I have noted the exchanges with Johannes below, who is convinced that the trivial amount of radiation released by manmade processes will somehow affect our atmosphere.

I keep trying...don't know why. I mean, the flaws are so OBVIOUS.

He seems to be immune to correction, either by virtue of math or by virtue of sheer common sense.

Does this make Johannes a dummy? By no means. I have seen a lot of people like him.

This phenomenon is more common and more complicated that it looks. Someone does a lot of math, and a lot of thinking, and arrives at a conclusion that is totally plausible within the parameters set. It is also totally wrong, since some critical parameter is missed somewhere along the line.

I used to smirk at the ancient Greek paradoxes, like Zeno's race between the tortoise and Achilles. His thinking was precise and held solidly to his rules of logic. Of course, any illiterate farmer would have told him that Achilles would blow the doors off the tortoise, but this paradox, according to the link, puzzled mathematicians for years. Cripes.

Now, it is important to note that Zeno was no idiot. So what's going on here?

When I read Jules Verne as a kid, I was impressed by the amount of math he brought to his books. He sat down and carefully calculated the details of his submarine and his moon ship.

Yet, it was obvious even to me then that a submarine built like the Nautilus would have been flattened like road kill at the depths it traversed, and that shooting a cannon shell to the Moon--inhabited yet--was impossible. But I didn't know a lot of engineering back then, and I found no math errors in Verne's work (not that I was a math whiz). And Verne was no idiot either.

Any engineer has had ideas that looked great on paper. But then...

Heck, Marxism works on paper.

Ayn Rand wrote that learning the nature of reality required both reason and observation, and that either one without the other can easily lead you in the wrong direction.

The notion of experimentation (observation) to validate a line of reasoning was not something the Greeks did, and frankly, I don't think Zeno would have cared if someone had outraced a rabbit right in front of him. Zeno lived in that mental state where ideas outweigh reality, which is why you don't want people like that in charge.