The original version of this story appeared in Quanta Magazine.
“Obviously” is a dangerous word, even in scenarios that seem simple. Suppose, for instance, you need to do an important computation. You get to choose between two computers that are almost identical, except that one has an extra hard drive full of precious family photos. It’s natural to assume that the two options are equally good—that an extra drive with no space remaining won’t aid your computation.
“Obviously, it doesn’t help, right?” said Bruno Loff, a computer scientist at the University of Lisbon.
Wrong. In 2014, Loff and four other researchers discovered that adding full storage
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