I think if you ask the experts who would claim that they know what the “correct” way to punctuate something is, they would tell you that a sentence may only have one terminal punctuation mark—that is to say, neither “?!” nor “!?” is correct.
So, no matter what order you use, you’ll never please those people. The Corpus of Contemporary American English has 3742 examples of “?!” and 1197 examples of “!?”. Clearly both orderings enjoy substantial usage, although it does appear that “?!” enjoys a majority of usage, probably because most sentences that get the double punctuation treatment are syntactically questions that have an exclamation point added for emphasis.
Edit: I checked in the British National Corpus, and it has 224 instances of “?!” and 121 instances of “!?”.
A question within a sentence should be preceded by a comma, and end with a question mark.
I am wondering, how long has that fish statue been there?
There are three important issues that this committee must address. What was the chairman doing in that YouTube video? is not among them.
If a question is particularly long or complex, then for clarity it could begin with a capital letter.
In the daydreams of my youth I would look at the clouds and wonder, Will I find happiness and fulfillment soon after getting a business administration degree, or must I amortize my well-being return on investment over the next seven to ten calendar years?
The sentence in the original question ends with a subordinate clause that does not, by itself, ask a question (“within which we can leverage our existing knowledge”). This is modifying a noun phrase that is part of the question (“set of simple computational rules”). Therefore, this subordinate clause is part of the original question, and should end with a question mark.
Putting all of this together, I would punctuate the sentence like this:
The question nagging me is, To what extent can we encapsulate all what we observe in nature into a set of simple computational rules, within which we can leverage our existing knowledge?
(Some of this advice is based on The Chicago Manual of Style 15th Edition §6.55 and §6.71.)
Best Answer
"Who knows?" is an example of a rhetorical question, because it is really a statement that does not actually ask for an answer.
The consensus is that it's sometimes OK to skip question marks for rhetorical question. Some people will say you shouldn't ever skip a question mark for a rhetorical question, and no one minds if you use a question mark, so I suggest that you do. (Personally, rhetorical questions without question marks always throw me off -- John Grisham has a habit of doing this and it causes me to read these sentences in a weird, sarcastic tone)
Here is more information from Wikipedia: