How would you answer if asked "How to eat a donut with only a hole left?" If you eat donuts, there is nothing left, not holes, and it's impossible to leave only holes. I wonder if such a question would react as stupid.

However, what should I do when I doubt the common sense here and, based on the knowledge of the academic discipline, "Is that really true?" The real pleasure of learning is that it overturns what everyone has taken for granted. In that sense, facing the question of "leaving only donuts in a hole" is the highlight of academic power.

The fields of researchers who have tackled this problem are diverse, including engineering, aesthetics, mathematics, history, and anthropology. I am amazed at how they face each other. "Is there a hole in the donut in the first place?" "Is the donut the modern nation itself?" Just say that. It wasn't something weird at all, but the result of pouring our findings into the “hole of the donut”.

Actually, this question is one of the standard stories in the discussion on the Internet. The fact that this topic has survived on the Internet, where information is repeatedly evolving and evolving, can be said to be the indication that new values ​​are being discovered through discussion. What kind of world can we see if we seriously tackle such "stuff" from an academic standpoint? Why don't you learn the essence of ideas and thoughts out of common sense from unique records of intellectual fighting?

Main points of this book


It's impossible to "eat a donut leaving only a hole." The real pleasure of learning is to doubt such common sense and overturn what everyone has taken for granted.


An engineer thinks about the limits of engineering cutting and considers various methods. Also, one aesthetician considers the holes in the edible donuts as "ideals" that never go away.


One mathematician claims that a four-dimensional space can leave a donut hole. On the other hand, in history, there are approaches that question the premise that "a hole is in the donut".

[Must read point!] To eat leaving only holes

Engineers "shave donuts"

In this summary, we will introduce some of the points from the content discussed by researchers in each faculty. First is engineering.

As a person involved in engineering, Takashi Takada, an associate professor at the Graduate School of Engineering, Osaka University, said he received the problem from the front when asked, "How to eat leaving only a donut hole." Specifically, after grasping the inner shape of the donut accurately, think about the limits of engineering cutting.

What kind of method can be used to cut donuts with high precision? With mouth and teeth, accuracy is limited to a few millimeters at best. Even if you use scissors or a knife, the accuracy will be about 1 mm at best.

What if you next try machining? What is effective is to soak the donut in a resin or the like to solidify it. It is no longer food at this point, but if you close your eyes, you can aim for about 0.1 mm by lathe processing. In addition, ablation processing, in which a laser is focused and irradiated for a short period of time, should reach the limit of several tens of millimeters.

If you pay attention to the point of "leaving only holes", you can use the method of "sputtering" instead of cutting. The surface of the donut is coated with a thin metal, and then the donut ingredients are dissolved with an organic solvent. This leaves a "hole" covered with a very thin coating.

In this way, there are various engineering methods even for the simple work of “cutting” and “cutting”. And there are many points to consider depending on the nature of the material.

Aesthetics Think "Donuts are Homes"

The essence of the academic field of "aesthetics" lies not in what we study, but in what we consider and what we consider.

According to Hitoshi Tanaka, an associate professor at the Graduate School of Letters, Osaka University, from an aesthetic standpoint, he would doubt about the premise that eating donuts would eliminate the holes in the donuts. This is because the edible donuts that actually exist are not the "doughnuts themselves". Even if you eat donuts, the only concept of "donuts" does not disappear. Since you can't eat "the donut itself," you can answer that the hole will never disappear.

From an aesthetic point of view, it is possible to focus on the aspect that "people can express various feelings" from the space of holes left after eating real donuts. The smell and taste of the donut in front of you will bring back the memory of the donut you ate before. The sweets that are familiar like donuts are likely to be easily tied to the space and home protected by love. In other words, it is possible to draw the conclusion that a donut is "a house" because of the existence of the hole.

Mathematicians formulate "leave a hole"

From a mathematician's point of view, how do you deal with the topic of "how to eat leaving only a donut hole"? According to Hideki Miyaji, an associate professor at the Graduate School of Science, Osaka University, it's simply not possible. In the world of mathematics, impossible is a very heavy word.

Originally, in mathematics, it is possible to delusion of anything as long as the thinking is developed according to the rules of logic. Therefore, by mathematically formulating a word such as "leave a hole," we can find hope that a solution can be found.

For example, let's say you can put a donut in a space called 4D. We usually live in a three-dimensional space in which we can recognize three essentially different directions: front and back, left and right, and up and down. The 4th dimension is another space with more axes that can move freely.

To recognize a donut hole, you need to make a ring through your finger and recognize that you cannot remove the finger and donut like a ring of wisdom. Here, let's define the "hole of the donut" as the gesture that keeps the fingers away from the donut. Then, the title of "how to eat leaving only the donut hole" can be translated into the title of "can you eat the donut while your friend recognizes the hole of the donut?"

If your friend loops his finger through a hole in a donut, the fourth dimension lets you eat the donut without touching his friend's finger. Here, we use a logical trick in the field of low-dimensional topology: "Two entangled rings can always be removed in four-dimensional space." This is one answer to the topic of eating donuts leaving only holes. Thus, in mathematics, logical thinking is free.

Learning from donut holes

Psychiatrist finds ideal in donut hole

The strange thing about human mental function is that reason and irrationality coexist. A person's heart wants resonance with the hearts of others. Nevertheless, you cannot pin a person's mind like a specimen. At the moment you think you're caught, you slip through your fingers and run away.

What does the human heart want in the first place? According to Yoichi Inoue, an emeritus professor at Osaka University and a doctor of medicine, it may be like a donut hole from a psychiatric and humanistic standpoint. With the donut hole, the road above the donut continues infinitely. We are travelers who circle around the hole. The existence of a hole gives us a glimpse of infinity in a finite life.

We humans are always trying to overcome the present, secure freedom, and hold on to the possibilities. And it is the passion and ideal to break through finiteness and go to the unknown that has moved humans and developed civilization so far. It is the ideal that sustains the hearts of people, and the last that remains even if all reality and materials change. It's like a hole in a donut that remains after the donut has been eaten. It's not the donut holes that disappeared when you bite the donut. The surrounding walls have disappeared. Just as the hole itself does not disappear, the ideal in the mind of a person does not disappear.

Historians suspect that donuts have holes

The essence of history lies in the perspective of things. Depending on how you look at it, the way you perceive and understand that object will change. So how do historians face the challenge of "how to eat leaving only a donut hole?"

According to Yoneyuki Sugita, a professor at the Graduate School of Languages ​​and Cultures of Osaka University, there are two approaches to history. One is a microscopic approach that deeply analyzes the given assumptions as correct ones. The other is a macro approach, in which the given premise itself is viewed with suspicion and a new perspective is devised.

Now, let's consider the question "why donuts have holes?" with a microscopic approach to history. At this time, two interpretations emerge: "creed (ideology)" and "concrete interests". The former interpretation suggests that the donuts may have been pierced as a means of showing patriotism and loyalty. With the latter interpretation, I think that someone may have made a hole because it gained politically and economically.

On the other hand, in the macro approach, I try to doubt the premise that "a hole is in the donut". This creates a different interpretation. In other words, the attitude of "seeing everything, including implicit assumptions, with suspicion" can be said to be the basis of academic learning.

Learning from donut holes

Chemists challenge environmental problems with "doughnut-shaped oligosaccharides"

As an application section, I will briefly introduce the research conducted by Associate Professor Toshiyuki Kida, Department of Applied Chemistry, Graduate School of Engineering, Osaka University. Mr. Kida is developing high-performance materials that are friendly to people and the environment.

So, we are using "cyclodextrin", a cyclic oligosaccharide made from starch. This material is shaped like a donut, about a billionth of a meter. This donut substance can take other substances into its hole by the action of "inclusion". Furthermore, the substance taken in the hole can be released by the action of "release". For example, commercially available deodorants utilize the action of inclusion of malodorous substances by cyclodextrin.

The size of the donut hole, or the ring of cyclodextrin, determines the substance that can be included. Therefore, chemists have established a technique to cut one part of a donut ring and insert another part into it, enabling inclusion of various substances. In addition, the inclusion effect has been realized even in oils that were thought to be impossible in the past. It is also expected to be useful in treating oils that are toxic.

Cyclodextrin is an environmentally compatible functional material that has little impact on the environment and has both recyclability and biodegradability. By exploiting this new function and making more effective use of its holes, we can contribute to the development of science. Furthermore, it is believed to help revitalize Japanese industry.

Judicial scholars look for precedents related to "donuts"

The starting point of law is the articles of law and the precedents. The reason for examining the precedents is that following the rules precedes justice, legal stability, and purpose. If there is no good reason to leave the precedent, it is safe to follow it.

Kunihiko Okubo, a professor at the Graduate School of International Public Policy, Osaka University, found the "Donut Case" by searching laws and court cases with "Donut" as the keyword. In this case, the meaning of "donut" was contested in court. Companies in the bedding industry argued whether the defendant's "donut cushion" mark infringed the trademark rights of the plaintiff's "donut" logotype. As a result, the court did not recognize the trademark infringement, the plaintiff lost the case, and the defendant won.

Here is the point of the judgment of this case. Donuts for Western confectionery can have various shapes. However, in the case of donuts used like "doughnut pillows" and "doughnut chairs", it usually means a circular or ring shape with a hole in the center.

Assuming donuts with a shape other than a ring shape, a new horizon will be opened for "how to eat donuts leaving only holes." For example, make a round donut with no holes, call the central part a "hole", and leave only that part for eating. That would legally leave only a hole for the donut.

Recommendation of reading

Students at Osaka University make plans and manuscripts written by various researchers are redlined by the students themselves. This book is a paperback edition of a book that was born from such original efforts. The authors include humanities and science researchers, as well as cross-disciplinary research. It is difficult for professional editors to put together manuscripts written by such diverse authors into expressions that anyone can understand.

In the production of this book, a group of librarians and science students read the manuscript in pairs and thoroughly discussed what they do not understand and how to express it in the form of a request for correction to the author. It is said to have returned. One such aspect of this book can be seen as embodying the university's mission of "exploring the truth in a community of researchers and students." It also teaches that learning is essentially about tackling problems for which you do not know the answer. Business people who struggle everyday with unanswered questions can learn fresh perspectives and ways of thinking.