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Why do we use base ten? Because we have ten digits on our hands. Maybe a shrug or open palms to mean “nothing”. But base ten has nine digits: 1 to 9 and a 0

Why do we use base ten? Because we have ten digits on our hands. Maybe a shrug or open palms to mean “nothing”. But base ten has nine digits: 1 to 9 and a 0 for nothing.

bagrow 5y ago
Zero is a digit.
- mvh 5y ago
  You’re right. There are two types of 0: the internal syntax denoting digit shift, like in 507, and the number representing nothing, as in 0. So in our number system, o isn’t just syntax, it’s also a number.
- Joker_vD 5y ago
  Which is precisely what enables the positional system at the conceptual level: not only you can have "gaps" in the middle, but it enables you to distinguish between 1 and 10 and 100. Babylonians, for example, didn't conceptualize 0 as a numeric quantity just like 1 or 5. So, when they invented a sign for gaps in the numbers, they didn't use it at the ending positions, so their "I" could mean 1, or 60, or 3600, or..., depending on the context. Neither was it used to signify the quantity of zero: empty space was used instead.
- gorgoiler 5y ago
  Yes, sorry, my point didn’t come across very well. What’s quite interesting is to ask pupils to assign numbers to their fingers and thumbs: 1 2 3 4 5 6 7 8 9 ... X? It’s a good way of introducing positional number systems, and the... paradox? quandary? quirk?.. of how base N never includes a symbol for N, and how N in base N is always ‘10’. See also: asking pupils to divide 12345* by 67, taught in the context of arithmetic and logical shifting. (*base 67)
rsj_hn 5y ago
Fun Fact: The babylonians used a base 6 (really, base 60) system. We still see echoes of this with 360 degrees in a circle (invented by Babylonians) as well as 60 minutes in an hour, 12/24 hours in a day, etc. Even the 7 day week is viewed as a 6 day work week plus an extra day for ceremonies (A "Sabbath" was invented by the Babylonians as well, although in a different form than the Jewish Sabbath - the Babylonian Sabbath barred work on the seventh day because it was considered unlucky). The theory is they did this because of their hands, but used one hand to count digits and the other hand to count groups of digits: for each of the 4 fingers they are divided into 3 segments. When you are counting, you can point to the four fingers with your thumb, thus giving 12 and a pointer to which finger you are on. Then in your other hand you can keep track of how many units of 12, so 5*12 = 60. A base 60 system. But there was no digit for zero, although of course they had a way of dealing with zero, it was just not considered a number.

Why do we use base ten? Because we have ten digits on our hands. Maybe a shrug or open palms to mean “nothing”. But base ten has nine digits: 1 to 9 and a 0 for nothing.

bagrow 5y ago

Zero is a digit.

mvh 5y ago
You’re right. There are two types of 0: the internal syntax denoting digit shift, like in 507, and the number representing nothing, as in 0. So in our number system, o isn’t just syntax, it’s also a number.
Joker_vD 5y ago
Which is precisely what enables the positional system at the conceptual level: not only you can have "gaps" in the middle, but it enables you to distinguish between 1 and 10 and 100. Babylonians, for example, didn't conceptualize 0 as a numeric quantity just like 1 or 5. So, when they invented a sign for gaps in the numbers, they didn't use it at the ending positions, so their "I" could mean 1, or 60, or 3600, or..., depending on the context. Neither was it used to signify the quantity of zero: empty space was used instead.
gorgoiler 5y ago
Yes, sorry, my point didn’t come across very well. What’s quite interesting is to ask pupils to assign numbers to their fingers and thumbs: 1 2 3 4 5 6 7 8 9 ... X? It’s a good way of introducing positional number systems, and the... paradox? quandary? quirk?.. of how base N never includes a symbol for N, and how N in base N is always ‘10’. See also: asking pupils to divide 12345* by 67, taught in the context of arithmetic and logical shifting. (*base 67)

rsj_hn 5y ago

Fun Fact: The babylonians used a base 6 (really, base 60) system. We still see echoes of this with 360 degrees in a circle (invented by Babylonians) as well as 60 minutes in an hour, 12/24 hours in a day, etc. Even the 7 day week is viewed as a 6 day work week plus an extra day for ceremonies (A "Sabbath" was invented by the Babylonians as well, although in a different form than the Jewish Sabbath - the Babylonian Sabbath barred work on the seventh day because it was considered unlucky). The theory is they did this because of their hands, but used one hand to count digits and the other hand to count groups of digits: for each of the 4 fingers they are divided into 3 segments. When you are counting, you can point to the four fingers with your thumb, thus giving 12 and a pointer to which finger you are on. Then in your other hand you can keep track of how many units of 12, so 5*12 = 60. A base 60 system. But there was no digit for zero, although of course they had a way of dealing with zero, it was just not considered a number.