[monorailz]

In the linked notebook http://nbviewer.jupyter.org/url/norvig.com/ipython/Countdown... when he says

>because there are 2 ways to make 27 with the numbers (10, 9, 8), namely, ((10+9)+8) and (10+(9+8))

why not also (10+9+8)?

[dalke]

+ is an associative binary operator. You have to decide which pair to add first.

[ibrahima]

To add on, I think he's writing from a Lisp perspective, not general math notation.

[moron4hire]

That doesn't matter. It's just the basic associative property of addition in arithmetic. As such, it's present in all programming languages.

[Dylan16807]

But in normal math it's easy to use n-ary addition.

[gjm11]

In Lisp too -- arguably easier than in most languages. To add 10+9+8 in Lisp you write (+ 10 9 8), a single 3-ary call to +. In, say, C you write 10+9+8 and the parser turns that into two 2-ary additions.

(Of course, in either language you end up with two 2-operand ADD instructions in the object code. Nothing has hardware for arbitrary n-ary adds!)

[B1FF_PSUVM]

Nowadays math mostly ends up in a CPU crunching two inputs at a time.

If you don't write it so explicitly, a compiler will do it for you anyway.

[monorailz]

Thank you both, that makes sense.

[zitterbewegung]

Think about when you evaluate the expression (10+9+8). You will either add 10+9 or 9+8 first and add 19 to 8 or 17 to 8. (10+9+8) is ambiguous because it can be parsed both ways.