Mike Manganello offers a useful critique of Car Talk, pseudocontext, and WCYDWT:
I can certainly accept working definitions that require clarification, but the Car Talk problem confuses the issue [of pseudocontext] (at least for me). I’ve only done a little tweaking to the Car Talk problem:
“The fuel gauge of an 18-wheeler is broken, so the driver decides to check the gas level of his cylindrical gas tank with a dipstick. When the level of the gas measures 20 inches high, the tank is completely full. What will the dipstick measurement be when the gas tank is one-quarter full?”
Based on the working definition of pseudocontext, this problem fails on both counts. It completely ignores reality: Why wouldn’t you just fix the gas gauge? Then the problem asks for an irrelevant measurement: Why would we need to know that the tank is one-quarter full?
I assumed the trucker wanted to know one quarter of a tank (rather than four fifths) so he’d know when he had to refuel. An arbitrary number maybe (why not one fifth of a tank?) but not irrelevant. As for ignoring reality, I know more about mid-century Russian architecture than I do about long-haul trucking, but it seemed plausible to me that the trucker couldn’t waste time fixing the gauge in the middle of a run. In both of these cases, I deferred to the authority of the radio hosts. If either of Mike’s complaints were valid, why wouldn’t the hosts have echoed them?
Mike has also misquoted the definition of pseudocontext in small but crucial ways.
Mike’s: “It completely ignores reality.”
Mine: “Context that is flatly untrue.”
Mike’s: “Problems that ask for an irrelevant measurement.”
Mine: “Operations that have nothing to do with the given context.”
Personally, I find the Car Talk problem kind of boring and not very mathematically rich.
Once again we find that a problem’s basis in either pseudocontext or context has nothing to do with how much anyone enjoys or profits from it. (Seems only to fair to mention, though, that Alex’s class had the opposite reaction.)
Another word of caution: Mathematics is part utility and part artistry. By limiting mathematical study to problems related to genuine physical phenomena can only serve to retard the growth of mathematics.
It’s worth clarifying my total agreement here. My blog covers math applications pretty much exclusively not because I think those are the only problems worth studying but because those problems are the easiest to create and teach poorly.