The magic, myth and math of magic squares | Michael Daniels | TEDxDouglas

Summary

The script explores the fascinating world of magic squares, dating back 4,000 years to Chinese legend, where they were believed to possess mystical powers. It delves into the Lo Shu square's significance in Chinese culture and its unique properties, such as the magic constant of 15. The script also discusses the intricate Janana square from Northern India, known as the most perfect magic square, and its diabolical intricacy with 52 ways to obtain the magic constant of 34. It touches on the historical use of magic squares for protection and in art, exemplified by Albrecht Dürer's Melencolia I engraving, which contains a magic square. The narrative concludes with the Siamese method for constructing magic squares, emphasizing their historical and mystical importance.

Takeaways

• 🔢 Magic squares are mathematical constructs where the sums of the numbers in each row, column, and diagonal are equal, known as the magic constant.
• 🐢 The concept of magic squares dates back to ancient Chinese legend, attributed to Yu the Great, who saw a pattern on the back of a tortoise, which is called the Lo Shu.
• 🧙‍♂️ Magic squares have been used in various cultures for mystical and protective purposes, such as in temples and as amulets for good luck and warding off evil.
• 🌐 The Lo Shu square is significant in Chinese philosophy, with its numbers arranged to represent the yin and yang principles.
• 💠 The 'Jana' or 'Chaisa Vatra' square is a 5x5 magic square with a magic constant of 34, notable for its intricate properties, including sums of 2x2 groupings within the square.
• 🎨 Albrecht Dürer incorporated a magic square into his engraving 'Melancholia I', which may symbolize a conflict between imagination and reason.
• 🔮 Cornelius Agrippa, a German occultist, published magic squares and attributed them to different planets, suggesting they could be used in rituals and to invoke powers.
• 🤹‍♂️ The 'Siamese method' is a simple technique to construct odd-order magic squares, which involves starting in the middle of the top row and moving up and right, with specific rules for when to move down or to the other end of a row.
• 📚 Agrippa's influence extended to figures like Dr. John Dee, and his work 'Occult Philosophy' circulated in manuscript form before its publication.
• 🤔 The speaker suggests that Dürer may have intentionally altered Agrippa's magic square in his engraving to avoid creating a pan-magic square, which might have been considered too powerful.

Q & A

What is a magic square?

A magic square is a grid of numbers where the rows, columns, and diagonals all add up to the same total, known as the magic constant.

What is the significance of the Lo Shu square in Chinese culture?

The Lo Shu square is significant in Chinese culture as it is believed to have been inspired by a pattern seen on the back of a giant tortoise. It is associated with the steps of Yu, the founder of the Xia Dynasty, and is used in religious practices and architecture for protection.

What is the magic constant of the Lo Shu square?

The magic constant of the Lo Shu square is 15, which is the sum of the numbers in each row, column, or diagonal.

How does the arrangement of numbers in the Lo Shu square relate to Chinese philosophy?

In the Lo Shu square, the odd (yin) numbers are placed in the corners, and the even (yang) numbers form a cross in the center, reflecting the balance of passive and active forces in Chinese philosophy.

What is a pan-magic square?

A pan-magic square is a type of magic square where not only do the rows, columns, and diagonals add up to the same total, but also every 2x2 grouping within the square adds up to the magic constant.

What is the significance of the number 34 in the Jana (Chia-Sa-Vatra) square?

In the Jana square, the number 34 is the magic constant, and it is significant because it can be obtained in 52 different ways from the square, including the sums of the 2x2 groupings.

What is the connection between the magic square in Albrecht Dürer's engraving 'Melencolia I' and Cornelius Agrippa?

Albrecht Dürer's magic square in 'Melencolia I' is believed to have been inspired by Cornelius Agrippa, a German occultist. Agrippa's influence on Dürer is evident in the engraving, which includes a magic square similar to one published by Agrippa.

Why is it impossible to create a 2x2 magic square?

A 2x2 magic square is impossible because each number in the square must be unique, and with only four cells, it's not possible to have different sums for the rows, columns, and diagonals.

What is the Siamese method for constructing odd-order magic squares?

The Siamese method for constructing odd-order magic squares involves starting in the middle of the top row, moving up and right, and if you cannot move up and right, you move to the end of the row and then down. If you move out of the square, you go to the opposite end of the row.

How were magic squares used in the past?

Magic squares have been used for various purposes in the past, including as protective symbols in buildings, as amulets for personal protection or healing, and in rituals to invoke the powers of the planets or summon supernatural beings.