A brief history of banned numbers - Alessandra King

Summary

The script explores the historical and cultural significance of numbers, showing how they have been seen as both powerful and dangerous throughout history. It begins with the ancient Greeks, who viewed numbers as keys to understanding the universe, and highlights the controversy surrounding irrational numbers, zero, and negative numbers. It also discusses the political and religious implications of numbers, such as the banning of certain numeral systems and the potential criminalization of numbers that represent sensitive information. Ultimately, the script reveals how numbers, like words, hold power in shaping societies and systems.

Takeaways

• 😀 The pen is mightier than the sword, but numbers have also been historically considered powerful enough to ban.
• 😀 In ancient times, tally marks evolved into more complex numerical systems as societies grew, especially in the context of agriculture and communal living.
• 😀 Pythagoras and his followers believed numbers were the key to understanding the universe, but the discovery of irrational numbers challenged this worldview.
• 😀 Hippasus, a follower of Pythagoras, discovered irrational numbers and was reportedly exiled or even drowned for revealing this 'threat' to Pythagorean thought.
• 😀 The concept of irrational numbers, like the diagonal of a square, was disturbing to philosophers who believed in a perfectly rational universe.
• 😀 During the Middle Ages, Roman numerals were used in Europe, but other cultures, like the Arabs, developed more advanced systems, including a symbol for zero.
• 😀 The introduction of Hindu-Arabic numerals in Italy faced resistance, as they were seen as easy to forge and had associations with the concept of debt and moneylending.
• 😀 In the 13th century, Florence banned Hindu-Arabic numerals for record-keeping due to fears of misuse and unfamiliarity.
• 😀 Negative numbers were dismissed as absurd for centuries and were not widely accepted until the 19th century, despite their mathematical utility.
• 😀 In modern times, certain numbers are banned for symbolic reasons (e.g., politically charged dates) or for their association with encrypted information, like in the case of decrypted DVD codes in 2001.

Q & A

What historical event is referenced to highlight the power of words?

The script references the outlawing of religious tracts, revolutionary manifestos, and the censorship and burning of books to emphasize how words have historically been seen as powerful enough to challenge the social order.

Why were some numbers considered dangerous in the past?

Certain numbers were considered dangerous because they challenged established beliefs or systems. For example, irrational numbers disrupted the Pythagoreans' view of a perfect, rational universe, and numerals from other cultures were initially rejected due to concerns over their potential misuse.

What was the significance of Hippasus' discovery?

Hippasus discovered that some quantities, like the diagonal of a square with sides of length one, couldn't be expressed as a ratio of whole numbers or fractions. This led to the concept of irrational numbers, which were seen as a threat to the Pythagorean view of a perfectly ordered universe.

What happened to Hippasus after his discovery?

Hippasus was reportedly exiled for publicizing his discovery of irrational numbers, and some legends claim that he was drowned by the gods as punishment for challenging the prevailing philosophical beliefs.

Why were Hindu-Arabic numerals initially banned in medieval Europe?

Hindu-Arabic numerals, which included the concept of zero, were banned in medieval Europe because they were easier to forge and unfamiliar to customers. Additionally, the concept of zero opened the door to negative numbers, which were controversial and associated with the recording of debt.

How did zero and negative numbers challenge existing beliefs?

Zero and negative numbers challenged existing beliefs by introducing new mathematical concepts that were difficult for many to accept. Negative numbers were dismissed as absurd well into the 19th century, and many mathematicians avoided using them, even though they would have made certain mathematical problems easier to solve.

Why did some governments ban certain numbers in more recent times?

Governments have banned certain numbers due to their symbolic significance, such as those connected to revolutionary dates or opposition political figures. Additionally, numbers representing encrypted data or proprietary information could be banned because they carry protected or sensitive information.

How did the decryption of DVDs relate to illegal numbers?

In 2001, a code used to decrypt DVDs was shared as a large prime number. This raised the idea that some numbers could be considered illegal if they represented or could be used to decrypt protected information, making the possession or publication of such numbers a potential criminal offense.

What is the relationship between numbers and information in the digital age?

In the digital age, just about any information—whether text, images, video, or executable programs—can be converted into a string of numbers. This means that even encrypted or proprietary information, which can be represented as numbers, may be regulated or restricted by authorities.

What is the significance of the phrase 'the mathematician's pencil grows stronger by the day'?

The phrase highlights how, in our increasingly algorithm-driven world, mathematics and calculations are becoming more influential. As algorithms and mathematical tools continue to shape our lives, the role of mathematicians in creating and understanding numbers becomes more powerful and important.