1 Work in groups. Discuss questions 1-3. 1 Does your country or culture use Arabic numbers (1, 2, 3, 4, etc.) or does ti have a different system of symbols? fI it has more than…
1 Work in groups. Discuss questions 1-3. 1 Does your country or culture use Arabic numbers (1, 2, 3, 4, etc.) or does ti have a different system of symbols? fI it has more than one system, when is each used? 2 What are Roman numerals? When and where are Roman numerals usually used? Which numbers are represented by the Roman numerals in photographs 1-3? 3 Most ancient number systems began with simple bars such as I, II, and, I. Why do you think this is? 1 Read Text 1. Complete the notes. Numbers 1-3 Most civilizations used ' System used in three historical civilizations: 2 and System now used in 3 Modern Arabic N u m e r a l s 1, 2, a n d 3 c o m e f r o m But join when S Number of bars humans see as separate without counting Effect on early written notation? 1 A numeral is a sign or symbol that represents a number. People have for many years been interested in the origin of such symbols. Take Roman numerals for instance. The first three numerals (I, Il and Il) use bar notation. This means that they follow the simple rule of containing as many bars as there are units. The numeral for four, IV, however, breaks the rule. Roman numerals are not alone in using this system. Ifrah (1998), in his book on the history of numerical notations, shows that in al civilisations, the first three numbers were initially denoted by repeatedly writing down the symbol for 'one, usually a bar, as many times as necessary. nI most civilizations, this was followed by a different symbol for four and beyond. Other examples of this are the Cuneiform numerals T. T. T and 7, used ni ancient Mesopotamia, and ancient Indian numerals (- = , and +). Today, the Chinese denote the numbers 1, 2 and 3 using one, two and three horizontal bars, yet they employ a different symbol for number .4 Even modern Arabic numerals (1, 2, 3etc.) derive from the same principle. The numeral for one is a single bar and the numerals for 2 and 3 derive from two and three horizontal bars that became joined together when they were hand written. 2 One theory that explains the evolution of numerals is subitization. Subitization is defined as the ability to determine the number of something without actually counting. Research has shown that subitizing becomes much more difficult after the number 3. In other words, humans can easily distinguish between the numerals ,I lI and Il but beyond this, bar notation becomes difficult and we are unable at a glance to accurately distinguish between, say, Il and IIIII. This difficulty may explain the effect on early notation, as 'new' numerals were created to make it easier for us to tell the difference between the numbers denoted.
Discussion Questions:
Arabic Numeral Usage:
- Many countries and cultures, including most of the world today, utilize Arabic numerals (1, 2, 3, 4, etc.) as their primary numerical system. Some cultures may employ additional numeral systems, such as Roman numerals (I, II, III, IV, etc.) for specific contexts like clock faces, book chapters, or major events. In certain Asian cultures, traditional numeral systems may also exist alongside Arabic numerals, often reflecting cultural heritage or religious contexts.
Roman Numerals:
- Roman numerals are a numeral system originating from ancient Rome, using combinations of letters from the Latin alphabet (I, V, X, L, C, D, M) to represent numbers. They are traditionally used in specific contexts such as clock faces, the numbering of chapters in books, or to denote significant events like the Super Bowl or the Olympics. The Roman numerals represented in photographs 1-3 would typically be based on their standard representation (for example, I = 1, II = 2, III = 3).
Evolution of Ancient Number Systems:
- The initial use of simple bars (I, II, III) in ancient number systems likely reflects an innate human cognitive ability to recognize small quantities at a glance, which is known as subitization. This principle may have facilitated early numeral systems, as humans tend to find it easier to perceive and differentiate between small groups of items. As quantities increase, however, the complexity grows, leading to the development of more sophisticated numeral systems to represent larger numbers distinctly.
Notes Completion:
Most civilizations used: simple bar notation or tally marks.
System used in three historical civilizations:
- Ancient Mesopotamia
- Ancient India
- Ancient China
System now used:
- Modern Arabic numeral system (1, 2, 3, etc.)
Modern Arabic Numerals 1, 2, and 3 come from:
- The principle of repeated bar notation, where each numeral is denoted by horizontal bars.
Distinctive number of bars humans see as separate without counting:
- Up to three bars; beyond this, humans have difficulty distinguishing between numbers without explicit counting (subitization theory).
Effect on early written notation?:
- Difficulty in distinguishing beyond three led to the creation of new symbols for larger numbers, adapting numeral systems to improve clarity and usability.
