What if you reversed the order of operations? Instead of PEMDAS it was SADMEP.
At first glance you would think the order of operations is arbitrary. A convention we agree upon for no reason other than that having a convention ensures (or at least tries to ensure) that expressions will evaluate the same way for one evaluator as they do for another.
I got to thinking about this tonight and came across a consequence of the idea that I couldn't wrap my head around.
3*4+5 regularly = 17.
3*4+5 inversely = 27.
But here's my question. Let's say you're faced with a real life situation.
You have a rectangular arrangement of stones 3 wide and 4 deep. In addition you have 5 more stones. The obvious arithmetic expression for how many stones there are is 3*4 + 5.
This is intuitive and obvious. Partly because we are used to PEMDAS.
But if the order of operations were SADMEP and we were faced with the same arrangement of stones, what would be the arithmetic expression for the amount of stones?
Since I can't think of an arithmetic expression for this situation, does it mean that PEMDAS is the logical (not so arbitrary after all) order of operations?
Or are there stone arrangements that would be equally hard to represent with PEMDAS but trivial to represent with SADMEP?