[TheRealDevonMcC]

The preceding discussion is a good example of "whoosh!" because it fails to understand that APL is an array language. It eschews scalar representation like "A1x1 + A2x2 ...". In APL, you would write this as something like "A +.× x".

The same lack of understanding of the array context also underlies the earlier comment favoring "standard" order of operation that works well for maybe five functions with three levels of precedence but quickly becomes unwieldy for more functions.

Someone else already alluded to this lack of scalability but the power of a strictly positional precedence - not "no precedence" - shows up in array operations. For example, consider reduction by a non-commutative function like "-/A".

In the "standard" order of precedence, since all the subtractions are at the same level, this can be restated as the first item in A minus the sum of the remaining items. This is not particularly interesting or useful.

However, positional precedence interprets this expression as an alternating sum: (2-3) + (5-9) (for the "A" above). Alternating sum is a common, useful construction in mathematics.