Dave told me one time that he solved part of his thermodynamics test with ratios instead of the method presented in the text. The instructor gave him a hard time about not using the correct method. Now I'm all for the 'proper' way, but come on, a right answer without cheating is a right answer. If the problem was trivial enough to be solved with an inferior method then it really wasn't a problem was it?
I think that Ratios is outclassed by symmetry. Just the other day I was reviewing some design changes for someone and it was symmetry that told me the person screwed up. Logic dictates conditional outcomes, If -> Then. thats usually not to hard to follow, where most people stop thinking is in the If -> Then -> Applies to ALL OF THIS mentality that symmetry has to offer.
Given my discussion on Symmetry I think I will give you an example of Symmetry mis applied. you see, one day I got a call from the city that said one of the fences that goes around my house was in violation of some building code. Upon close inspection of the code I determined that indeed it may be. The fence existed before I ever moved in and was not erected by my hand or my $. The big question was WHY NOW, why did the city all of a sudden care? well, someone down the way was applying for a permit to build a fence very similar to mine. when the city did not issue a permit (against code) this person walked around the neighborhood and turned in every one that was in 'violation'. This guy tried to use Symmetry to get the permit. the city was bound to code and thus he never got it. an inspecter never showed up to review my fence. The correct application of symmetry would have been to build a fence in violation like the rest of the neighborhood and never apply for a permit. you see logic dictates that if the city turned a blind eye to everyone else, he should have tried without a permit.
Do you have a good application of Symmetry? if so, post.