Ancient Domains Of Mystery, forum overview / General / Paradoxes
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Caladriel Registered user ReGiStErEd UsEr Last page view: 4907 days, 18 hours, 52 minutes and 13 seconds ago. |
I am spawning this from Any Physicists Out There [Edited 1 time, last edit on 5/29/2008 at 21:06 (GMT -5) by Caladriel] |
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Caladriel Registered user ReGiStErEd UsEr Last page view: 4907 days, 18 hours, 52 minutes and 13 seconds ago. |
Hendar wrote: OK, heres one: A hare and a tortoise have a race, but the tortoise gets a meter head start. Assuming the both start simultaneously, the hare cannot catch up with the tortoise. Why? Well, even if the hare moves at light speed, it must take some finite amount of time to catch up to the tortoises starting point. If the tortoise is moving at all, no matter how slowly, in that small unit of time it will cover some distance - no matter how microscopically small - before the hare gets to the tortoises starting position. Then they are back to square one. The hare has narrowed the lead of the tortoise, but the same situation will repeat itself, the distance between the hare and the tortoise getting ever smaller but never reducing to zero. So how the hell do fast objects overtake slower objects?????? [Edited 1 time, last edit on 5/29/2008 at 21:45 (GMT -5) by Caladriel] |
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Caladriel Registered user ReGiStErEd UsEr Last page view: 4907 days, 18 hours, 52 minutes and 13 seconds ago. |
Caladriel wrote: Hendar: Classic! I love it. (although I heard about it as Achilles and a tortoise) Your problem is that at the start of each 'step' in the race, the hare will have to reach the starting point of the tortoise from that step (the hare actually has to pass that point, but, in order to pass that point, the hare first has to reach that point) Each time, when the hare reaches the tortoise' starting point for that step, the tortoise will have moved a little forward, thus creating a new starting point for the next step that the hare will have to reach. By the time the hare reaches that new starting point, the tortoise will have again moved a little bit forward. etc. Each time, that "little bit forward" will be smaller, but it will always be there. I think I have an intuitive grasp of a solution, but I do not know if I can verbalize it. The paradox exists because you are viewing the race as an infinite series of finite steps. It is actually a continuum. A continuous wave rather than a set of discrete plateaus. The distance that the Hare has to travel reduces to 0, at which point the hare overtakes the tortoise. ie. if you continually chop a tree branch in half, you will never reach the trunk, you will simply wind up with smaller and smaller discrete chunks of wood as you get closer and closer to the trunk. However, if you sand the branch instead of chopping it, you will reach the trunk and wind up with a pile of sawdust. |
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Caladriel Registered user ReGiStErEd UsEr Last page view: 4907 days, 18 hours, 52 minutes and 13 seconds ago. |
Darren Grey wrote: The problem was invented by the ancient greeks, and they never solved it. The problem lies in the concept of infinity, and the human mind's difficulty in grasping it. The Greeks didn't realise that adding up an infinite series of numbers could lead to a real number - they thought that an infinite sum must be infinite itself. This is not true. If you add up the sum of 1/(2^n) (ie 1/2 + 1/4 + 1/8 +...) for an infinite value of n you will get 1. In pure maths this is generally expressed as the infinite series converging on a real number. More commonly you could simply look at it as a form of integration - the area under a curve is the sum of infinite small slices. In the example presented imagine that the distance between the hare and the tortoise is halved each time, and you will have the same mathematical series as above. There is no paradox - just a lack of understanding of adding infinite numbers. |
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Caladriel Registered user ReGiStErEd UsEr Last page view: 4907 days, 18 hours, 52 minutes and 13 seconds ago. |
Here's one: My next post is true |
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Caladriel Registered user ReGiStErEd UsEr Last page view: 4907 days, 18 hours, 52 minutes and 13 seconds ago. |
My previous post is false. Which is true and which is false? |
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Caladriel Registered user ReGiStErEd UsEr Last page view: 4907 days, 18 hours, 52 minutes and 13 seconds ago. |
Here's one: I have a book that catalogues all book catalogues which do not list themselves. Should my catalogue list itself? (If it does list itself, then it is a catalogue that lists itself, so it does not belong and shouldn't be listed. If it does not list itself, then it is a catalogue that does not list itself, so it does belong, so it should be listed) [Edited 1 time, last edit on 5/30/2008 at 15:31 (GMT -5) by Caladriel] |
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Hendar23 Registered user Last page view: 5867 days, 14 hours, 34 minutes and 8 seconds ago. |
Thanks for the answer Darren! I can't remember where I heard that problem but it's been annoying me since high school. Thinking of infinitely halving things...I remember playing with my grandfathers vice as a small kid, I was fascinated that you could move it extremely small distances with a relatively large turn of the lever. I used to try and get the two surfaces of the vice as close to each other as possible without touching. I started wondering if such a thing as 'as close to as possible' could exist, as any distance -no matter how small - could always be halved again. Darrens answer kinda covers that. As a kid I got to thinking that distance and maybe time could be reduced to an indivisible discrete unit. A friend and I figured out something very weirdly when we were about five years old. We were talking about really small things after we found a tiny tiny bug. We decided there had to be things too small to see, but we also decided that even if something appears to be absolutely still, if you zoomed in small enough it was actually constantly vibrating. We both agreed this was pretty self evident, and as I grew up I found out it was true. Was it coincidence? Or spooky childrens intution? "Men are born for games. Nothing else. Every child knows that play is nobler than work" - Cormac McCarthy, Blood Meridian [Edited 1 time, last edit on 5/30/2008 at 13:32 (GMT -5) by Hendar23] |
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Darren Grey Registered user Last page view: 4450 days, 30 minutes and 33 seconds ago. |
The vice thing... well, let's look at it in terms of a real situation instead of simple maths. The particles have a sort of force on each other regardless of distance, but further away it may as well be forgotten. Once they get within a certain range though (say a few micrometres) then there will be a certain force felt between them - it could be attractive or respulsive, or it could just be a general friction force that makes it slightly harder to bring them together and slightly harder to pull them apart. However on the macroscopic scale this would be unobservable - these are the sort of forces that keep solids bound together, and that on the basic levels of things cause collisions and contact forces etc. So, overall, there's no definite point to say where the gap ends. The actual molecules will never "touch", but they will develop repulsive forces at some point, and even before that they may exert other forces on each other. Waldenbrook, the dwarven shopkeeper, mumbles: "I'd offer 9 gold pieces for yer dwarven child corpse." |
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Hendar23 Registered user Last page view: 5867 days, 14 hours, 34 minutes and 8 seconds ago. |
Oh yeah I was thinking more generally. I knew the vice didn't even have a perfectly flat surface. I was thinking more if such a thing as a perfectly flat surface could exist. Of course, physically it can't. Interesting if you re thinking about moving two atoms closer and closer together though....the boundary point must be a pretty cool thing to study. Makes me think of strange attractors for some reason. "Men are born for games. Nothing else. Every child knows that play is nobler than work" - Cormac McCarthy, Blood Meridian |
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Kingsdragon Registered user You smelt it you dealt it! Last page view: 5981 days, 7 hours, 10 minutes and 54 seconds ago. |
Liar paradox. You are asked to say one thing, it may only be a true or false statement. If it's true I will cut your head off, if it's false I will strangle you. Your answer? You are going to strangle me. Behind every successful man is a woman, behind her is his wife XD |
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Kingsdragon Registered user You smelt it you dealt it! Last page view: 5981 days, 7 hours, 10 minutes and 54 seconds ago. |
A Cretan says "All Cretans are liars" Many documents contain pages on which the text "This page is intentionally blank" is printed, thereby making the page not blank. If there is an exception to every rule, then every rule must have at least one exception, the exception to this one being that it has no exception. Behind every successful man is a woman, behind her is his wife XD |
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Kingsdragon Registered user You smelt it you dealt it! Last page view: 5981 days, 7 hours, 10 minutes and 54 seconds ago. |
Why time travel is IMPOSSIBLE You travel back in time and kill your grandfather before he meets your grandmother which precludes your own conception and, therefore, you couldn't go back in time and kill your grandfather. Behind every successful man is a woman, behind her is his wife XD |
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Kingsdragon Registered user You smelt it you dealt it! Last page view: 5981 days, 7 hours, 10 minutes and 54 seconds ago. |
I once had to do a essay on Paradoxes and we had to make up our own, mine wasn't too good imho it was this; Everyone does something on SOME level of wanting/will. The lady who buys her kid a lolly pop tells him/her she doesn't want to get it, but she gets it anyway. In my opinion that means she DID want to get it on some level, otherwise she wouldn't have done it. Behind every successful man is a woman, behind her is his wife XD |
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Caladriel Registered user ReGiStErEd UsEr Last page view: 4907 days, 18 hours, 52 minutes and 13 seconds ago. |
Kings Dragon: Hmmmmm . . . Liar's Paradox. Actually, you could first strangle me (making the statement true) then you could cut my head off. (You didn't say "I will strangle you if and only if the statement is false", or "I will not strangle you if it is true") Cretan: The Cretan is lying. Only some cretans are liars. Time Travel: Or you spawn off a new time stream. :-) Lollipop: I would say that that is closer to irony. [Edited 1 time, last edit on 6/19/2008 at 08:55 (GMT -5) by Caladriel] |
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The Real J. Registered user The faceless swordsman Last page view: 5824 days, 7 hours, 27 minutes and 9 seconds ago. |
I'm not sure if this will qualify, but something I just thought of: What color is an invisible dog ? If you can tell the color then surely the dog can't be invisible. OTOH, since the dog is invisible it is impossible to specify its color. Sytytä toiselle tuli ja hän pysyy lämpimänä jonkin aikaa. Sytytä hänet palamaan ja hän pysyy lämpimänä loppuelämänsä. |
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Maelstrom Registered user The Knight of the Black Rose Last page view: 3327 days, 19 hours, 59 minutes and 45 seconds ago. |
Something that does not absorb visible light has no colour. No paradox there. A pessimist sees a dark tunnel. An optimist sees a light at the end of that tunnel. A realist sees a train. And the train driver sees three idiots on the tracks. |
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Silfir Registered user Writer of Overly Long Guides Last page view: 4279 days, 1 hour, 12 minutes and 43 seconds ago. |
The dog could have a potential colour, as in the colour it would have if you were to pour the contents of a potion of visibility in its food... You drop the golden ball. You kick the golden ball. It slides to the west. Suddenly Harry Potter, the apprentice wizard, appears! "That's not how you play Quidditch! are you even listening?" Which direction? (123456789) 4 Harry Potter, the apprentice wizard, is hit by a bolt of acid! Harry Potter, the apprentice wizard, is annihilated. You hear the ecstatic cries of a large crowd! |
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Caladriel Registered user ReGiStErEd UsEr Last page view: 4907 days, 18 hours, 52 minutes and 13 seconds ago. |
Or if you have the "See Invisible" intrinsic. |
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Morio Registered user Holy Champion of ADoM Last page view: 4108 days, 22 hours, 46 minutes and 33 seconds ago. |
"Or if you have the "See Invisible" intrinsic." Or more commonly, being high/drunk "I don't know what World War 3 will be fought with, but I know World War 4 with be fought with sticks and stones." - Albert Einstein |
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Kingsdragon Registered user You smelt it you dealt it! Last page view: 5981 days, 7 hours, 10 minutes and 54 seconds ago. |
@ Caladreil Lol you can't spawn another future, you already have one. As for the lollipop you might be right there... it is a bit of irony, but that actually happens a lot sadly :( Behind every successful man is a woman, behind her is his wife XD |
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Maelstrom Registered user The Knight of the Black Rose Last page view: 3327 days, 19 hours, 59 minutes and 45 seconds ago. |
Let's not start a debate wether time has only one dimention or not. Either you spawn a new future, or you cannot travel in time and no paradox there. A pessimist sees a dark tunnel. An optimist sees a light at the end of that tunnel. A realist sees a train. And the train driver sees three idiots on the tracks. |
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Kingsdragon Registered user You smelt it you dealt it! Last page view: 5981 days, 7 hours, 10 minutes and 54 seconds ago. |
I like debates about the future *snubs nose* haha Behind every successful man is a woman, behind her is his wife XD |
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Caladriel Registered user ReGiStErEd UsEr Last page view: 4907 days, 18 hours, 52 minutes and 13 seconds ago. |
Hmm, re: Time Travel paradox, if the creation of alternate time streams cannot occur, there is still a way around the paradox. The Grandfather paradox does not prove that time travel is impossible; it simply shows that going back in time and killing your grandfather (or making any changes, for that matter) is impossible. Thus, if you told me that you were going back in time to kill your biological grandfather before your father was born, I would point out that anything you do in the past has already happenned, so you obviously failed/will fail to kill your biological grandpappy. [Edited 1 time, last edit on 6/25/2008 at 17:29 (GMT -5) by Caladriel] |
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Silfir Registered user Writer of Overly Long Guides Last page view: 4279 days, 1 hour, 12 minutes and 43 seconds ago. |
And the reason you will have failed to kill your biological grandpappy is that time travel is impossible :) You drop the golden ball. You kick the golden ball. It slides to the west. Suddenly Harry Potter, the apprentice wizard, appears! "That's not how you play Quidditch! are you even listening?" Which direction? (123456789) 4 Harry Potter, the apprentice wizard, is hit by a bolt of acid! Harry Potter, the apprentice wizard, is annihilated. You hear the ecstatic cries of a large crowd! |
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Darren Grey Registered user Last page view: 4450 days, 30 minutes and 33 seconds ago. |
Chaos theory in general would suggest that going back in time is impossible - change is inevitable. When it gets down to the atomic scale our whole notion of time becomes rather fuzzy, so it's hard to even think about it from a physics point of view. Waldenbrook, the dwarven shopkeeper, mumbles: "I'd offer 9 gold pieces for yer dwarven child corpse." |
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Kingsdragon Registered user You smelt it you dealt it! Last page view: 5981 days, 7 hours, 10 minutes and 54 seconds ago. |
Haha. Simple enough. I myself don't, and won't believe in time travel. However it is possible to view the past, going far back enough in space. BUT you have to travel faster then the speed of light and look back at earth and see the light coming towards you from earth with some powerful telescope thingy. So say you go back 10 times faster than light and go back far enough to catch up with the light thats moving 200 years ago and look at England, you might just see people going about there business on horses. Gagh... I'm tired so I don't know if I explained that right. Behind every successful man is a woman, behind her is his wife XD |
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Darren Grey Registered user Last page view: 4450 days, 30 minutes and 33 seconds ago. |
But of course travelling faster than light is utterly impossible - it's one of the laws of the universe. However since distant objects reflect light so in theory they'll be relfecting back observations of the Earth from previous years. Impossible to actually discern those reflections, never mind get any detail from them, but still interesting to think about. Waldenbrook, the dwarven shopkeeper, mumbles: "I'd offer 9 gold pieces for yer dwarven child corpse." |
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Maelstrom Registered user The Knight of the Black Rose Last page view: 3327 days, 19 hours, 59 minutes and 45 seconds ago. |
That law of the universe is quite stupid, since light doesn't have one speed :P Light in vacuum travels faster then light in atmosphere - since it's impossible to travel faster then c, why isn't c a constant number? That's as close to a paradox as we can get ;) A pessimist sees a dark tunnel. An optimist sees a light at the end of that tunnel. A realist sees a train. And the train driver sees three idiots on the tracks. |
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Darren Grey Registered user Last page view: 4450 days, 30 minutes and 33 seconds ago. |
That's not true - light always travels at c. The speed of propogation of light through a material is something different than the speed of light - the light rays in this instance are affected by the electromagnetic fields of the atoms. In essence they get bounced around a bit, slowing their progress through the medium, but never altering their actual speed. Waldenbrook, the dwarven shopkeeper, mumbles: "I'd offer 9 gold pieces for yer dwarven child corpse." |
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