System: How about “Inverse Parentheses”? We can write the entire article without ever defining what it means. Nerds will be unable to resist.
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.
a = 2 *
3 + 4 list = [
1,2,3,
[ 4, 5 ],
6
]
=
a
*
2
+
3
4
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.
A . B : C :. D
((A B) C) D
What if you need to nest parentheses? Then you use more dots. A double dot (:) is like a single dot, but stronger. For example, we write ((1 + 2) × 3) + 4 as 1 + 2 . × 3 : + 4, and the double dot isolates the entire 1 + 2 . × 3 expression into a single sub-formula to which the + 4 applies.²
A dot can be thought of as a pair of parentheses, “) (”, with implicit parentheses at the beginning and end as needed.
In general the “direction” rule for interpreting a formula ‘A.B’ will be to first indicate that the center dot “works both backwards and forwards” to give first ‘A).(B’, and then the opening and closing parentheses are added to yield ‘(A).(B)’. The extra set of pairs of parentheses is then reduced to the formula (A.B).³
So perhaps one way of thinking about it is that more dots indicates more separation.
¹ https://plato.stanford.edu/entries/pm-notation/dots.html
² https://blog.plover.com/math/PM.html
³ https://plato.stanford.edu/entries/pm-notation/dots.html
See also https://plato.stanford.edu/entries/pm-notation/index.html and https://muse.jhu.edu/article/904086.
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Well done.