Since this doesn't exist in practice, shouldn't the article author first explain what they mean by that?

> 1 + )2 * 3(

(1 + 2) * 3

I love the twist: reversing the friendly levels gives you a classic parser, and it opens up crazy experiments like whitespace weakening. Have you tested it on non-arithmetic ops (logical/bitwise) or more complex expressions like ((()))?

If you have the expression 1+2*3 you have three elements with two operands. You need to choose a rule to pick one of them first.

In mathematics, the rule is "*/ then +-" and then from left to right. This means that usually first you do 2*3, then 1+.

But what if you do want to make 1+2 first?

There is another alternative, parenthesis. Those mean "do the thing inside first" so (1+2)*3 changes the precedence and now you do 1+2 first, then *3

The post is asking: with parenthesis you can increase the precedence of operations. What if you could decrease it?

Let's use «» as another operand (the blog uses parenthesis, but that makes it really confusing) this operand means "do the thing inside last". So the expression 1+«2*3» means "do 1+ first, then 2*3.

The issue is...this doesn't make sense, what the blog is really saying is to reduce the precedence of operators. Think the expression 1+2«*»3 or 1+2(*)3 and now the rule is "the parenthesized operators have one precedence less" so 1+2(*)3=(1+2)*3

Instead of ordinary brackets, one can also use the dot notation. I think it was used in Principia Mathematica or slightly later:

  (A (B (C D)))

  A . B : C .: D

However, this is only a replacement for ordinary parentheses, not for these "reverse" ones discussed here. Maybe for reverse, one could use groups of little circles instead of dots: °, °°, °°°, etc.

1 + (2 * 3) forces 2 * 3 to happen first.

Without them, operator precedence decides. The post asks a deliberately strange question:

What if parentheses did the opposite — instead of grouping things tighter, they made them bind less tightly?

Clearly, this was the worst possible time for me to come across this brain damaging essay.

I really can’t afford it! My mathematical heart can’t help taking symmetrical precedence control seriously. But my gut is experiencing an unpleasant form of vertigo.

For example,

    (1 + 2) * (3 + 4)

    1) + (2 * 3) + (4

    (1) + (2 * 3) + (4)