Today is a Friday, so we’ll take a little pause from our ppmmc series and discuss something a little bit light. We’ll pick up the ppmmc series on Monday.

The following (fragment) statements have different meanings: \((x + 3)\dot\ 7\) vs \(x + 3\dot\ 7\) and this is because of the parentheses in the first statement. Some grade schoolers learn the mnemonic PEMDAS for “order of operations” — parentheses, exponents, multiplication, division, addition, and subtraction. (And, of course, there are other operations not covered in PEMDAS, but that’s besides the point.) The statement \((x+3)\dot\ 7\), for example, doesn’t really mean anything by itself because it doesn’t resolve to anything. If instead one wrote \(f(x) = (x+3)\dot\ 7\), then this would be syntactically more meaningful because at the least, the expression \((x+3)\dot\ 7\) is being assigned to \(f\) and hence we have a statement. But mathematical statements don’t typically end with a specific type of punctuation (maybe QED to denote the end of a proof), they just end. Though often times, there are “words” surrounding the mathematical symbolism and there is a feeling of a sentence so the typical punctuation marks of “!”, “?”, or “.” are used to denote the end. So, this looks fine: what does \((x+3)\dot\ 7\) equal if \(x = -3\)?

Now, a quick change of gears. Punctuation is just a way of allowing the reader to understand where the breaks are. Take for example, (and now the rant begins), the use of quotes. Consider the following sentence:

Fred exclaimed, “There is no extra credit in my class!”

This is typically how such a sentence would be written. Notice the use of the comma to explain to the reader that the author is stating what Fred exclaimed. Then notice the use of the quotes to tell the reader what Fred exclaimed. Since Fred was exclaiming something, the sentence encapsulated in the quotes is terminated by an exclamation point. But, where did the whole sentence end? Apparently, it ended with the close quotes. But this makes no sense! This is bad syntax. Here’s how the sentence really should be written.

Fred exclaimed, “There is no extra credit in my class!”.

Ahhhh, that feels so much better. The sentence has ended with a glorious period as it should. The exclamation point was to convey a sense of exclamation in Fred’s voice when he, well, made his exclamation. The period denotes the end of the sentence which states without exclamation what Fred had exclaimed. This is syntactically consistent. Aesthetics be damned.

So now suppose someone wanted to quote the author about Fred’s exclamation. How should that be written? In this author’s view, it would be written like this.

Did the author write, “Fred exclaimed, “There is no extra credit in my class!”.”?

And a response could be

Yes, the author did write, “Fred exclaimed, “There is no extra credit in my class!”.”.

. ← I need this period because it ends the sentence that began with, “And a response could be …”. 😀

How would this be done in the “standard” way? I have no idea. It would be ugly, inconsistent, and confusing. Probably something non-sensical like

Did the author write, “Fred exclaimed, ‘There is no extra credit in my class!'”

Maybe the person would be bold and put a question mark at the end. Who knows.

The same reasoning works for parenthetical statements or sentences. (This self-referencing example shows that this sentence is encapsulated inside the parentheses, so the period comes first.) Whereas if there were a sentence embedded in a parenthetical while inside of another sentence (This is an another example of self-referencing.), then the punctuation should look like the way it does for this sentence. And what happens if there is a parenthetical sentence inside of a sentence, but it ends the sentence (This is a contrived scenario, but it can happen.)? ← That’s how the punctuation should work! Finally, there is one more layer of nesting like this (And what happens if there is a parenthetical sentence inside of a sentence, but it ends the sentence (This is a contrived scenario, but it can happen.)?). “Ugly.”, you say? Not in the slightest! This is clear, beautiful, logical syntax.

– Truly, you have a dizzying intellect.
Wait till I get started! Now where was I?
– Logical syntax.
Yes, logical syntax.

What about abbreviated words or phrases at the end of a sentence? Consider the sentence below.

I had to get groceries, go to the bank, go to the post office, get my car from the repair shop, etc.

Where did this sentence end? Did it end with “etc.”? How could it? The period following “etc” ends the abbreviation for “et cetera”. There needs to be another period. The sentence should look like

I had to get groceries, go to the bank, go to the post office, get my car from the repair shop, etc..

. See doesn’t that make so much more sense and isn’t it consistent now? Don’t you feel warm and fuzzy inside now? If this sentence happened to be interrogative or exclamatory, then we’d have no problem writing “etc.?” or “etc.!”, respectively. What probably happens though, because of people’s irrational phobia of consecutive punctuation marks, is that “etc.?” would be written as “etc?” or some other equivalent, inconsistent way. Here is the same sentence inline as a quote: “I had to get groceries, go to the bank, go to the post office, get my car from the repair shop, etc..”. You may ask, “Did you just write, “”I had to get groceries, go to the bank, go to the post office, get my car from the repair shop, etc..”.”?”. Yes. Yes, I did and you had better write it that way too.

Anyway …

It is doubtful that the world would be any better off if punctuation rules were syntactically consistent, but who knows how much easier people would find working with mathematics if they had been taught logical systems and then were allowed to use them consistently early on? In any case, I will continue to use the “standard” punctuation, but don’t be surprised if you see, from time to time, a little rebellion on that front. Please let me know if you see any punctuation gaffes here. I’ll promptly fix them.