{"id":34,"date":"2023-06-05T15:29:32","date_gmt":"2023-06-05T15:29:32","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/tulsacc-math1473\/chapter\/why-it-matters-historical-counting-systems\/"},"modified":"2023-07-05T19:38:24","modified_gmt":"2023-07-05T19:38:24","slug":"why-it-matters-historical-counting-systems","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/tulsacc-math1473\/chapter\/why-it-matters-historical-counting-systems\/","title":{"raw":"Why It Matters: Historical Counting Systems","rendered":"Why It Matters: Historical Counting Systems"},"content":{"raw":"

Why do historical counting systems still matter today?<\/h2>\r\nWhen you check that balance in your bank account, or when you glance at the speedometer in your car, or even when you look for your child\u2019s number on the back of jerseys during a pee wee football game, you are reading numerals in the Hindu-Arabic counting system<\/strong>. \u00a0We are all familiar with those ten digits, 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. \u00a0What\u2019s more, when we read a number like 352, we know that it stands for three groups of a hundred, five groups of ten, and two ones\/units. \u00a0Our numerals are arranged according to a positional base 10 (or decimal) system<\/strong>\u2026 most of the time, anyway.\r\n\r\n\"Digital<\/a>\r\n\r\n \r\n\r\nTelling time requires a slightly different system. \u00a0While there are still Hindu-Arabic numerals involved, the way that they behave is decidedly different. \u00a0There are 60 seconds in every minute and 60 minutes in every hour. \u00a0So if your watch displays 10:04:59 right now, then you expect it to read 10:05:00 a second later.\r\n\r\n \r\n\r\nWe are so used to telling time in groups of 60 that it seems natural. \u00a0But have you ever wondered why there are not 100 seconds in each minute, or 100 minutes in an hour? \u00a0In the late 1700s, a French attorney by the name of Claude Boniface Collignon suggested a system of decimal time measurement in which each day has 10 hours, each hour lasting 100 minutes, and each minute having 1000 seconds. \u00a0Of course the actual duration of these new hours, minutes, and seconds would be much different. \u00a0In particular, the decimal second, would last 0.864 of a normal second. \u00a0On the upside, time conversions would be trivial; for example, 6 decimal hours = 600 decimal minutes = 600,000 decimal seconds.\r\n\r\n \r\n\r\nSo why does our system of telling time not conform to the usual base 10 counting system that governs most other aspects of our life? \u00a0Blame it on the Babylonians!\r\n\r\n \r\n\r\n\"Babylonian<\/a>\r\n\r\n \r\n\r\nThe Babylonians were one of the first cultures to develop a positional numeral system. \u00a0However instead of having only 10 distinct numerals and groups in powers of 10, their system was based on groups and powers of 60 (which is called a sexigesimal system<\/strong>). \u00a0The Babylonian system spread throughout most of Mesopotamia, but it eventually mostly faded into history, allowing other number systems such as the Roman numerals and the Hindu-Arabic system to take its place.\r\n\r\nOn the other hand, there are still vestiges of the sexigemisal counting system in the way that we keep time as well as how we measure angles in degrees. \u00a0There are 360 degrees in a full circle (and [latex]360^{\\circ} = 6 \\times 60^{\\circ}[\/latex]). \u00a0Furthermore, there are 60 arc minutes in one degree and 60 arc seconds in one arc minute. \u00a0This system of degrees, arc minutes, and arc seconds is also used to locate any point on the surface of the Earth by its latitude and longitude. \u00a0So even though our numerals are Hindu-Arabic, we still rely on the Babylonian base 60 system every second of the day and everywhere on the globe!\r\n\r\nIn this unit, we will try to focus on three main ideas. The first will be an examination of basic number and counting systems and the symbols that we use for numbers. We will look at our own modern (Western) number system as well those of a couple of selected civilizations to see the differences and diversity that is possible when humans start counting. The second idea we will look at will be base systems. By comparing our own base-ten (decimal) system with other bases, we will quickly become aware that the system that we are so used to, when slightly changed, will challenge our notions about numbers and what symbols for those numbers actually mean. The third will be an examination of measurement systems.\u00a0 We will look at the U.S. customary measurement system and the metric system.","rendered":"

Why do historical counting systems still matter today?<\/h2>\n

When you check that balance in your bank account, or when you glance at the speedometer in your car, or even when you look for your child\u2019s number on the back of jerseys during a pee wee football game, you are reading numerals in the Hindu-Arabic counting system<\/strong>. \u00a0We are all familiar with those ten digits, 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. \u00a0What\u2019s more, when we read a number like 352, we know that it stands for three groups of a hundred, five groups of ten, and two ones\/units. \u00a0Our numerals are arranged according to a positional base 10 (or decimal) system<\/strong>\u2026 most of the time, anyway.<\/p>\n

\"Digital<\/a><\/p>\n

 <\/p>\n

Telling time requires a slightly different system. \u00a0While there are still Hindu-Arabic numerals involved, the way that they behave is decidedly different. \u00a0There are 60 seconds in every minute and 60 minutes in every hour. \u00a0So if your watch displays 10:04:59 right now, then you expect it to read 10:05:00 a second later.<\/p>\n

 <\/p>\n

We are so used to telling time in groups of 60 that it seems natural. \u00a0But have you ever wondered why there are not 100 seconds in each minute, or 100 minutes in an hour? \u00a0In the late 1700s, a French attorney by the name of Claude Boniface Collignon suggested a system of decimal time measurement in which each day has 10 hours, each hour lasting 100 minutes, and each minute having 1000 seconds. \u00a0Of course the actual duration of these new hours, minutes, and seconds would be much different. \u00a0In particular, the decimal second, would last 0.864 of a normal second. \u00a0On the upside, time conversions would be trivial; for example, 6 decimal hours = 600 decimal minutes = 600,000 decimal seconds.<\/p>\n

 <\/p>\n

So why does our system of telling time not conform to the usual base 10 counting system that governs most other aspects of our life? \u00a0Blame it on the Babylonians!<\/p>\n

 <\/p>\n

\"Babylonian<\/a><\/p>\n

 <\/p>\n

The Babylonians were one of the first cultures to develop a positional numeral system. \u00a0However instead of having only 10 distinct numerals and groups in powers of 10, their system was based on groups and powers of 60 (which is called a sexigesimal system<\/strong>). \u00a0The Babylonian system spread throughout most of Mesopotamia, but it eventually mostly faded into history, allowing other number systems such as the Roman numerals and the Hindu-Arabic system to take its place.<\/p>\n

On the other hand, there are still vestiges of the sexigemisal counting system in the way that we keep time as well as how we measure angles in degrees. \u00a0There are 360 degrees in a full circle (and [latex]360^{\\circ} = 6 \\times 60^{\\circ}[\/latex]). \u00a0Furthermore, there are 60 arc minutes in one degree and 60 arc seconds in one arc minute. \u00a0This system of degrees, arc minutes, and arc seconds is also used to locate any point on the surface of the Earth by its latitude and longitude. \u00a0So even though our numerals are Hindu-Arabic, we still rely on the Babylonian base 60 system every second of the day and everywhere on the globe!<\/p>\n

In this unit, we will try to focus on three main ideas. The first will be an examination of basic number and counting systems and the symbols that we use for numbers. We will look at our own modern (Western) number system as well those of a couple of selected civilizations to see the differences and diversity that is possible when humans start counting. The second idea we will look at will be base systems. By comparing our own base-ten (decimal) system with other bases, we will quickly become aware that the system that we are so used to, when slightly changed, will challenge our notions about numbers and what symbols for those numbers actually mean. The third will be an examination of measurement systems.\u00a0 We will look at the U.S. customary measurement system and the metric system.<\/p>\n\n\t\t\t

\n\t\t\t

Candela Citations<\/h3>\n\t\t\t\t\t
\n\t\t\t\t\t\t
\n\t\t\t\t\t\t\t
CC licensed content, Original<\/div>