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I have two thoughts on this topic. They are: "deriving works on your own" and "using other answers to help guide my answer".
Deriving Works On Your Own: frequently through high school I often derived for myself methods for solving problems I didn't know had answers already. When I was young I had a tricky method of calculating the base 2 log of a number (to work out how many bits it contained). It wasn't until later in high school that I learned about the logen over loge2 method of doing the same.
Likewise, with programming tasks, I have often found myself inventing ways of doing things, only to discover later on that there is an existing standard way of doing it.. and in fact it may well be patented.
A lot is said for "original discoveries", that is, you can't obtain a Ph.D without contributing something new to the world of knowledge. Indeed, you are not allowed to use a patented method because the theory is the patent owner "discovered" the method and therefore owns it.
But I believe there is value in discovering things for ourselves, even if they were discovered by someone else. In fact I believe the basis for a patent should be invalidated if someone discovered something on their own without having to learn about the patent through reading it.
Using Other Answers to Guide My Answer: I am a perfectionist by nature.. now in this world of the internet there are a lot of answers out there, and sometimes they are the best darn answer one could reasonably expect to use. There are many top quality tools on the internet but, time and again, I find the exact answer I'm looking for isn't there, or it doesn't suit my exact needs.
Thus I feel that yes the internet does make our lives easier in that it is easier to find answers to questions we would have otherwise spent a lot longer trying to answer.
But I don't believe that the answers provided on the internet are always, or indeed usually, the answer we are looking for. Often answers are pointers to get us thinking about what exactly we'd like to concoct.
I believe civilisations that used to conquer many nations would take the best of the cultures they'd invaded and mixed that into daily life; so it is with the internet - in this global village we have more opportunity to pick the best of what is out there for our needs, and weave that into an answer (the weaving is still up to the individual, however).