patisserie effectDuring my French study summer in Pau, France, in 1961, I found myself one afternoon in the company of one of the girls in our group, Diane Ayache. To the left, you can see the only picture I can find of Diane, which I scanned from a slide (I didn't take many pictures that summer). I'm sorry that it's rather out of
focus. Diane and I wanted to get to some event that was scheduled to take place in Pau's Unfortunately, the bicycle was not one that two people could comfortably ride. We started out walking together, with me pushing the bicycle, but then I had a better idea - a way we could get there faster, while still arriving at the same time. We could do that if we each bicycled half way, and walked half way. To do that, I consulted my map of the city of Pau, and picked a point along our route that seemed to be half way to the So Diane set off, carrying the bicycle lock, but leaving me the key. I proceeded to walk to the agreed upon corner, and as I arrived there, I was pleased to see the bicycle, chained to a pole. My brilliant idea was working! But just as I unlocked the bicycle, who should step out of a nearby doorway but Diane. I looked at the sign above the door - it was a It seemed that upon arriving at the designated corner, Diane had noticed the Let me add that Diane was not alone in being magnetically drawn to Pau's That's my main story for this entry, and if you're not at all into math, you may want to stop reading here, and scroll to the footer to decide what to do next. If you continue reading, you'll learn how that evening, being a mathematically-oriented MIT student, I proceeded to compute the optimal place to leave the bicycle, given my walking and cycling rates, and Diane's. This was of course more an interesting mathematical exercise than anything of practical value. I'm someone who invents and solves math problems for my own amusement. I find it relaxing. As I worked through the algebra, it quickly became clear that rather than working with our walking and riding
In electrical engineering, some components have an electrical property called "resistance", which is given in "ohms" (named after Georg Simon Ohm, a German physicist). But the reciprocal of resistance Anyway, below I'll develop the formula I came up with. Looking at our trip to the I've defined D _{C}p
+ D_{W}(P-p) = L_{W}p + L_{C}(P-p)If you remember your algebra, you can then show that p/P equals: _{W} - L_{C} _{W} - L_{C}) + (L_{W} - D_{C})And that's what I called "the Ayache formula", in honor of Diane. For example: suppose Diane and I both walk at a speed of 4 km/hr, meaning a "slowth" of 15 minutes/km, and we both cycle at three times that speed, that is taking only 5 minutes/km. Then we should leave the bicycle the following fraction of the way to the final destination: In fact, if our walking rates are equal, and our cycling rates are equal, a glance at the formula shows that it will yield a value of 1/2 no matter what those rates are. That seemed obvious to me before I had worked through the math. If our walking rates are the same, and our cycling rates are the same, and we each cycle half the distance and walk half the distance, we're going to arrive at the same time. But suppose that although we both walk at 15 minutes/km, Diane proves to be a speed demon on the cycle, taking only 3 minutes/km, while I'm a slowpoke at 6 minutes/km. Then the formula gives That is, we should pick a point to leave the bicycle that's only about 43 percent of the way to the final destination, instead of half way. Since Diane is a faster cycler, for us both to arrive at the same time, she has to cycle less and walk more. But damn that Footnotes (click [return to text] to go back to the footnote link)
A resident of Pau is "palois". The names of city residents are often irregular, in English as well as French. The residents of both Cambridge, England and Cambridge, Massachusetts (USA) are "Cantabrigians". I once explained to a Frenchman that while the residents of New York are "New Yorkers", the residents of Boston are "Bostonians". Then, to see if he knew "Chicagoan", I asked if he knew what the residents of Chicago are called. "
But in 1971, it was decided to rename the unit of conductance the "siemens", after the German inventor Ernst Werner von Siemens. I'm an old-timer, and I still use the "mho", myself. [return to text] |