It's important in reading Liu to "literally" read the text - because Liu tries his best to describe the most abstract science(-fiction) in the most "literal/direct" way possible (even in the Singer Chapter), except maybe in explicit cases like Yun Tianming's fairy tales. IOW, the amount of rope remains constant, you've just "engineered" a way to burn it up ("evenly") 4 times faster. The variation in thickness at any point becomes irrelevant when you fold & burn it as a ONE SINGLE "new" rope just as the variation in thickness at any point is irrelevant to the fact that the original/ "old" rope would take one hour to burn up IN ITS ENTIRETY. all things remaining constant), would burn up in HALF an hour- so burning it from both ends would only take 15 minutes. TL DR: After you fold a rope, you simply have ONE SINGLE "new" rope (of variable thickness) only HALF the length of the unfolded/"old" rope which, pari passu (i.e. IOW, you went off the deep end thinking it was some (abstract) logic riddle, when it's NOT - it was just a "engineering" issue (AA was an engineer, right?) and engineering is also a science (hence part of STEM), you know.Īctually VISUALIZE (aka "model/simulate") the rope, instead of thinking "in the abstract" (or "sense", as you put it) - what do you have when a rope (of variable thickness), which would burn up in one hour, is PHYSICALLY folded in half? LOL, glad that you thought of the possibility of a translation error but you've just suffered a complete lapse in basic "visualization", in your decision to pursue (abstract?) logic or (common?) "sense". To think of it another way, there are always four ends from which the rope is burning, meaning that the rope will burn at 4x the rate it would if only burned from one end, and therefore will be burned in 1/4 the time. The limit of this process, as the number of iterations approaches infinity, is fifteen minutes.
When this happens, light the remaining rope somewhere in the middle. Unless you're very lucky, one rope will burn out faster than the other. The flame in the middle will split the rope into two ropes, each of which is burning from both ends. Light the rope at each end, and light the rope somewhere in the middle. Folding it in half is doing exactly this, and so doesn't work as an answer. They make a big deal out of the fact that the rope is of non-uniform thickness, and therefore you can't just divide the rope by length and have that translate to time. The solution presented in the book, as written, is wrong, at least in English (I can't speak for the original phrasing of the problem). This might be a dead thread, but it's one of the first hits on google, so maybe someone else will see this. Keep in mind that in theory you might need to ignite the remaining part infinite number of times (and also infinitely fast in the end, which would create a nice link with question 1) in case no 2 parts finish burning at the same time. The canonical solution to the problem is to start burning the rope from both ends and anywhere in the middle at the same time and then repeatedly ignite the remaining part after the other one has been burnt, anywhere in the middle, until the whole rope is burnt. On the other hand if they mean that the both halves should touch and the faster burning part will ignite the slower burning parts, this does not work either because the faster burning part would ignite the slower part in multiple places, leading to faster-than-15 minutes burning of the entire rope. If by folding they mean to combine them and create a new, shorter rope from these 2, then we cannot be sure what the burning time is for such a constructed rope.
I had the same issue with the solution from the book.
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