Poincare conjectures. Moreover, it can be considered to be reduced to the question of if S^4 has an exotic smooth structure.

Technically, Poincare never asserted this conjecture. He only stated it was an interesting problem. So perhaps it should be called Poincare’s Egregious Problem. (With thanks from the sources: http://www.openproblemgarden.org/op/smooth_4_dimen… , http://www.technologyreview.com/featuredstory/5316… and https://en.wikipedia.org/wiki/Poincar%C3%A9_conjec… )

Now, while I have been researching from about 3 decades on the A’, A, A-A’ and A-A Systems of the Density Operators with A (A’-A’), AA, AA-A, AA-AA, I have found that it can be called the Quantum Potency in Homeopathy and the Twelve Tissue Remedies along with 15 Cell Salts, Bach Flower, Electra-homeopathy, Ayurveda, Herbalism, Nutraceuticals, Food and Diet Supplements, and for any creation of Quantization of Eatables and Drinks, and or what we eat, drink, creams, toothpastes, shampoos, conditioners, and thus manufacturer’s manual of manufacturing the quantized products. I have been practicing it all particularly Homeopathy, Twelves Tissue and Cell salts with Quantum Potency of say 1x. Though I have submitted an application for patent at USPTO Office, USA of it in the name of Philselfology, the Single Model and Theory of Everything, but my follow ups are very poor due to lack of huge funds, attorney fees and or otherwise.

In this regard, the homeopathy and tissue salts of 1x are use in the eye drops, toothpastes, soaps, facial creams, skin care creams, mouth washers, malt drinks, shampoos and conditioners, skin care powders, and other uses which use say 1x, the 10mg in 100mg. I have used all of these products for say 20-25 years with very good results and prescribed to thousands of people, who also received the same or better results.

In any case, the Nano Potency of A’, A-A’, A-A, and the higher potency and the dimensions can go to the level of millions of A’, A-A’ and A-A Dimensions through the Triturations Processes of A’-A’ as through going all the way say as A’, 2A’, 3A’, 4A’, 5A’, 6A’, etc. up to CM A’ and higher Nano Potency, which we have also discussed in the meeting of last week of July, 2015 with Steven Ferrel​, CEO Life Dynamix, Manu Bhardwaj​, CEO, Bhrigu Sons Pharmaceuticals​, Dr. Vaidya Mahan Singh​, Dr. Gur Kamal Kaur, Kuldeep Kaur​, M.P.Ed, B.Ed in Yoga, Noni Kaur​ and Raji Seerha​ went through this kind of manufacturing of medicines and the food and diet supplements as making of all products through Nano Potency of A’, A, A-A’ and A-A Systems, which has a close relation with popular trituration process of manufacturing the same say as 1x, 2x, 3x, 4x, 6x and the higher potency systems otherwise. With my personal practice of this systems and that our people who are involved in this kind of Research and Developments (R&D;’s), our proposed Nano Potency assumes good mixing through triturations as A’ as the base with other medicinal products added to it say as A’, A, A-A’, A-A or the higher concentrations to end up in the Nano Potency Systems.

“Nanochemists and nanotoxicologists have discovered that smaller particles and more dilute solutions are sometimes more powerful chemically and biologically than more concentrated solutions of nanoparticles. This observation stems partly from the ability of dilution to keep the highly reactive surfaces of each nanoparticle from physically colliding with another particle in solution and inactivating each other. (Please read more from the source our (Life Dynmix R&D;) thanks: http://www.amcofh.org/research/basic and say also http://homeopathystudyguide.weebly.com/research—… )


Please also read the following research report: Adaptive Network Nanomedicine: An Integrated Model for Homeopathic Medicine

“Activation of stress response effectors, including heat shock proteins, inflammasomes, cytokines and neuroendocrine pathways, initiate beneficial compensatory reactions across the interconnected networks of the organism as a complex adaptive system. Homeopathic remedies act by stimulating hormetic adaptive rather than conventional pharmacological effects. Updating terminology from “homeopathy” to “adaptive network nanomedicine” reflects the integration of this historical but controversial medical system with modern scientific findings.” (With thanks from the source: http://homeopathystudyguide.weebly.com/research—… )

I have also considered it all say the A’, 2A’, 3A’, 4A’ as the A, E, O, AE, the Life Dipole of Health Care, Cure and Wellness Systems in all world therapies, both the modern and the ancient ones.



The A’-A’ at various levels of manifolds and dimensions also act as the Phonon Systems:



(Please read more about the Phonon Systems from the sources with our thanks: https://en.wikipedia.org/wiki/Phonon and https://en.wikipedia.org/wiki/Normal_mode )


We will edit and add.


The Previous Part of the Series: How Quantum Schwa of A’-0-A’ Helps in Quantum Bit, Flip, Phase Error Detection, Correction with IBM Researches: Quantum Computing, Education and Research: Quantum Theory of DNA, TGD and TQC : Gurmukhi and Be Happy Philselfologically 167

The Next Part of the Series: How Sachwa Vowels of A’, A, 2A in Linguistics Explain Differential Topology, Homotopy, Nano Particles, Cobordism, Manifolds, Quantum Qubit, Dimensions, Parameterization, Coordinatiozation, and World Line: Gurmukhi and Be Happy Philselfologically 169


Thanks for your time!

Be Happy Philselfologically while listening to Good Quality Music Everyday! 

Dr. Harmander Singh
Author: Dr. Harmander Singh

Be Happy Philselfologically: The Research on Free and Renewable Energy as Quantum, Classical and Sacred Systems! 🙂

Pin It on Pinterest

Share This
0
Would love your thoughts, please comment.x
()
x