the sense you mean is a different sense of the word index - meaning, to crawl. Yes, of course it does that too.
Google, no doubt, has a very sophisticated way of querying against their cache of the WWW and it has probably evolved over time. However, it is inappropriate to say Google does a join over the entire internet for one query. It is much more reasonable to say that Google checked your query string against their gigantic index of terms, and it took a while to dig that deep into the pile. The performance hit such a complex query takes is more like unzipping a large archive to get a specific megabyte's worth of info, rather than saying it smashed all the files together and then searched for the exact term like notepad.
Anyway, think about it for a while, it's clearly a cool issue in search, and programs and algorithms do not have to visually search things as humans must.
I recommend reading the Stanford paper[0] (page 12), which spells out in a lot of detail exactly what they were doing.
In short, your pathological query would have searched for every document which contained one of your words, discarded those which didn't match all, and then sorted by word proximity. I expect for a literal phase search, there would be a final pass to look for the exact phrase in order.
The reason my search took 30 seconds is because it started by getting a list of every site with "from" on it, every site with "what" on it, and so on, intereseecting them all. That's how it ended up finding my quote. how else do you think it did it?
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to find the string "from what it is to a" which occurs only hidden in the middle of shaespeare's texts -- what do you think they do?
In my opinion they combine the list of sites that have every word - starting with the least common ones. It's easier if you search for something that has a few uncommon words. Then you start with a small list, and have to combine it with other small lists.
When every word in the phrase has billions of sites (there are billions of pages that have the word "to" on them, same for "from", "what", "it", "is", "a"), you have to combine them all. Then you have to do a string search within the resulting set, since I put it in quotation marks. There is no easy strategy. Hence the long search time.
what else could they be doing?