Number Names Obtained by Counting in Twos

Transcript

Number Names Obtained by Counting in TwosA group of indigenous people in Australia called the Gumulgal had the following words for their numbers Gumulgal (Australia) urapon ukasar ukasar-urapon ukasar-ukasar ukasar-ukasar-urapon ukasar-ukasar-ukasarHow are the numbers formed? Their system was built by "counting in 2s": 1: urapon 2: ukasar 3: ukasar-urapon (which is 2 + 1) 4: ukasar-ukasar (which is 2 + 2) 5: ukasar-ukasar-urapon (which is 2 + 2 + 1) 6: ukasar-ukasar-ukasar (which is 2 + 2 + 2) For any number greater than 6, they simply used the word "ras". Interestingly, similar "counting in twos" systems were developed by the Bakairi people in South America and the Bushmen in South Africa, despite the vast geographical distance and lack of contact. Historians theorize they may have had common ancestors who used this system. Why Grouping Evolved (And Its Limitations) The text suggests a reason why humans started grouping numbers. The Limit of Perception: Most humans find it difficult to immediately know the size of a collection "at a glance" if it has 5 or more objects. A More Efficient System: This "limit of perception" may be what prompted people using tally marks to start grouping them (for example, making a new symbol for every 5 marks). This is more efficient than a simple tally system. However, this method also has a major drawback. The Problem with a Single Group Size The text asks what the difficulty would be for a system that only counts in groups of a single size, like 5. To represent the number 1345 in a system that only counts by 5s, you would have to write the symbol for "5" a total of 269 times (1345 ÷ 5 = 269). Conclusion Even though grouping is better than a simple tally, a system based on only one group size "can still become cumbersome for larger numbers". This leads to the need for a refinement of this idea, which would be the next step in the evolution of number systems (such as using multiple landmarks, like the Roman system, or a place value system).