Tiered Ties; Why The Five is Mathematically Odd and Untouchable, Euclid, and Initiation

The Five is an institution that gathers scientists and intellectuals in our country. If the total number of members of The Five is compared to the total population of the country of Deutschtonia, the ratio is very far off. The Five members number a maximum of 216 people, which is 0.00027 percent of the population of Deutschtonia, which is around 80 million people.

To be able to become a member of The Five, you must meet very strict requirements. There is an unwritten rule that applicants must have at least two postgraduate degrees in two different fields. Of course, other aspects besides academic aspects are also taken into consideration.

I have three academic degrees at the postgraduate level. The three degrees are symbolic systems, aerospace engineering, and history and philosophy of science. Symbolic systems itself is an interdisciplinary degree that includes the disciplines of computer science, linguistics, mathematics, philosophy, psychology, and statistics.

As for non-academic aspects, I have the skills to be a story writer and comic creator. I have published one comic that has achieved satisfactory sales. Satisfactory here means that the royalties from the comic are equivalent to about two weeks of my salary. I decided to donate 54 percent of the royalties to a non-governmental organization engaged in education and literacy.

The title of the comic is "Tiered Ties." The comic is aimed at readers aged 18+. The mystery and thriller genre comic includes many mathematical topics, especially regarding knot theory and graph theory. The comic was one of the topics of my conversation with Mrs. Rostand at the end of December last year.

I still remember one of the sentences Mrs. Rostand said at that time, "Knowing that there are two hundred other people like Mr. Schonewolken in The Five, it is not strange that The Five is called an odd and untouchable institution. Even mathematics calls it that way."

The meaning of 'mathematics also calls The Five odd and untouchable' is because in mathematics, there are terms for odd numbers and untouchable numbers.

For odd numbers, I think since childhood, many people have known that the number five is an odd number. Odd numbers are integers with the form n = 2k + 1, where k is an integer. In other words, an integer is an odd number if it is not divisible by 2. 5 is not divisible by 2; therefore, 5 is an odd number.

An untouchable number is a positive integer that cannot be expressed as the sum of all proper divisors of any positive integer. In other words, these numbers are not included in the aliquot addition function. Because we are using aliquots, the calculation of the untouched numbers must use the number 1 as one of the numbers in the addition operation.

For example, the number 7 is not untouchable, as it is equal to the sum of the proper divisors of 8: 1 + 2 + 3 = 7. Meanwhile, the only way to write 5 as the sum of several positive integers, including 1, is 5 = 1 + 4. But if we use the number 4, the factor list must contain 4 and 2. Because if 4 divides a number, 2 also does. So, 1 + 4 cannot be the sum of all of any number's proper divisors. Therefore, 5 is an untouchable number.

The existence of these untouchable numbers has been a research topic for mathematicians since ancient times. A mathematician named Abu Mansur ibn Tahir of Baghdad, who lived more than a millennium ago, studied the existence of untouchable numbers. I remember that information from papers and lectures from one of my previous lecturers named Mr. Jacques Sessionsano.

It should be noted that the maximum number of members of The Five is 216 people. The number 216 itself is one of the untouchable numbers. However, 216, like other untouchable numbers, is an even number. In comparison, the number 5, to date, is the only untouchable number that is also an odd number.

The number five is the number of sides of the shape that is the logo of The Five. Yes, we use the five-sided polygon shape, aka a pentagon, as our institutional logo. The pentagon that we use has the same interior angle of 108° and also has the Schläfli symbol {5}. It's an equilateral and equiangular pentagon. Or, in simpler terms, we use a regular pentagon.

On the bottom line on the inside of the regular pentagon of the Five symbol, there is the writing "DIE FÜNF.” The writing means “The Five” in Deutschtonia. Meanwhile, on the other four sides of the pentagon in sequence, there are words that will read "CRESCAT SCIENTIA VITA EXCOLATUR." The words are from Latin, which is one of the ancient languages. These four Latin words have become our official motto and have the meaning "May knowledge grow and life be enriched."

Five and pentagon were chosen to be related to The Five because of the names of two ancient mathematicians, Euclid and Plato.

Five is a symbol of the five postulates and five common notions from Euclid's famous book, entitled The Elements. From these basic things, Euclid developed them into many constructions of geometric shapes. It fits our motto of wanting to develop knowledge.

When someone is inaugurated as a member of the Five, they must perform certain procedures. They will perform the inauguration ceremony for the Five at the Five headquarters. The ceremony is held in a room called the “Einleitung” room or “Initiation” room.

I think the ceremony is not complicated but rather very enjoyable. We only need about ten minutes to complete the entire procedure. For me, the most interesting thing is when the prospective members practice the movement of making geometric shapes from Proposition 11 of Book IV of Euclid’s Elements with a giant compass and a giant protractor.

Proposition 11 of Book IV of Euclid’s Elements discusses how we can write an equilateral pentagon and an equilateral pentagon in a given circle. The circle is a symbol of the Earth. While the pentagon, of course, is a symbol of the Five. What's the meaning of that? You can guess for yourself, right?

I performed the ceremony in the living room of the Five headquarters on the first floor, witnessed by several people who were already members of the Five. Of the three floors in the Five's headquarters, the central room on the second floor is used as the Einleitung room for the High of Five or Big Five members. The central room on the third floor is the meeting room for the five Big Five members.

Just like the initiation chamber on the first floor, the central rooms on the second and third floors are also related to the pentagon, mathematics, and philosophy. But that's a story for later, okay?

Speaking of the initiation room, you could say the room is located in the middle of our country. The room is located in the middle of the Five central headquarters. While our central headquarters is located in a place named Niederdorla. Niederdorla is none other than the geographical center and geometric center of the Federal Republic of Deutschtonia.

The geometric center itself has other names, namely ‘centroid’ and ‘center of figure.’ Therefore, Centroid and Center of Figure are other nicknames for The Five. Although the nickname most widely used by the public is, of course, ‘odd and untouched.’

Speaking of nicknames, High of Five is an unofficial title. Officially, every member of High of Five is given the title of ‘Wissenschaftsfeldmarschall,’ which means ‘science field marshal.’