punctuation - "Life changes; memories don't." A comma would be better?

I came across this sentence on a blog.

Life changes; memories don't.

The first time I read this sentence, I knew something was wrong. If I'm not wrong, a semicolon is used between two independent clauses, but memories don't isn't an independent clause.

Now the correction could be

Life changes, memories don't.

OR

Life changes. Memories don't.

Have I analyzed the mistake properly? Could there be any other possible way of writing this sentence?

Answer

Memories don't is indeed an independent clause, meaning "memories don't change". The auxiliary verb don't licenses the ellipsis of the following verb phrase. In linguistics, this is often referred to as VP ellipsis or post-auxiliary ellipsis:

1a. Have you seen Titanic? I have seen Titanic.
1b. Have you seen Titanic? I have seen Titanic.

The presence of an auxiliary like have allows you to omit the rest of the predicate. Of course, this only works if the listener can figure out what you've omitted! So it depends on context, too.

In your example, both conditions are met. We have the auxiliary verb don't, and it's clear from context what the rest of the sentence should be:

2a. Life changes. Memories don't change.
2b. Life changes. Memories don't change.

So what we actually have here is a sequence of two independent clauses. They can, of course, stand independently as complete sentences, separated by a period:

3a. Life changes. Memories don't.

We can also join them with a semicolon, like any pair of complete sentences. This is most appropriate when the two sentences are closely related:

3b. Life changes; memories don't.

We have a third option, too. When sentences are very closely related, and especially when they're short and parallel or contrastive in structure, we can join them with a comma:

3c. Life changes, memories don't.

This is called asyndetic coordination, and as a rhetorical device it is often referred to as asyndeton. In this form of coordination, you put constituents together without an overt coordinator like and or or. You've probably seen it in some famous quotes:

4a. I came, I saw, I conquered.

As you can see, these coordinates are closely parallel, similar in meaning and form. When this isn't true, asyndetic coordination is less acceptable, and people often use the term comma splice to refer to the resulting sentence. Unfortunately, there's no hard-and-fast rule for when it's acceptable and when it's not.

But in this case, I think the comma works fairly well. Your coordinates are similar in form and in meaning:

3a. Life changes. Memories don't.
3b. Life changes; memories don't.
3c. Life changes, memories don't.

I think all three are fine.