What's the historical origin of the left-to-right order of operations?
4
$begingroup$
I would assume this question has been answered before, but no combination of Googling and searching StackExchange yielded an actual response.
The Facebook problem 6/2(1+2) is boring to discuss in terms of PEMDAS/BODMAS/PEMA, but a friend of mine gave me a question I couldn't answer. There are plenty of articles on the origin of this convention. But they always mention in passing that aside from that you evaluate left-to-right.
Where does this come from? I'm assuming this convention was introduced in a country that reads left-to-right. Has there been a time when mathematicians in Arabia, Japan, China, etc. evaluated in a different order?
notation math-history
asked Dec 1 '18 at 6:52
CodeMonkeyCodeMonkey
1214
$endgroup$
|
show 1 more comment
4
$begingroup$
I would assume this question has been answered before, but no combination of Googling and searching StackExchange yielded an actual response.
The Facebook problem 6/2(1+2) is boring to discuss in terms of PEMDAS/BODMAS/PEMA, but a friend of mine gave me a question I couldn't answer. There are plenty of articles on the origin of this convention. But they always mention in passing that aside from that you evaluate left-to-right.
Where does this come from? I'm assuming this convention was introduced in a country that reads left-to-right. Has there been a time when mathematicians in Arabia, Japan, China, etc. evaluated in a different order?
notation math-history
asked Dec 1 '18 at 6:52
CodeMonkeyCodeMonkey
1214
$endgroup$
$begingroup$
Similar question asked in the past, math.stackexchange.com/questions/1246798/…
$endgroup$
– Gerry Myerson
Dec 1 '18 at 7:12
2
$begingroup$
Most western languages write horizontally. In that case, it is preferable to write from left to right to allow freshly written characters in ink more time to dry. In ancient time, chinese text are written vertically from top to bottom and then right to left. Their arithmetic problem are also presented in this order. e.g. see picture on 九章算術 on wiki. Due to strong influence of chinese to japenese culture. I believe same thing happens to ancient japanese. No idea about various cultures in middle east.
$endgroup$
– achille hui
Dec 1 '18 at 7:36
$begingroup$
@GerryMyerson Thank you, I saw that one, but it doesn't really contain answers. Also it doesn't specifically address the left-to-right order I'm interested in. There's one data point in the comments, but the one answer has no substance.
$endgroup$
– CodeMonkey
Dec 1 '18 at 8:02
$begingroup$
@achillehui That's very cool, I'm wondering for how long they kept this up, considering the Chinese numbers are already inherently base 10, making them much more useful for math than Roman numerals. Also I studied some Chinese in university (nothing to write home about), and it's fascinating that most of the characters are still recognizable, while I couldn't read whatever my forefathers wrote ~2000-3000 years ago (if they wrote at all).
$endgroup$
– CodeMonkey
Dec 1 '18 at 8:08
$begingroup$
There is remarkable exception from the "left-to-right" convention: This is the composition of functions. Given functions $f : X to Y$ and $g : X to Z$, their composition is written as $g circ f : X to Z$ although we first apply $f$ and in the second step $g$. Obviuosly this is the price for writing $f(x)$. This enforces writing $g(f(x))$ which lead to use $g circ f$ for the functuon assigning to $x in X$ the value $g(f(x)) in Z$.
$endgroup$
– Paul Frost
Dec 1 '18 at 12:00
|
show 1 more comment
4
4
4
$begingroup$
I would assume this question has been answered before, but no combination of Googling and searching StackExchange yielded an actual response.
The Facebook problem 6/2(1+2) is boring to discuss in terms of PEMDAS/BODMAS/PEMA, but a friend of mine gave me a question I couldn't answer. There are plenty of articles on the origin of this convention. But they always mention in passing that aside from that you evaluate left-to-right.
Where does this come from? I'm assuming this convention was introduced in a country that reads left-to-right. Has there been a time when mathematicians in Arabia, Japan, China, etc. evaluated in a different order?
notation math-history
asked Dec 1 '18 at 6:52
CodeMonkeyCodeMonkey
1214
$endgroup$
I would assume this question has been answered before, but no combination of Googling and searching StackExchange yielded an actual response.
The Facebook problem 6/2(1+2) is boring to discuss in terms of PEMDAS/BODMAS/PEMA, but a friend of mine gave me a question I couldn't answer. There are plenty of articles on the origin of this convention. But they always mention in passing that aside from that you evaluate left-to-right.
Where does this come from? I'm assuming this convention was introduced in a country that reads left-to-right. Has there been a time when mathematicians in Arabia, Japan, China, etc. evaluated in a different order?
notation math-history
notation math-history
asked Dec 1 '18 at 6:52
CodeMonkeyCodeMonkey
1214
asked Dec 1 '18 at 6:52
CodeMonkeyCodeMonkey
1214
edited Dec 1 '18 at 7:02
CodeMonkey
asked Dec 1 '18 at 6:52
CodeMonkeyCodeMonkey
1214
asked Dec 1 '18 at 6:52
CodeMonkeyCodeMonkey
1214
asked Dec 1 '18 at 6:52
CodeMonkeyCodeMonkey
1214
1214
$begingroup$
Similar question asked in the past, math.stackexchange.com/questions/1246798/…
$endgroup$
– Gerry Myerson
Dec 1 '18 at 7:12
2
$begingroup$
Most western languages write horizontally. In that case, it is preferable to write from left to right to allow freshly written characters in ink more time to dry. In ancient time, chinese text are written vertically from top to bottom and then right to left. Their arithmetic problem are also presented in this order. e.g. see picture on 九章算術 on wiki. Due to strong influence of chinese to japenese culture. I believe same thing happens to ancient japanese. No idea about various cultures in middle east.
$endgroup$
– achille hui
Dec 1 '18 at 7:36
$begingroup$
@GerryMyerson Thank you, I saw that one, but it doesn't really contain answers. Also it doesn't specifically address the left-to-right order I'm interested in. There's one data point in the comments, but the one answer has no substance.
$endgroup$
– CodeMonkey
Dec 1 '18 at 8:02
$begingroup$
@achillehui That's very cool, I'm wondering for how long they kept this up, considering the Chinese numbers are already inherently base 10, making them much more useful for math than Roman numerals. Also I studied some Chinese in university (nothing to write home about), and it's fascinating that most of the characters are still recognizable, while I couldn't read whatever my forefathers wrote ~2000-3000 years ago (if they wrote at all).
$endgroup$
– CodeMonkey
Dec 1 '18 at 8:08
$begingroup$
There is remarkable exception from the "left-to-right" convention: This is the composition of functions. Given functions $f : X to Y$ and $g : X to Z$, their composition is written as $g circ f : X to Z$ although we first apply $f$ and in the second step $g$. Obviuosly this is the price for writing $f(x)$. This enforces writing $g(f(x))$ which lead to use $g circ f$ for the functuon assigning to $x in X$ the value $g(f(x)) in Z$.
$endgroup$
– Paul Frost
Dec 1 '18 at 12:00
|
show 1 more comment
$begingroup$
Similar question asked in the past, math.stackexchange.com/questions/1246798/…
$endgroup$
– Gerry Myerson
Dec 1 '18 at 7:12
2
$begingroup$
Most western languages write horizontally. In that case, it is preferable to write from left to right to allow freshly written characters in ink more time to dry. In ancient time, chinese text are written vertically from top to bottom and then right to left. Their arithmetic problem are also presented in this order. e.g. see picture on 九章算術 on wiki. Due to strong influence of chinese to japenese culture. I believe same thing happens to ancient japanese. No idea about various cultures in middle east.
$endgroup$
– achille hui
Dec 1 '18 at 7:36
$begingroup$
@GerryMyerson Thank you, I saw that one, but it doesn't really contain answers. Also it doesn't specifically address the left-to-right order I'm interested in. There's one data point in the comments, but the one answer has no substance.
$endgroup$
– CodeMonkey
Dec 1 '18 at 8:02
$begingroup$
@achillehui That's very cool, I'm wondering for how long they kept this up, considering the Chinese numbers are already inherently base 10, making them much more useful for math than Roman numerals. Also I studied some Chinese in university (nothing to write home about), and it's fascinating that most of the characters are still recognizable, while I couldn't read whatever my forefathers wrote ~2000-3000 years ago (if they wrote at all).
$endgroup$
– CodeMonkey
Dec 1 '18 at 8:08
$begingroup$
There is remarkable exception from the "left-to-right" convention: This is the composition of functions. Given functions $f : X to Y$ and $g : X to Z$, their composition is written as $g circ f : X to Z$ although we first apply $f$ and in the second step $g$. Obviuosly this is the price for writing $f(x)$. This enforces writing $g(f(x))$ which lead to use $g circ f$ for the functuon assigning to $x in X$ the value $g(f(x)) in Z$.
$endgroup$
– Paul Frost
Dec 1 '18 at 12:00
$begingroup$
Similar question asked in the past, math.stackexchange.com/questions/1246798/…
$endgroup$
– Gerry Myerson
Dec 1 '18 at 7:12
$begingroup$
Similar question asked in the past, math.stackexchange.com/questions/1246798/…
$endgroup$
– Gerry Myerson
Dec 1 '18 at 7:12
2
2
$begingroup$
Most western languages write horizontally. In that case, it is preferable to write from left to right to allow freshly written characters in ink more time to dry. In ancient time, chinese text are written vertically from top to bottom and then right to left. Their arithmetic problem are also presented in this order. e.g. see picture on 九章算術 on wiki. Due to strong influence of chinese to japenese culture. I believe same thing happens to ancient japanese. No idea about various cultures in middle east.
$endgroup$
– achille hui
Dec 1 '18 at 7:36
$begingroup$
Most western languages write horizontally. In that case, it is preferable to write from left to right to allow freshly written characters in ink more time to dry. In ancient time, chinese text are written vertically from top to bottom and then right to left. Their arithmetic problem are also presented in this order. e.g. see picture on 九章算術 on wiki. Due to strong influence of chinese to japenese culture. I believe same thing happens to ancient japanese. No idea about various cultures in middle east.
$endgroup$
– achille hui
Dec 1 '18 at 7:36
$begingroup$
@GerryMyerson Thank you, I saw that one, but it doesn't really contain answers. Also it doesn't specifically address the left-to-right order I'm interested in. There's one data point in the comments, but the one answer has no substance.
$endgroup$
– CodeMonkey
Dec 1 '18 at 8:02
$begingroup$
@GerryMyerson Thank you, I saw that one, but it doesn't really contain answers. Also it doesn't specifically address the left-to-right order I'm interested in. There's one data point in the comments, but the one answer has no substance.
$endgroup$
– CodeMonkey
Dec 1 '18 at 8:02
$begingroup$
@achillehui That's very cool, I'm wondering for how long they kept this up, considering the Chinese numbers are already inherently base 10, making them much more useful for math than Roman numerals. Also I studied some Chinese in university (nothing to write home about), and it's fascinating that most of the characters are still recognizable, while I couldn't read whatever my forefathers wrote ~2000-3000 years ago (if they wrote at all).
$endgroup$
– CodeMonkey
Dec 1 '18 at 8:08
$begingroup$
@achillehui That's very cool, I'm wondering for how long they kept this up, considering the Chinese numbers are already inherently base 10, making them much more useful for math than Roman numerals. Also I studied some Chinese in university (nothing to write home about), and it's fascinating that most of the characters are still recognizable, while I couldn't read whatever my forefathers wrote ~2000-3000 years ago (if they wrote at all).
$endgroup$
– CodeMonkey
Dec 1 '18 at 8:08
$begingroup$
There is remarkable exception from the "left-to-right" convention: This is the composition of functions. Given functions $f : X to Y$ and $g : X to Z$, their composition is written as $g circ f : X to Z$ although we first apply $f$ and in the second step $g$. Obviuosly this is the price for writing $f(x)$. This enforces writing $g(f(x))$ which lead to use $g circ f$ for the functuon assigning to $x in X$ the value $g(f(x)) in Z$.
$endgroup$
– Paul Frost
Dec 1 '18 at 12:00
$begingroup$
There is remarkable exception from the "left-to-right" convention: This is the composition of functions. Given functions $f : X to Y$ and $g : X to Z$, their composition is written as $g circ f : X to Z$ although we first apply $f$ and in the second step $g$. Obviuosly this is the price for writing $f(x)$. This enforces writing $g(f(x))$ which lead to use $g circ f$ for the functuon assigning to $x in X$ the value $g(f(x)) in Z$.
$endgroup$
– Paul Frost
Dec 1 '18 at 12:00
|
show 1 more comment
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$begingroup$
Similar question asked in the past, math.stackexchange.com/questions/1246798/…
$endgroup$
– Gerry Myerson
Dec 1 '18 at 7:12
2
$begingroup$
Most western languages write horizontally. In that case, it is preferable to write from left to right to allow freshly written characters in ink more time to dry. In ancient time, chinese text are written vertically from top to bottom and then right to left. Their arithmetic problem are also presented in this order. e.g. see picture on 九章算術 on wiki. Due to strong influence of chinese to japenese culture. I believe same thing happens to ancient japanese. No idea about various cultures in middle east.
$endgroup$
– achille hui
Dec 1 '18 at 7:36
$begingroup$
@GerryMyerson Thank you, I saw that one, but it doesn't really contain answers. Also it doesn't specifically address the left-to-right order I'm interested in. There's one data point in the comments, but the one answer has no substance.
$endgroup$
– CodeMonkey
Dec 1 '18 at 8:02
$begingroup$
@achillehui That's very cool, I'm wondering for how long they kept this up, considering the Chinese numbers are already inherently base 10, making them much more useful for math than Roman numerals. Also I studied some Chinese in university (nothing to write home about), and it's fascinating that most of the characters are still recognizable, while I couldn't read whatever my forefathers wrote ~2000-3000 years ago (if they wrote at all).
$endgroup$
– CodeMonkey
Dec 1 '18 at 8:08
$begingroup$
There is remarkable exception from the "left-to-right" convention: This is the composition of functions. Given functions $f : X to Y$ and $g : X to Z$, their composition is written as $g circ f : X to Z$ although we first apply $f$ and in the second step $g$. Obviuosly this is the price for writing $f(x)$. This enforces writing $g(f(x))$ which lead to use $g circ f$ for the functuon assigning to $x in X$ the value $g(f(x)) in Z$.
$endgroup$
– Paul Frost
Dec 1 '18 at 12:00