Are any of these non-mainstream opinions? Of course the first three are now, but that doesn't matter (I don't care to think what "mainstream" opinions of computing limits are). I'd wager you can't find a successful person from one hundred or two hundred years ago who had an opinion that would today be considered non-mainstream. It's like when people try to argue against Darwin, saying he was racist -- it was the mainstream opinion of the time.
Besides, all four quotes are bad examples. Nietzsche's quote has to be looked at in the context of the 1880s. Certainly that opinion was quite mainstream then -- the first woman to be awarded a PhD in Mathematics was only in 1886 (source: http://www.agnesscott.edu/lriddle/women/firstPhDs.htm).
Carnegie's quote -- ignoring the part about race -- is a simple history question. Was there ever a "danger of war" between Germany and others? I won't try to answer it, as I don't know. Either way, what matters is what other people thought at the time.
Einstein's quote is simply about facts. Was there the "slightest indication" that nuclear energy was possible? Science marches on -- before the industrial revolution, was there the slightest indication that horseless carriages were possible?
Von Neumann's quote makes more sense when you think about the theory of computation. Computers today still run on the Von Neumann architecture from the 30s and 40s -- any progress has been optimization, and does not push the limit any farther. You still can't sort a list in less than O(n log n) time, or sum n values in less than O(n) operations. As far as I know it, the only thing to push the limits of computing is quantum computing, which is currently in its infancy.
Of course, none of this means that you should think only "mainstream" thoughts -- if you never ask what else is possible, you won't do anything new. But progress marches on -- everyone has mainstream opinions today that will be non-mainstream decades hence.
Interesting, I agree with your facts but I read the author is meaning the exact opposite.
I.e. the author was asking us to take note of these mainstream opinions that brilliant people had and how wrong they are. In other words, even if brilliant people think you are wrong, you may still be right.
Wrong doesn't necessarily correlate with "non-mainstream". There's a point to be made here, but all I'm getting from this article is "famous people can be incredibly wrong too".
Besides, all four quotes are bad examples. Nietzsche's quote has to be looked at in the context of the 1880s. Certainly that opinion was quite mainstream then -- the first woman to be awarded a PhD in Mathematics was only in 1886 (source: http://www.agnesscott.edu/lriddle/women/firstPhDs.htm).
Carnegie's quote -- ignoring the part about race -- is a simple history question. Was there ever a "danger of war" between Germany and others? I won't try to answer it, as I don't know. Either way, what matters is what other people thought at the time.
Einstein's quote is simply about facts. Was there the "slightest indication" that nuclear energy was possible? Science marches on -- before the industrial revolution, was there the slightest indication that horseless carriages were possible?
Von Neumann's quote makes more sense when you think about the theory of computation. Computers today still run on the Von Neumann architecture from the 30s and 40s -- any progress has been optimization, and does not push the limit any farther. You still can't sort a list in less than O(n log n) time, or sum n values in less than O(n) operations. As far as I know it, the only thing to push the limits of computing is quantum computing, which is currently in its infancy.
Of course, none of this means that you should think only "mainstream" thoughts -- if you never ask what else is possible, you won't do anything new. But progress marches on -- everyone has mainstream opinions today that will be non-mainstream decades hence.