Riddles & Brain Teasers
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By Committee
Member # 4233
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written Thursday, October 27 2005 03:45
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quote:Electric cars don't have engines though - they have motors. Posts: 2242 | Registered: Saturday, April 10 2004 07:00 |
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...b10010b...
Member # 869
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written Thursday, October 27 2005 03:54
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Technically, any machine capable of doing mechanical work can be called an engine. A purely electric car doesn't have an internal combustion engine, of course. -------------------- My BoE Page Bandwagons are fun! Roots Hunted! Posts: 9973 | Registered: Saturday, March 30 2002 08:00 |
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Electric Sheep One
Member # 3431
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written Thursday, October 27 2005 03:59
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A famously mysterious line of Milton: "And that two handed engine by the door Stands ready to strike once, and strike no more." Possibly he meant some kind of ambiguous reference to both a clock and a headsman's axe, but it has never really been clear. The reference to the door just doesn't help; 'door' seems to be there just in order to rhyme. Some poems just never quite work, even if you're Milton. Anyway, archaically an engine can be pretty much any device. -------------------- It is not enough to discover how things seem to seem. We must discover how things really seem. Posts: 3335 | Registered: Thursday, September 4 2003 07:00 |
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By Committee
Member # 4233
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written Thursday, October 27 2005 04:25
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Have you ever heard of an electrical engine though? I do know that electrical motors don't tend to make much noise until current is applied, and then they're doing their job, which in a car's case is moving it. They don't have pistons that fire while they are "idling." At any rate, I think it's a copout answer to build a riddle around. No offense, Aran! :) [ Thursday, October 27, 2005 04:34: Message edited by: Drew ] Posts: 2242 | Registered: Saturday, April 10 2004 07:00 |
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Electric Sheep One
Member # 3431
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written Thursday, October 27 2005 05:23
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As a peace offering: modern diesel locomotives use diesel engines to drive electrical generators that power electric motors. Yay! -------------------- It is not enough to discover how things seem to seem. We must discover how things really seem. Posts: 3335 | Registered: Thursday, September 4 2003 07:00 |
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By Committee
Member # 4233
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written Thursday, October 27 2005 05:31
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Huh - I was not aware of that. Is that more effecient than having the engine directly power the wheels? I imagine that such a set up wouldn't allow for acceleration as rapid as a diesel engine directly powering the wheels, but then that's not really what a locomotive is all about. [ Thursday, October 27, 2005 05:32: Message edited by: Drew ] Posts: 2242 | Registered: Saturday, April 10 2004 07:00 |
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La Canaliste
Member # 5563
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written Thursday, October 27 2005 06:08
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If I remember correctly, and it was a long time ago that I studied these things, it is because the electric motor has higher torque at low revs than the diesel. This could be a hallucination due to too much tea, though. -------------------- I am a pale shadow of the previous self. quote: Deep down, you know you should have voted for Alcritas! Posts: 387 | Registered: Tuesday, March 1 2005 08:00 |
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BANNED
Member # 4
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written Thursday, October 27 2005 08:17
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Aran- "Besonderwagen" ist die Name der Autos, die die National Sozialisten benützt haben, um die Jüden zu vergiften. ... >_> -------------------- 私のバラドですそしてころしたいいらればころす Posts: 6936 | Registered: Tuesday, September 18 2001 07:00 |
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Electric Sheep One
Member # 3431
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written Thursday, October 27 2005 23:55
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Urp; I have no idea why locomotives work that way, except that it must obviously be more efficient because railways are themselves ruthless engines of capitalism. Except perhaps on the island of Sodor; and even there, you can't help wondering whether they just don't show you what happens to engines that aren't Really Useful. One more thing I noticed about the monks problem: unlike other versions of the same puzzle, in which the entire problem is set up on day 0, in this case most of the situation has been going on for years, before the tourist arrives. Suppose there are at least two red-eyed monks; then every monk, including the red-eyed, has known for ages that at least one monk has red eyes. So it seems as though the tourist tells the monks nothing that they haven't all already known, for a long time, from observation. So why does the suicide calendar only start counting down when the outsider delivers this non-news? -------------------- It is not enough to discover how things seem to seem. We must discover how things really seem. Posts: 3335 | Registered: Thursday, September 4 2003 07:00 |
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Electric Sheep One
Member # 3431
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written Friday, October 28 2005 00:01
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Literally, "Besonderwagen" is just "special car". Needless to say, in German one must now think of some other name for this reasonable basic concept. As my knowledges of German history and the German language have not yet met, I am indebted to TM for saving me from a faux pas I might well have made at some point. -------------------- It is not enough to discover how things seem to seem. We must discover how things really seem. Posts: 3335 | Registered: Thursday, September 4 2003 07:00 |
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Shaper
Member # 5450
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written Friday, October 28 2005 00:44
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quote:Because of the fact that the red-eyed monks did not know that they had red eye syndrome. The puzzle makes us assume that the RES sufferers did not know about their...illness. -------------------- Mugglenet--The ULTIMATE Harry Potter Site. Polaris-- New location. Posts: 2396 | Registered: Saturday, January 29 2005 08:00 |
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Law Bringer
Member # 2984
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written Friday, October 28 2005 01:20
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Because before the tourist made his statement, there was no way for a monk to deduce his own eye color from the others' actions. Once he did, the monks knew that one monk would kill himself on the first night, and n on the nth night, and could therefore draw conclusions. Or, in a mathematical sense, the "true for n=1" statement only became true with the tourist's statement. But once it was true for n=1, it immediately became true for all other numbers. -------------------- The Encyclopaedia Ermariana <-- Now a Wiki! "Polaris leers down from the black vault, winking hideously like an insane watching eye which strives to convey some strange message, yet recalls nothing save that it once had a message to convey." --- HP Lovecraft. "I single Aran out due to his nasty temperament, and his superior intellect." --- SupaNik Posts: 8752 | Registered: Wednesday, May 14 2003 07:00 |
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Shaper
Member # 32
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written Friday, October 28 2005 04:25
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quote:I imagine it's easier to carry the energy around using electricity instead of having the engine directly connected. It also means you have less parts to replace in case one of them goes bad... -------------------- Lt. Sullust Cogito Ergo Sum Polaris Posts: 2462 | Registered: Wednesday, October 3 2001 07:00 |
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Electric Sheep One
Member # 3431
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written Friday, October 28 2005 13:03
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Aran is of course right, but the point of my last question was to address specifically the apparent paradox that the tourist seems to convey no new information to the monks. Evidently the tourist actually somehow does inject new information into the system; but yet the direct content of the tourist's revelation may well be familiar to all the monks. So, uh, what's up with that? What might help, here: would it be the same if there were no tourist, but one night one of the monks can't stand the hypocrisy any longer, and spray paints the refectory walls with the message, "Some of us have red eyes!"? Now again one of the monks has written nothing but what all the monks already know. So how could this change anything? But if it can't, what's so different about the tourist? -------------------- It is not enough to discover how things seem to seem. We must discover how things really seem. Posts: 3335 | Registered: Thursday, September 4 2003 07:00 |
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...b10010b...
Member # 869
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written Friday, October 28 2005 13:10
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quote:Well, in the case of there being only one red-eyed monk, the tourist does provide new information; the red-eyed monk didn't previously know there was at least one red-eyed monk. And since the entire inductive chain relies on the fact that if there is only one red-eyed monk, he will know he has red eyes, this is important information. If one red-eyed monk wouldn't know to kill himself, then two can't know to kill themselves, and if two can't know then three can't know, and so on. [ Friday, October 28, 2005 13:17: Message edited by: Explode Thuryl Now ] -------------------- My BoE Page Bandwagons are fun! Roots Hunted! Posts: 9973 | Registered: Saturday, March 30 2002 08:00 |
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Electric Sheep One
Member # 3431
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written Friday, October 28 2005 13:41
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Sure, but you just dance around the thing that bothers me. Only with more than one red-eyed monk is anything about this whole puzzle less than obvious, so skip the single-red case. In the more-than-one-red-eyed case, what new info does the tourist provide? And would it be the same if one of the monks blurted out the same line? To put it another way: the monks do already know that at least one of them has red eyes. So this must not be precisely the new information conveyed to them by the tourist. What is the new information, then? -------------------- It is not enough to discover how things seem to seem. We must discover how things really seem. Posts: 3335 | Registered: Thursday, September 4 2003 07:00 |
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...b10010b...
Member # 869
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written Friday, October 28 2005 13:52
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I don't think we can skip the one-red-eyed-monk case; not entirely, at least. The logic of all the rest of the solution relies on what would happen in that case. Look at the case of two red-eyed monks: the new information the tourist has (eventually) provided in this case is actually that there are two red-eyed monks, because if there were only one he'd have killed himself on the first night. Admittedly, this information is only new to the two red-eyed monks themselves, but they're the ones who need to know. Now look at the case of three red-eyed monks: each red-eyed monk can only conclude that he's red-eyed based on the fact that two red-eyed monks will kill themselves on day 2. If they haven't killed themselves on day 2, there must be 3 red-eyed monks. But without the tourist telling them that at least one has red eyes, he has no way of defining when day 2 is. Basically, the tourist's input is important because without it, the red-eyed monks can't be relied upon to kill themselves at a specific time -- and the monks' suicide relies on the monks knowing that the reason the red-eyed monks haven't all killed themselves at a specific time is because there's one more red-eyed monk than each red-eyed monk can see. Any other method of conveying the information, including a monk blurting it out, would work just as well, as long as every monk received the information at the same time. [ Friday, October 28, 2005 13:57: Message edited by: Explode Thuryl Now ] -------------------- My BoE Page Bandwagons are fun! Roots Hunted! Posts: 9973 | Registered: Saturday, March 30 2002 08:00 |
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Law Bringer
Member # 335
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written Friday, October 28 2005 14:08
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It can't be skipped. This is mathematically an inductive proof. You have to prove it's true for n = 1 and for n + 1 if it is true for n, from which you can conclude that it is true for all n >= 1. The entire series depends on the n = 1 case. It seems weird and I can't get my brain to accept it intuitively, but it's true mathematically. [Edit: But wait! Suppose all the monks come together one day, see each other monk, and learn about the curse, then start living together. None die even though they all know that there are some red eyes and learn it at the same time (assuming more than one monk has red eyes), they all know that they know it (assuming more than two monks with red eyes), they all know that they know that they know it (assuming more than three monks)...] —Alorael, whose mind hurts now. [ Friday, October 28, 2005 14:12: Message edited by: Apologenesis ] Posts: 14579 | Registered: Saturday, December 1 2001 08:00 |
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...b10010b...
Member # 869
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written Friday, October 28 2005 14:11
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It actually makes a little more sense when you realise that a red-eyed monk thinks there's one less red-eyed monk than there really is. And a red-eyed monk who thinks he isn't a red-eyed monk thinks that the red-eyed monks who think they aren't red-eyed monks think there are two less red-eyed monks than there really are. And a red-eyed monk who thinks he isn't a red eyed monk also thinks that the red-eyed monks who think that they aren't red-eyed monks think that other red-eyed monks who think they aren't red-eyed monks think there are three less red-eyed monks than there really are. See how you get back to the case of 1 red-eyed monk that way? Consider four monks: A, B, C and D. All four have red eyes. All four assume that they themselves don't have red eyes (since otherwise they'd have to kill themselves). Monk A thinks Monks B, C and D think that there are two red-eyed monks in the monastery, since A thinks that A isn't red-eyed. Monk A thinks that Monk B, working on the same reasoning as Monk A, thinks that C and D think there's only one red-eyed monk in the monastery, since A thinks that A isn't red-eyed, and A also thinks that B thinks that B isn't red-eyed. Monk A also thinks that Monk B thinks that Monk C, working on the same reasoning as Monk B, thinks that D thinks there are no red-eyed monks in the monastery, since A thinks that A isn't red-eyed, and A also thinks that B thinks that B isn't red-eyed, and A also thinks that B thinks that C thinks that C isn't red-eyed. In other words, the reasoning for the monks not killing themselves relies on the fact that there could be a monk who thinks that another monk could think that there are no red-eyed monks. And so we're back to the one-monk case. Note that it isn't important that any monk actually does think there are no red-eyed monks; only that another monk thinks that there could be a monk who thinks there aren't any. Actually, not even that, merely that there could be a monk who thinks that there could be a monk who thinks that there aren't any. Or that there could be a monk who thinks that there could be a monk who thinks that... you get the idea. ... Wow. That's a weird argument. I'm going to have to give it some more thought. [ Friday, October 28, 2005 14:29: Message edited by: Explode Thuryl Now ] -------------------- My BoE Page Bandwagons are fun! Roots Hunted! Posts: 9973 | Registered: Saturday, March 30 2002 08:00 |
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Shock Trooper
Member # 5969
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written Friday, October 28 2005 15:18
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If there were a hundred monks with red eyes, though, then nobody could possibly think that someone else could think that there weren't any.... right? -------------------- A C, an E flat, and a G walk into the Tower of the Magi. Ambrin runs up to them and says, "Hey, look! It's the Triad!" Kelner snorts and says "Pretty minor Triad if you ask me." Posts: 242 | Registered: Thursday, June 16 2005 07:00 |
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...b10010b...
Member # 869
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written Friday, October 28 2005 15:28
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Okay, I'm NOT going to go through the full chain of reasoning for 100 monks -- it was hard enough for 4. But the same logic applies. All that's necessary is that each red-eyed monk doesn't know that he himself is red-eyed. So suppose there are 100 red-eyed monks. Let's look at it from the perspective of Monk #1. As far as he knows, Monk #2 sees 98 red-eyed monks, and thinks there are only 98 red-eyed monks. (Monk #2 actually sees 99 red-eyed monks, but Monk #1 has no way of knowing this.) Now, think about what Monk #1 thinks that Monk #2 is thinking. As far as Monk #1 knows, Monk #2 is thinking that Monk #3 sees 97 red-eyed monks (everyone except #1, #2 and #3, since #1 knows that #2 doesn't know #2 is red-eyed, and #1 doesn't know that #1 is red-eyed, and we're still looking at this from #1's perspective). Monk #3 actually sees 99 red-eyed monks, and Monk #2 actually thinks that Monk #3 sees 98, but Monk #1 has no way of knowing either of these things. Think about what #1 thinks that #2 thinks that #3 is thinking. As far as #1 knows, #2 thinks that #3 thinks that #4 sees 96 red-eyed monks (everyone except #1, #2, #3 and #4, since #1 knows that #2 doesn't know #2 is red-eyed, and #1 knows that #2 knows that #3 doesn't know #3 is red-eyed, and #1 doesn't know that #1 is red-eyed, and we're still looking at this from #1's perspective). Monk #4 actually sees 99 red-eyed monks, Monk #3 actually thinks that Monk #4 sees 98, and Monk #2 actually thinks that Monk #3 thinks that Monk #4 sees 97, but Monk #1 has no way of knowing any of these things. Continue this chain of reasoning down to #100, and you see that #1 thinks that #2 thinks that #3 thinks (long chain of monks omitted) that #99 thinks that #100 sees 0 red-eyed monks (since #1 doesn't know that #1 is red-eyed, and #1 knows that #2 doesn't know that #2 is red-eyed, and #1 knows that #2 knows that #3 doesn't know that #3 is red-eyed...) There you go. Proof by recursive empathy. Not sure if this is less brain-hurting than the original explanation, but it seems more satisfying. [ Friday, October 28, 2005 15:42: Message edited by: Explode Thuryl Now ] -------------------- My BoE Page Bandwagons are fun! Roots Hunted! Posts: 9973 | Registered: Saturday, March 30 2002 08:00 |
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Shock Trooper
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written Friday, October 28 2005 15:47
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Ah, I see. Red-Eyed Monk #1 thinks there are 99, so he thinks that #2 thinks there are 98 and that #2 thinks that #3 thinks there are 97... so someone has to be thought to be thought (&c) to think there are zero. =) (Edit: Hey, whaddaya know? Post #50! ^_^) [ Friday, October 28, 2005 16:08: Message edited by: Explore the Surface Now ] -------------------- A C, an E flat, and a G walk into the Tower of the Magi. Ambrin runs up to them and says, "Hey, look! It's the Triad!" Kelner snorts and says "Pretty minor Triad if you ask me." Posts: 242 | Registered: Thursday, June 16 2005 07:00 |
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Law Bringer
Member # 335
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written Friday, October 28 2005 17:28
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Well, not quite. Every non-red monk sees the correct number of red eyes, but they're irrelevant and we can ignore them. Every red-eyed monk sees the same number of red-eyed monks: one less than there actually are. Every day they don't die means there are at least that many red eyes visible to each monk. Once it's day N, every monk knows that the other monks can't have seen N-1 red eyes or they'd all be dead. So then all the monks commit suicide. —Alorael, who can't even explain this coherently. It's really much less brain-breaking if you just accept that induction works and stop trying to think about reality. Posts: 14579 | Registered: Saturday, December 1 2001 08:00 |
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...b10010b...
Member # 869
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written Friday, October 28 2005 17:37
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Which is why it has to be possible for some monks to believe that there are no red-eyed monks at all. (Or rather, for some monks to believe that some monks believe that some monks believe (etc.) that there are no red-eyed monks at all.) Certainly, the conditions of the puzzle specify that there are in fact red-eyed monks, but they do not specify that all the monks know that there are in fact red-eyed monks; only that a monk must kill himself if he knows he has red eyes, which is quite a different matter altogether. Once the possibility that anyone could believe that anyone could believe (etc) that no monks have red eyes is removed (that is to say, once the tourist makes his statement), the countdown to mass suicide begins. The key to this is that the red-eyed monks don't actually all have the same information to begin with; the (n-1) pairs of eyes they see is a different -1 for each monk. Furthermore, every monk has to have perfect knowledge about what every other monk knows in order for the suicides to occur. [ Friday, October 28, 2005 17:57: Message edited by: Explode Thuryl Now ] -------------------- My BoE Page Bandwagons are fun! Roots Hunted! Posts: 9973 | Registered: Saturday, March 30 2002 08:00 |
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Electric Sheep One
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written Friday, October 28 2005 23:36
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I think we're getting somewhere, but ... can anyone give a succinct answer to the question, "Precisely what new information does the tourist convey to the monks?" Until that gets answered, I'd like to take up Alorael's observation that if you just stick with the induction argument all seems clear, but then if you force yourself to look at the problem from another perspective, such as my information question, you can be totally confused. One runs into this sort of thing all the time in physics, where you can find one way of looking at the problem, according to which everything is clear, but then from other perspectives it isn't clear at all. Or worse, from other perspectives it seems just as clear, but incompatibly different. In such cases, some people seem to have the idea that what you should do is find the clear perspective as fast as possible, then insist on it alone, declaring all other perspectives bad. Others (or to be more precise, me, because I haven't found too many other people that are like this to my degree) can't rest until they have clarified the problem from all known perspectives. People of the second type tend to be quite slow to understand anything, because they spend much of their time deliberately trying to confuse themselves. When at last they become unable to confuse themselves, however, they emerge with an unusually full understanding of the problem. The disappointing thing about this, though, is that when you understand something that thoroughly it always seems so simple that you just feel really dumb for not having understood it right away. If you happen to discuss this problem with someone who hasn't gone through all your grief, your clear explanations make them think you're a genius. If those same people encounter you while you're still confusing yourself with a perverse perspective on the problem, they think you're an idiot. -------------------- It is not enough to discover how things seem to seem. We must discover how things really seem. Posts: 3335 | Registered: Thursday, September 4 2003 07:00 |