What Is the Meaning of Imaginery Number with Nucleotide Bases as Regards to Quantum Perspective Model?


This paper attempts to express imaginary number with chemical nucleotide bases (A T, G, C and U) as regards to Quantum Perspective Model. At first, the exact Euler’s formula was written just like as in here “exi = cos(x) + i·sin(x)”. Secondly, twin pi is substituted for x(x = 2Π). Thirdly, the result of this process equals to “e2iπ = cos(2Π) + i·sin(2Π)”. Fourthly, sort up this formula just like as in here: “e2iπ = 1 + i0” = +1. Fifthly, multiply both sides of the equation by minus one’-e2iπ = -1. Sixthly, this expression equals to “i2”. These numbers can be expressed as genetic codes [Adenine (A), Thymine (T), Guanine (G), Cytosine (C) and Uracil (U)]. Seventhly, after converting process of this formula can be expressed as “AATGGGCCCUUGAAGAACUUUAAGTTTGGG”. Eighthly, after searching these sequences in the NCBI (The National Center for Biotechnology Information) database, the NCBI search result was similar to bony fishes (“Danio Rerio” and “Danio Aesculapi”) and flat worms. Ninthly, the common feature of the NCBI search result for some irrational numbers is that Euler numbers are the same as these results, as is the case with Pi in particular. Tenthly, let’s not forget that some irrational numbers in the gene database are similar to these creatures, and that there is a genetic link between Fibonacci sequences in Mathematics and Euler numbers. Finally, this article proved not only the relationship between imaginary number and nucleotide bases, but also the common relationship between NCBI database search “Danio Rerio” and “Danio Aesculapi” of some irrational numbers. In sum, could this similarity lead to a new paradigm for the imaginary number as a new dimension, i.e. if we take time as the fourth dimension, could it be the fifth dimension? As a result, the expression of imaginary number with genetic codes reaches striking meaningful results that will shed light on the Quantum Perspective Model, which is a new research method among Quantum Physics, Biology and Electricity and Mathematics.

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Ölmez, T. (2023) What Is the Meaning of Imaginery Number with Nucleotide Bases as Regards to Quantum Perspective Model?. Open Access Library Journal, 10, 1-20. doi: 10.4236/oalib.1109792.

1. Introduction

Prior to this article the relations between some constant numbers and genetic codes were researched by K. Köklü [1] and T. Ölmez [2] . At first, relations between Pi numbers and genetic codes were published by K. Köklü [3] . Secondly, the relations between Planck’s numbers and genetic codes were revealed by T. Ölmez [4] . Thirdly, relations between basic atomic weight of particles (proton, neutron and electron) and nucleotide bases were put forth by T. Ölmez [5] . Fourthly, the relations between Bohr Magneton and Boltzmann constants and nucleotide bases were researched by T. Ölmez again [5] . Lastly, the the relations between Euler’s Identity and imaginary number and nucleotide bases and bony fishes will be explained by this article at next pages.

Complex numbers (a + bi) are used in Mathematics, Physics, engineering, electrical engineering and Quantum Physics. Fields include describing complex electrical currents, designing music synthesizers that calculate wavelengths, engineering analysis of stress on beams. Calculation of the movement of shock absorbers, design of dynamo and electric motors, creation of Mandelbrot sets (see Figure 1) and manipulating large matrices used in modelling. Especially, in this article cited in electrical engineering denotes complex numbers with a “j” because “i” is already in use to represent current a + bi becomes a + bj. In electricity; AC (Alternating Current Electricity) changes between positive and negative in a sine wave. (Remember, Euler’s Identity also consist of both cosines and sinus wave!). In fact, in real life, complex numbers are used by engineers and physicists to measure electrical currents, analyze stresses in structures such as bridges and buildings, and study the flow of fluids. When combining two AC currents, it may not match properly. Namely, it can be very hard to figure out the new current. But using imaginary numbers and real numbers together makes it a lot easier to do the calculations (The Quadratic Equation can give results that include imaginary numbers). In sum, imaginary numbers are used in the real world. Engineers use them to describe electrical currents. In electricity, circuit components such as resistors, inductors and capacitors all oppose the flow of the current. This opposition is called resistance for resistors and reactance for inductors and capacitors. A circuit’s total opposition to current flow is impedance. All

Figure 1. Mandelbrot sets (https://images.app.goo.gl/k3TqgQRyY2bnkqGC8).

of these quantities are measured in ohms. There are some rules about electricity, these are conservation of energy and voltage, Kircoff’s law and generalized conservation of power, Kircoff’s voltage law (KVL) and Kircoff’s current law (KCL). But an article cited by J.L. Williams exploring the relationship between the fundamental laws of circuit theory (Kircoff’s voltage law (KVL) and Kircoff’s current law (KCL) and Tellegen’s theorem or generalized conservation of power principle), active and reactive current components and their corresponding active and reactive powers. It is emphasized that the active and reactive currents do not satisfy Kircoff’s current law (KCL). The concept of active and reactive currents has not only been defined for sinusoidal currents and voltages but also for situations such as the case of the instantaneous currents and the case of periodic nonsinusoidal currents [6] .

2. Methods

The representation of nucleotide bases (AT, G, C, and U) according to the Quantum Perspective Model is explained by chemical formulas. Regarding these chemical formulas, it was calculated according to the atomic masses of the elements. However, this article aims to investigate the relationship between imaginary numbers and nucleotide bases. In summary, the purpose of this research article is to explore the relationships between atomic weights, number base systems, and chemical formulas of nucleotide bases of imaginary numbers and Euler’s Identity.

The chemical structures of nucleotide bases consist of Carbon(C), Nitrogen (N), Oxygen (O) and Hydrogen (H) [7] . For the representation of nucleotide bases (A, T, C, G and U) in chemical atoms; please, see Table 1.

The Calculation of the Euler’s Identity and Imaginary Number as Nucleotide Bases

At first, the exact Euler formula was written as here “exi = cos(x) + i・sin(x)”. Secondly, the twin pi is substituted for x (x = 2Π). Thirdly, the result of this operation is equal to “e2iπ = cos(2Π) + i・sin(2Π)”. Fourthly, order this formula as follows: “e2iπ = 1 + i0” = +1. Fifthly, multiply both sides of the equation by minus one’-e2iπ = −1. Sixthly, this expression is equal to “i2”. These numbers can be expressed as genetic codes [Adenine (A), Thymine (T), Guanine (G), Cytosine (C) and Uracil (U)] (please, see Table 2). Seventhly, the operation of this formula after conversion can be expressed as “AATGGGCCCUUGAAGAACUUUAAGTTTGGG”. After searching for these sequences in the NCBI (National Center for Biotechnology Information) database, the NCBI search result was similar to bony fish and some other creatures.

In sum, as regards to Quantum Perspective Model, after the expression of imaginary number as nucleotide bases, some important consequences were reached by this article. This result will be put forth in next pages.

3. Results and Discussion

3.1. Results

Before this study; Kevser Köklü has published articles on the Quantum Perspective Model, not only about the square of the speed of light [1] , but also about the nucleotide-based Pi numbers [3] . In addition to these; Pi numbers once again extended version [8] , golden ratio numbers [9] , Euler numbers [10] , square root of two [11] , square root of three [12] , square root of five [13] , square root of seven [14] , square root of ten [15] and Fibonacci numbers [16] were also published by Tahir ÖLMEZ. Even the Euler Identity [17] and the extended golden ratio numbers [18] were also calculated. In summary, the codes of all these irrational numbers explained by a genetic sequence (mentioned above) can be found in this diagram (see, Table 3).

Table 1. The representation of nucleotide bases (A, T, C, G and U) in chemical atoms.

Table 2. The calculation of the Euler’s identity and imaginary number as nucleotide bases (A, T, C, G and U).

Table 3. The summary of some irrational numbers and nucleotide bases.

According to Quantum Perspective Model, prior to this article, the relationship between the square of the speed of light (c2) [1] by K. Köklü and Planck’s constant numbers [2] , Avogardo’s Number [4] , the atomic weight of proton [4] , the atomic weight of electron [4] , the atomic weight of neutron [4] , the Boltzmann constant [5] . The Bohr magneton constant [5] genetic codes were studied by T. Ölmez (please, see Table 4). At first, the calculation of the Faraday’s constant numbers [19] as nucleotide bases also can be expressed with Uracil (U) and Guanine (G) nucleotide base and Adenine (A) and Guanine (G) “AG” nucleotide base [7] Secondly, after searching this sequence at NCBI (The National Center for Biotechnology Information) database [please, see (Figure 14)], the consequences are many living organisms. Fourthly, these are flat worms, flies, mothseudicots, bivalves, gastropods, butterflies, caecilians, primates, mites, stonycorals, stoneflies, spiders, bees, crustaceans, starfish, rodents, hymenopterans, birds, placentals, nematodes, lancelets, viruses, segmented worms, beetles and especially bony fishes (Danio Rerio and Danio Aesculapi) (see, Table 3) and please, see (Figures 2-14) [20] . Lastly, NCBI (The National Center for Biotechnology Information) search result of golden ratio numbers sequences “ACATCC” are very interesting model organism consequence just like as “Symphodus melops” (Corking Wrasse). See (Figure 7) [18] .

3.2. Discussion

According to Quantum Perspective Model, prior to this article, the relationship between Planck’s constant numbers [2] and genetic codes were studied by T. Ölmez. The consequence of this article can be expression of Planck’s constant numbers as both Adenine (A) and Thymine (T) nucleotide bases. Besides, calculation of Faraday constants as nucleotide bases can be expressed in terms of nucleotide bases Uracil (U) and Guanine (G) “UG” or Adenine (A) and Guanine (G) “AG” [19] . Previously, this twin result may be explained by Quantum Superposition. But also the link between some irrational numbers and genetic codes were researched by Tahir Ölmez, too (please, see Table 3). Not only the NCBI database results of some irrational numbers (√2, √3, √5, √7, √10, Pi, Euler’s and golden ratio numbers) are bony fishes ,but also the NCBI database result of the Faraday’s constant numbers are silk worms [21] [22] [23] . Both of these consequences of the NCBI explosion are crucial model creatures for the genetic analysis model. Let alone previous explanations, the expression of imaginary numbers as genetic codes “AATGGGCCCUUGAAGAACUUUAAGTTTGGG” also consist of stop codons [24] just like as “UAG” and “UAA”. In addition, while pi numbers are expressed as genetic codes, they also consist of the genetic codes of some of the Euler numbers (please, see Table 3). A common feature of some irrational and complex numbers is that NCBI blasts consist of bony fish, particularly Danio Rerio and Danio Aesculapi (please, see Table 5).

Table 4. The summary of some constant numbers and nucleotide bases.

Table 5. The NCBI (National Biotechnology Information Center) summary and genetic sequences of some irrational numbers.

Figure 2. The NCBI blast results for danio rerio [20] .

Figure 3. The NCBI gene bank for “Danio Aesculapi” [20] .

A Universe is a population of galaxies joined by networks of dark matter and energy. In a Universe of ∞ scales―hence of Absolute Relativity―the i-number is relative to the limits of the perception of the observer that classifies them. We can also establish a relative i-scale to study Living Systems and the Human World. Thus the main energy and 0-clocks of time of each scale for physical and biological worlds will be:

1st Scale: Open strings of energy and closed time strings: Strong Forces & Gravitational space-time.

2nd Scale: Bosons: Light and O-Photons.

Figure 4. The NCBI taxonomy organism results [20] .

Figure 5. The NCBI gene search results [20] .

Figure 6. The NCBI gene search results [20] .

Figure 7. The NCBI gene search results [20] .

Figure 8. The NCBI gene search results [20] .

Figure 9. The NCBI taxonomy report search results [20] .

3rd Scale: Fermions: Electrons & O-quarks.

4th Scale: Atomic Organisms: Periodic Table.

5th Scale: Inorganic and Organic Molecules

6th Scale; Life Cells. States of Mater: Energetic Gas, Ex Liquid and Informative Solids.

7th Scale. Life organisms; Energetic Plants; Informative Animals. Organic Metal-Machines.

8th Scale: Planets. Human Civilizations; Economic Systems, Stars & O-Black holes.

9th Scale: Galaxies, which might be the beginning of a new Scalar Game.

10th Scale: Universe, which might be a Gas cloud of Atoms of the new Scalar game [24] .

Figure 10. The NCBI taxonomy report search results [20] .

Figure 11. The NCBi taxonomy report search results [20] .

Figure 12. The NCBI taxonomy report search results [20] .

Figure 13. The NCBI taxonomy report search results [20] .

The Life-Death Cycle is very important for evolutionary development. A glimpse to the birth and death phases/ages of the existential cycle. The physicists ignore the black hole paradox so they don’t understand that protons, neutrons and all other particles do not live eternally. On the contrary their life/death cycle is their complementary cycle between informative states and energetic states, either the clock of particle/wave complimentarily or the clock of particle/antiparticle, past to future and future to past cycles. If considering time as a fourth dimension, then what can be the next fifth dimension? As a result, this is a new paradigm. Can fifth dimension consist of imaginary numbers? A new paradigm changes

Figure 14. The NCBI data search screen for “AATGGGCCCUUGAAGAACUUUAAGTTTGGG” nucleotide bases [20] .

our view of the Universe. This paradigm will define all the life and death cycles of change of form of the Universe. There are two arrows of time, two possible modes of change towards the future: the arrow of entropy, which is the only one understood by physicists, which increases motion. (Remember, the binary number system consists of two numbers, “0” and “1”, as in the binary unmeasured case in the superposition principle.) The arrow of information, which increases form, the arrow of biology and evolution. And this duality is also essential to expand our understanding of the Universe. Limits of physics in its study of time, as a single, lineal clock: the ∞ space times of the Universe. Because of such limited definition of time as “what a clock measures” and only as change in motion, the fourth dimension paradigm does not allow to study all the phenomena related to time. Things like evolution or history that happens in time cannot be understood with Relativity. The form of beings: biological time, as in evolution or in the life/death cycle or a change in the motion of beings: physical time, measured by clocks as in Galileo’s formula: V = s/t. So time as change studies together all time related changes in all disciplines from Biology to Physics. In physics the instrument physicists use to measure time, a clock, becomes essential to model all times changes similar to the clock’s rotational frequency, a “cyclical geometry” of space. Time becomes synonymous with circular space and the Universe [25] .

Why do we evaluate the modules and argument of imaginary numbers? Complex numbers are used to model real world phenomena as it relates to electricity and generate interesting patterns. The mathematics used in Electrical Engineering to add together resistances, currents or DC voltages used what are called “real numbers” used as either integers or as fractions. But real numbers are not the only kind of numbers using especially when dealing with frequency dependent sinusoidal sources and vectors. In addition to using normal or real numbers, complex numbers were introduced to allow solving complex equations with numbers with the square root of negative numbers (√−1); the system of complex numbers is based on the so-called imaginary unit. It is equal to the square root of minus one. In electrical engineering, this type of number is called an “imaginary number” and distinguishes an imaginary number from a real number the letter “j” known commonly in electrical engineering. A complex number then consists of two different but much related parts, a “real number” plus an “imaginary number”. Although people did not believe in the solution of √-1 for many years, today it is called the “imaginary number” [26] .

When calculating Euler Identity and imaginary numbers, if “2π” is taken instead of “x”, the result of this operation would be exactly like this: “2iπ = 0” (As to this in exponential numbers, only one number to the zero power is equal to one “e2iπ = 0”, so e˚ = 1). Also, Euler’s Identity doesn’t just consist of cosine and sine formulas, quantum particles and imaginary numbers can also be expressed as waves and particles!

4. Conclusions

This paper tries to shed lights on the relationships between some constant numbers (please, see Table 4) just like as the imaginary number and nucleotide bases [Adenine (A), Thymine (T) Guanine (G), Cytosine (C) and Uracil (U)]. According to Quantum Perspective Model, the chemical formulas of nucleotide bases [Adenine (A), Thymine (T) Guanine (G), Cytosine (C) and Uracil (U)] consist of Carbon(C), Nitrogen (N), Oxygen (O) and Hydrogen (H). Carbon is the structural reproductive atom that shapes the body and forms the membranes of organic cells. In machines made of metal, atoms of silicon and gold are informative atoms that act as the brains of advanced robots; iron is structural atom, maximum the ionization energy that forms the “membrane” or body of the machine; copper and silver carry electrical energy that feeds the body/brain systems. (Remember gold and silicon are very good conductors for electricity) [25] . Complementary, organic molecules given their affinity, they give birth to more complex molecular systems and make up most of the molecules in the Universe. Maximum affinity occurs between atoms with relatively similar atomic, brain, weight, and orbital body form in the atomic table. There are three component regions in living organisms. One of them is the oxygen we breathe and the water component that fills the interstitial spaces of the cell. The second is Nitrogen, the informative atom found in excess in DNA and brain cells. As cellular beings, we are also defined by a language of repetitive information written in the DNA foundations that make up the genetic code. In the simple molecules of life, Carbon, Oxygen and Nitrogen are the top predator central atoms that act as carriers of their relative energy and information, trapping and surrounding themselves with the weaker Hydrogen atoms that form the outer “membrane” of their molecular structure with the dominant atoms. Nitrogen heads, carbon bodies and oxygen energy make up the simplest living entities, amino acids. Even lineal proteins evolved according to the inverse laws of transcendental, social evolution, forming self-replicating hollow membranes with cyclic, stationary forms. Indeed, once the nucleotide, the third informative horizon of molecular life, evolved, the protein’s simple brains short-lived its top predator status. The economist, sociologist and business guru A. Toffler, who defined humanity’s transition from hunting-gathering to agriculture as the first wave, the industrial revolution as the second wave and the information revolution as the third wave. According to Alvin Toffler, those who first began agriculture dominated hunter-gatherers, and those who preceded industry dominated agrarian societies [27] .

The most illuminating analysis of Multiple Space-Time is the objective evaluation of man, another fractal part of the Universe, in unity with his cycles of existence and organic laws: like all other living organisms, we humans have two energy poles and circular and linear form, body and head knowledge. Considering man as a fractal organisms; medicine and physiology deals with the sensory functions of the human organism, the three networks that activate our arrows of time: Digestion, the Energy System depend on the senses of smell and taste; hormonal, blood, reproductive system are connected to the senses of touch, and the 6th emotional sense and Nervous, Information System are connected to the higher senses of vision and sound. Humans are made of simple atoms closely related to nuclei C = 6, N = 7, O = 8, which follow the law of proximity in their electronic body orbits. All of these atoms are filled with sp orbital’s, which together create complex complementary organisms based on body-brain affinity. Thus, the parallel electronic cover connects these atoms externally depending on the proximity of their orbits, forming the 4 structures of organic molecules. The affinity law also describes inorganic molecules and other metal energy and information structures. For example, machines made of metal are formed with atoms of similar nucleic number. On the other hand, atoms with different atomic weights associate in hierarchical structures in which the lighter atoms become enslaved by the others. For example, the macro-energetic proteins of life, Hemoglobin and Chlorophyll, have 2 central, dense atomic nuclei, Iron and Mg, which dominate lighter carbohydrate “arms”, used to jail oxygens, the energy atoms of living beings [25] . As a result, there are cyclical systems based on not only atoms at the micro level, but also circular systems at scale for the physical and biological worlds at the macro level.

Cells are made of energetic amino acids found in their nuclei, reproductive proteins that form membranes and informative nucleotides (Remember, Faraday constants [19] can be expressed as the cocoon of the silkworm (Bombyx Mori) [28] ). Suffice it to say that in any active organism with more than one scale, in the informative code, in this case the genes of biological super-organisms encode multiple hierarchical levels of the organism, with the basic triple code forming their simplest scale (case of life, amino acids) [25] .

Our perception of size is constantly changing over time. Initially, two-dimensional unknowns can be represented both as width and height, and as “0 and 1” in binary based system. In addition, if the binary number system is taken as “0” as death and life as “1”, the death-life cyclical system can emerge. Also, the most complex nucleotide heads are Purines: binary, pentagonal, and hexagonal nitrogen rings are joined by a strong covalent C = C wall forming binary pairs called Adenine and Guanine, adding an external nitrogen antenna with two unknown Hydrogen eyes. Within this number system, is there an object which, when squared, gives −1? Yes. It is the pair (0, 1). When you square it using the above rule of multiplication, you get (0, 1)(0, 1) = ((0)(0) − (1)(1), (0)(1) + (1)(0)) = (−1, 0) (THE RESULT IS MINUS ONE’-1’) [29] . Then three-dimensional unknowns (width, length and height) and time can be shown as the fourth dimension. But finally, can imaginary numbers be represented as the fourth dimension today? Because basically, the element set of imaginary numbers also consists of four basic numbers (1, −1, i, −i). One of the formulas of this basic set of numbers in mathematics is the formula where the fourth power of x is equal to the number “1” [(x2 − 1)(x2 + 1) = 0]. In fact, the expression of the Universal Genetic Code Table, which consists of triple writing of genetic codes, in the fourth dimension is expressed as “REVERSE” (please, see Table 2). Even, only the “reverse” process is not seen in genetic codes, there are shadows that can be counted as the fourth dimension, just like its reflection in a mirror. If you look at convergent or divergent mirrors at the same time, you can detect that the size of things can be seen in different dimensions in the mirror, which could indicate the illusions of the observer in Quantum Physics? Even normally single entities can give two or more images of these entities depending on the number of mirrors; can this point to the definition of superposition in Quantum Physics? “Is the imaginary number trying to mathematically model these unobservable aspects of Nature?” It may be asked. It is also worth mentioning there is an asymmetry in exponential rules, where 2−1 = 1/2, while 21 = 2 and −2−1 = −1/2 and −21 = −2. In other words, the asymmetry is found in several of the basic rules of mathematics. This article written by E.G. Haug and Pankaj Mani highlights an interesting asymmetry in the basic mathematical rules between positive and negative numbers. Also, by showing that an alternative numerical system exists, basically the same as today’s system, but positive numbers outweigh negative numbers, It is trying to describe a system of the current number system, such as mirror symmetry. Asymmetry in both of these systems can lead to imaginary results and complex numbers. An alternative number system with fully symmetrical rules is also proposed. The superiority of negative numbers over positive numbers or vice versa, and even here imaginary and complex numbers is no longer needed. This number system seems to be superior to other numerical systems because it brings simplicity. Like this, and logic is returning to areas dominated by complex rules for much of the history of mathematics. It was also discussed how the Riemann hypothesis could be related to the asymmetry in the current number system. As with numbers in space-time and quantum mechanics, two hitherto obscure areas of physics. In order for such a number system in this mystery to be freed from phantasm, may need more to describe nature [30] . Imaginary numbers are defined by squaring a negative number that is not possible in the set of real numbers. Applying the quantum state of quantum particles in the unmeasured state, known as superposition, to a real number produces a complex number that exists in both positive and negative forms simultaneously, thus producing a negative real number quantity when squared. Imaginary numbers are defined by the result of squaring, which produces a negative number that is not possible in the set of real numbers. The application of the quantum state of quantum particles in an unmeasured state known as superposition to a real number produces a complex number that exists in both positive and negative forms simultaneously thus producing a negative real number quantity when squared. In sum, for these reasons, Euler’s Identity has been applied in the expression of the imaginary number and the “REVERSE” operation has been applied in the expression of the genetic codes. “I seem to be the only scientist who thinks that time velocities are different in different parts of the universe,” said Einstein, and eventually formulated this by this author in the systems science setting to make it useful for hard science with new math and logic tools. However, like all new paradigms of science, the current phase of fifth dimensional studies is limited to a few researchers and is being discussed by practitioners of the previous paradigm [25] .

Initially, the expression of the imaginary number as nucleotide bases is “AATGGGCCCUUGAAGAACUUUAAGTTTGGG”. Secondly, the NCBI results of the imaginary number are bony fish and flatworms and bees. Thirdly, not only are NCBI results of imaginary numbers bony fish (especially Danio Rerio and Danio Aesculapii), but also NCBI results of some irrational numbers are bony fish [20] . Fourthly, the NCBI resultant expression of Faraday constant numbers is silkworms (especially Bombyx Mori), which is also related to the electric membrane in terms of cocoons of silkworms [21] . (Remember, one of the NCBI blast results of the imaginary number are worms that evolve, which, like other circular systems, change from worm to butterfly). Fifthly, let alone the previous explanations, given the implications of this, some irrational numbers and some universal constants (see, Table 4) are both very important genetic models for many scientific studies. In fact, the bee’s chromosomes do not change to the number “16” and the number “16” is also obtained from the fourth power of the two numbers (“16” = 22 × 22). Can the fourth base be also valid for bees? [31] “(x4 − 14) = (x2 − 1)(x2 + 1)” Sixthly, not only Faraday’s fixed numbers are electrically related, imaginary numbers are electrically related as well. After ordering the Euler Identity’s formula “exi + 1 = 0” using “2π” instead of “x”, this important change is attributed not only to the link between the Faraday constants in Electrochemistry, but also to the link between the binary positions of the Superposition in Quantum Physics. Seventhly, the emergence of imaginary numbers from the Euler Identity [32] is very interesting, as both are associated with sine waves. One of research article reveals the sine value in Euler’s formula and the relations of sine and cosine trigonometric functions with imaginary number [33] . Because “exi” has been reached for a variable that’s integral and derivative are the same. So, given this information about “exi”, the point (derivative) or area (integral) of this formula is the same as the other operation! Eighthly, whether there is actually a relationship between the imaginary number and the Mandelbrot set can be a further research topic in terms of fractals and Chaos Theory (Remember, K. Köklü also related pi numbers to Chaos Theory, too [3] ). In summary, can these cyclical results and this new Quantum Perspective Model paradigm shed light on the interrelationships between sciences such as Quantum Physics, Biology [34] and Electrochemistry, and Mathematics? As for math, this solution could be a cornerstone for a new dimension. That is, the infinite series expression of some irrational numbers, such as golden ratio numbers, Euler numbers, and Pi numbers, can be a sign of a new dimension, including imaginary numbers. The common features of some irrational numbers have infinite sum ratios (E, Pi, Phi…etc) [35] . But some infinite series are indeed finite, there is a small problem for Taylor series that only works when −1 < x < 1. (Remember, the solution set of imaginary numbers is also in the range of minus one to plus one) [36] . In conclusion, if time is treated as the fourth dimension, could the fifth dimension be imaginary numbers? So, these results may shed light on the new paradigm of science! That is, the interrelationships of the Sciences?

Conflicts of Interest

The author declares no conflicts of interest.


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