# Calling all you PEMDAS (or BEDMAS, or PERMDAS) fans…

Consider the expression:

$256^{(\frac{1}{2})^{3}}$

Is its value 2 or 4096?

And can we all agree that this question doesn’t matter? Can we agree that it’s like debating the meaning of a poorly written sentence, when we should really be reprimanding the person who wrote it and imploring them to be more clear next time?

In short, can we allow Vi Hart to lead us into the light on this one?

### 4 responses to “Calling all you PEMDAS (or BEDMAS, or PERMDAS) fans…”

1. Christopher

What I’m saying is that if you wrote that expression, you either meant: $(256^{(\frac{1}{2})})^{3}$ or you meant $256^{((\frac{1}{2})^{3})}$. You should have written what you meant.

2. Yes, let’s please agree that this is the mathematical equivalent of a dangling participle or a misplaced modifier. The whole point of a (let’s face it, largely arbitrary) convention like PEMDAS is to avoid ambiguity. If your English sentence is unclear, it’s not the reader’s fault; if your mathematical expression is unclear, it’s not the evaluator’s fault. A sentence/expression should be as concise as convention allows, but no more so. And parentheses are free.

Debating the correct interpretation of this expression is about as informative, as a mathematical exercise, as it would be for English students to debate whether the fact that Latin infinitives are incapable of being split means that we also shouldn’t split them in English. There might be an answer, but it’s trivial and unrelated to the real issue: How can we best communicate what we mean?

3. Christopher

Lusto:

How can we best communicate what we mean?

A: With copious use of bold type, evidently.

• My thoughts cannot be contained by puny, standard-width fonts. Sometimes I even use extra serifs, just to catch any overflowing emphasis.