It saddens me that the most accessible repositories of information are those that, allegedly, dumb me down.
There is A LOT of information in printed books that is not on the Internet.
There was a project to put all books on the Internet -- Google Books -- but that famously got tied up in lawsuits.
As a result, if your information diet consists of the Internet and not books, you're missing out.
I occasionally write something "obvious" from a book on my blog, and people are like "wow how did you figure that out" ?
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For what Knuth is doing, he certainly doesn't need to read much on the Internet. Most of it is in books, or at the Stanford library (or whichever library he goes to).
He's probably so busy with books that the Internet seems UNINTERESTING.
If you want access to newer publications, the Internet is more efficient, but those are also available to the library. (Sadly, Scihub is the best source for those without university access.)
So yeah I'd say 3 main repos of knowledge are: the open Internet, printed books, and Scihub, and many people today only use the first one.
As an aside, ThriftBooks has been amazing for increasing my collection! I;ve gotten so many books for cheap
No ads lol!
It's honestly sad to me when I see people scrolling through terrible web pages with tiny morsels of information, which are often "interested" or wrong.
The question was how the phases add or subtract when looking at a phase graph of a cosine wave modulated DFT transform, not exactly rocket science.
It seems like the internet has dumbed down to the point where its front page is very surface level and always requires additional research assistance in the form of SearxNG, AI chats, or turning to less SEO prone engines like marginalia or even wiby to get good and honest results. I don't think adapting to human toxic environments like the current internet is a good model for the future, when we already have the tools to filter the wheat from the chaff.
But I've also used the internet to great effect when getting up to speed on a research topic because I had lots of access to high quality texts and tools (citation manager for tracking, spreadsheet for glossary of terms). Notably that didn't involve any communications, just searches.