I wrote a (very long) blog post about those viral math problems and am looking for feedback, especially from people who are not convinced that the problem is ambiguous.
Itโs about a 30min read so thank you in advance if you really take the time to read it, but I think itโs worth it if you joined such discussions in the past, but Iโm probably biased because I wrote it :)
Donโt need any extra letters - just need people to remember the rules around expanding brackets in the first place.
Obviously more letters would make the mnemonic worse, not better. I was making a joke.
As for the brackets โthe rules around expanding bracketsโ are only meaningful in the assumed context of our order of operations. For example, if we instead all agreed that addition should be before multiplication, then aร(b+c) would โexpandโ to aรb+c, because the addition is before multiplication anyway and the brackets do nothing.
I was making a joke.
Fair enough, but my point still stands.
if we instead all agreed that addition should be before multiplication
โฆthen you would STILL have to do multiplication first. You canโt change Maths by simply agreeing to change it - thatโs like saying if we all agree that the Earth is flat then the Earth is flat. Similarly we canโt agree that 1+1=3 now. Maths is used to model the real world - you canโt โagreeโ to change physics. You canโt add 1 thing to 1 other thing and have 3 things now, no matter how much you might want to โagreeโ that there is 3, thereโs only 2 things. Multiplying is a binary operation, and addition is unary, and you have to do binary operators before unary operators - that is a fact that no amount of โagreeingโ can change. 2x3 is actually a contracted form of 2+2+2, which is why it has to be done before addition - youโre in fact exposing the hidden additions before you do the additions.
the brackets do nothing
The brackets, by definition, say what to do first. Regardless of any other order of operations rules, you always do brackets first - that is in fact their sole job. They indicate any exceptions to the rules that would apply otherwise. They perform no other function. If youโre going to no longer do brackets first then you would simply not use them at all anymore. And in fact we donโt - when there are redundant brackets, like in (2)(1+2), we simply leave them out, leaving 2(1+2).
I believe youโre conflating the rules of maths with the notation we use to represent mathematical concepts. We can choose whatever notation we like to mean anything we like. There is absolutely nothing stopping us from choosing to interpret a+bรc as (a+b)รc rather than a+(bรc). We donโt even have to write it like that at all. We could write a,b,cร+. (And sometimes people do write it like that.) Notation is just a way to communicate. It represents the maths, but it is not itself the maths. Some notation is more convenient or more intuitive than others. ร before + is a very convenient choice, because it easier to express mathematical truths clearly and concisely - but nevertheless, it is still just a choice.
