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Comment by roelschroeven | Hacker News Reader

Off-topic, a question about the notation used for multiplication in this article.

I'm used to see multiplication written as 3⋅12 or sometimes 3×12, but recently I encountered this notation using parentheses, 3(12), and now I see that in this article too. Is that commonly used? It looks weird to me, and not very readable, perhaps just because I'm not used to it. To me 2⋅2⋅2⋅3⋅7 is much more readable than 2(2)(2)(3)(7) (which at first sight looks like function calls to me). Is the parentheses-notation used just to get rid of the explicit multiplication sign?

I guess there are situations where you can't easily use a proper multiplication sign, in which case I can see the parentheses notation as an effective alternative. But I've seen it used in handwritten equations too, so that can't be the only explanation.

Just wondering.

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which at first sight looks like function calls to me

This is at least consistent. Let's try to think of numbers as functions. Then dots or juxtaposition must mean function composition, right? Then, f(x)=f⋅x is consistent with arithmetic as we know it and this dual interpretation of dots. I suspect that it's also the only such consistent mapping from numbers to functions, but couldn't prove this right away.

I usually only recall seeing it where it's the expansion or replacement of a variable with the actual value, when solving equations or similar. It's not great. I've seen it used in a text talking about programming, with letters: so a(x) was actually multiplication but looked exactly like a function. Ugh!

It’s not uncommon to write a x b as ‘ab’. So if you wanted to put two literals together using this syntax you could wrap one in brackets.

Yes, it is extremely common. What country are you from?

It is used particularly in things like 3(x + 5) or (a + b)(a - b).

In your examples, it's not the brackets signifying the multiplication. It's the adjacency that signifies the multiplication (as in e.g. 3x) and in they happen to need brackets to highlight the precendence which would be lost in e.g. 3x + 5.

The notation of the article logically follows because e.g. (4) = 4 but using that as a "cheat" to enable multiplication of numeric literals using adjacency is very rare I think.

No, it's not rare. It's still quite common when you have people manipulating literal numbers. The literal numbers are what's rare.

You say it's not rare, but I can't remember ever seeing it before reading this article.

Likely because you haven't encountered it since junior high school. It's not uncommon notation in pre-algebra and occasionally beginning algebra.

Yes, of course, I do know that. It's not what I meant.

Suppose we expand that first example. I would write: 3(x + 5) = 3x + 3⋅5 The notation I'm talking about writes: 3(x + 5) = 3x + 3(5)

It's that 3(5) instead of 3⋅5 I'm talking about.

I prefer to use a dot like you, but find calculations like "let x=5, then 3(1+x) = 3(1+5) = 3(6) = 18" acceptable, because each equation is just a lock substitution

In (high energy) physics the digits in the parenthensis states the error bar.

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