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You are not logged in. #1 20130809 00:24:41
ShoelaceA shoelace is lying on the floor, and attached you can see its shadow. If I pull it, what is the probability that it will produce a knot? #2 20130809 01:03:53
Re: ShoelaceHi anna_gg The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #3 20130809 01:18:25
Re: ShoelaceAll I can tell is that there are 7 intersections, so there are 2^7 =128 possible ways the shoelace can cross itself. Of these, we should keep only the ones that are "over/under/over" and "under/over/under", which will produce a knot. But I cannot figure out how many these are. #4 20130809 01:30:46
Re: ShoelaceUm, have you seen my answer? The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #5 20130809 01:46:38
Re: Shoelace
Yes, but I do not understand how you calculate it #6 20130809 04:29:18
Re: ShoelaceWell, I looked at the two parts separately, because they are virtually independent. For one, there are 8 possibilities for one and 16 for the other. Then I just combine them. The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #7 20130810 03:47:55
Re: Shoelace
So you mean that in the right part there are only 3/16 possibilities that a knot is produced? Because at the left part I see there are 2/8, that is 4/16. #8 20130810 03:51:50
Re: ShoelaceNo, both probabilities are 1/4. The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #9 20130810 04:48:28
Re: Shoelace
So, how do you get 7/16? Am confused #11 20130813 02:55:28
Re: ShoelaceHow did you get 7 / 16 by multiplying? In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #12 20130813 17:28:11
Re: Shoelace
The probability for both parts NOT to produce a knot is 3/4 for each (since the probability to produce a knot is 1/4). Therefore the total probability NOT to have a knot is 3/4*3/4 = 9/16, thus giving us probability to have a knot 19/16 = 7/16. #13 20130813 18:09:32
Re: ShoelaceHi; In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #14 20130818 23:32:09
Re: ShoelaceI understand that the left part has a probability of 1/4 to produce a knot, since only two of the eight possible ways produce a knot (over/under/over and under/over/under). However, how the right part has also 1/4 probability; You mean that from the 16 possible ways, 4 of them produce a knot; 