We are constantly getting into trouble by mixing up our mental models (mathematical or not) with "actual reality". One obvious example was our assumption that space is "Euclidean". We really hit the wall with this in Quantum Mechanics, which seems to defy human logic itself (The EPR Paradox). I see it all the time when respectable physicists fail to grasp the idea that the Universe may actually be infinite or disallow actual singularities. My favorite example of this is the canard that someplace in an infinite universe there "must" be another version of me typing an identical e-mail to another version of you. Although the analogy is far from exact, I enjoy thinking about this in the same way I enjoy the proof that there is an infinite number of prime numbers. In my imagination at least, an infinite universe implies an infinite number of "situations" at every scale. The idea that two "situations" are identical is a construct of the h...