The Big X - Numberphile

Summary

In this engaging video script, the presenter explores 'The Ground of Arts,' a pioneering arithmetic book by Robert Record, published in 1542. It aimed to bring England's arithmetic skills in line with the rest of Europe by introducing the Indo-Arabic numeral system, including the revolutionary concept of 'cipher' or zero. The script also delves into the historical significance of the cipher, its impact on arithmetic, and its playful references in Shakespeare's works. The presenter speculates on the origin of the multiplication symbol and its possible connection to Record's times table technique, offering a unique perspective on the evolution of mathematical symbols.

Takeaways

• 📚 'The Ground of Arts' is a significant historical arithmetic book written by Robert Record in 1542, aimed at the general public in English to explain arithmetic concepts.
• 🌐 The book was a response to England's lag in arithmetic knowledge compared to the rest of Europe, particularly due to the country's break from the Catholic Church and the Renaissance's influence.
• 🔢 It introduced the Indo-Arabic numeral system to the English public, including the concept of place value and the revolutionary 'cipher' or zero, which simplified arithmetic significantly.
• 🎲 Robert Record made learning arithmetic more approachable by incorporating verses and a friendly tone, demystifying the subject for the general populace.
• 📖 The term 'cipher' for zero was not universally used; it was a term that emerged later, and at the time, people referred to it as 'nothing' or 'nil'.
• 🤔 The script ponders the origin of the multiplication symbol, suggesting it might have been inspired by the 'X' shape of the times table technique introduced in 'The Ground of Arts'.
• 🎨 Shakespeare, who was part of the first generation to learn this new arithmetic, made references to it in his plays, indicating the impact of the cipher and arithmetic on culture.
• 🧩 The script highlights the ingenuity of the times table technique for tricky multiplications, such as 8 * 7, and demonstrates how it works with an algebraic explanation.
• 📐 It also discusses the practical application of arithmetic in the book, including long multiplication and word problems that reflect the everyday life of the Elizabethan era.
• 🤓 The video script speculates on the influence of 'The Ground of Arts' on the development of mathematical symbols and the cultural significance of arithmetic during the English Renaissance.
• 🔍 The script encourages viewers interested in the intersection of mathematics and culture to explore further resources, such as Rob's book on numbers and the Objectivity channel.

Q & A

What is the book 'The Ground of Arts' about?

'The Ground of Arts' is an arithmetic book first written in 1542 by Robert Record. It was the first book aimed at the general public in England to explain how to do arithmetic using the new Indo-Arabic numeral system.

Why was 'The Ground of Arts' significant in England during its time?

The book was significant because it helped England catch up with the rest of Europe in arithmetic, which was important since England had fallen behind due to the Reformation and the break from the Catholic Church.

What numeral system does 'The Ground of Arts' introduce?

The book introduces the new Indo-Arabic numeral system, which included the use of zero, referred to as 'cipher' in the book.

How does Robert Record explain the concept of zero in his book?

Robert Record refers to zero as 'cipher,' a term derived from Arabic. He explains that this symbol, despite representing nothing, is crucial in making numbers large and revolutionizing arithmetic.

What multiplication technique does Robert Record introduce in 'The Ground of Arts'?

Record introduces a technique for doing times tables, which involves drawing diagonals and using number bonds to make multiplication easier. This method was particularly useful for multiplying single-digit numbers.

Does Robert Record's multiplication technique work for numbers outside the range of 6 to 9?

Yes, the technique works for numbers outside the range of 6 to 9, though it may seem unnecessarily complex for such cases. The algebra behind the method shows that it is valid for any numbers.

How were long multiplication problems addressed in 'The Ground of Arts'?

The book includes practical word problems that require long multiplication. Record demonstrates how to solve these problems without the modern multiplication symbol, which had not been invented yet.

Who is credited with inventing the multiplication symbol, and how might Robert Record's work have influenced this?

William Oughtred is credited with inventing the multiplication symbol around 1630. It's suggested that he may have been inspired by Record's technique of drawing diagonals, which resembles an 'X'.

How does Shakespeare reference arithmetic in his plays, and what might this indicate?

Shakespeare refers to arithmetic in his plays, such as 'Romeo and Juliet' and 'Henry V'. This indicates that he was likely familiar with arithmetic concepts from 'The Ground of Arts', which was published shortly before his time.

What is a notable mathematical reference in Shakespeare's 'Henry V'?

In 'Henry V', the chorus refers to himself as a 'crooked figure a one' and the other actors as 'ciphers'. This reflects the arithmetic concept introduced by Record that small symbols, like zero, can significantly expand numbers.

Why is the term 'cipher' significant in the context of Robert Record's work and Shakespeare's plays?

The term 'cipher' is significant because it represents the concept of zero, which was a new and revolutionary idea in arithmetic. Shakespeare's references to 'cipher' in his plays suggest that he found this concept intriguing and important.