The more I read on-line, the more I think the mathematicians have it right. The meaning of 4+3*6 is perfectly well defined. You have to do the multiplication first.
If you want to force the addition to be be done first, you just slip in some parentheses: (4+3)*6.
Sadly, text isn’t like that. And with the internet encouraging writing by all and sundry, and forcing hurried writing by those who should know better, it’s easy to produce potentially ambiguous statements like this, from a piece about the need to encourage social inclusion by reading, on the London Book Fair site:
Not only are those who read less likely to be divorced, but they are less likely to smoke and be unemployed
My original reading of the first phrase parsed “those who read less” as a unit, and the phrase apparently claimed members of this group were “likely to be divorced”.
Of course, reading as far as the end of the sentence made it clear I’d got it wrong and the group under discussion is “those who read” who are “less likely to be divorced”.
If only there were some kind of notation that allowed us to group words in the way that mathematicians group expressions:
Not only are [those who read] [less likely] to be divorced, but they are less likely to smoke and be unemployed.
Yes, that’s pretty ugly, but at least it’s unambiguous.
(You could, of course, add in additional square brackets elsewhere for further clarity, in the same way that the calculation quoted earlier could be written 4+(3*6) although the parentheses are not required.)
I’m a product of an age when punctuation and grammar was barely taught in schools, so I am never sure whether I am doing things right. I am, however, a great fan of commas for clarification. So, when I noticed the same kind of ambiguity in my phrase “a piece about the need to encourage social inclusion by reading on the London Book Fair site”, I patched it by adding the comma after “reading”.
If I had more time, I’d probably be re-phrasing the whole thing. If I hadn’t spent so long in Spain, I probably wouldn’t be tempted to write complex sentences with so many clauses that I get tied in knots.