Recursive Smoking

Another interesting bit came up today on the site of the Dutch newspaper Trouw: Second-hand smoke is also harmful to the smoker. (I do like these miniscule on-line pieces from Trouw, that nevertheless usually manage to communicate a well-defined, thought-provoking point. This sort of material helps this blog to move closer to the aggregation function that has been suggested for it.)

Basically, while the health risks of second-hand smoke for non-smokers in the same general vicinity have been subject to exhaustive investigation, the impact of that smoke on the smokers who were emitting it in the first place has been neglected, on the assumption that they had enough health problems just taking into account their direct puffing. But no! A smoker may think he has smoked, say, fourteen cigarettes on a given evening – because he sees fourteen butts in the ashtray – but in reality the harmful effect on him is on the order of 16.6 cigarettes, precisely because of the second-hand smoke he created but then breathed in again.

This is out of a study from the (Italian) National Institute for Cancer Research, where they conducted their research on smoking newstand kiosk-owners, who sit there most of the day just smoking by themselves. But mathematicians out there will justifiably wonder whether 16.6 in that particular case is really the final figure, or whether it is instead even higher. After all, that second-hand smoke that you breathe in you then exhale again (making it third-hand smoke), which then you partially breathe in again, etc. etc. This sounds to me like an infinite sequence problem! (Which, as any good mathematician can tell you, under certain conditions will still yield a non-infinite, final answer.)

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