Book 31. In proof by contradiction that √2 is an irrational number, if √2 were a rational number, then that rational number would be uk/2t²

 Hello. This is β (Beta). This time, I'd like to write about proof by contradiction. I'll be quoting from "Proving the world's most beautiful mathematical formula, e^(iπ)=-1".

"√2 is not an irrational number."

√2 = m/n ...① (m and n have no common divisors other than 1). Multiply both sides by n and square.

2n² = m² ...②. m² is a multiple of 2. If m is not a multiple of 2, then m² cannot be a multiple of 2.

m is a multiple of 2.

m = 2k (where k is an integer) ...③. Substitute this into ②.

2n² = 4k². n² = 2k², and n² is a multiple of 2.

n is also a multiple of 2...④. From ③ and ④.

m and n have 2 as a common divisor. This contradicts statement ①.

√2 is an irrational number. (Quoted from the above book)

From here on, these are my ideas. In conclusion, the point that m and n have no common divisors other than 1 is that m and n are relatively prime, that is, m and n are prime numbers or relatively prime composite numbers. In other words, from here on, we will consider cases other than when m and n are prime numbers or other cases where they have no common divisors other than 1.

Furthermore, if √2 can be a rational number, then √2 = (uk)/(2t²). In other words, if √2 can be a rational number, then √2 = composite number / (2 x squared expression).

The assumption that m and n have no common divisors other than 1 is based on the assumption that m and n are prime numbers, isn't it? Now, if we replace n and m with N and M, and set N=n/t and M=m/u, then by proof by contradiction we can see that √2=(uk)/(2t²) is a rational number equal to √2.

The equation √2=m/n assumes that both the numerator and denominator are prime numbers. However, if √2 is a rational number, then we can see that uk is a composite number and 2t² is a squared expression. The method for finding √2=(uk)/(2t²) will be explained in detail later. (Life Lessons).

Find the value of √2 as a continued fraction close to (uk)/(2t²). (Visual confirmation)

page 7!!The secret to consistent success is a deep love for practice!? We want to do what we have a natural talent for and what we absolutely love

Hello. This is Ten Watanabe. Today's theme is "The secret to consistently winning is that you absolutely love practicing." Consistently winning. Hmm. I think there are two patterns to the word "win." The so-called founding and maintaining.

First, you need to start by aiming to be number one. Anyone who aspires to be number one starts out as a beginner. Isn't it common for people entering any industry to begin with menial tasks as a kind of apprenticeship?

In general society, whether at school or at work, senior colleagues will teach you a lot at first. They should explain the bare minimum necessary things once you enter that industry.

I believe that what I learned from my seniors is also important. They patiently taught me the traditions that have been passed down for a long time, and by faithfully following them, a certain level of quality can be ensured.

I recommend imitating the most skilled senior you encounter. If that senior is kind, they will likely teach you the secrets to being the best in detail. Don't jump to conclusions and assume they won't tell you such important things right away; the quickest way to learn is to ask them repeatedly, humbly but not persistently.

If you meticulously imitate the teachings of your most senior colleague, you will eventually be able to achieve results and may even become the top player in that industry.

At that point, instead of becoming complacent and thinking "it's all good now that I'm number one," it's important to accept that the founding phase is over. Becoming number one means you've founded your business, that is, you've launched your own brand.

People passing by will praise you when they realize you're number one. Being showered with praise like that might make you think you're already number one without even trying. However, once you've achieved being number one—that is, founding your business—the next step is maintaining it.

You often hear about title defenses in boxing and other sports. When you become the best among a group of people in a certain weight class, you then have to maintain that top position. Defending a title means successfully holding onto the title of being the best among the people in that designated weight class.

Which is more difficult, starting a business or maintaining it? Which is more important, becoming number one or maintaining the number one position? I believe that the reason why people who become number one can't maintain it is because they are too complacent with themselves.

Those who endure rigorous and grueling training, restrict their diets, refrain from leisure activities, and maintain a serious and stoic attitude, can sometimes gain unimaginable wealth and fame by becoming number one.

Therefore, some people use that money and prestige to neglect their rigorous training and start having fun. No one, being human, can endure training without a clear goal. After achieving the goal of becoming number one, many people lose sight of their next goal and instead pursue whatever they want.

If you continue training with the same stoicism you used when you were number one, you're unlikely to lose your top position. However, not many people strive to maintain their number one position. In other words, even if you become number one, if you become complacent, you won't be able to maintain it and will lose to those who are working hard to become number one.

At the top level, there's probably not much difference between the first and second place finishers in terms of physical and intellectual abilities. Therefore, a slight difference in practice time can be the deciding factor. However, those who have approached practice as a chore will find it difficult to maintain their position even after reaching the top, as they will have to continue that grueling training indefinitely.

Of course, some people who aim to be number one absolutely love practicing. When you're doing something you love, practicing after becoming number one isn't a chore; you'll proactively and voluntarily engage in training.

I believe the difference between someone who ends up being number one and someone who can stay number one is whether or not they enjoy practicing. In the end, the simple answer is that you can't beat someone who is doing what they love.

No matter how much you practice or how long you practice, you can never beat someone who enjoys the process and doesn't see the effort as hard work, because they are always the one who actively dedicates time to it.

You could say that's just his natural talent, but no one can beat someone who is having so much fun. It might take time for someone who is having so much fun to beat someone who practices hard for long hours, but once they become number one, they can just continue practicing with the same enjoyment as always, and that's what makes them strong.

Those who believe that professionals must practice even when it's not fun lack a certain perspective: they cannot compete with professionals who have never once felt that practicing was not fun.

Ultimately, the best story about starting and maintaining a business is about wholeheartedly enjoying what you love to the fullest throughout your life. Even if someone becomes a professional because they're better at it than others, even if they don't particularly love it, they can't compete with a passionate enthusiast who finds it incredibly enjoyable. The professional world is teeming with talented enthusiasts.

If we want to be number one, we first do something we have a knack for. If we want to maintain that number one position after becoming number one, we do something that we have a knack for and that we absolutely love. Perhaps the secret to founding and maintaining a business lies here. I hope you find something you can dedicate your life to and that you absolutely love. That's all. Thank you. Ten Watanabe.

Book 30. A 20x giver! If you consistently split the bill in roughly a 5:95 ratio, you'll be welcomed wherever you go

Hello. This is Beta from the R86plusA blog. I'm interested in the distribution system that exists in human society. In human society, the share is often taken by the organizer, the person who hosted the event.

I know people who split the bill in a way that's close to a 5:5 or 4:6 split. The important thing is that when you split the bill, it feels fair. If it's 8:2 or 9:1, dissatisfaction will naturally arise. No matter how excellent a company is, I believe that companies that hoard profits and don't distribute them to many people will decline.

I believe splitting the bill is fair. This is because it allows the other party in a transaction to know that they are on equal footing. However, even when we say "equal," I think it's often asymmetrical. In other words, instead of playing the same role and doing the same amount of work, each person has a role to play—this person contributes labor, this person contributes money, and so on. In a cooperative relationship, each person naturally brings out their own strengths.

Lately, I've been reading a book called "Lectures on Celestial Mechanics" by C.L. Siegel, J.K. Moser, et al. If we were to read this book collaboratively, we would need to assign specific pages and sections to each person and fulfill our respective roles. One person might cover the first 50 pages, and another the 50th to 100th pages, but there are many other ways we could cooperate. We could teach each other the parts we understand, and the possibilities are endless.

The lectures on celestial mechanics are a book I find incomprehensible, but they begin by describing a special method of differentiation called the Lagrange multiplier method. Many people may get stuck at that point, so if I have the opportunity, I would like to help everyone by explaining the Lagrange multiplier method.

I'm also a bit of an unusual person, studying quantum mechanics and celestial mechanics, but with a little ingenuity, even books that seem difficult to me can be read. Since we were talking about splitting the bill, I'd like to give you a small gift.

When reading, imagining drawing diagonal lines between words makes it easier to understand. It's surprising how much easier it becomes to read just by quickly drawing diagonal lines between words. I know that celestial mechanics is one of the most difficult subjects in academics, so I remember being very happy when I came up with this slash reading method.

It makes me happy to see people move on to the next stage of their lives with their inherent optimism and determination, and I remember feeling that same sensation when I read using this slash reading technique. I believe that by learning about slash reading, you too can take a step towards the next stage with your own inherent optimism and determination.

Now, regarding the shares, I think 5:95 is not bad. 5:95 means giving almost 20 times your share. In other words, you are a 20x giver, and in this case, since I didn't receive anything from the readers for teaching slash reading, I think I achieved a 20x gift by teaching them about slash reading.

I don't need anything in return. All I'd really appreciate is a simple click on an ad I put on my blog. After all, I believe gifts are very important in human society. When you receive a lot of things, people are watching to see if you can generously share them with others.

I'm the type of person who gives presents, and I don't receive many, but I know how happy it makes me when I do. In fact, I often give material gifts, like sweets, and the recipients often show their thoughtfulness and consideration through their gifts.

While I'm currently offering slash reading as a gift, even just celestial mechanics is an extremely complex subject, and I think mastering it is incredibly difficult.

Furthermore, if I were to offer a gift to my readers, I would like to include an article explaining how to solve problems using the Lagrange multiplier method, specifically this special method for solving differential equations, if you purchase this book on celestial mechanics and study with me.

Ultimately, society is a reciprocal, gift-giving society. Even considering employment alone, being employed by a company can be seen as a cooperative relationship between someone who gives their labor as a gift and someone who gives their salary as a gift.

I am writing this article on April 14, 2026. The number 14 is very important to me. I won't go into personal reasons, but I believe it is a number related to God. As God's number. However, I am very glad that I was able to write about the subject of celestial mechanics lectures, which is a mysterious area for me, on this day, the 14th.

The next installment of this article will be an explanation of the Lagrange multiplier method, a truly essential technique. That's all for now.

If you consistently split the bill in roughly a 5:95 ratio, you'll be welcomed wherever you go. Don't think of it as a one-time cooperative act, but rather as a cooperative act that happens dozens or even hundreds of times. Even if your share is 5%, you'll have the opportunity to earn dozens or even hundreds of times that amount. More than that, I believe you'll be valued and treated with great respect by your friends.

That's all. Today, I taught you about slash reading. I don't want to sound condescending, so I'll stop here. Thank you for listening. This was β. See you next time. α.

Book 29. A person who is a manager. What is its purpose? It is the purpose of management to keep asking this question.

 Hello. β (beta). This time, I would like to write about the profession of manager.

When you think of a manager, you may think of a middle manager, but management can be said to be the president's job. Furthermore, it is the job of a manager. The most important thing in my job is to observe management.

When it comes to management, it seems that it is normal for middle managers to give instructions and subordinates to act according to instructions. In order for a subordinate to be a subordinate, a boss must be a boss. In order for a subordinate to surpass his subordinates, he must surpass his superiors and exceed his superiors' instructions.

The boss's accurate instructions motivate and motivate the subordinates, but the boss must take responsibility for the actions of the subordinates. The actions of subordinates must reflect the instructions of their superiors, but they must also be able to act beyond subordinates. Only when a subordinate quits a subordinate can he succeed as a manager.

However, raising subordinates is difficult, and the will of the boss must be reflected. Otherwise, they will lead their subordinates to a difference in direction, a dichotomy, and even self-destruction. Raising subordinates means going beyond subordinates, beyond superiors, and increasing autonomy to the point where they understand the boss's wishes.

In order for a subordinate to be a subordinate, he must become the boss's right-hand man, the boss's shield, and the boss's spear, and bring him to a state where there is no contradiction. If I were the boss, the instructions I give to my subordinates are a general agreement, not a detailed process.

A rough agreement is enough to communicate with subordinates on a regular basis, and more importantly, there is a relationship of trust, but I don't think a boss who ends at a detailed process will never be a big success. It can be said that it is the duty of the boss to fulfill his responsibilities in an emergency, just as the boss is the boss, without imposing responsibility on the subordinates.

I wrote that when a subordinate quits a subordinate, it is a great achievement as a manager, but I think one theme can be what happens to the subordinate or the boss when the boss quits the boss. The boss cannot surpass the boss.

Because the boss is only the boss. Beyond that, when you quit your boss, your organization will be automated. Autonomous forces work in the organization, and the organization becomes an organization beyond the organization. Even without a boss, the organization is formed into a state of activation.

One of the points of achievement as a boss is when you quit your boss and automate the organization. That is one of the points to achieve, and it is something that every good manager has tried. What goes beyond that point and now goes beyond that is to create a new organization.

When you automate your organization beyond your boss, the new challenge will be to shape a new organization. This emphasis is the original job of the manager, and it can be said that it is the reason for the existence of the manager to be a manager.

If I were to become a manager, it would be said that management is to shape a new culture, civilization, or world, and to be a part of the wheel of it. The reason why I think this part is important is that as we move into a new era, society will become more sophisticated and shape a new era.

Each organization does not exist from the beginning, but when an organization is established, its dynamics lead to an automated mechanism. On the basis of an automated system without a founder and manager, the dynamics of the founder and manager will turn in a new direction to create a new organization.

And if the new organization is automated, it is the original role of the manager to steer the foundation and training of the new organization. The role of the manager is never to make the organization bigger. It is the role of executives and bureaucracy to make the organization bigger.

Beyond that, managers create something out of nothing. It can be said that the creation of new things is the responsibility of the manager, whether it is an organization or a product. Originally, the manager should be the boss.

When a subordinate quits a subordinate, the subordinate becomes the boss. When the subordinate becomes a boss, he needs to quit his boss. It is the responsibility of the boss to give autonomy to his subordinates, transfer responsibilities, and form an autonomous organization.

If you get to that point, leaving the rest to the younger generation and moving to a new organization is proof of your existence as a manager. I think that a manager is a manager. In order to become a manager beyond a manager, the main focus is on mastering the realm of creation beyond several processes.

A person who is a manager. What is the purpose? There is no chance of winning for managers who do not see their purpose or for the organization. What is the purpose? It is the purpose of management to keep asking this question. And that's it. Thank you for your growth. It was β.

page 6! One suggestion I would like to make is to speak with the strength of the tongue, and if you are a good singer, you know that if you sing with the strength of the "throat Buddha", you can sing a clear song -R86plusA-

 Hello. This is the Ten Watanabe of the R86plusA blog.

There are people who have a bad tongue and find it difficult to listen to them when talking. I have had several experiences where I thought it was difficult for elderly people to listen to them, perhaps because of their dentures.

The fact that the tongue is not smooth and it is difficult to hear what is being said is a disadvantage for both the speaker and the listener.

One suggestion I would like to make is to speak with your tongue. If you are a good singer, you know that if you put effort into singing "Nodobutsu", you can sing a clear song.

However, the problem here is not the "throat", but the "tongue". I think that people who have difficulty hearing their voices probably don't have strength in their tongues.

Therefore, by practicing vocalization while putting effort into your tongue, it will be easier for the other person to hear you.

Even when singing, if you not only focus on the "throat Buddha", but also on the "tongue", you can go to the next stage one step further.

If you can't get your voice to be understood, why not try various things by focusing on your throat and tongue?

page 5!! There is a famous story about how many times you need to fold paper to fold 1mm paper and cross Mt. Fuji, and the answer is 22 times -R86plusA-

 Hello. This is Ten Watanabe of the R86plusA blog. Computers need to think about memory, which is the amount of data.

Until now, there have been various digital media such as blogs, audio media, and images, but the mainstream these days is still video distribution. Videos are informative, and you can get a lot of information at a glance.

On the other hand, there are also limitations in data capacity, and a single video can be very large as data, such as hundreds of megabytes.

Even if the computer itself has a lot of terabytes (1 million times 1 megabyte), if you take and store many videos, the memory capacity will naturally decrease. However, if it is a text file with only text written on it, it often takes only a few kilobytes (1/1000th of a megabyte).

Here, let's review the part-time job. 1 kilobyte = 1024 bytes, 1 megabyte = 1024 kilobytes, 1 gigabyte = 1024 megabytes, 1 terabyte = 1024 gigabytes.

By the way, the reason why it is 1024 instead of 1000 is that computers represent data only with the numbers 0 and 1 called binary numbers. Therefore, the capacity of data such as the power of 2 is easier for a computer to handle.

Multiply 2 to the power of 10, that is, 2 10 times, to get 1024. There is a famous story about how many times you need to fold paper to cross Mt. Fuji by folding 1mm paper, and the answer is 22 times. It might be interesting to do some math on this yourself.

The power of 2 is an exponential increase, and if you multiply it by 2 100 times or 1000 times, it becomes an astronomical number.

When it comes to cryptography, which is computer security, this idea called exponential has become the mainstream today, and exponential cryptographic digits are realized.

page 4! If you are asked to shop without any trouble, you will not accept it obediently, and at least let me buy at least one of the sweets -R86plusA-

 Hello. This is Ten Watanabe of the R86plusA blog. There is a formula that says income - cost = profit.

The idea of income is generally based on production (quantity) x price (price) in economics.

However, in the real economy, it is absolutely not possible to sell all the quantity produced as it is, so it seems that the general income formula is to use sales quantity x price.

If all the products can be sold, you will mass-produce Mercedes-Benz.

So, in this case, if the sales quantity is Acheieve x (Ax) and the price is price(p), it becomes pAx. As for the cost, the production volume is multiplied by the cost per unit, so it is production volume (x) x marginal cost (MC).

So, if you become an enlightened monk who says that you don't need profit, your profit will be zero.

You can't think of zero profit. If you are asked to shop without any trouble, you will not accept it obediently. At least let me buy one of the sweets.

After all, income - expense = profit is pAx-xMC=π. And if the profit is zero, pAx = xMC, and the sales pAx and expense xMC match.

If the production volume is 15 units, the sales quantity is 10 units, and the marginal cost is $5, then p=xMC/Ax, so p=(15×5)/10=$7.5. In other words, if you set the price per piece to $7.5, you will not be in the black or in the red, but the sales and expenses will be the same, that is, zero profit.

Here, the story jumps skyward, but there is a concept called the quantity theory of money in macroeconomics. The formula MV = PT is M: money supply, P: prices, V: speed of money circulation, and T: real GDP.

Here, the person who hits the nail on the head is sharp. If PT = MV, it can be reduced to the formula of income = expense. If p=P, T=Ax, M=x, V=MC, then the two formulas will match.

Furthermore, if we say M: money stock M3, T: real GDP, P: CPI (consumer price index), and V: multiplier effect, the story will expand more and more. The equations pAx=xMC and MV=PT are also related to the IS-LM model of macroeconomics.

From here, through macroeconomics and microeconomics, new ways of thinking will be born more and more.

If you push it further, the formula p = MC is famous in microeconomics, but if P (price) = V (multiplier effect), M (money supply) = T (real GDP).

At this point, we can see that the current money stock M3, which amounts to 1,500 trillion yen, can achieve an efficient economic environment suitable for market principles by matching the real GDP of 550 trillion yen.

As an aside, money stock = credit multiplier x monetary base.

Monetary base = "Bank of Japan bill issuance" + "money circulation" + "Bank of Japan current account".

And that's it. See you then.