From Nate Silver's "The signal and the noise:"
The amount of information was increasing much more rapidly than our understanding of what to do with it, or our ability to differentiate the useful information from the mistruths.
Why is there a comma before or? Isn't the second clause dependent, since it refers to the increasing amount of information (so it's not self-contained)? If it is indeed independent, how exactly do you tell when a clause is dependent?
The second clause is neither independent or dependent as there is no verb in the phrase "our ability to differentiate the useful information from the mistruths". This sentence is a compound sentence and is equivalent to writing "I don't like signal, or noise".
I see two possibilities of why there is a comma:
Provide clarity in a long sentence. It helps break up the sentence for easier reading and gives the reader a place to pause for a mental or real breath.
Style choice, either by the author or the editor.
No, it is not an independent clause. In fact, it isn't even a full clause:
Or our ability to differentiate the useful information from the mistruths.
There is no main verb in this phrase. It's just our ability to do something. This is a nominal phrase, not a clause or a sentence.
There is another issue: the use of or there makes the sentence more complicated, and I would consider it inadvisable. And should have been used, and even and than after a comma. The comma is optional: it is probably frowned upon by some, but it certainly make the sentence easier to read. (Without the comma, remove than.)
The amount of information was increasing much more rapidly than our understanding of what to do with it, and than our ability to differentiate the useful information from the mistruths.
The reason is that the information was increasing more rapidly than our understanding what to do, and it was increasing more rapidly than our ability to differentiate: that's what you get when you fill in the ellipsis. It is both-and, not either-or.
The reason that or was used is here is probably that than suggest an implicit negation: after all, the thing you compare it to ("our understanding") is not increasing more rapidly than the thing compared ("the amount of information"). In older French, a negation would be used after than in the same kind of comparison, as in: "this house is larger than that house isn't". Of course we do not do this in English, but the mental inclination is there. And in negative sentences with as, you woulduse or:
This house is not as large as your house or my house.
SUPPLEMENTAL:
Both Bill Franke and Cerberus have provided excellent analyses of the structure of this sentence; but I must dissent from their understanding of Silver’s or.
English or is ambiguous: it may act as either what logicians call an exclusive or, denoting “one and only one among alternatives”, or an inclusive or, denoting “one or more among alternatives”.
In a very rigorous discourse where such ambiguity is intolerable — a legal document, or a treatise on logic — additional words are required to eliminate the ambiguity: “one or the other, but not both”, for instance. But in ordinary discourse, which sense is intended will be clear from the context. If I display two theatre tickets and ask
Should I take Bob or Carol or Ted or Alice?
no hearer will suggest I invite all four, or any three or two. If, on the other hand, I assert (truthfully) that
My rutabaga is bigger than Bob’s or Carol’s or Ted’s or Alice’s.
no hearer will be in any doubt whose vegetable is the largest.
Accordingly, I think you may dismiss the strictures against the use of or here; it is perfectly clear that Silver employs or rather than and to express, in fewer words, the same quality of disjunction as “on the one hand ... on the other hand”.
