The simple journey log

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Mathematical progress

Until now, new findings in the field of physics and chemistry have been discovered by observations in natural events and experiments. On the other hand, new knowledge of mathematics has been discovered through thought experiments. Mathematical findings were mathematics, geometric axioms and theorems, truths of logic and solving equations. Calculations have been performed to predict the motion of objects and the motion of celestial bodies, where the computational solution techniques have developed. Analysis of motion such as dynamics and astronomy has been developed together with mathematics and physics, so it relates to events in the natural world. On the other hand, the purely abstract mathematics field has nothing to do with events of nature events. The subject is not around himself or in the natural world. In short, mathematics is like metaphysical scholastic philosophy.

Regarding the relationship between mathematics and physics / astronomy, Galileo Galilei clearly expressed "Mathematics is the language in which God has written the universe". That is, mathematics is a language. He laid the foundation of physics as a modern discipline. Things that can be described in the language of mathematics, although it is logical, rules our universe as a reason of nature. Therefore, attitude towards science of analysis and comprehension is established. Nevertheless, since you can write a certain equation with arbitrary parameters, in which the hypothesis is not necessarily true in nature. About this, Von Neumann and Torahiko Terada have said similar things, I agree with them exactly.

Advancement in mathematics is said to be slow compared to other science. But what about it? I think that I will never be late. In the first place, quick discovery can not be obtained from thought experiments. At the root of the essence of thinking lies the philosophical method of thinking while asking yourself. There was also a bias of religious view there. However, human beings who have acquired the language "mathematics" suitable for logical thinking have found truths with tools of thought experiments that do not rely on experience but making use of analogy. Mathematics that make new discoveries in thought experiments, since ancient times to modern times, there is not much change in environmental conditions. However, today, with the development of computers, leaving the computation to the computer allows the simulation to go far beyond thinking experiments and discover and verify new facts. This is a paradigm shift.

Jan 13, 2019

From medieval mathematics to today’s mathematics

Examination math as an education that many of the baby-boomers have learned is, of course, mathematics until the 18th century. Most mathematics taught in compulsory education are calculation techniques and geometry from Greek era to medieval times. Even mathematics studied in the science and engineering of the university does not touch the essence of modern mathematics. Except for mathematicians, only students who major in mathematics or graduate students in science may have touched the essence of modern mathematics. In this respect, mathematics and history are similar. Why is this delay behind? It is because modern mathematics is too complex and detailed to differentiate.

Meanwhile, advances in knowledge in physics, life science, and other state of the art science fields are extensive. However, mathematical progress seems to be less seemingly glorious than those. A mathematical history researcher says modern mathematics is too technical. It is said that even if there are breakthrough progress such as physics, astronomy and life science, it should be appropriate. He has a point, but that is not all.

Once, allegation that mathematics was not science, metaphysics, scholastic philosophy was mainstream. The object of science must be touched by eye. There are no thickness, size and weight in the lines and points handled in mathematics. The numbers are abstract to the last. Mathematics that is only a thought experiment is not science. Therefore, there was no exhibition on mathematics in the science museum. However, in modern times, that view is no longer mainstream. Today, mathematical science, computational science are positioned as the foundation of modern science. They are taking on the role of leading science such as elementary particle theory, super string theory, cosmology theory. Their success puts the young people into curiosity for science and longing for mathematicians. For example, a wonderful mathematical physicist gives children the power to see the world by mathematics.

On the other hand, even now, there may be old style mathematicians who cast older sutras on stereotypes. Indeed, it can be seen that they are performing artistic lessons that do not feel the sense of science. In other words, it is a class that will show off memory skill like exam examination math. Unless there is something curious about the secret or puzzle of logic, If not, it is just sutras. Most mathematical solution techniques can be found from the site database. Why, it is important to think about what you thought of the solution so that it will be useful for the next try, but it is hardly done.

In other words, it does not mean that conventional realm other than mathematical science is not necessary. The opposite is true. Learning number theory and geometry, etc. is to understand the essence of the number, what does it mean to count? What is space? Is the space full of symmetry? Focusing on prime numbers also changes the recognition of space.

As Einstein developed the theory of relativity in the Minkowski space, in order for us to tell the further universe, we need a number theory like p-adic number and Riemann zeta ζ functions, supersymmetry, new geometry, etc. . In other words, we must refine mathematical knowledge which is the basis of mathematical science. And, so far it might have been a purpose forcedly. Because continuing thinking of mathematics is just fun. I guess it is an instinct to solve a mystery. It's like a puzzle to enjoy without reason. Especially for elder mathematicians who retire from active service and work for STEM education volunteers, it is an everyday custom that I do not want to change.

Jan 12, 2019

Advice to young students

In my approach to science, the most important thing is curiosity. Besides, humility is important for our efforts. The central activity of education for elementary mathematics should be calculation. Nevertheless, it should not be making too much of calculation practice. It is important to acquire the habit of thinking. It is interesting to change the way of calculation like the common core that has been advanced in the United States. However, there seems to be confusion with the teacher in the field.

By the way, I will refer to science education. STEM for grade school students is important for industrialized countries and advanced scientific countries to maintain international competitiveness. In particular, I have argued in various postings that mathematics as basic science is important. This perception is high in overseas developed countries, but this country is no so. I think that future differences will emerge.

There used to be "affordable education" in primary education of this country, which means that students would be able to do without difficulty. The philosophy was close to the common core in the United States as mentioned above. So was the aim of education was placed emphasis on putting the ability to think, but seems to have been unsuccessful. It was because there was no ability to make teachers think deeply. Once, elementary school mathematics education which let kids remember 3.14 ... as 3 was criticized. Integer and irrational number are different. Pi, is because it was important to to understand a transcendental number.

On the other hand, in many engineering calculations, the calculation ability of approximation is utilized. But meets the government's education policy aimed at technology-oriented nation, this is a different story. To aim for prevailing scientific nation, you should not dishonor mathematics education.

Well, math education for junior high and high school students is still exam examination math. It is skilled and memorizes formulas and solutions. Despite having solved such a difficult mathematical problem, I am surprised that they do not maintain mathematical sense when they become university students and become adults. It is said that tools not used will be forgotten.

Mathematics is the science of thinking, but metaphysics. Language is metaphysics. Language is accompanied by culture. The language of mathematics comes with the culture of mathematics. Those who learn mathematics should remember the language to talk about mathematics and constantly be conscious of mathematical culture and make it their own.

For mathematical culture, area theory, topos, model theory, expression theory and so on are interesting. Research in mathematics field is aloof. Therefore, it is troublesome for research that imitates and follows overseas research. Creativity is important for selecting research themes.

It has become an era where computers can be used for new mathematics. Large-scale calculation and simulation are left to the computer, mathematicians should concentrate to think about his concerns and new ideas as possible as you can.

Jan 11, 2019

Moderate stress is necessary for the life

He has reached old age now and cleared his almost dreams and goals since boyhood. Every time he accomplished the task, mental stress due to the sense of mission was supposed to be lighter. However, he realize that even after reaching the goal, stress will not go away. People always strives to set goals and achieve them. He should have given up some activities that were unaffordable commensurate with economic power, but still he's taken a lot of hobbies. Some hobbies require licenses. In case of his hobby life he had to pass the governmental exams. So far, he has acquired the highest qualifications in all.

Recently, he feels a decline in the memory capacity of the brain. That's why the newly challenge of acquiring qualifications that require memory is almost impossible. On the other hand, thinking abilities have been sharpened over the years. The ability of writing is definitely improving. People would like to send a stress free life, but it is said that it will become senile dementia as soon as stress is gone. For him who has lived a life without honor and status, writing and mathematical research is a pleasant stress. The curiosity to numbers was from elementary school students. When an old man gently touches his heart and touches the secret of the number, he feels as if he became a hermit.

Jan 1, 2019

Universal Property

I introduce good texts to people who want to learn the field of new mathematics. Tom Leinster's Basic Category Theory can be recommended. Let me introduce the beginning of the introduction.

Category theory takes a bird’s eye view of mathematics. From high in the sky, details become invisible, but we can spot patterns that were impossible to detect from ground level. How is the lowest common multiple of two numbers like the direct sum of two vector spaces? What do discrete topological spaces, free groups, and fields of fractions have in common? We will discover answers to these and many similar questions, seeing patterns in mathematics that you may never have seen before.

The most important concept in this book is that of universal property. The further you go in mathematics, especially pure mathematics, the more universal properties you will meet. We will spend most of our time studying different manifestations of this concept.

Like all branches of mathematics, category theory has its own special vocabulary, which we will meet as we go along. But since the idea of universal property is so important, I will use this introduction to explain it with no jargon at all, by means of examples. For novice, it is useful for studying that the first example of a universal property is very simple.

Dec 31, 2018

Internationalization of this country may be behind

At the end of the year, I looked for some handy notes that would be useful. I thought if I had an iPhone at hand, I thought that a notebook was unnecessary, but again, I can not throw away the paper notebook.

By the way, on the front cover, there is a display, such as a note book or hand book, which seems to be English. I noticed it after purchasing the notebook, but I no longer feel like using that notebook. Because of misspell, it is a notebook, not a note book. It is not a hand book but a handbook. It is a pity that such funny English is still missing in the publications.

Dec 23, 2028

"Exquisite adjustment" and Anthropic principle

Very cool and exciting articles were published in Asian mathematics magazines, so I will refer to it and introduce some in summary. Pascal considered the issue of faith as to to which or not to believe in God by using probability theory. Recently, there are also arguments like the following with a scientific mood at first glance using probability theory. The latest influential physics theory which exceptionally explains all phenomena in this world contains multiple constants without exception. These constants are free from the theory itself, may be other values without inevitability, free parameters in that sense. However, in any theory, if even a small number of these parameters deviate from the actual values, The air is supposed to be in the world remarkably obvious or destructive. No complex atom or molecule could be composed or any star may naturally have any life. Since the probability that a parameter that could have been any value will become this value of reality is extremely low, this "exquisite adjustment fine tuning "is not a coincidence. Therefore, It is impossible to believe in the existence of "Intelligent Designer." If you think carefully, there are several holes in this discussion. Is it so rare, may there be other explanations?

How about the following argument? Let's admit that the chance of accidentally getting such an exquisite value is very low. However, it is precisely what we are arguing that we exist severely. Otherwise, we just did not have this problem itself either. Therefore, there is nothing surprising, there is nothing to explain in 'exquisite adjustment'. We refer to this argument as "anthropic principle" Well, is this discussion correct? To imagine your feelings, it is stupid to prove the existence of "intelligent designers", but it is probably somewhere that the principle of human beings is too much. The cause is probably too crude and ambiguous assertion to say logic. However, on the other hand, I feel that I point out important issues. There are various variations and strengths of assertions in the human principle, but the essence is that if it is other than an observer. It is based on the fact that "I" is automatically sampled. Can we make a reasonable inference based on this human principle, or is it an obvious argument that "I am because I am?" Seriously, you will not receive the "intellectual designer" hypothesis for "exquisite adjustment" problems, but how about the multi-space hypothesis that there are multiple or infinitely many universe. By the way, this is the latest cosmology But it is regarded as a powerful theory. If there are lots of universe, there will also be a specially good universe that happens to have exquisite parameters by chance, with high probability, and there will be intelligent observers like us in that good universe. So the question is, does the human principle support somewhat this hypothesis? Let's say that the development of theoretical physics narrowed the powerful universe to two. If the difference from each is the only universe of our universe,

Is Anthropic principle nonsense? Since the reader of this journal will have deep interests and empathy in mathematics, it may have been said that such discussion was nonsense in the first place. Indeed, it is certain that these problems are not mathematical problems, as it is an issue that the appropriate probability space is not well understood. However, such a matter of choosing an observer exists in an unexpectedly wide range, often sneaking in unaware of myself. For example, why do columns that you lined up at supermarkets always grow longer? Longer rows have more observers, so the probability that you are in a long row is higher. For example, why does entropy always increase? The higher the entropy, the higher the probability, the more observers there are.

Furthermore, why is the entropy around us so low? We exist because we are in a state with low entropy. For example, why the life on the earth has evolved to such a complex existence like human being so quickly, because we are strictly here, the premise that creates intelligent observers is the reference space Yes, of course, its probability is high. I do not necessarily claim that the above discussion is correct. However, there is no doubt that the effect of observer selection relates to these problems, and it is certain that the temptation of such discussion is strong. This problem inherently lurks in this field not only in cosmology but also in a wide range of fields of natural science. Although it is true that "I am an observer is always a sample" indeed has information for probabilistic reasoning in many cases, it is very difficult to make correct reasoning, and this problem is troubling.

Dec 19, 2028

Old boy’s dreams

He gotta keep on thinking math idea. So he is a math geek and a jack of all trade but master of none. Because he was doing very well in various fields such computer science, aerodynamics, and mathematics. So, he is still active in the front lines of science and education. Well, once a person gets elderly and can lose sex appeal and greed, it will return to elementary school students. Moreover, it seems that it is a sequence of becoming an infant i.e., second childhood and going dead when you get older. As suggested by the theorem of maximum value, now his derivative coefficient, that is, the slope of life is minus, so how he can draw a life locus after this. When calculated by Poisson distribution, it becomes zero on December 25, 2030. If it is a normal distribution his death will be shorter.

The story derailed from the beginning, but today's topic is an old boy’s hobby. In student days it was complicated and it was troublesome to keep thinking Math, but it became fun. Now then it make him happy. He sometimes gets ridiculous if he get to a novel idea.

Language is same as well. It is fun to memorize not only English but also various words. Those are skills that have few opportunities to use though, I’m keeping it, even if I know that human’s brain can not have a new linguistic vision after youth.

This elderly man is good at Rubik 's cube. Not only 3 × 3 × 3 but also 4 × 4 × 4 can be taken immediately. Because he clarified the solution algorithm of Rubik 's cube from the group theory. He is strong also on puzzle rings.

Girls aged 10 to 16 years older than boy solve puzzle rings quickly. Girls' brains are growing faster than boys. Surely old boy can be solved, however, it will be forgotten as time passes. Even though an old boy has wisdom, he can not maintain his memory.

In addition, the old boy loses to them at the speed of thinking, but if he competes for abstraction ability it is likely to win.

He used to be a flying mathematician in the past. Now the wings are folded. Although he has not flew around the world, He is dedicated in writings in the study. The theme is mathematics, focusing on telling Universe, number theory, category theory and discrete mathematics than geometry and analysis. At the science museum he is striving to find gifted boys. He is also interested in stars and galaxies. Therefore, he keeps volunteering activities on planetarium commentary. While looking at the stars, it is the dream of the old man to indulge in fancy.

- Dec 18, 2018

Orion and the stage of art technologies

TV drama called Downtown Rocket is quite interesting, isn’t it? The meaning of downtown rocket is advanced technologies made by a SME, small and medium enterprises located in downtown. I rarely watch TV, so until recently, I didn’t know this drama of precision machinery Industry with distinguished development speed. A story that the technical capabilities of SMEs compete with the tyranny of a large industrial companies and survive is comfortable. However, it seems to be different from reality.

The space industry is a promising field for manufacturers. In the sequel, the subject shifted to development competition in the agricultural field of mobile machinery. However, it is not enough that the focused technology is an engine or a mission, not to mention artificial intelligence deeply. Also, I wanted to refer to remote sensing technology in relation to space technology and agriculture.

The capital strength that can be invested in research and development is key. Even if basic technologies, designs and prototypes can be made, the production capacity of the production line is necessary for actual production. Quality control and maintenance cost as much as development. Comprehensive strength is required for manufacturing technology instead of Crafting.

R & D of basic technology depends on excellent technicians. However, SMEs are hard to secure talented people In order to recruit talented personnel, corporate brand power and future prospects are required. It is not enough to use technology alone. For innovative science and technology, comprehensive scientific power and mathematics are important. For that purpose, higher education is inevitable. Therefore, it goes without saying that large corporations are superior to SMEs. The key of this drama always emphasizes the technological capabilities related to manufacturing, but in order to survive in the global market, advanced science capability is more important than manufacturing technology.

Orion is a symbol of the hero. By the way, in the drama, a main actor casting the president of

high technology fabrication is wearing only shirts and suits lies down on the ground and a scene watching Orion is coming out, but this would be wrong. It is the season of severe cold around February to look on Orion constellation. The actor may be frozen and dead.

- Dec 17, 2018

Closed collective and ostracism

Closed collective is called "Mura-Shakai" in Japan means

The so-called "Mura uneven society" refers to a closed community closed collective with units of activity. It does not depend on the geographical size. However, as you can see from the etymology, it comes from a rural community.

Originally, the community is not open-minded. It seems that interpreting is difficult, and it is such expression that is translated fairly wrong. As a translation, I encounter lite literal translation with village community, small town community and so on.

That's stupid!

"Mura community" means that the closed social structure that the boss dominates, ruled by the convention Trying to exclude others, bullying of newcomer newly in a bad mood which is an insidious forms of bullying, surmise the clout of dominant person, ruled by the custom which stem from local convention, and escape unforgivable. That is, collectivism seeking harmony, cooperation. Those who can not do that are made to village ostracism. It is a group of inward mentality called “silo mentality” without seeing outside society.

Such a community is also everywhere in the country. It is a characteristic of society that has been made up of agriculture. By being afraid of group odor, it becomes obedient to the collective, bullies the vulnerable, conjecture dominants in order to share the dominant’s interest, get the concessions and maximize self interests. Even in the local community, the company, the elderly association, and the expert group, there is a closed collective. Especially insidious is seen in the group of children and old people. It seems that they move more instinctively. In the case of a group of researchers, they slander and eliminate excellent people in the organization. Then, they want to make groups more than necessary. It seems they can not ban anxiety about being independent.

Well, from a mathematical point of view, things that can be flipped have properties like singularity, isolated point, cusp point. Regularization is performed on the side that plays. The degree is like finding eigenvalues. There is only one real eigenvalue in the real square matrix whose components are positive depending on the degree. Speaking of p - ary, there is a near and far distant, near p - ary distance. The distance feeling is determined by the remainder divided by the prime number. The prime number becomes the head of the group. Those far from this prime can not be opponent. However, those who are excluded do not have any anxiety.

Well, from a mathematical point of view, things that can be flipped have properties like singularity, isolated point, cusp point. By blow-up, singularities can be gentle. Regularization is performed on the side that plays. The degree is like finding eigenvalues. There is only one real eigenvalue in the real square matrix whose components are positive depending on the degree. Speaking of p - ary, there is a near and far distant, near p-adic distance. The distance feeling is determined by the remainder divided by the prime number. The prime number becomes the head of the group. Those far from this prime can not be opponent.

-Dec 12, 2018

Mathematician condemned in spying, and being knowledgeable about Sanskrit

André Weil, French mathematician who was one of the most influential figures in mathematics during the 20th century, particularly in number theory and algebraic geometry. His teaching career was even more international. He was professor of mathematics in India, and thereafter taught at São Paulo, Brazil, and Chicago. He joined the Institute for Advanced Study, Princeton in 1958, becoming professor emeritus in 1976. During World War II, he refused military service and was condemned for spying charges. In order to avoid a five-year sentence in a French jail, Weil volunteered to return to the army. In 1941, after reuniting with his wife, Eveline, Weil fled with her to the United States after suffering.

He was also a gifted linguist who read Sanskrit and many other languages, and he was a sympathetic expert on Indian religious writings. Mathematicians who had knowledge of Indian philosophy and could read the Sanskrit language were only André Weil.

Mathematical physicist Hermann Weyl in the same era and André Weil were similar in name. That's why Weil was jokingly saying, "Mathematical historians will have intense debate over whether he and I are the same person." Moreover, he does not know that he was to be confused with Andrew John Wiles who solved Fermat's final theorem later. Even if French, German, English and languages change, the etymology called Weil, Weyl, Wiles will be the same.

Weil found value only in pure mathematics, and he was not interested in applied mathematics. He is famous for Bourbaki's early members, but he himself is very proud of himself, and his daughter' s name was also Nicolette's name from Nikola Bourbaki. Mathematics progresses with a few geniuses, and mathematicians below the two streams are said to be only resonance boxes. In the discussion he said straightforwardly and too ready to criticize others. Sometimes he get person's antipathy. Genius is not cooperative. However, he said he continued mathematics in prison while being sentenced to death by spy charges. Empathy with mathematicians who continued mathematics even in the limited time.

-Dec 11, 2018

Is categorical theory Platonic?

In the word Platonic Love, I feel purity! In the first place, in Platonism change is evil. In other words, what can be studied is the essence that does not change, and all changes, exercise, actions and processes should have been abandoned.

But in modern times science thinking of dynamic change will be mainstream. The common language that connects different fields of modern science is categorical theory, but then it can be said that the theory of categories is not Platonic ... Well, what do you do? Yes, the categorization theory is not Platonic. Plato is not noticed more than romance.

So, somewhere is the science field near here, computer science? The programmer naturally comes into the categorization theory from the state transition diagram. On the other hand, it is difficult to enter geometry and other things that are doing homology. Even though we acknowledge the achievements of Plato and Euclid, we must forget them in the new scientific field.

- Dec 9, 2018

The power of pondering

Teaching kids philosophy makes them smarter in math and English. It is the power of pondering. Schools face relentless pressure to up their offerings in the STEM fields—science, technology, engineering, and math. Few are making the case for philosophy. Maybe they should. Nine- and 10-year-old children in England who participated in a philosophy class once a week over the course of a year significantly boosted their math and literacy skills, with disadvantaged students showing the most significant gains, according to a large and well-designed study. It is said that more than 3,000 kids in 48 schools across England participated in weekly discussions about concepts such as truth, justice, friendship, and knowledge, with time carved out for silent reflection, question making, question airing, and building on one another’s thoughts and ideas.

- Dec 8, 2018

Authoritarianism behind the sign display

When I was walking down the street, I found such sign, “The University of Цукуба Hospital.” Цукуба is the name of this area. so that hospital is attached to Цукуба University. However, a sense of discomfort remains a little. I can read it with Цукуба Hospital University. I'm sure the hospital has the university attached to. I guess it's relatively a big hospital.

On the other hand, at the entrance of the university, it is written as “University of Цукуба”. Still this sign also has discomfort. On the website of this university, it was written as “The Цукуба university.” It seems that signs are not unified. Generally, the name of university and its hospital is written like this. “University of Michigan Hospitals”, “The University of Michigan's hospital.” College names are like “Stanford University”, “The University of Chicago.”

For proper nouns, it is natural not to attach the definite article “the”. When emphasizing the attribution of University using the preposition "of", I will attach a definite article. Still it can be attached in sentences, but University of Chicago is natural without displaying the name when displaying the name of the university. For instance, Tokyo’s Bay is called “Tokyo bay“ or “The bay of Tokyo.”

The hospital at the beginning, “Цукуба University Hospital” would be natural. Or give the impression of a big hospital with only one in the neighborhood would be The University of Цукуба's Hospital. However, there is no need to attach the definite article to the small area’s university hospital. How do you feel hidden authoritarianism of national universities.

I checked other university hospitals in this country. The University of Tokyo Hospital, The Tohoku University Hospital, University Hospital, Kitasato University Hospital. . . Most private university hospitals are given natural notation. The University of Tokyo Hospital is the same notation as the university hospital at the beginning. Tohoku University Hospital is on hand with “the.” By the way, I was pronouncing the University of Tokyo as “Todai” in our conversation, so I thought that it was Todai University.

- Dec 7, 2018

The deviant who ran into simplification became a troublesome exclusion of others

Cauchy who neglected Galois' contributions twice was a troublesome but Leopold Kronecker also had many enemies. Kronecker did not acknowledge the set theory of Cantor and afflicted Cantor so crazy. However, formalism, which makes mathematics simple and beautiful, makes sense in response. It is also in my mathematical view. Although Kronecker was stubborn, the philosophy of Kronecker who loves natural numbers became a source of intuitionism. He was never an unskilled mathematician.

Kronecker said that natural numbers were made by God, but others were made by humans (= Die ganzen Zahlen hat der liebe Gott gemacht, alles andere ist Menschenwerk.) In addition, by solving the dream of Kuronekka's dream of. youth, it is know that Sadaharu Takagi has developed a theory of class.

Originally Kronecker was interested in simplifying the existing theory and making it more sophisticated. And it gradually became sharp, constitutive, it began to feel suspicious unless it proved to perform only finite operations. Therefore, he took Bolzano-Weierstrass' s theorem i.e., the bounded real number sequence has a converging subsequence was not recognizable. Furthermore, if it is not a number that can be obtained by performing a finite operation from an integer, it is regarded that it does not exist. He writes that the proof of the transcendence of pi (π) by Lindeman (1882) is "beautiful, but meaningless, because no transcendental number exists." (Of course, most of the numbers are transcendental numbers.)

At the University of Berlin, his colleague Weierstrass was opposed to the long-term. In addition, there were times when we did not post research on Dedekind which was close to Kronecker's own research field in the magazine. In addition, in the field of mathematical foundation theory, it is known to have attacked the set theory of Georg Cantor.

Cantor proved that there are infinite transcendental numbers, but from his point of view, this result was completely meaningless. Kronecker is a person who puts his thoughts into action, refuses to post Cantor's paper in his magazine, openly criticized Cantor and Dadekint's theory on real numbers, and even Cantor's personality. Cantor was badly scratched by this, which also became a factor that Cantor became mentally unstable later.

The view of Kronecker was by no means totally dogmatic, but later Henri Poincaré and Blauer became the basis for developing mathematical intuitionism which states that mathematics should be assembled more intuitively. According to Andre Weil's research book, it was pointed out that the later Kronecker was inspired by Eisenstein's elliptic function theory and was developing its own elliptic function theory.

Economically, after acquiring the degree, he took over the deceased uncle's bank and farm and succeeded in management, making it successful financially. In the article of 1853 we re-arranged the Galois theory and given a simple proof that the quintic equation can not be algebraically solved and this is the simplest as a proof that the quintic equation can not be algebraically solved Although it is being done, it is forgotten in the present mathematical history.

Dec 6, 2018

A scientist only on the surface, a shallow scientist at the bottom

It is the basis of mathematical science to be able to handle mathematical equations such as differential equations. It is fundamental skill, but it is not science to explain the phenomenon by finding the appropriate differential equations without knowing the meaning and choosing the parameters appropriately. Those who are harmful to physics and mathematics applied to physics If you talk about parameters, the simulation of the solution looked like a phenomenon. “I can draw a curve of any solution.” Von Neumann says, "Give me four parameters, apply one image of elephant, if I have five parameters, shake the nose of that elephant." Von Neumann cited here is the creator of computer theory and my favorite mathematician. Because it is a deep mathematician, please do not misunderstand. Hiraku Toyama says that "Knowledge of differential equations would be great if it became the culture of this country." However Common sense must be good sense. Additionally, "Differentiating seeing the future, and integrating viewing the past" is my word. Present-day mathematician Tadashi Tokieda who is always contributing to the math seminar wrote above stories in the sentence at the end of the article. In particular, he said complaints "Do not try to solve the differential equation before the solution can be seen." That's right. This is a reason that many pseudo-scientists can only see the surface and understand lightly.

Dec 5, 2018

A scientist only on the surface, a shallow scientist at the bottom

It is the basis of mathematical science to be able to handle mathematical equations such as differential equations. It is fundamental skill, but it is not science to explain the phenomenon by finding the appropriate differential equations without knowing the meaning and choosing the parameters appropriately. Those who are harmful to physics and mathematics applied to physics If you talk about parameters, the simulation of the solution looked like a phenomenon. “I can draw a curve of any solution.” Von Neumann says, "Give me four parameters, apply one image of elephant, if I have five parameters, shake the nose of that elephant." Von Neumann cited here is the creator of computer theory and my favorite mathematician. Because it is a deep mathematician, please do not misunderstand. Hiraku Toyama says that "Knowledge of differential equations would be great if it became the culture of this country." However Common sense must be good sense. Additionally, "Differentiating seeing the future, and integrating viewing the past" is my word. Present-day mathematician Tadashi Tokieda who is always contributing to the math seminar wrote above stories in the sentence at the end of the article. In particular, he said complaints "Do not try to solve the differential equation before the solution can be seen." That's right. This is a reason that many pseudo-scientists can only see the surface and understand lightly.

Dec 5, 2018

Genomic editing ignoring ethics

Those who are driven love of conquest by ambition and not being humble are ineligible in scientists. A Chinese researcher reportedly edited the human’s genome contrary to the rule and went on to the birth of twin babies. In contact with this news, I could not forbid the feeling disgust. . . Operation that embeds genes into healthy eggs has problems. When the engineered gene is diffused, even if it is known as dangerous, it can not return. It causes dangerous consequences for mankind.

Too self-assured person are unreliable. much less scientist. Such person is always in the surroundings. Even if he was the president, he would prioritize himself as it was overbearing enthusiasms. When discussing, his nature can be seen. Some scientists convictively do very dangerous acts as much like concerned doctor. Even if there is a possibility that the action can have irreparable results, they will not consider the subsistence of all human being. There is no rule to suppress such human beings without responsibility. We must wait for their conscience and consciousness.

- Dec 4, 2018

Self-esteem and conscience of professionals

The detection of tampering with the inspection data of its own products by engineers in this continues. Engineers must be proud of their skills. Even so, I think what is wrong with tampering the data and making the quality of the product sesame. Tampering is called falsification in English. Also, the word fabrication manufacturing has a meaning of. OK, back to the subject, he wrote the inspection data appropriately without checking to keep the deadline of the delivery date. To the inspection division in the company, since the delivery date is directly linked to turnover, the bias of keeping the delivery date is strongly applied. Companies that cheat the quality of the products to be shipped lose credibility and will be excluded from the market.

For a tamper engineer, was not there anything that had led to despairing the data? If not, this person in charge would not be a technician.

Tampering with research data by scientists is also occasionally reported. For researchers, experimental data, analytical data, observational data are precious. I think whether there is no conscience of the researcher to tamper with it, to omit the inconvenient data to conclude, or to change the numerical value. By the way, data falsification is also called doctor. The doctor has meaning to do the mixing. The word of “doctors” say that there are a lot of suspicious things. Returning the story, tampering the data and announcing remarkable research results, even if it is temporarily evaluated, it will definitely be a lie. I do not understand why they do such a thing.

- Dec 3, 2018

Obsession or some kind of courage to live

When anyone gets old-age, preference gets narrowed. Age, illness, and what has stopped being unaffordable is flying. The obsession with flying seems to have diminished. Instead, the obsession for mathematics became stronger on behalf of flying. The premonition has been from the boyhood, but it became dominant in the old age.

It may seem that it is a weird person to be immersed in mathematics in the old age. I think that the satisfaction of a person can be measured by breaking his obsession. In my case, there are other encouragement that gives that will be worth living. For example, commentary on stars at science museums, STEM educational activities, etc. will be worth living. Math and programming discourse makes something in my life worth living for.

Moreover, preference changes with time. One thing to find mathematical tasks, thinking and thinking. Continue to challenge the most difficult national examination. in fact, I took the exams all day last Sunday. Continue to be involved in multiple languages and different cultures. They are worth living for. Well, let's find a way to live from what we can do at hand.

Dec2, 2018

The tool left behind from support

HTML editor and FTP uploader are essential to updating the Internet serve, however I have a difficulties on them. The FTP tool, called FTP on the Go Pro failed on the iPad that I use all the time. This utility can repair any line of HTM files on the web. It is a difficulty with a fee-based utility called God's software that is no longer possible to upload files to the internet server.

Most recently packages like Wordpress are on the market, but I would like to manage the web with traditional pages and FTP. Since Pages can be converted to PDF and ePub files, I can just upload them without using HTML. However, the need for simple HTML does not decrease.

Precisely, my MAC server has no HtML editor. Editors purchased so far are not compatible with MAC. It's costly to purchase again. So I bought a cheapest editor, FTP on the Go pro for iOS.

HTML editing is to be done on the iPad. Luckily, editing work became possible even in bed. This tool was useful. However, this tool is still running normally on the iPhone. It seems that maintenance has not been done for more than six months against iOS update.

I have written trouble information to Application store, but no response from the developer.

At any late, I attempted to access the developer's Internet site, but I could not. The site may have already been deleted. It is really irresponsible that support for paid applications isinterrupted without notifying users.

If Apple's Pages has an Export feature to HTML file, I don’t need to purchase an additional HTML creator. However, at the moment HTML editing is not possible on my iPad, but I can still write HTML tags with the TEXT editor directly. So converts TEXT files to HTML files sing Notepad, then upload it using the FTP function of Good Reader which is called another application of God. It takes time and effort, but I am able to manage to keep working.

- Dec 1, 2018

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