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Where and When Did the Symbols "+" and "–" Originate?

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Re: Where and When Did the Symbols "+" and "–" Originate?

#41

Post by scott_s »

rootbear wrote: post #35
pavlov wrote: post #5

What fascinates me most about this story is how it illustrates what a young race we humans are intellectually. If we ever want to be anything more than warring tribes, we must learn to accumulate knowledge together. Universal symbols for addition and substraction are the first small step on that very long road, yet it's only been a few hundred years since we took that step. On the scale of the universe, we are like a…

And we're still using '*' for multiplication in our programming languages instead of '×' because using anything other than ASCII for programming is just too hard, or too weird, or whatever.

To be fair, I prefer dots over crosses for multiplication of scalars in when I write it myself. I tend to assume a cross means cross product instead of scalar multiplication. (But, oddly, I do not assume that a dot means dot product.)

Re: Where and When Did the Symbols "+" and "–" Originate?

#42

Post by sp332 »

rootbear wrote: post #35
pavlov wrote: post #5

What fascinates me most about this story is how it illustrates what a young race we humans are intellectually. If we ever want to be anything more than warring tribes, we must learn to accumulate knowledge together. Universal symbols for addition and substraction are the first small step on that very long road, yet it's only been a few hundred years since we took that step. On the scale of the universe, we are like a…

And we're still using '*' for multiplication in our programming languages instead of '×' because using anything other than ASCII for programming is just too hard, or too weird, or whatever.

We already tried going full-APL but it only proved that it wasn't a good idea. I mean this is impressive https://www.youtube.com/watch?v=a9xAKttWgP4 but I still think the notation is too obscure.

Re: Where and When Did the Symbols "+" and "–" Originate?

#43

Post by rmccue »

rootbear wrote: post #35
pavlov wrote: post #5

What fascinates me most about this story is how it illustrates what a young race we humans are intellectually. If we ever want to be anything more than warring tribes, we must learn to accumulate knowledge together. Universal symbols for addition and substraction are the first small step on that very long road, yet it's only been a few hundred years since we took that step. On the scale of the universe, we are like a…

And we're still using '*' for multiplication in our programming languages instead of '×' because using anything other than ASCII for programming is just too hard, or too weird, or whatever.

More likely, it's because we don't have them on our keyboards. Programming languages are usually about reducing friction for programmers, but using the proper multiplication/division symbols would increase that for most people.

Re: Where and When Did the Symbols "+" and "–" Originate?

#44

Post by milliams »

scott_s wrote: post #41
rootbear wrote: post #35

Earlier quoted context omitted.

And we're still using '*' for multiplication in our programming languages instead of '×' because using anything other than ASCII for programming is just too hard, or too weird, or whatever.

To be fair, I prefer dots over crosses for multiplication of scalars in when I write it myself. I tend to assume a cross means cross product instead of scalar multiplication. (But, oddly, I do not assume that a dot means dot product.)

But even in that case, people are using the full-stop '.' rather than the middle dot '·'

Re: Where and When Did the Symbols "+" and "–" Originate?

#45

Post by kps »

yaix wrote: post #37

> Overall, what is perhaps most impressive in this story is the fact that symbols which first appeared in print only about five hundred years ago have become part of what is perhaps the most universal “language.” They appeared just at the right time to be carried around the world by conquista and colonialism. Same goes for time notation, etc.

They appeared just at the right time to be carried around the world by movable type. Same goes for non-mathematical punctuation.

To put it another way, mass production of text froze the symbols that happened to be in use at the time.

Re: Where and When Did the Symbols "+" and "–" Originate?

#46

Post by tel »

sp332 wrote: post #42
rootbear wrote: post #35

Earlier quoted context omitted.

And we're still using '*' for multiplication in our programming languages instead of '×' because using anything other than ASCII for programming is just too hard, or too weird, or whatever.

We already tried going full-APL but it only proved that it wasn't a good idea. I mean this is impressive https://www.youtube.com/watch?v=a9xAKttWgP4 but I still think the notation is too obscure.

Full APL isn't just unicode, though, it's also a total commitment to single-character operators as the primary language construct. Take a look at some Agda or Unicode-enabled Haskell code to see it really improving readability... though hampering type-ability.

Re: Where and When Did the Symbols "+" and "–" Originate?

#47

Post by Gormo »

lmm wrote: post #10

I always felt the origin of the equals sign was wonderful: "I will sette as I doe often in woorke use, a paire of parralles, or Gemowe lines of one lengthe, thus : ==, bicause noe 2, thynges, can be moare equalle."

> bicause noe 2, thynges, can be moare equalle

Which is not to say that a higher degree of equality can't be attained; it's just that then you'd have one thing instead of two.

Re: Where and When Did the Symbols "+" and "–" Originate?

#48

Post by chiph »

yaix wrote: post #37

> Overall, what is perhaps most impressive in this story is the fact that symbols which first appeared in print only about five hundred years ago have become part of what is perhaps the most universal “language.” They appeared just at the right time to be carried around the world by conquista and colonialism. Same goes for time notation, etc.

One of the interesting things is why are there 24 hours in a day, 60 minutes per hour, etc?

Mathematically, those values are useful because they can be factored in many ways. But who picked them?

I was at the British Museum one time, and they had an horological exhibit (clocks throughout the ages), so I asked one of the curators. He said it was the Babylonians that chose those values.

But since this thread is about notation, I should be asking who picked the colon (:) as the time separator that is generally used. And are there other conventions for this?

Re: Where and When Did the Symbols "+" and "–" Originate?

#49

Post by kps »

mseebach wrote: post #29
mich41 wrote: post #19

Earlier quoted context omitted.

Everybody uses juxtaposition for multiplication (or dot when some separation is required) and horizontal line for division. * and / are poor man's substitutes when all you have is ASCII. × is used for vector products, Cartesian products and products of algebraic structures in general. The only place I've ever seen × or ÷ being used in arithmetics was primary school. No idea why they use them.

> The only place I've ever seen × or ÷ being used in arithmetics was primary school. No idea why they use them. Perhaps because the other prominent use is on the buttons of every single calculator in the world.

I recall using × and ÷ in primary school, before the advent of portable calculators.

I know that's mere anecdotal evidence, but I believe there do exist reliable documentary sources from that era.

Re: Where and When Did the Symbols "+" and "–" Originate?

#50

Post by kps »

manish_gill wrote: post #36
yaddayadda wrote: post #31

The next logical question is, "Where did × and ÷ originate?" From there, I've always wondered how multiplication migrated from "×" to "∗"? And recently, I've wondered if we will migrate "-" to something else? (This last derives from having to annotate a range of numbers including positive and negative. When "-" is used for both range and negative, it causes confusion.) p.s. I tried to post this to the original poster…

I always thought the * was used for multiplication to avoid confusing × with the English alphabet X. We can usually distinguish them while writing equations on paper(I write x in a cursive, for example).

* was used for multiplication because there weren't enough bits to fit every symbol everyone would have liked into ASCII, so compromises were made, including preference for symbols that could be 'overloaded' with multiple meanings in different contexts.
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