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48 NECİP ERDOĞAN Why would a person who could not swim jump from the second floor of a jumping tower? When I took a few strokes and came near him, he was suspended in the water, eyes open awaiting death. Some people love to open their eyes underwater, when you dive to the bottom and evacuate the air from your lungs, you have to wait patiently in the middle of the bubbles until the water brings you back to the surface. Jonny was waiting patiently like this until I came near him, not quite all the way down, but not getting to the surface either. Extending your arms, you push your body upwards and feel the transition from death to life. The blue of the sea is so vivid when you feel the sunlight! My father's life is based on numbers, why did he attempt suicide? I thought of the book Uncle Petros and the Goldbach Conjecture, which I read when I was a kid. Goldbach's Conjecture states that each prime number on the number axis can be written as the sum of two even numbers. Unsuccessful and devoting his life to prove the conjecture, Uncle Petros finds the cure in suicide. Another subject that extinguishes people's joy of life is the fifth postulate. Let us now return to Saccheri's issue of self-contradictory proof. He strove to prove Euclid's fifth postulate. There are many examples in mathematics where the principle has been successfully applied. One of the most famous of these dates back to the Pythagoreans and was solving a mathematical problem in a way that greatly annoyed them. 49 KIBUTZ AND TRAUMA When some problems were solved, it was considered appropriate to keep the solution a secret. The most important of these problems: Is it possible to find a rational number whose square is 2? is the question. The Greeks were beginning to realize that rational numbers were not sufficient for the correct development of their ideas of geometry. Today we do not needlessly worry that a given geometric quantity cannot simply be measured with rational numbers alone. This is because the concept of real numbers is very familiar to us. Although our pocket calculators only express numbers as a finite number of digits, we recognize that this is an approximation that is forced upon us by the fact that the calculator is a finite object. We are prepared to allow the ideal mathematical number to require strictly decimal expansion to continue indefinitely. This is, of course, true even for the decimal representation of most fractions. 1/3 = 0.3333 29/12 = 2.416666 9/7 = 1.285714285714285714... 237/148 = 1.601351351351… The decimal expansion for a fraction is always ultimately periodic, that is, after a certain point the infinite sequence of digits goes to infinity. means that it consists of some finite sequence repeated. The repeating sequences in the examples above are 3, 6, 285714, and 135, respectively. Decimal expansions were not available for the ancient Greeks 50 NECIP ERDOĞAN, but they had their own way of dealing with irrational numbers. What they actually adopted was a system of representing numbers in terms of what are now called continuous fractions. It is not necessary to go into all the details here, but some brief comments are appropriate. Continuous i is a fraction, finite or infinite expression: a + (b + (c + (d +…) -1)-1)-1 where a, b, c, d are positive integers. Any rational number greater than 1 can be written to terminate an expression like this: 52/9 = 5+ (1+ (3+ (2) -1)-1)-1 and less than 1 to represent a positive rational , we let the first integer in the expression be zero. To express an irrational real number, we let the continued fraction expression go on indefinitely. Some examples: √2 = 1 + (2+ (2+ (2 +….)-1)-1)-1 7-√3= 5+ (3+ (1+ (2+ (1+ (2+) (1+ (2…) -1)-1)-1)-1)-1)-1) - 1) π = 3 + (7+ (15+ (1+ (292+) (1+ (1+) (1+ (2 +…)-1)-1)-1)-1)- 1)-1) - 1) As noted above in the familiar decimal notation, it is rational numbers that ultimately have periodic expressions. 51 KIBUTZ AND TRAUMA On the other hand, we can see that rational numbers now always have a finite definition, a strength of the Greek fractional representation. A natural question to ask in this context is: What numbers ultimately have a periodic continuous fraction representation? This is a remarkable theorem, which proved for the first time to our knowledge by the great mathematician Lagrange, that numbers whose representation in terms of continued fractions are ultimately periodic are what are called quadratic irrationals. What is quadratic irrational and what is its significance for Greek geometry? A number that can be written in the form a+sqrt(b) where a and b are fractions and b is not a perfect square. Such numbers are important in geometry because they are the most important rational numbers encountered in ruler and compass structures. Special examples of quadratic irrationals are when a = 0 and b is a natural number or rational greater than 1. The continuous fractional representation of such a number is particularly striking. Including quadratic irrationals gives us a correct path to sufficient numbers for Euclidean geometry, but it does not provide all the necessary information. Numbers like sqrt(a + sqrt(b)) are extensively covered in Euclid's tenth and most difficult book. The Greeks had found a way to describe numbers that turned out to be sufficient for Euclidean geometry. These numbers are actually real numbers in modern terminology. 52 NECIP ERDOĞAN Although a fully satisfactory definition of these numbers was not found until the 19th century, Eudoxos, one of the students of the plateau, the great ancient astronomer, had already acquired the basic ideas in the 4th century. It would be appropriate here to say a few words about the ideas of Eudoxos. First, we must remember that numbers in Euclidean geometry can be expressed in terms of ratios of lengths, not directly in terms of lengths. My father always warned me and my sister Din about this. The first step in Eudoxan theory was to provide a criterion for when an aspect ratio a:b would be greater than a c:d ratio. Eudoxos actually had a real concept of numbers in terms of length ratios. It also provided rules for the sum and multiplication of such real numbers. There was a fundamental difference in perspective, but between the Greek real number and the modern one, the Greeks saw the irrational number given to us as the concept of distance in physical space. Real physical objects existing in this space inevitably lagged behind the Platonic ideal. Maybe it was the Platonic world of ideas that drove my father to suicide. I must read the notebook we have used since childhood, relive its memories until the morning. I remember drawing a square on the first page, something like a square drawn in sand or a cube hewn out of marble, and Din had drawn a circle. 53 KIBUTZ AND TRAUMA My father Nec always said, "The measure of distance in simple geometry will be something to be determined accordingly, it would be convenient to try to deduce the concept of real numbers from the geometric units of an assumed Euclidean space to be given." he would say. In fact, this is what Eudoxos accomplished! My father, Nec, used to say that Jews could be forced to leave the country where they were born and raised at any time, so they should not be content with knowing a language that is not spoken in any other country or laws that are not applied anywhere else, and that they should choose professions that will work for them in any situation. That's why we had to become doctors, engineers, or traders, because that's what will keep you alive, regardless of what our neighbors say about you. People always talk about the Jews, claiming that we have snatched other people's jobs, loaned money at interest, exploited workers, and taken over the world economy. Science and economics, in particular, must be in our hands if we are to survive independently. My grandmother's pregnancy was risky. Diabetes and high blood pressure were causing problems. At that time, the symptoms were quite effective, and deaths due to pregnancy poisoning were common. Little was known about the health of pregnant women about cigarettes and viruses, which means that although the Nazis had advanced knowledge about conducting live experiments on Jews, they did not advance enough... 54 NECİP ERDOĞAN İ

People's reactions to these deaths in those years were also very different. It was not common practice to terminate a pregnancy when the woman's life was in danger. When my grandfather risked death, he did not immediately tell his wife about this, he could not restrain his desire for a son, he had to devote his life to his son (if he was a man, of course), he was ready to forget the pain he had experienced, the pressure and insults of the Nazis. The patient doctors of hospitals in Nazi Germany tell that cesarean section is risky. They defend the thesis that there will be no postpartum poisoning and try to calm the fearful expectant mothers. My father often talked about the hardships suffered by the German Jews, in fact, the Arabs living in our country were suffering the same troubles. He would describe how a home invasion in Germany was perceived as an exceptional case, and how the star of David that appeared on the door of your workplace one morning caused death. , I think our difference from the Germans was that we were not doing this work in a systematic way. Stefan Zweig dreamed of a Jewish-only country and unfortunately he didn't live to see it, he lost his joy of life when he saw the Nazis growing stronger, whereas we have a small country surrounded by Arabs, the dark days of the Second World War are over, my grandfather is sitting at one end of the living room in his wealthy house, at the big dining table, in his home where languages other than German are spoken, servants wandering around and happy last days, because soon the Nazis will come to power, glasses are clinked, and while we look to the future with hope, my grandfather is waiting for his grandchildren. he speaks of one day being an all-Jewish country, from the promised land that we all dream of, there are many ways to know what really happened, God hasn't promised land to anyone, maybe we're all like the children of a poor family living in a hut. However, we are told on the Kibbutz that we are distinguished people, that the gifted are all Jews, for example, Judaism does not take much effort to recruit new members, you need to prepare yourself for long readings, coexistence with the Jewish community, conversations with rabbis. . All of my grandfather's relatives died in concentration camps, there is no information about the camp itself, explaining what my grandfather did there and why he was not taken to the gas chamber. Despite everything, my father hates Arabs rather than Germans. My grandfather didn't write anything about Judaism, I think he converted to save his life, he's at the head of a Nazi officer and says he has only one chance to live; donate all your possessions to the Nazis and become a Christian! How hard it was for him to change religion. Books to understand this religion, attempts to understand the belief in the three Gods, nightmares at night, rabbis whispering that he will burn in hell because of his conversion… My father became interested in this subject after my grandfather died, and given the circumstances, he must have been as curious as I was. . The fact that his father never spoke about Judaism and did not go to the synagogue, leaving him free to choose, seems to be proof of this situation. I don't know when my grandfather started journaling, it probably started after he escaped from the concentration camp. My father started working after my grandfather died, he went into business as an adolescent who had nothing in financial terms and a miracle happened; His financial situation improved rapidly, from then on he turned to science and focused on genetic engineering, which he saw as the profession of the future. I learned later that it wasn't a miracle, that his biological father was RO THSCHILD. Thus I became the heir to an empire. *** I'm always thinking about fatherlessness tonight, how does it feel to be without it? We were very lucky to have brought him to the hospital early, early intervention brought him back to life. My father would often sit by the lake and meditate, gazing at the distant lights of the boats that drove tourists across the lake, traveling to distant worlds. When I was a kid, I used to witness what he was always sitting alone in a dark room thinking about. What was going through your mind? 57 KIBUTZ AND TRAUMA I'm sure he was thinking about prime numbers. A prime number is a number that is not divisible by 1 and any number other than itself. The number of your hands is the first prime number; It is not divisible by any number other than 1 and itself. Another important point is that there are no even prime numbers other than 2. Prime numbers are just as important to mathematics as elements are to chemistry. Because there are at least two prime numbers in the list of materials required to produce a number, and the number you will get is not a prime number. For example, 13 and 5 are prime numbers, and if we multiply them, we get 65. 65 is not a prime number because it has a number other than 1 and itself, if you wish." said. The mathematician also asked the ruler to put 1 grain of rice in the first chess square, 2 in the second, 4 in the third, 8 in the fourth, and 16 in the fifth, so that the number of rice in each square would be twice the number of rice in the previous square. . The monarch, who was very surprised by such a simple request, started to place the rice grains. He could easily place the rice in the first squares, but as he progressed through the squares, he began to have difficulty. When he came to the 16th square, he asked his servants for 1 kilo of rice. In the following frames, the butlers had to bring the rice with wheelbarrows. As a result, the ruler could not reach the last square, the 64th square. Then he had to give half of his fortune to the mathematician. If we decided to do this experiment today, by the time we reach square 64, the total amount of rice would be approximately the amount of rice produced in the last thousand years. Let's come to the relationship between our myth and prime numbers. Ever since Greek mathematicians tried to prove that prime numbers go to infinity, mathematicians have developed formulas to find very large prime numbers. One of these formulas was developed by the French Pastor Marin Mersen. Mersenne was like an e-mail server in the 17th century. He was examining the letters he received from all over the world and conveying the ideas in these letters to people he thought could improve them further. The formula developed by Mersenne said that if you move as many squares on the chessboard as the prime number and add the number of rice in the squares as you progress, you will get a prime number. If we go as far as the first prime number, we get 1+2=3 grains of rice and this is a prime number. Similarly, if we move up to the fifth square, we get 1+2+4+8+16=31 rice grains. This is also a prime number. Mersenne was devoted to this method, but it did not work. 11 is a prime number and if we move forward 11 squares, we will count 2047 62 NECIP ERDOĞAN grains of rice. However, this number is equal to 23 multiplied by 89 and is not a prime number. It's true that the formula doesn't always work, but it did help discover some great prime numbers. 63 PART 2 Hello, I am E1, I know for what purpose I came to this world and how I came to this world, but the people working in the science center are not aware of this, me and my friend N1 are the product of the project. We are copies of geniuses from the past. I learned this truth first, you don't have to believe me, but you may have heard of the concept of soul transformation. There are memories of a Jewish genius who escaped from the Nazi persecution, which I do not know from where, these memories never leave me, my original Albert EINSTEIN whispers in my ear; He says that he is always in favor of peace, that he wishes for people to give up racism, and that no race is a superior race. I told him the purpose of the people working at the science center, I told him that the atomic bomb that was made in the past was replaced by biological weapons, a lot of what I said affected him of course, but he was most impressed by the cloning of himself and he told me about his life, of academics who understood that he was very smart. He said that they did not give a chair out of jealousy, that he sought a job for years, but that he was a civil servant and that he made history with the articles he wrote in his spare time. Contrary to what is known, he is not someone who dedicates his life to numbers and complex formulas, but loves love very much. Einstein tells me his childhood memories: "When we go hunting, we will catch a small animal we call x because we don't know its name. We'll catch him and give him his real name." said my uncle. The math book he gifted me was very fun, reading Calculus is as good as reading a very fluent detective novel, I recently read the proof of the Pythagorean theorem after my bath and had a lot of fun. I will ask Uncle Jakob to give new problems. We've been in hiding for more than a year, I don't have the opportunity to tell you everything, my dear clone, I was also interested in the millennial problems that could not be solved in your time, especially the Riemann-Zeta function, if I had the opportunity to return to the world again, I would try this function, who knows maybe We can also solve problems after the soul leaves the body, after all, we are solving questions in sleep, and sleep is half-death. When I was a child, bedtime was nine in the evening. There is always hustle and bustle in the room. Tables are lifted, beds are made, blankets are laid, nothing stays in its position in the morning. I sleep on a small sofa so my feet are bare, I found the method of adding chairs last night. A terrible noise comes from the next room, the sound of the bed being folded. We need more blankets to sleep comfortably on the chipboards. When my uncle sleeps, he pulls his bed near the window to get the night air, now it's time to draw the blackout curtain… When I was sixteen, I only started reading Calculus and I was very happy, a happy man, a woman who couldn't think about the future from the moment she was in.

stay satisfied. I'm dreaming while solving the integral; I'm studying physics and mathematics at the same time after I won the university, then I become the youngest professor of the Polytechnic Institute. I always preferred to be alone. I never felt like I belonged in Germany. I persistently stayed away from language, religion and race relations. A person who lives like this has, of course, lost something of his social life energy. On the other hand, by making himself independent from the opinions of others, he did not base his stance on these foundations. Six forty-five alarm sounds and everyone wakes up, mom turns off the alarm, puts water on and washes her face. I lift the blackout curtain and a new day begins in the room, my uncle takes the fountain pen and writes history in his diary, he let me take this pen to school when I was ten but I had to keep this pen a year later, my homeroom teacher only let me use the school pen. We signed diaries and compositions with this fountain pen, and most importantly, I wrote the formula E=m.c2, which went down in history, with this pen. Something happens every day, but I have no cure to tell you, my dear clone, you are living in the future that I always dreamed of when I was young, actually I always predicted the future! Yes, that's right, you can predict the future dear E1, at first this ability sounds great, predicting how the first human colonies on Mars will live, knowing that the distribution of prime numbers will be found, and knowing that the Poincare conjecture will be solved by Perelmann, who is Jewish like me. Would you like to predict what the civilizations on earth will be like in 500 or a million years, but to learn the details of the painful events that await you? Would you like to know the date when your mother or father will die? Don't worry my dear clone E1, I've dealt with this issue for you, if my invention of quantum physics is correct, it will not be possible to predict the future no matter how perfect computers are made by humans, 1905 was the year my life changed for me, the principle behind photocells that convert sunlight into electricity I just published my article explaining it. In this article I have said that light is now made up of invisible bundles of energy called quanta. I explained that light is absorbed when it comes into contact with matter. Newton had also worked on light before me. I'm talking about Isaac NEW TON, the original of your friend clone N1. My article received a great response in the first days, but after a while it turned out that I was right. Quantum physics tells us that you cannot know everything you want to know about subatomic particles all at once. Matter consists of electrons, neutrons, and protons, and what we can know about them is limited by nature. You can only calculate the consequences of events. Yes, quantum physics is my invention, but this invention will not last forever, my dear clone E1, a day will come, the improbable world hidden under the world will be discovered. "After you died, people named manifolds with certain properties after you. An Einstein manifold is a manifold that has a fixed ratio between curvature and metric." said E1. 67 KIBUTZ AND TRAUMA When he got no answer, he began to think that the spirit of the gifted man had left him. "Why me?" he said to himself. "There are many cloned people like me, but none of them talk about soul transformation." "You have to stop them!" said Einstein, the genius physicist back in E1's body, which startled the poor clone. "You have to stop them, innocent people died because of my mistake in 1945, if you don't stop the science center, history will repeat itself, I want you to get together with copycats like you and organize them." E1 seemed to see the famous scientist with his tongue sticking out and graying hair while hearing these words. The person he was closest to at the science center was N1, a replica of Isaac Newton. Every day we would shut up in our room and spend hours studying the Riemann–Zeta function, trying to figure out how the prime numbers were distributed. The science center wanted the solution of "MILLIUM PROBLEMS". These problems represent the deepest mysteries in mathematics today. They think some of these questions will lead to useful applications in effective drug treatments, strict cybersecurity encryption standards. Our simulations with N1 showed that there is a mass gap in the solution of the Yang-Mills equations relative to their quantum version. I would very much like to contact Einstein right now. What are their thoughts on Yang-Mills equations? 68 NECIP ERDOĞAN "Mathematics and physics always mutually benefit each other E1, remember that…" "I don't believe it, you're back Einstein, hearing your voice again is an indescribable happiness for me!" "Advances in mathematics often lead to new approaches to physical theories. In the science center you mentioned, you have to take this into consideration first. New discoveries in physics are also investigating the mathematical relationships that underlie them in more detail.

encourages the. Quantum mechanics is arguably one of the most successful physical theories in history." "One of the pillars of your quantum mechanics is Yang–Mills equations, my dear original." said E1. After thinking for a few seconds, "Do you mind if I call you original?" asked. Einstein began to look around and pretend to be the host waiting for guests. He continued to think aloud. "Yang-Mills theory provides a mathematical basis for our understanding of elementary particle physics. Without it, we can't tell how many particles there are or what masses they should have. But there is a problem. Experiments and computer simulations, such as the Large Hadron Collider at CERN near Geneva, Switzerland, suggest that there is a minimum mass that particles can have. However, the distance between this mass and zero—the so-called mass gap—does not appear to be constrained within the framework of Yang-Mills theory. Solving the problem involves justifying the existence of this gap mathematically." 69 KIBUTZ AND TRAUMA "I haven't heard of these equations, my dear clone." "I am speaking, my dear original, of a set of equations formulated by Chen-ning Yang and Robert Mills in your last year on earth—in 1954—that describe the profound nature of matter. These equations are the higher dimensions of Maxwell's equations." "We need to work on it, E1, but I want you to promise me that the science center must not cause another disaster, I don't want a second atomic bomb." "Bio weapons have replaced the atomic bomb, my dear original. Now I have to meet with N1 and work on Maxwell's equations first." said E1. "Do you think Plato's mathematical world is real?" "This was an extraordinary idea for its time, and it turned out to be very powerful." "But does the platonic mathematical world really exist in any sense?" asked E1. "I thought we were going to study Maxwell's equations." said N1. "Many people, including philosophers, see such a "World" as pure fiction, only a product of our boundless imagination, and the owner of the science center, Nec, who is severely manic-depressive, is an imaginative man. The platonic perspective is indeed extremely valuable. It tells us to be careful to distinguish precise mathematical entities from the approaches we see around us in mathematical entities from those we see around us in the world of physical things." 70 NECİP ERDOĞAN N1, "So you are claiming to me that a rectangular prism-shaped matchbox does not exist in reality but only exists in Plato's world of ideas?" said. "I'm just saying that we're going to make a mapping between the platonic world and the physical world. The platonic world provides us with the blueprint that modern science has carried on ever since. Scientists will come up with models of the Earth, or rather certain aspects of the Earth, and these models can be tested against previous observations and the results of the carefully designed experiment. Models are considered appropriate if they pass such rigorous scrutiny and, in addition, if they are internally consistent constructs. The important point about these models for our present discussion is that they are basically purely abstract mathematical models. In particular, the question of internal consistency of a scientific model is one that requires it to be mathematical, otherwise you cannot be sure that these questions have well-defined answers." "I'm curious, you claim to be talking to Albert Einstein, E1, tell me about his views on the platonic world." Einstein said, "If any kind of existence is to be assigned to the model itself, that existence lies within the platonic world of mathematical forms. Of course, the opposite point of view can be taken: that is, the model itself may simply occupy a place in our minds as having a reality of its own, rather than accepting Plato's world as absolute and real in any sense. For our individual minds are notoriously vague, unreliable, and inconsistent in judgment. The precision, reliability, and consistency that our scientific theories require requires something beyond any of our individual minds. In mathematics we find a much greater robustness than can be found in a given mind. Still, an alternative view may be accepted that the mathematical world does not have an independent existence and consists only of certain ideas distilled from our various minds, which are found to be completely reliable and accepted by all. Whether they are actively doing research or using results obtained by others, those who work at it often feel like they are just explorers in a world that extends far beyond their own." said. When Einstein finished speaking, E1's gaze returned to normal, now that the trance-ridden soul had left his replicated body. N1 didn't know that souls would enter a different body but read it online According to the report, last week, in a city in southern Turkey, three people claimed to have been reincarnated for the second time at the same time. According to the belief of reincarnation, the same soul started to live in different bodies and learned some lessons in each life and rose to the levels of holiness, the aim was to reach God. Seven billion people were formed, perhaps, by a limited number of souls traveling to and from the world in a certain time cycle. It's like each of the infinite number of numbers is actually written as a product of prime numbers! N1 was actually thinking neither of Maxwell's equations nor of the Zeta function. In his world, there were only numbers 72 NECIP ERDOĞAN. He was cut off from life when he started working on number theory. The relations between arithmetic and geometry fascinated him, the geometry of the elements was a separate research topic. When they started working on number theory with E1, the simple relationship they found between arithmetic and geometry impressed him. *** The greatest discovery of the world of numbers began with the question: Can we find a fractional number whose square is exactly two? The number with exactly two squares was expressed as 1.414213562373095048 80168872... and the numbers after the comma were definitely not repeating. In this case, "Is this number a fractional number?" The answer to the question was negative. All fractional numbers would continue forever after the comma, like the number above, for example, the number we call half was 0.5000... or a quarter 0.2500... Then what was the difference in the number above? In fractional numbers, the same digit was always repeated after the comma, while there was no REGULAR repeating number after the double squared comma, yes, it continued forever and continued irregularly forever. Therefore, this new type of number took its place in the history of science: irrational numbers. 73 KIBUTZ AND TRAUMA E1 said that there is another spelling of this irrational number; 1+1/(2+1/(2+...) infinitely looped the serial software: 1, 2, 2, 2, 2... Whereas for any rational number, for example. number was also a quadratic irrational number. Similarly, the square numbers 3, 5, 6, 7, 8, 10, 11... were also quadratic irrational numbers. Meanwhile, the number 14 came to mind, my lucky number is 14. The square is 14. I thought about the number that is the number that is the number that goes like 3+1/(2+1/(6+...), so the sequence of the numbers is: 3, 1, 2, 1, 6, 1, 2, 1, 6, 1, It could be written as 2, 1, 6, 1, 2, 1, 6, 1, 2, 1,... The above palindromic sequence starts with 3, then comes the triple of 1, 2, 1, then comes the double of the three and 1, 2, The numbers 1 came back and continued like this. So the sequence is A, B, C, D, 2A, D, C, B, 2A, B, C, D, 2A, D, C, B, 2A, B, C, D was repeating as 2A, D, C, B, 2A,... E1 said that his lucky number was 17 and he wanted to do the same for 17. He took the pen in his hand to find the serial expansion of the number whose square is 17. 7 was a prime number and to me all primes were unlucky despite being the building blocks of numbers. After finding the serial expansion, he turned his back on me like a child who did not want to share his homework with his friends. "Well, if we add up infinitely many rational numbers (fractional numbers), will the number we find be rational or irrational? What is your opinion?" asked. 74 NECIP ERDOĞAN I had already prepared my best answer to E1 in my mind. It was like the life invention form of arithmetic geometry. E.g; When we focus on the infinite sum of 1/1-1/3+1/5-1/7+1/9-1/11+1/13-1/15+... We could immediately notice that the ratio of a circle's circumference to its diameter (the number pi) was equal to one quarter. "Here is E1, this is a relation between arithmetic and geometry!" I said and handed the pen to him. "It's your turn, make your move!" E1 began to describe the thoughts conveyed to him by Einstein: "The mathematics itself seems to have a robustness that goes far beyond what any mathematician can perceive. Whether they are actively researching or using results obtained by others; those who work on this subject often feel that they are merely explorers in a world that lies far beyond them – a world with an objectivity that transcends mere sight. What I mean by this existence is really only the objectivity of mathematical truth. Platonic existence, as I see it, refers to the existence of an objective external standard that does not depend on our individual views or our particular culture. Such existence may also refer to things other than mathematics, such as morality or aesthetics, but here we should only be concerned with mathematical objectivity, which seems to be a much more obvious issue. Let me explain this topic by taking a famous example of a mathematical truth and relate it to the problem of objectivity. In 1637, Pierre de Fermat proclaimed Fermat's last theorem, which he wrote in the margin of his copy of Arithmetica by the third-century Greek mathematician Diaphontos.

He made his famous claim. "The equation xn + yn = zn has no solution in integers when n is greater than two." In a margin, Fermat further noted: "I cannot include this evidence here, as this margin is too narrow to include the proof." Fermat's claim remained unconfirmed for more than 350 years, despite the efforts of numerous outstanding mathematicians. A proof was finally published by Andrew Wiles in 1995, and this proof is now accepted as a valid argument by the mathematical community." Before Einstein died in 1955, he whispered to E1 that he was dealing with this problem but could not find a solution. Unsolvable problems would arise as long as humanity existed. The relation of the world of numbers to the physical world has attracted attention since Plato. N1, "Do you think PLATO's mathematical world is real?" said. "This was an extraordinary idea for its time, and it turned out to be very powerful." said E1. "But does the platonic mathematical world really exist in any meaningful sense?" 76 NECIP ERDOĞAN "Many people, including philosophers, can see such a world as pure fiction—it is only a product of our boundless imagination. Yet the platonic perspective is indeed extremely valuable. It tells us to be careful to distinguish precise mathematical entities from the approximations we see around us in the world of physical things. Moreover, it provides us with the blueprint that modern science has been going on ever since. Scientists will come up with models of the Earth, or rather certain aspects of the Earth, and these models can be tested against previous observations and the results of the carefully designed experiment. Models are considered appropriate if they undergo such rigorous scrutiny and, in addition, if they are internally consistent constructs. The important point about these models for our present discussion is that they are basically purely abstract mathematical models. In particular, the problem of internal consistency of a scientific model is one that requires the model to be undetermined. The precision required requires that the model be mathematical, otherwise you cannot be sure that these questions have well-defined answers." *** If any kind of existence is to be assigned to the model itself, that existence lies in the Platonic world of mathematical forms. Of course, the opposite point of view can be adopted: that is, the model itself simply exists in our various minds, rather than taking Plato's world as absolute and real in any sense. 77 KIBUTZ AND TRAUMA Yet there is something important to be gained about the fact that mathematical structures have a reality of their own. Our individual minds are notoriously vague and unreliable and inconsistent in their judgments. The precision, reliability, and consistency that our scientific theories require requires something beyond any of our individual minds. Einstein: "We find in mathematics a much greater robustness than can be found in any given mind. Doesn't that point to something outside of us with a reality beyond what any individual can achieve?" said. The gifted physicist's interest in Plato's world of ideas got E1 and N1 excited. E1, "An alternative view can be made that the mathematical world does not have an independent existence and consists only of certain ideas that have been cleared of our various minds and are completely reliable and accepted by all." said. "The mathematics itself actually seems to have a robustness that goes far beyond what any mathematician can perceive. Whether they are actively researching or using results obtained by others, those who study it often feel that they are merely explorers in a world that lies far beyond them—a world with an objectivity that transcends mere sight, no matter how expert others may be. their own or others' opinion." said N1. E1, "It may be useful if we present the true existence of the Platonic world in a different way. What I mean by this existence is actually the objectivity of mathematical reality. Platonic existence as I see it implies the existence of an objective external standard that does not depend on our individual views or our particular culture." said. "You are absolutely right." said Einstein, suddenly sticking out his huge tongue. "In elementary school, my teachers thought I was stupid, but after I studied Calculus and wrote an article, the neutral perspective of mathematics confirmed my giftedness." "Such existence may also refer to things other than mathematics, such as morality or aesthetics, but I am only concerned here with mathematical objectivity, which seems to be a much more obvious issue. Let me explain this issue by taking a famous example of a mathematical fact and link it to the problem of objectivity." "I allow it." said Einstein, tongue still sticking out. "Suppose the validity of Fermat's claim is actually a subjective matter. So X did this in 1995.

It would not be absurd to find a real and specific counter-example to Fermat's claim for another mathematician X, as long as he had done it first. In such a case, the mathematical community would have to accept the truth of X's counterexample. From then on, any attempt by Wiles to prove Fermat's claim would be futile as X had taken this argument first, and as a result Fermat's claim would now be false!" "Wiles will be very angry if he hears these words, it occurred to me is Wiles Jewish?" Finally, Einstein pulled his tongue in. 79 KIBUTZ AND TRAUMA Nec suddenly emerged from behind the curtain in which he was hiding his thick notebook with frayed pages. "I have been listening to you for a long time. I also have something to say about this. I think that almost all mathematicians, regardless of their attitude towards Platonism, would consider such possibilities plainly absurd. Of course, it may still be the case that Wiley's argument actually contains an error and Fermat's claim is indeed false. Or there may be a fundamental error in Wiley's argument, but Fermat's claim is true nonetheless. Or, Wiley's argument, while true in its foundations, may involve non-rigorous steps that will not conform to the standards of some future rule of mathematical acceptability. However, these issues do not address the point I have reached here. The question is not whether the neutrality of Fermat's claim itself will be convincing for a given mathematical ensemble of any given time." E1, "What do you mean, so Wiley doesn't deserve the award? If so; Say two integers whose cubes add up to the cube of another integer!" said. N1, "I think of 1729, it is the sum of the cube of 9 and the cube of 10." said. "It is also the cube of 12 and the cube of one." Nec said, "I know the story guys, Hardy comes to visit Ramanujan who is sick, Ramanujan asks what number of taxi he took. Hardy says 1729 is an ordinary number. Ra manujan says that this number is not an ordinary number. It says 93 +103 =13 +123 =1729. NECIP ERDOĞAN adds that there is no smaller integer that provides this feature. Who knows, the magic number we're looking for may be 1729. If the cube of a single integer is 1729, Wiley has deceived the whole world." said. "I think you are right." said Einstein. "From the point of view of mathematical logic, it should be noted that Fermat's claim is in fact a mathematical statement of a particularly simple kind, whose objectivity is particularly evident. Only a small minority of mathematicians may consider the veracity of such claims to be in any way subjective, but there may be some subjectivity about the kinds of arguments that will be considered convincing. However, there are other types of mathematical claims whose truth can reasonably be considered a matter of opinion. Perhaps the best known of such claims is the axiom of choice. While most mathematicians probably accept the axiom of choice as true, others may view it as a controversial claim that may even be false. Still others would take it as a claim whose truth is a mere matter of opinion, something that can be considered one way or another, depending on what system of axioms and the rules of a procedure one chooses to adhere to. Mathematicians who support this last point of view would be relatively weak Platonists. Those who adhere to neutrality about the correctness of the axiom of choice will be the stronger Platonists. Although not much touched upon in physical theory, I will return to the axis of choice as it has some relevance to the mathematics underlying the behavior of the physical world. 81 KIBUTZ AND TRAUMA For the moment it would be appropriate not to worry too much about this. If the axiom of choice can somehow be resolved by an appropriate form of indisputable mathematical reasoning, then its truth is indeed a purely objective matter." "Shut up now!" shouted Einstein suddenly, only E1 could see him, relaying what he was whispering to himself. "I think Mr. Superintelligence is bored." said Nec. E1, "On the other hand, if the axiom of choice is only a matter of opinion or arbitrary decision, then the Platonic World of absolute mathematical forms contains neither the axiom of choice nor its negation. The mathematical claims that might belong to Plato's world are certainly those that are objectively true. Indeed, I take mathematical objectivity, mathematical Platonism, for what it really is. To say that some mathematical claims have a Platonic existence is only to say that they are objectively true." said. N1, "You did a lot of philosophy, I feel like I'm reading Sofinin's World." said. "A similar interpretation applies to mathematical concepts—for example, the concept of the number 7, or the multiplication rule of integers, or the idea that some set contains an infinite number of elements—all of which have a platonic existence because they are objective concepts. in my opinion

According to him, Platonic existence is simply a matter of objectivity, and so it should certainly not be seen as something mystical or unscientific, although some people may see it that way. However, as with the 82 NECIP ERDOĞAN axiom of choice, questions about whether a particular proposition for a mathematical entity should be regarded as having objective existence can be delicate and sometimes technical. However, we certainly don't need to be mathematicians to appreciate the general soundness of many mathematical concepts. The Mandelbrot cluster is extraordinarily detailed, but it is not just any human design." "You're right," said Einstein. "Why didn't I think of it before I died? Pick a random complex number, square it, then add the constant c, mark the result on the plane, then square the number you found, add the constant c, mark it on the plane, repeat the same process forever and you'll have a perfect shape! Ah, if I had lived a little longer, maybe I would have found a fractal too." "Remarkably, this structure is described by a mathematical rule of a certain simplicity. We will come to this clearly, but if I try to provide this rule in detail now, it will distract us from our current goals." said Nec. E1, "The Mandelbrot set is certainly not an invention of any human mind. The set has taken its place on computer screens objectively in mathematics itself. If it makes sense to assign a real existence to the Mandelbrot set, then the existence is not in our minds, because no one can fully understand the infinite variety and boundless complexity of the set. said. It can exist only in the Platonic world of mathematical forms. I am aware that there will be many readers who will have difficulty assigning any real entity to mathematical structures. N1, "Do you have any requests from such readers, Mr. Duplicated Einstein?" asked. "Let me ask such readers only to broaden their notion of what the term existence might mean to them. The mathematical forms of Plato's world do not have the same kind of existence as ordinary physical objects such as tables and chairs. They do not have spatial positions; they do not exist in time either." "Do you and I, as two clones, belong to the Platonic world or the physical world? Ask the inventor of RELATIVITY that only you saw?" E1 pretended not to hear the question and began to write in Nec's worn notebook: "Objective mathematical concepts should be thought of as timeless entities and not as existence the moment they were first perceived by humans. So mathematical existence is different not only from physical existence, but also from an existence determined by our mental perceptions. Yet existence as beings belonging to three separate worlds has a deep and mysterious connection with each other—physical, mental, Platonic. I write down some of my beliefs or prejudices regarding these mysteries. Concerning the first of these mysteries, which relates the platonic world of mathematics to the physical world, it may be noted that I allow only a small part of the mathematical world to be concerned with the workings of the physical world. It is a case that the enormous superiority of the activities of naive mathematicians today has no obvious connection with either physics or any other branch of science, although one can often be surprised by important applications, although inexperienced. Likewise, with regard to the second mystery in which mindset definitively arises, I am not claiming that most physical structures need to stimulate mindset. While a cat's brain does indeed awaken mental qualities, I don't want the same for a rock. Finally, for the third mystery, I readily admit that only a small part of our mental activity should deal with absolute mathematical truth! These three truths are represented in the smallness of the basis of the connection between each world with subsequent worlds taken clockwise in the diagram. But it is the encirclement of each world in its connection with the world before it that reveals my prejudices. The entire physical world is portrayed as governed by mathematical laws." Einstein suddenly picked up the pencil, his graying hair stood up, looked like he was crazy, drew three different worlds on the big picture paper and drew secret tunnels connecting these worlds. "Do your friends see this picture?" "Even though they can't see you, they see what an interesting picture you've drawn." said E1. "Everything in the physical universe is actually governed in full detail by mathematical principles, perhaps by equations as we will learn in the chapters that follow, or perhaps by some mathematical concepts fundamentally different from the concepts we would label today with the term equations. If this is true, then even our own physical actions will be fully subject to such ultimate mathematical control that control can still allow." He had completed the picture, an unseen e The picture being drawn by l was terrible for everyone but E1. Nec looked at the carefully drawn picture. "This drawing also allows for the belief that there can be a mindset that is not rooted in physical structures. Finally, it allows for the existence of genuine mathematical claims whose truth is in principle inaccessible to reason and insight. This enlarged picture presents potential mysteries that lie beyond even what I allow in my own preferred picture of the world. I think the more tightly organized scientific perspective of the figure has enough mysteries. These mysteries do not go away by switching to the more relaxed order of the sketch drawn by a ghost. Because it remains a profound enigma why laws should be applied to the world with such extraordinary precision. What's more, it's not just the precision but also the subtle complexity and mathematical beauty of these successful theories that are so mysterious. There is, of course, a deep mystery as well, how this properly organized physical material arose—and I am specifically referring here to the living human brain—may somehow evoke the mental quality of conscious awareness." E1 suddenly stopped. "Friends, I said these words, but the owner of these words is Albert Einstein. I don't know how much you believe in the concept of soul transformation, but the spirit of a gifted man is with me." said. Nec said, "There is a mystery about how we perceive scientific truth. It's not just that our brains are programmed to calculate with reliable methods. For example, zero, one, two, three, four, etc. There is something much deeper than the insights even the brightest among us have when we appreciate the true meanings of terms." said. E1, "What is that depth?" asked. "Let this remain a secret between us." said. "19. In the 20th and 20th centuries, the view emerged that the mathematical concept of number should be separate from the nature of physical space. Since it has been shown that mathematically consistent geometries other than Euclid's exist, this made it inappropriate to insist that the mathematical concept of geometry must necessarily be deduced from the pseudo-nature of real physical space. Moreover, it can be very difficult, if not impossible, to detect the detailed nature of this supposedly fundamental platonic physical geometry in terms of the behavior of imperfect physical objects. To know the nature of numbers by what geometric distance to describe, for example, it would be necessary to know what happens at both infinitesimal and infinitely large distances. "Even today, these questions do not have a clear solution." said E1. "Therefore, it was much more convenient to develop the nature of a number in a way that did not refer directly to physical measures. Accordingly, Richard DEDEKIND and Georg CAN TOR developed their ideas of what real numbers are, using concepts that do not refer directly to geometry. DEDEKIND's definition of real numbers is expressed in terms from the infinite set of rational numbers. Basically we think that both positive and negative rational numbers will be arranged in an order of magnitude. We can imagine this ordering to occur from left to right, where we think negative rationals are denoted indefinitely to the left, zero in the middle, and positive rationals go forever to the right. Dedekind imagines a cut that neatly splits this screen in half, with those to the left of the cut smaller than those to the right. We say that the cut defines an irrational real number when the blade does not hit a real rational number but falls between them. More precisely, it occurs when those on the left do not have a true largest member and those on the right do not have a true smallest member. The complete family of real numbers is obtained when the irrational system defined in terms of such deductions is adjacent to the rational number system we already have. Dede kind's procedure leads directly to the laws of addition, subtraction, multiplication and division for real numbers with simple definitions. Moreover, (1/1)-(1/3)+( 1/5)-(1/7)+(1/9)-… allows things like the infinite continuous fraction we saw before to go further and define boundaries. Real number meanings can be given. In fact, this sum is equal to the irrational number π/4. Although its roots go back to ancient times, science, which we can describe as a type of knowledge and thinking and which is a product of civilization, is actually a new concept. Spiritual like religion, legend, mythology, philosophy in ancient times; It is difficult to talk about an understanding of science, which is called science today, and which is essentially based on observation and thinking, apart from efforts to meet daily needs such as handicrafts. However, it cannot be ignored that the knowledge, techniques and concepts obtained as a result of these efforts are the source of scientific concepts and processes that became evident in later ages. In fact, there are two needs at the core of scientific thinking and invention, one being the curiosity of understanding the world, and the other, making life comfortable and safe." Nec,"

We will make life safe only for the Jews!" said. Einstein started whispering in my ear. "You have to stop him, E1, you are humanity's only hope. If the millennium problems are solved, the genetic codes of many viruses that are considered harmless will be in the hands of Nec. Block this sick man now, move with N1!" I didn't know if N1 could help me, or rather how. I had to deliver Nec's workbook to his daughter Din and son Avn. He believed that the virtual daughter he had created in his brain had been killed in a terrorist attack last year. Religion had checked the names of the victims one by one. There was no victim named Shem. N1 "It was his daughter Din, whom he bought goat milk ice cream after school." said. E1, "Nec was on the pier, looking out over the lake when the ferry exploded." she said. "Frightened by the explosion, he believed that the imaginary personality had been killed." said Einstein. "I talked to Avn and Din, he needs to be taken to the psychiatric ward urgently." said E1. 89 KIBUTZ AND TRAUMA Nec could not hear what was being said, he was focused on one spot on the ceiling. He suddenly started talking. "The first of these needs has created a technical tradition that includes various forms of life and skill that has been transferred from generation to generation in the history of humanity, and the second has created a spiritual tradition that gathers the feelings, beliefs and thoughts of human beings. These two traditions were separated from each other in the beginning and in different hands for a long time, and as a result, they could not find the opportunity to interact with each other. Even in the heyday of the ancient Greek civilization, it is seen that there were craftsmen who used manual skills and simple techniques, on the other hand, poets, politicians and philosophers who formed the world of feeling, belief and thought. This separation continued throughout the Middle Ages, but began to disappear at the beginning of the new age. After the merger and mutual interaction of the two traditions, science in the modern sense began to emerge. It is based on an effective fusion of the two traditions of scientific thinking and research effort, the technical skills that enable experimentation, and the theoretical work that leads to conceptual thinking. Man's desire to dominate nature and his effort to understand are as old as human history. The birth of modern science awaited the union of these two aspirations. However, even in the life of the first man it is difficult to say that these two wishes were completely separate. Because the first people used their simple technical skills in their relationship with nature, as well as resorted to some irrational ways such as magic. The purpose of magic was to destroy the enemies in the past, the purpose of science today is to defeat the enemies, throughout human history the feeling of killing and destroying does not disappear! We humans are not mammals but a member of the virus class 90 NECIP ERDOĞAN; We enter the habitat, destroy the host, use all the possibilities, and after destroying the beauties of nature, we look for a new habitat." We can find the same purpose in fairy tales or stories about the existence and order of the world, such as myths that persist from place to place in various cultures. The reason for the creation and existence of the Sun, Moon and stars has been imagined as eliminating the fear of human beings in the face of life and death, providing the confidence and comfort they seek. Even in magic, there was always the idea that nature did not change according to its wishes and that it had to obey some laws. Early humans knew that they could not save themselves from the fact that fire always burns, water wets, the sun is bright, winters are cold and summers are hot. However, magic and myth are not directly the cause of the birth of science. The birth of science was caused by the passion for understanding and knowing as well as the effort to control nature. Although the roots of science go back to ancient times, science, which we can describe as a type of knowledge and thinking and which is a product of civilization, is actually a new concept. Spiritual like religion, myth, philosophy in ancient times; It is difficult to talk about an understanding of science, which is called science today and is based on observation and thinking, except for the efforts to meet daily needs such as handicrafts. However, it cannot be ignored that the knowledge, techniques and concepts obtained as a result of these efforts are the source of scientific concepts and processes that became evident in later ages. In fact, at the core of scientific thinking and invention lie two needs, one being the curiosity of understanding the world, and the other, making life comfortable and safe. The first of these needs has created a technical tradition that includes various forms of life and skill that have been transferred from generation to generation in the history of humanity, and the second has created a spiritual tradition that gathers human feelings, beliefs and thoughts. These two traditions were separated from each other in the beginning and in different hands for a long time, and as a result, they could not find the opportunity to interact. Even in the heyday of the ancient Greek civilization, it is seen that there were craftsmen who used simple techniques, and poets, politicians and philosophers who created the world of feeling, belief and thought.

is This separation continued throughout the Middle Ages, but began to disappear at the beginning of the new age. After the merger and mutual interaction of the two traditions, science in the modern sense began to emerge. It is based on an effective fusion of the two traditions of scientific thinking and research effort, the technical skills that enable experimentation, and the theoretical work that leads to conceptual thinking. Man's desire to dominate nature and his effort to understand are as old as human history. The birth of modern science awaited the union of these two aspirations. However, even in the life of the first man it is difficult to say that these two wishes were completely separate. Because, the first people used their simple technical skills in their relationship with human-nature, as well as resorted to some irrational ways such as magic. In fact, the purpose of magic is to influence nature: to heal the dying patients, to prevent expected natural disasters, to destroy the enemies, etc. We can find the same purpose in fairy tales or stories about the existence and order of the world that persist in various cultures from place to place. The reason for the creation and existence of the Sun, Moon and stars is imagined as eliminating the fear of human beings in the face of life and death, providing the security and comfort they seek. Even in magic, there was always the idea that nature did not change at will, that it had to obey certain laws. Early humans knew that they could not save themselves from the fact that fire always burns, water wets, the sun is bright, winters are cold and summers are hot. However, magic and myth are not directly the cause of the birth of science. The birth of science was caused by the passion for understanding and knowing, as well as the effort to control nature. "What is the history of science and technology?" We can briefly define the answer to the question as the birth and development story of science and technology. The purpose of the history of science and technology; to examine the emergence, dissemination and conditions of use of objective knowledge and technique, and to provide a certain direction, a way of thinking, and even a broader perspective. The history of science and technology tries to achieve its purpose not by listing the results achieved in various branches of science, but rather by explaining these results in the context of the conditions they depend on. Its task is not to be a catalog study of facts and inventions, but to follow and reveal the birth and development of scientific concepts, theories, techniques and understanding. I was snapped out of my thoughts when Din suddenly entered. "How are you dad? I've been reading the workbook for days, why is it so important to you to solve millennium problems?" 93 KIBUTZ AND TRAUMA Religion had reached everything I tried to hide, the genetic codes of the biological weapon we had created were now deciphered. "I only shared this secret with my daughter Shem, Din." "You don't have a daughter named Shem, the memories you wrote belong to me, you need treatment, you're sick dad!" Religion was jealous of my daughter Shem, I was going to leave the science center to her, Shem was my only heir. My daughter would use our weapon, the vaccine of which is only in the Israeli Government, where necessary, my life may not be enough for this, but I trusted Şem. "Call me Shem, Din, now!" At this time, the security guards and paramedics of the science center had entered, and Din began to cry. "I beg you, don't hurt my father!" Avn was waiting behind the white-coat attendants, avoiding my eyes. He took my hand as if I were a small child and handed me over to the officers. END