Bill Stewart <[EMAIL PROTECTED]> wrote : >At 08:22 AM 01/25/2002 -0800, Tim May wrote: >>On Thursday, January 24, 2002, at 09:06 PM, [EMAIL PROTECTED] wrote: >>>I've concluded that you can't answer Tim's riddle >>>without knowing the radius of the drill --but I may >>>put myself open to ridicule for suggesting this. >> >>But if you were devious enough, you would realize that >>"can't answer Tim's riddle without knowing the radius of the drill" >>allows for offering the infinitesimal drill bit "trick" >>as a valid solution to the problem. > >It's quickly obvious that *if* there is a solution, >it's either dependent on "d", the radius of the drill bit, or it's not. >If it is, the infinitesimal drill bit is the obvious calculation method. >But it's a counter-intuitive answer, and real-world problems >don't usually have answers that neat, and the mind that is not merely >devious but also curious says "that's interesting, let's explore this, >have I got some paper to draw pictures on, wonder how someone noticed >a surprising result like this...". > >Alternatively, the mind that is not curious but merely plodding says >"OK, if there's an answer, that's it, but let's check to be sure >before sending Tim the answer", which leads to almost as much work >as doing it from scratch :-) > Curiosity is what gets one to pursue the problem in the first place.
Economics can influence the method. Starting with the devious solution which is obviously the cheapest you can choose to invest in some qualitative reasoning. In Tim's puzzle what happens to the thickness of the collar ( which becomes infinitesimally thin as the drill gets larger ) can be pondered without putting pencil to paper or fingers to keys. This easy investment can lend some degree of confidence at minimal cost. The level of investment should be proportional to the value of the correct answer. I think starting with the devious approach is the more effective in that investment is comitted in phases, if any one phase shows that further investment is clearly not a good choice you can stop and cut your losses. Starting right in with the plodding solution might turn out to be a very heavy investment in a guaranteed failure that could have been spotted sooner. Mike
