The connection to the St. Petersburg paradox is pretty tenuous.<p>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.
"A chain is only as strong as its weakest link"<p>And if you model a rope or fiber as multiple chains side-by-side (and on a molecular level they kinda-sorta are) then the longer the chain the more likely you end up with multiple parallel/concurrent defects.<p>It's an interesting finding in that few would ever intuit it but once told about it they'll say it's "obvious". At least that's what I thought!
> Materials typically contain lots of small imperfections, but it’s the rare, large defects that cause a material to fail.<p>Ok so.... we need to know more about the rare large defects! Unfortunately that's the last we hear about them in this paper.