The Evolution of Numbers: From Ancient Civilizations to Modern Technology

The hero of this story is a master of disguise, appearing as a wedge or a cone, but always being the number one. His story is a tale of struggle, knowledge of the origin of numbers, and how he helped create the first cities and empires.

The speaker delves into how the combination of ones and zeros dominates the modern digital world, from coding text on a computer to transmitting images on a digital television.

The history of the number one dates back to around 20,000 years ago when solid evidence of its existence for counting emerged. The 'bone of the monkey' found in Congo with 60 marks on each side suggests early humans used it for counting, giving them an advantage over other mammals.

By converting the number one into a mark, early humans could count beyond what other mammals could, giving them a cognitive advantage. This ability to count freely without limits allowed humans to surpass predators like lions and tigers.

As humans evolved and began constructing their own homes instead of living in natural caves, the history of the number one was forever changed. The transition from natural caves to constructed dwellings marked a significant shift in human development.

Around 4000 BC in ancient Sumeria, the Sumerians played a crucial role in giving independence to the number one. This period marked a pivotal moment in the history of the number one, shaping its significance in human civilization.

Around 6,000 years ago, the Sumerians invented a counting system using tokens made of cones to represent numbers. This innovation allowed them to perform arithmetic operations like addition and subtraction, marking a significant advancement in human history.

The Walpiri indigenous people of Central Australia lived without using numbers for approximately 30,000 years. Their language lacked numerical terms, and they measured quantities through songs and the position of the sun, showcasing a unique cultural approach to mathematics.

The contrast between the Walpiri people's numerical absence and the Sumerians' development of mathematics highlights how cultural context shapes the need for mathematical concepts. While the Walpiri thrived without numbers, the urban lifestyle of the Sumerians necessitated arithmetic for organization and taxation purposes.

The urban environment of Sumerian cities demanded mathematical systems for managing resources, such as storing and distributing grains, calculating profits and losses, and levying taxes. This urban lifestyle led to the creation of numerical tokens and the emergence of arithmetic as a vital tool for civic administration.

The Sumerians devised a method of writing numbers by making marks on clay tablets to represent numerical values, eliminating the need for physical tokens. This innovation allowed for the permanent recording of complex calculations and marked the birth of written numerical records in human history.

Since childhood, the Sumerians developed a powerful and wealthy elite that laid the foundation for modern accounting practices. The Sumerians introduced the concept of the certified accountant, who played a crucial role in building empires and shaping economies.

Around 3000 BC in Egypt, the Sumerian numerical system was further developed. The Egyptians used intricate symbols to represent numbers, with different symbols for daily work, aristocrats, and the pharaoh. They even had a symbol for a million, a concept unimaginable to the Sumerians.

To ensure precision in construction, the Egyptians defined their own version of the unit 'one.' Known as the 'cubit,' it was based on the length of a man's arm from elbow to fingertip plus the width of the hand. This standard unit, the 'cubit,' was meticulously preserved in temples and distributed across the empire for construction projects.

By transforming the 'one' from a counting unit to a measurement unit, the ancient Egyptians revolutionized various industries like tailoring and carpet making. The 'cubit' became the universal measure for construction, enabling the Egyptians to execute vast projects with astonishing accuracy, enhancing the grandeur of wonders like the pyramids.

Over time, the 'one' evolved into a divine concept, symbolizing unity and the essence of the universe. In ancient Greece, Pythagoras introduced mathematical theories that elevated the 'one' to a fundamental element in geometry, demonstrating its significance in shaping philosophical and scientific thought.

Pitágoras had a school where students renounced material possessions, ate only vegetables, and swore to never touch beans, believing it would purify their souls. He founded a vegetarian mathematics school in Greece around 520 BC, exploring the wonders and mysteries of numbers.

Pitágoras was the first to distinguish between even and odd numbers, assigning unique characteristics to each. He also delved into integers, noticing how certain integer combinations formed pleasing shapes like triangles and squares, leading to the concept of a magic triangle.

Pitágoras believed that everything was made of numbers, including music, contrary to other philosophers who thought substances like fire, air, or water were fundamental. He saw numbers as the essence of all things, including the harmony in music.

Pitágoras demonstrated the relationship between harmonious sounds and integer ratios using different-sized containers. He showed that beautiful harmonies resulted from integer ratios, while dissonance came from non-integer ratios, emphasizing the role of mathematics in explaining musical harmonies.

Pitágoras believed that the beauty of music rested on integers, suggesting that the universe was also constructed from essential materials represented by the number one. He attributed the harmony in music to the grouping of ones, highlighting the importance of integers in understanding the cosmos.

Despite his admiration for the number one, Pitágoras' belief system ultimately failed. His famous right-angled triangle became the evidence of his mistake, as he struggled to make each side an exact number of units, leading to the realization that the core of the triangle did not align with his theory of the number one as the essence of everything.

Pitágoras believed that the world was based on units, but this was proven false. He thought the square of the hypotenuse of a right triangle was equal to the sum of the squares of the other two sides, which was debunked by his favorite geometric figure. Pitágoras couldn't conceive numbers without them representing real things, unlike later mathematicians who were liberated from this constraint.

Arquímedes, a renowned mathematician, brought mathematics to unimaginable realms by playing with numbers. He engaged in mathematical games that seemed trivial but yielded practical results. For instance, he pondered the difference in area between a sphere and a cylinder, which led to significant advancements in cartography, transforming the globe into a flat map.

The Romans, unlike the Greeks, were more interested in practical matters than abstract mathematics. They utilized numerical systems for military organization, with the 'centurias' consisting of 100 men and 'manipules' of 200 soldiers. Even punishments were based on numerical principles, such as 'decimation,' where one in ten soldiers was killed regardless of individual guilt.

Roman numerals, an improved version of ancient tally marks, were primarily used for counting and inscriptions. The system lacked the efficiency of Arabic numerals, with symbols representing values up to a million. While suitable for tomb inscriptions, Roman numerals were not conducive to advanced mathematical calculations.

The Romans faced complications in theoretical mathematics due to the inefficiency of their numeral system. Writing one billion in Roman numerals took around 16 minutes, highlighting the impracticality of their system. Unlike the Greeks, the Romans did not have prominent mathematicians. The Roman numeral system expanded with the empire's power, but it was not suitable for complex calculations, leading to the use of counting boards similar to ancient abacuses.

The Roman numeral system spread across Europe over 500 years, from Spain to Turkey, as the Roman Empire expanded its control. Even after the empire's fall, the Roman numeral system persisted in various forms, showcasing its enduring legacy in European culture.

Around 500 AD, Hindu numerals, with distinct symbols for 1 to 9, emerged from India. These numerals were capable of handling large numbers efficiently, showcasing advancements in mathematical notation. The Hindu numeral system laid the foundation for the modern Arabic numerals used today, which were adopted around 500 AD.

Although known as Arabic numerals, they originated in India around 500 BC. The Arabic numerals were a significant innovation that revolutionized mathematics. The introduction of zero, a new number, marked a pivotal moment in history, transforming the concept of nothing into a numerical value.

The invention of zero, represented as '0', was a groundbreaking development that changed the course of mathematics and the world. For the first time, nothingness was quantified as a number, symbolizing a profound shift in human understanding. The inscription mentioning a garden's dimensions in terms of '0' highlighted the practical applications of this new numerical concept.

The concept of zero (0) by itself may seem meaningless, but when combined with one (1), the magic of numbers unfolds. The Hindu numerical system, with just 10 digits, allowed for the representation of infinitely large and small numbers, a feat not achievable by the Roman numeral system. The combination of zero and one revolutionized mathematics and laid the foundation for significant advancements in science and astronomy.

The Indian numerical system, including zero, one, and the rest of the digits, enabled Indian scientists to make groundbreaking discoveries. Indian astronomers were centuries ahead of their Christian counterparts, accurately determining Earth's movements and dimensions. Their precise calculations, with an error margin of less than 1%, showcased the power and sophistication of the Indian numerical system.

Around 762 AD, the Indian numerical system, including the numeral zero, made its way to Baghdad, under the rule of the great Caliph Al-Mansur. The introduction of Indian numerals to the Islamic world marked a significant advancement in mathematics and science, allowing for more precise calculations and complex mathematical operations.

In Islamic society, the implementation of Islamic law, which required intricate mathematical calculations, posed challenges due to the limitations of the existing numeral system. The need for precise calculations in matters like inheritance distribution highlighted the importance of a more advanced numerical system.

An Indian ambassador presented the Indian numerical system to the Islamic world, including the concept of zero, which fascinated Muslim scholars. The Indian numerals, with their unique properties and versatility, opened up new possibilities in mathematics, leading to the development of advanced mathematical techniques and solutions.

Islamic scholars, particularly Al-Khwarizmi, were deeply impressed by the Indian numerical system, embracing the concept of zero and the other digits. They learned new mathematical tricks, equations, and algebraic concepts, paving the way for significant advancements in mathematics and science within the Islamic world.

The introduction of Hindu-Arabic numerals in Europe marked a significant shift in mathematical and astronomical advancements. While the Indian system gained popularity in the Islamic world, Europe, dominated by Roman numerals, resisted the change. The clash between the two numeral systems was inevitable and would alter the course of Western history.

The adoption of Hindu-Arabic numerals in Europe signaled the beginning of the end for Roman numerals. Merchants in North Africa quickly embraced the new system for their transactions, leading to widespread use by the 12th century.

Leonardo Fibonacci, a young Italian diplomat's son in Algeria, was captivated by Hindu-Arabic numerals. Upon returning home, he introduced these numerals to Europe through his book 'Libro del Calculo' in 1212. Fibonacci's work was instrumental in popularizing the Indian numeral system in Europe.

Fibonacci's book not only introduced Hindu-Arabic numerals but also provided practical applications for merchants. In a time when capitalism was emerging in Europe, Fibonacci's work became essential reading, demonstrating how to leverage Indian numerals for calculations like profit estimation.

Despite Fibonacci's efforts, many Europeans clung to Roman numerals out of comfort and tradition. The complexity of transitioning to a new system, especially for merchants dealing with diverse currencies, posed challenges. The distrust towards unfamiliar Indian numerals further hindered widespread adoption.

The use of Indian numerals faced skepticism and resistance in Europe. Merchants, accustomed to Roman numerals, hesitated to adopt the new system due to concerns about accuracy and trust. The city of Florence even went as far as banning merchants from using Indian numerals, reflecting the deep-rooted skepticism towards change.

The use of Roman numerals was prevalent, but the number zero sparked suspicion. It was considered a sign causing confusion and difficulty. The zero was referred to as a 'cifra' and associated with secret codes or ciphers.

The days of the old system using abacus and Roman numerals were numbered due to human greed. Traditionalists resisted the shift to Indian numerals and the concept of charging interest on loans, which was once considered a sin by the Catholic Church.

With the Protestant Reformation, churches softened their stance on business practices like charging interest, leading to a shift in Christian resistance to capitalism.

The debate arose on whether Indian numerals or the abacus were more convenient for calculations involving loans and interest. A mathematician and an abacus expert were tasked with solving a financial scenario involving interest calculations.

The abacus expert and the mathematician were given a financial problem involving compound interest. The abacus expert, using a modern model but following 16th-century techniques, provided a precise answer with attention to compound interest nuances.

Centuries after the introduction of Indian numerals to Europe, they triumphed over Roman numerals due to their speed, versatility, and compatibility with zero and one. The old Roman numeral system eventually became obsolete.

The introduction of Indian numerals facilitated navigation for European sailors, enabling them to calculate latitude accurately. This advancement encouraged exploration, leading to the discovery of America.

Christopher Columbus mistakenly believed he had reached Japan when he actually arrived in the West Indies. This error, like many others, highlighted the ongoing challenge of human fallibility in navigation and exploration.

Gottfried Wilhelm Leibniz, a renowned mathematician, aimed to free humanity from the curse of human error by inventing a mechanical calculating machine. He believed that by using only the numbers 0 and 1, he could eliminate human error and developed the binary system.

Leibniz was convinced that the universe could be represented by the numbers 0 and 1. He developed a system consisting only of ones and zeros, known as the binary system, to achieve any mathematical dream and eradicate human error.

In the binary system, numbers are expressed using only ones and zeros. Each column represents powers of 2, with each digit indicating the presence or absence of that power. For example, the number 9 in binary is represented as 1001.

The binary system's mechanical process of using ones and zeros is ideal for machines, as they can efficiently add numbers regardless of their size. This system, being perfect for machines, simplifies the handling of large numbers.

Leibniz designed a binary machine using metal marbles and slots instead of eggs and cups. This machine was intended to revolutionize computation and pave the way for the digital era, but unfortunately, it was never constructed.

Colossus, the first binary computer in the world, was created during World War II in 1944 in the north of England. It was installed at the British intelligence headquarters in Paisley Park. Colossus operated on electronic signals of 1s and 0s, performing rapid calculations to decipher enemy codes, aiding the Allies in gaining intelligence advantage over the Germans.

Computers have revolutionized technology by enabling complex calculations such as resolving percentages, currency conversions, and compound interests. They have surpassed the capabilities of ancient minds in handling mathematical tasks efficiently, changing the world forever.

In the era of computers, our world operates on a stream of ones and zeros, from managing bank accounts and medical records to scanning barcodes on pet food. The dominance of binary code has relegated other numerical systems to history, showcasing the power and efficiency of the binary system in modern society.

Computers have become integral in modern society, with their influence extending to various aspects of life. They have streamlined processes, enhanced efficiency, and transformed how we interact with technology, marking a significant shift towards a digital-centric world.