The connection to the St. Petersburg paradox is pretty tenuous. All the paper seems to suggest is that strength of a fiber is proportional to log(length_fiber)

The connection to the St. Petersburg paradox is pretty tenuous. All the paper seems to suggest is that strength of a fiber is proportional to log(length_fiber). But the St. Petersburg paradox doesn't just come from observing that the odds of getting log_2(n) heads in a row is 1/n. Instead, you're multiplying that quantity by an exponentially growing quantity and then taking an expectation (i.e. summing) and getting an unbounded sum. I don't see a clear analogy to that in material strength.