It is better to do the right problem the wrong way than to do the wrong problem the right way.
Richard Hamming quoted, Julian Havil, Impossible: Surprising Solutions to Counterintuitive Conundrums (50)
I was deep into my morning walk a few weeks ago when a powerful craving for doughnuts caught up with me. But proper doughnuts require a little time and a small crowd to partake in the pleasure, so I waited until the right moment.
For every complex problem, there is a solution that is simple, neat, and wrong (H.L. Mencken quoted, 82).
I find that I tend to read a math book or two every year. I’m not sure what it is in me that compels me to plow through the complex equations that I have little to no real understanding of, but I do it anyway. I like the ideas that the math symbolizes, I suppose. I take a strange pleasure in relating events in my life to mathematical equations.
A recipe is like a math equation: n( x + y) (s/t/r) + nfº = Ne (That’s n ingredients, multiplied by speed and time of rotation, plus n degrees fahrenheit, equals the nectar of mathematics: in this case: Apple-cider doughnuts.). Of course we ran into some problems.
Now that we have complex numbers properly placed and our mind receptive to lurking difficulty, we will consider what should be a simple computation for a calculator (44).
Ah yes, the lurking difficulty. Well, that is something one must always be prepared for. I had my heart set on apple cider doughnuts. My children and I were all visiting friends who had kindly procured all the necessary ingredients. I only needed 1/2 cup of apple cider (which I would reduce to 2T) and my friend wondered what to do with rest as they didn’t care for cider. I told her not to worry, my boys would take care of that. The next morning, I awoke, ready to prepare the dough when I realized our error. I neglected to tell the boys that there had been a reason, other than their enjoyment and ever-lurking thirst, for the purchase of the cider. They had made quick work of it. Good communication is important. In math, baking and life—that holds true.
Put succinctly, to increase the chances of success the team must adopt the somewhat counterintuitive strategy of being wrong together, not correct together (53).
Something strange that I love about math, as it feeds some sort of philosophical truth I seek, is that not only can there be multiple ways to reach a solution, but there are multiple solutions to a problem. It just depends on what system, matrix, or units of measurement and/or data you are using. There is not as much firm ground as we like to think. There are just abstract ideas and evolving methods of problem-solving.
Of course making apple cider doughnuts is not that complex of a problem. I solved the equation, in fact, by a simple adjustment of words. Rather than making Apple-cider Doughnuts I replaced the 2T reduced apple cider with milk and renamed the solution: Plain Doughnuts.
*title from p 128: “Certainly, [the proof] is more secure and in looking at it we can taste the nectar of mathematics…”