As an applied physics major in college, one of the things that I found difficult was solving many of the more complex equations that you would come across in mechanics (Orbital equations), E&M (Maxwell's equations), quantum mechanics (Schrodinger's) and the like. This is not to say that I didn't like or wasn't any good at math. But when solving such equations, you invariably needed to reduce some number of terms to zero because they were negligible relative to the other terms, and I just never could wrap my head around that. (As an example, take a look at equations 4.53-4.55 here)
At what point does it really become negligible? A hundred to one? A thousand? I mean, it's non-zero, right? That means it's gotta have some kind of effect, or so I thought.
Advice to people wishing to become smarter: Get in the habit of assuming that everything is more complex than you imagine.
Anyway, it makes some interesting points on how to evaluate risk -- beyond just straight probabilities and expected ROI -- using examples of the lottery, insurance and... Russian Roulette. The author suggests that, as a thought experiment, you might consider how much you value your own life, in very tangible, quantitative terms:
Suppose you have the option to play Russian Roulette, in return for which you will receive a fee of x. The gun has one million chambers, one of which holds a bullet. If you get the bullet, you die. Otherwise you collect the fee. What is the minimum value for x that will induce you to play? Would you play if x were one million dollars?The author says he'd do it for a million. (the discussion follows with another step or two.) Me, I couldn't find a workable number for x. I'm sure part of that stems from a lesson I learned a number of years ago that can be summarized in a fortune that read: "an ounce of gold cannot buy an ounce of time." (Let's just say bonus plans can be evil. In essence, for a carrot, THEY OWN YOU. Ok, lesson learned.) But, I think a larger aspect is that even when you're talking about a million to one odds, IT'S STILL ONE -- a finite number. Non-zero, baby. And you know what? Shit happens. Shit happens to me. And I guess maybe I value life too much. Perhaps under other circumstances, my response might differ. But given my present circumstances, I value life, my life, too much. Or at least I value it more than money.