But....(hey, you know that was coming, right?)
You take exception to using the law of averages in determining future events based on prior circumstances. And you specifically use the example of airline safety stating, "[a]n airline passenger who has made many safe flights is due for a crash.”
. . .
And really the same does hold true for lotteries because of the law of large numbers. If you play the lottery over enough times you are
guaranteed to eventually win. The universe may have devolved into a vacuous expanse of free quarks by then, but you will be a multi-millionaire (less the many hundreds of billions of dollars spent on purchasing the bi-weekly tickets.) For me, it is worth two bucks per week for that vanishingly minuscule opportunity to be able to tell a sizable number of people to piss off before my atomic structure completely disassociates.
It becomes a function of noise in the system which presents itself as a feedback loop, something not found in purely random, unassociated events.
With airplanes, the chances of either of us getting on a plane destined for failure on a given flight are the same. But if I fly more than you, my exposure to the potential failure increases each time I fly. When comparing two individuals the probability in a single event is the same. But when considering a single individual over time where the probability is cumulative, I stand a greater chance of crashing than someone who flies only once or infrequently.
Or have I got this all wrong for some reason I can not see? I presume that may be the case since you and Socrates are tormenting me on this fine Saturday morning. :)
However, if two people buy lottery tickets today, they have an equal chance of winning, even if one of them has purchased more tickets in the past. If two people take randomly selected airline flights today, they have the same probability of crashing, even if one of them has flown more in the past.
The fallacious law of averages, in contrast, says that if two people buy lottery tickets today, the one who has lost the most money in the past has the greater chance of winning, and that if two people take airline flights today, the person who has taken more flights in the past without crashing has the greater chance of crashing.
So yes, we are both on the same page in both instances.
And I thank you for this exchange, not only in taking the time to converse with me, but in also giving me the excuse to delay a whole boatload of idiotic, domestic chores my wife has planned for me today.
And again, you have produced an excellent, well written and engaging book.