### Multiplication by Juxtaposition

#### Evaluating 8÷2(2+2) in Haskell (and some other languages)

We interrupt the irregularly scheduled philosophical posts for some programming memes:

Over the last few days, the Internet has divided itself over what the value of the expression 8÷2(2+2) should be. Some say it should be evaluated as (8÷2)×(2+2) = 16. Some say it should be evaluated as 8÷(2×(2+2)) = 1.

At the risk of belaboring the obvious, the core dispute here is not really mathematical. There is not some sequence of mathematical operations that produces some number, where mathematicians disagree about what number it produces. Instead, this is a dispute about mathematical notation: what sequence of mathematical operations the expression corresponds to the way it’s written. Specifically, it is a dispute about whether multiplication written as juxtaposition (how “2” is written right next to “(2+2)”) has strictly higher precedence than division. It is closer to a linguistic or typographical dispute than a purely mathematical one, and the correct answer to the dispute is that whoever wrote the expression that way should learn to write math better.

This debate is not even new. The internet had fun arguing over 48÷2(9+3) and 6÷2(1+2), which are functionally identical ambiguous expressions, eight years ago. I don’t know why the debate is resurging now and why we still haven’t gotten tired of it.

But life is short, so since we’re here anyway, let’s make some additional memes.

### Asking the computer

Some of my coworkers had the idea to ask some programming languages what the answer was. The results were underwhelming.

```
$ python3
Python 3.6.7 (default, Oct 22 2018, 11:32:17)
[GCC 8.2.0] on linux
Type "help", "copyright", "credits" or "license" for more information.
>>> 8/2(2+2)
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
TypeError: 'int' object is not callable
```