In this post, notes of “Unit 2: Science: Contestation and Exchanges” from “GE – 2: Science, Technologies, and Humans: Contested Histories” are given which is helpful for the students doing graduation this year.
Decimal and Zero
Origins and Early Development
Ancient Number Systems
- Egyptian Numbers
The ancient Egyptians had a number system based on ten. They used special symbols for 1, 10, 100, 1000, and so on. These numbers helped them in trade, taxes, and writing on monuments. Their system added values of the symbols together. For example, two symbols for 100 meant 200. - Babylonian Numbers
The Babylonians used a base-60 number system, which is different from our base-10 system. This system helped them with math and astronomy. They divided circles into 360 degrees, which we still use today. In their system, the position of a number showed its value. They also had a form of zero as a placeholder, but it wasn’t fully developed like our zero today. - Chinese Rod Numbers
Ancient Chinese mathematicians wrote numbers with rods on bamboo or silk. The numbers were placed vertically, and their position showed their value. The Chinese had an early version of a place-value system and used zero as a placeholder, but it wasn’t completely standardized yet.
Early Ideas of Zero
- Mesopotamian Placeholders
Around 300 BC in Mesopotamia, the Babylonians started using a space or a special symbol to show an empty place in their number system. This helped tell apart numbers like 20 and 200. However, this symbol did not mean zero as a number, just a way to avoid confusion. The real idea of zero as a number took a long time to develop. - Mayan Use of Zero
The Maya civilization, around the 4th century AD, was one of the first to use zero as an actual number, not just a placeholder. They used zero in their calendars, understanding it as an important part of their math and astronomy. This was a big step forward in using zero as both an idea and a number.
In summary, the early number systems show different ways cultures used numbers, with placeholders used in Mesopotamia and more advanced uses of zero in the Maya civilization.
The Indian Contribution
Bakhshali Manuscript
- First Known Use of Zero as a Number
The Bakhshali Manuscript is an old Indian math book from around the 7th century CE (some think it might be older). It shows the first clear use of zero as both a number and a placeholder. The manuscript mainly focuses on basic math and algebra. In it, zero is represented by a small dot, which is different from earlier cultures like the Babylonians. This manuscript is important because it shows a big change in math, recognizing zero as both a placeholder and a number on its own. - Math Topics and Their Importance
The manuscript talks about different topics like number sequences, simple algebra, and how to solve quadratic equations. It shows that Indian math was advanced during the medieval period. The way it handles zero helped develop more complex math methods, showing that Indian mathematicians were creating a deeper understanding of numbers that would later impact the world.
Brahmagupta’s Innovations
- Rules for Math with Zero and Negative Numbers
Brahmagupta (born in 598 CE) was an important Indian mathematician and astronomer known for his work on math involving zero. In his main book, Brahmasphutasiddhanta, he set rules for how to do math with zero and negative numbers. Some of these rules are:- Adding zero to any number gives the same number (a + 0 = a).
- Adding any number to zero gives the same number (0 + a = a).
- Subtracting zero from any number gives the same number (a – 0 = a).
- Subtracting zero from zero gives zero (0 – 0 = 0).
- Multiplying any number by zero gives zero (a × 0 = 0).
- Dividing by zero is not allowed (a ÷ 0 is undefined).
- Multiplying two negative numbers gives a positive number, while multiplying a positive and a negative number gives a negative number.
These ideas helped build later math systems in both Eastern and Western cultures. Brahmagupta’s rules for zero and negative numbers were groundbreaking, as they expanded the number system and helped solve difficult math problems.
- Zero’s Role in Equations and Calculations
Brahmagupta’s work also included more complex areas like algebra. He found solutions to quadratic equations that sometimes included zero. One important idea was treating zero as a real number in these equations, which was not commonly accepted in other places at that time. His approach to zero in equations showed that it was not just a placeholder but also an important part of math operations, creating a stronger way to solve equations and helping develop algebra.
In conclusion, Indian contributions to the idea of zero were very important. The Bakhshali Manuscript shows the first clear use of zero as both a placeholder and a number, while Brahmagupta built on this with his rules for math involving zero and negative numbers. These contributions were crucial in shaping the math systems used for many years.
Transmission to the Islamic World
House of Wisdom in Baghdad
- Translation Movements under the Abbasid Caliphate
From the 8th to the 13th centuries, during the Abbasid Caliphate, Baghdad became a key place for learning, especially at the House of Wisdom. Scholars from different cultures and religions came together to translate important texts from Greek, Sanskrit, Persian, and other languages into Arabic. These translations included works on philosophy, mathematics, astronomy, and medicine, introducing ideas like zero and new numbers. Islamic scholars built on these translations, expanding knowledge of the Indian numeral system and zero. - Scholars like Al-Khwarizmi and Their Works
A notable figure from this time was the Persian mathematician Al-Khwarizmi (c. 780–850 CE). His important book, Al-Kitab al-Mukhtasar fi Hisab al-Jabr wal-Muqabala (The Compendious Book on Calculation by Completion and Balancing), introduced algebra (the term comes from “al-jabr”), Indian numbers, and the concept of zero. Al-Khwarizmi’s work laid the foundation for modern algebra and helped spread the use of zero and the Hindu-Arabic number system throughout the Islamic world and into Europe.
Adoption and Adaptation
- Development of Algebra
Al-Khwarizmi’s work was crucial for the growth of mathematics. He created a clear method for solving equations, including those using zero. Algebra arose from the need to solve real-life problems, like measuring land and dividing inheritance, with zero being key to these solutions. The Indian number system with zero became integral to this, making calculations easier. - Enhancement of Astronomical Tables
Islamic scholars improved the astronomical tables they received, using zero and the Hindu-Arabic number system for better accuracy. Scholars like Al-Battani and Al-Tusi used these methods to enhance their observations and models, which advanced astronomy. The use of zero allowed for better measurements and calculations of celestial movements, influencing later European scientists like Copernicus.
Journey to Europe
Contact Through Trade and Crusades
- Cultural Exchanges in Andalusia and Sicily
In the 10th and 11th centuries, places like Andalusia (in modern Spain) and Sicily became important for cultural exchange between the Islamic world and Europe. Through trade and new schools like the Medina Azahara and the University of Palermo, Islamic math and science texts were brought to Europe. Scholars such as Ibn Rushd (Averroes) and Ibn Sina (Avicenna) shaped both Islamic and European thinking, including the spread of zero and Arabic numbers. - Introduction via Translations of Arabic Texts
In the 12th century, many Arabic math and science texts were translated into Latin, mainly by scholars in Spain and Sicily. These translations were vital for bringing knowledge of zero, the Hindu-Arabic number system, and algebra to Europe. For example, translating Al-Khwarizmi’s work into Latin helped share his ideas on arithmetic and algebra, making zero and Arabic numbers known to European scholars.
Fibonacci’s Liber Abaci
- Popularizing Hindu-Arabic Numerals
A significant moment for introducing zero to Europe was the publication of Fibonacci’s Liber Abaci in 1202. Fibonacci, an Italian mathematician, learned about the Hindu-Arabic number system during his travels in North Africa. In his book, he showed how this system, along with zero, was much better for calculations than the cumbersome Roman numeral system. Liber Abaci helped make Hindu-Arabic numbers popular in Europe. - Impact on European Commerce and Mathematics
The adoption of the Hindu-Arabic number system, including zero, changed European trade and accounting. It made calculations easier and faster. Fibonacci’s work played a key role in developing more advanced math techniques and helped mathematics grow in Europe, leading to the Renaissance and beyond.
Contestation and Resistance
Cultural and Religious Opposition
- Suspicion of Arabic Numerals
Despite their usefulness, Arabic numerals (including zero) faced pushback in Europe, especially at first. Many European scholars and clergy were wary of these numbers because of their ties to the Islamic world. Some medieval thinkers worried they would disrupt the traditional Roman numeral system. Religious and cultural biases against Arabic culture also contributed to this resistance. - Prohibition in Some Merchant Guilds
In some regions of Europe, merchant guilds initially banned Arabic numerals, sticking to Roman numerals for trade and accounting. This resistance came from not understanding the practical benefits of the new system, as well as some groups being hesitant to accept change. Nevertheless, over time, the efficiency of the Arabic numerals became clear.
Gradual Acceptance
- Efficiency in Calculations Overcoming Resistance
Over time, the practical benefits of the Hindu-Arabic number system—like being simple and easy to use—began to outweigh the earlier resistance. As European merchants, mathematicians, and scientists recognized that the Arabic system made complex calculations quicker and more precise, its use grew. This change was vital for accounting, trade, and scientific work, where accuracy became increasingly important. - Integration into Scientific Works
Eventually, the use of Arabic numerals, including zero, became common in scientific and mathematical writings. Notable mathematicians like Rene Descartes, Isaac Newton, and Leibniz adopted the system, making it standard in European scientific texts. By the time of the Scientific Revolution in the 16th and 17th centuries, the Hindu-Arabic number system and the idea of zero were well established in European math and science.
In summary, the journey of zero and the Hindu-Arabic number system from India through the Islamic world to Europe was complex. From early efforts in Baghdad’s House of Wisdom to the work of European scholars like Fibonacci, the acceptance of zero and the Hindu-Arabic number system faced challenges. However, their eventual acceptance led to major advancements in math, trade, and science worldwide.
Global Impact and Legacy
Standardization of Numerical Systems
- Global Trade Improvement
The use of the Hindu-Arabic numeral system, which includes the number zero, has greatly helped global trade. This system became the main way to do accounting, business, and math, allowing people from different cultures to work together easily. Because numbers could be written and understood simply, international trade and finance grew, helping the world’s economy connect better. This common system made it easier for merchants to share financial information accurately, setting the stage for today’s global economy. - Base for Modern Math and Computing
The Hindu-Arabic numeral system, especially with zero, is the foundation of modern mathematics. The addition of zero helped develop algebra, calculus, and advanced math, which are vital for science and engineering. The system’s clarity and flexibility allow mathematicians to explore complex ideas. Also, zero is crucial in computing, where binary code (made of ones and zeroes) is essential for all digital devices, like computers, phones, and the internet.
Philosophical Interpretations
- Zero in Philosophy
Zero has also impacted philosophy, as it represents ideas of nothingness and emptiness. Philosophers discuss what nothing means, and in some Eastern beliefs, zero symbolizes the void or infinite possibilities. In Western thought, zero’s link to nothingness raises questions about its meaning—whether it’s just an absence or something with potential. This reflects our complex views on nothingness, existence, and the universe. - Cultural Symbolism
Different cultures have different views on zero, often connecting it to bigger ideas. In Indian philosophy, zero (or śūnyatā) can mean emptiness or the source of all things. In Western religion during medieval times, zero sometimes symbolized God’s ability to create from nothing. Overall, zero represents a wide range of ideas, from emptiness to creative potential, highlighting the mystery of existence.
Contemporary Relevance
Zero in Computer Science
- Binary Code and Programming
Zero is very important in computer science, especially in binary code, which is how all digital computers work. Binary code uses two symbols—0s and 1s—to show electrical states of off (0) and on (1). This system allows computers to do math, save information, and run programs. Zero is also used in programming to represent false values and to manage different conditions in logic.
Mathematical Innovations
- Importance in Calculus and Advanced Math
Zero is key not just in basic math but also in advanced fields like calculus. In calculus, zero is involved in limits, derivatives, and integrals. Understanding how things behave as they get close to zero is crucial. Calculus is essential for modern physics and engineering and wouldn’t exist without zero. It’s also used in advanced theories in areas like topology and number theory, continuing to push mathematical discovery forward.
Summary of Zero’s Global Impact and Legacy
Zero has greatly influenced many areas of thought and activity. It has helped global trade, shaped modern math, and sparked deep philosophical ideas in different cultures. Zero is the foundation of our number systems, making scientific and technological growth possible. In today’s digital world, zero remains crucial in computer science, and its importance in advanced math is still strong, showing that the simple idea of “nothing” is actually a vital part of everything.
Importance of Documentation
Power in Documentation
- What is Documentation?
Documentation includes written records and texts that help keep and share knowledge. These records are seen as “official” knowledge and hold power in shaping how society understands things. Who makes these documents and how they are viewed affects how knowledge is shared. - Control of Knowledge Creation
Power decides who gets to record history and knowledge, leaving some voices out. In science and academics, certain people often control what knowledge is accepted, which affects research and cultural stories.
Colonial Documentation Practices
- Collecting Records
During colonial times, powerful nations built museums and libraries to collect items and records from colonized areas. This collection not only showed their power but also changed how knowledge from local people was viewed and used. - Studying Indigenous Cultures
The study of native cultures often treated them as objects. By looking at them through a colonial viewpoint, these studies made indigenous cultures seem strange and separate from the “civilized” world.
Standardization and Its Effects
- Classifying Knowledge
Systems like the Linnaean classification in biology organized plants and animals, which helped control how people understood the natural world. - Official Records
Colonial governments used documents like censuses to manage and control people. These records helped in enforcing rules and classifying individuals, making local knowledge a tool for governance.
Silencing Voices
- Loss of Oral Traditions
Written records have often overshadowed oral traditions, causing many indigenous knowledge systems to be forgotten. This has led to a loss of cultural heritage and different ways of understanding. - Language Power
The use of European languages in academics has pushed local languages aside. Colonial powers not only suppressed local languages in their regions but also in global academia, creating language inequalities.
Resistance from Marginalized Groups
- Preserving Knowledge
Even with colonial pressures, many communities fought to keep their knowledge alive through secret schools and alternative teaching methods. - Other Ways of Documenting
Many marginalized groups use oral histories and storytelling instead of written records. Art, music, and performances also help keep their cultural knowledge alive.
Digital Age and Equal Access
- Using Technology for Change
The digital age provides new chances to share and preserve knowledge. Online archives and open platforms let marginalized voices tell their stories globally, challenging traditional control. - Barriers to Access
However, not everyone has equal access to technology. Some groups can share their knowledge, while others cannot due to lack of resources or internet access. This creates new inequalities similar to past colonial issues.
Revisiting Power Structures
- Looking at History Critically
A postcolonial view examines past documentation practices. By questioning biases in archives and education, scholars and activists aim to include more diverse cultures and histories. - Ethical Issues
Documenting indigenous knowledge raises important questions about ownership, consent, and fair representation. Concerns about how this knowledge is used and potential exploitation are critical in today’s discussions on ethics.
This overview shows the complex ties between power, knowledge, and documentation. It illustrates how control over records has often led to dominance and exclusion, but also how marginalized people have resisted and found new ways to share knowledge. Today, technology offers both opportunities and challenges in balancing these power dynamics.