[math-fun] Finding other people
The recent discussion of giving directions to people who don't know where they are reminded me of a problem that I think is original with me. Suppose a large number of people are placed randomly in an immense forest. There are no landmarks, the ground is level, and it's always heavily overcast so there's no way to tell which way is north. You can leave marks. People and marks can be seen iff you get within 10 meters of them. If everyone knows the above before they're transported to the forest, so they can discuss the problem with the others, what would be a good strategy? There isn't necessarily one best answer. But some answers are better than others.
This sounds somewhat similar to the radio-mesh-networking problem, where everyone has a cellphone radio, but there aren't any cellphone towers, so the only way to communicate is to talk to other cellphones to build up some sort of model and then pass your message off to some % of the cellphones that you can see and communicate with. Of course, you may be completely out of range of every other cellphone, so you may be incommunicado until either you move, or someone else moves closer to you. At 08:34 PM 5/17/2017, Keith F. Lynch wrote:
The recent discussion of giving directions to people who don't know where they are reminded me of a problem that I think is original with me.
Suppose a large number of people are placed randomly in an immense forest. There are no landmarks, the ground is level, and it's always heavily overcast so there's no way to tell which way is north.
You can leave marks. People and marks can be seen iff you get within 10 meters of them.
If everyone knows the above before they're transported to the forest, so they can discuss the problem with the others, what would be a good strategy?
There isn't necessarily one best answer. But some answers are better than others.
On 5/17/2017 8:34 PM, Keith F. Lynch wrote:
The recent discussion of giving directions to people who don't know where they are reminded me of a problem that I think is original with me.
Suppose a large number of people are placed randomly in an immense forest.
Scattered at random, or all put in one random place?
There are no landmarks, the ground is level, and it's always heavily overcast so there's no way to tell which way is north.
You can leave marks. People and marks can be seen iff you get within 10 meters of them.
If everyone knows the above before they're transported to the forest, so they can discuss the problem with the others, what would be a good strategy?
Clear land, build a cabin and hope civilization doesn't find you. Brent
There isn't necessarily one best answer. But some answers are better than others.
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My ultimate rendezvous problem: You and your partner are located at separate locations somewhere in the milky way galaxy. You have a ship capable of acceleration to light speed in negligible subjective time, and a beacon that can be detected over any distance its light reaches. Rendezvous for a victory drink before either of you dies of old age.
This reminds me of the very first rendezvous problem I heard, in a little book on probability by Frederick Mosteller (et al.?) from the 1960s: ----- You have agreed to a rare meeting in New York City with an old friend at a date and time both of you will have no trouble remembering. When the arrangement was made, however, the location of the was to be determined, and now that the date and time are upon you, you realize that a) no place was ever set for the meeting and b) you have no way of communicating with your friend now that you are both somewhere in New York City unbeknownst to the other. Problem: What do you do to maximize the chance of meeting the other person at the appointed time? ----- —Dan ———— Note: Wording of problem is my own, as I don't know which book I saw it in.
On May 17, 2017, at 10:58 PM, Dave Dyer <ddyer@real-me.net> wrote:
My ultimate rendezvous problem:
You and your partner are located at separate locations somewhere in the milky way galaxy. You have a ship capable of acceleration to light speed in negligible subjective time, and a beacon that can be detected over any distance its light reaches.
Rendezvous for a victory drink before either of you dies of old age.
A little Googling reveals that Mosteller's book is called "Fifty Challenging Problems in Probability with Solutions", and it was first published in 1965. Dover reprinted it at some point. The problem in question is #12, and is called "Quo Vadis?" I am somewhat annoyed by the problem statement. This is not Dan's problem; he remembered the relevant circumstances well enough. But the poser clearly expects us to generate our own "rules of the game", and it's not clear what's on the table and what's not. How many "locations" are there in New York City? How long does it take to check one to see if it contains your friend? Does the "structure" of New York City (other than it being a set of possible locations) matter? If the New York City of the problem has a "geometry", how fast can one move through it? On Fri, May 19, 2017 at 2:29 PM, Dan Asimov <asimov@msri.org> wrote:
This reminds me of the very first rendezvous problem I heard, in a little book on probability by Frederick Mosteller (et al.?) from the 1960s:
----- You have agreed to a rare meeting in New York City with an old friend at a date and time both of you will have no trouble remembering. When the arrangement was made, however, the location of the was to be determined, and now that the date and time are upon you, you realize that a) no place was ever set for the meeting and b) you have no way of communicating with your friend now that you are both somewhere in New York City unbeknownst to the other.
Problem: What do you do to maximize the chance of meeting the other person at the appointed time? -----
—Dan ———— Note: Wording of problem is my own, as I don't know which book I saw it in.
On May 17, 2017, at 10:58 PM, Dave Dyer <ddyer@real-me.net> wrote:
My ultimate rendezvous problem:
You and your partner are located at separate locations somewhere in the milky way galaxy. You have a ship capable of acceleration to light speed in negligible subjective time, and a beacon that can be detected over any distance its light reaches.
Rendezvous for a victory drink before either of you dies of old age.
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Nice googling, Allan. Interesting how much I forgot of this problem (Mosteller's wording): ----- Two strangers who have a private recognition signal agree to meet on a certain Thursday at 12 noon in New York City, a town familiar to neither, to discuss an important business deal, but later they discover that they have not chosen a meeting place, and neither can reach the other because both have embarked on trips. If they try nevertheless to meet, where should they go? ----- And you make an interesting point, Allan, about unspoken rules to what the problem really is. Yet even though I might have trouble stating the rules, I suspect many people can solve it in the way the poser intended. So even without stating the rules, I think this is the kind of problem that AI will be able to eventually tackle after being given a lot of other typical word problems and their solutions as a training sample. —Dan
On May 19, 2017, at 12:58 PM, Allan Wechsler <acwacw@gmail.com> wrote:
A little Googling reveals that Mosteller's book is called "Fifty Challenging Problems in Probability with Solutions", and it was first published in 1965. Dover reprinted it at some point. The problem in question is #12, and is called "Quo Vadis?"
I am somewhat annoyed by the problem statement. This is not Dan's problem; he remembered the relevant circumstances well enough. But the poser clearly expects us to generate our own "rules of the game", and it's not clear what's on the table and what's not. How many "locations" are there in New York City? How long does it take to check one to see if it contains your friend? Does the "structure" of New York City (other than it being a set of possible locations) matter? If the New York City of the problem has a "geometry", how fast can one move through it?
On Fri, May 19, 2017 at 2:29 PM, Dan Asimov <asimov@msri.org> wrote:
This reminds me of the very first rendezvous problem I heard, in a little book on probability by Frederick Mosteller (et al.?) from the 1960s:
----- You have agreed to a rare meeting in New York City with an old friend at a date and time both of you will have no trouble remembering. When the arrangement was made, however, the location of the was to be determined, and now that the date and time are upon you, you realize that a) no place was ever set for the meeting and b) you have no way of communicating with your friend now that you are both somewhere in New York City unbeknownst to the other.
Problem: What do you do to maximize the chance of meeting the other person at the appointed time? -----
—Dan ———— Note: Wording of problem is my own, as I don't know which book I saw it in.
On May 17, 2017, at 10:58 PM, Dave Dyer <ddyer@real-me.net> wrote:
My ultimate rendezvous problem:
You and your partner are located at separate locations somewhere in the milky way galaxy. You have a ship capable of acceleration to light speed in negligible subjective time, and a beacon that can be detected over any distance its light reaches.
Rendezvous for a victory drink before either of you dies of old age.
Don't know what it says about me, but the placement of the line-break in Allan's email (right after the word "Fifty") made me imagine a book by Mosteller called "Fifty Shades of Probability". Jim On Fri, May 19, 2017 at 3:58 PM, Allan Wechsler <acwacw@gmail.com> wrote:
A little Googling reveals that Mosteller's book is called "Fifty Challenging Problems in Probability with Solutions", and it was first published in 1965. Dover reprinted it at some point. The problem in question is #12, and is called "Quo Vadis?"
I am somewhat annoyed by the problem statement. This is not Dan's problem; he remembered the relevant circumstances well enough. But the poser clearly expects us to generate our own "rules of the game", and it's not clear what's on the table and what's not. How many "locations" are there in New York City? How long does it take to check one to see if it contains your friend? Does the "structure" of New York City (other than it being a set of possible locations) matter? If the New York City of the problem has a "geometry", how fast can one move through it?
On Fri, May 19, 2017 at 2:29 PM, Dan Asimov <asimov@msri.org> wrote:
This reminds me of the very first rendezvous problem I heard, in a little book on probability by Frederick Mosteller (et al.?) from the 1960s:
----- You have agreed to a rare meeting in New York City with an old friend at a date and time both of you will have no trouble remembering. When the arrangement was made, however, the location of the was to be determined, and now that the date and time are upon you, you realize that a) no place was ever set for the meeting and b) you have no way of communicating with your friend now that you are both somewhere in New York City unbeknownst to the other.
Problem: What do you do to maximize the chance of meeting the other person at the appointed time? -----
—Dan ———— Note: Wording of problem is my own, as I don't know which book I saw it in.
On May 17, 2017, at 10:58 PM, Dave Dyer <ddyer@real-me.net> wrote:
My ultimate rendezvous problem:
You and your partner are located at separate locations somewhere in the milky way galaxy. You have a ship capable of acceleration to light speed in negligible subjective time, and a beacon that can be detected over any distance its light reaches.
Rendezvous for a victory drink before either of you dies of old age.
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Pavlov had some stuff to say about that sort of thing. —Dan
On May 19, 2017, at 1:20 PM, James Propp <jamespropp@gmail.com> wrote:
Don't know what it says about me, but the placement of the line-break in Allan's email (right after the word "Fifty") made me imagine a book by Mosteller called "Fifty Shades of Probability".
On Fri, May 19, 2017 at 3:58 PM, Allan Wechsler <acwacw@gmail.com> wrote:
A little Googling reveals that Mosteller's book is called "Fifty Challenging Problems in Probability with Solutions", and it was first published in 1965. Dover reprinted it at some point. The problem in question is #12, and is called "Quo Vadis?"
I am somewhat annoyed by the problem statement. This is not Dan's problem; he remembered the relevant circumstances well enough. But the poser clearly expects us to generate our own "rules of the game", and it's not clear what's on the table and what's not. How many "locations" are there in New York City? How long does it take to check one to see if it contains your friend? Does the "structure" of New York City (other than it being a set of possible locations) matter? If the New York City of the problem has a "geometry", how fast can one move through it?
On Fri, May 19, 2017 at 2:29 PM, Dan Asimov <asimov@msri.org> wrote:
This reminds me of the very first rendezvous problem I heard, in a little book on probability by Frederick Mosteller (et al.?) from the 1960s:
----- You have agreed to a rare meeting in New York City with an old friend at a date and time both of you will have no trouble remembering. When the arrangement was made, however, the location of the was to be determined, and now that the date and time are upon you, you realize that a) no place was ever set for the meeting and b) you have no way of communicating with your friend now that you are both somewhere in New York City unbeknownst to the other.
Problem: What do you do to maximize the chance of meeting the other person at the appointed time? -----
—Dan ———— Note: Wording of problem is my own, as I don't know which book I saw it in.
On May 17, 2017, at 10:58 PM, Dave Dyer <ddyer@real-me.net> wrote:
My ultimate rendezvous problem:
You and your partner are located at separate locations somewhere in the milky way galaxy. You have a ship capable of acceleration to light speed in negligible subjective time, and a beacon that can be detected over any distance its light reaches.
Rendezvous for a victory drink before either of you dies of old age.
Dan, when you say, "Many people can solve it in the way the poser intended," I feel a little sad because I'm not one of them. Is there *anything* you can say about this obvious-to-some interpretation that will shed some light on it for me? At the moment, I haven't a clue. I have a vague model of people trying places sequentially, where there are N places, and so each trial gives a probability of N^(-2) of success. I am guessing that there is some intended trick that allows one to do better than that. On Fri, May 19, 2017 at 4:39 PM, Dan Asimov <dasimov@earthlink.net> wrote:
Pavlov had some stuff to say about that sort of thing.
—Dan
On May 19, 2017, at 1:20 PM, James Propp <jamespropp@gmail.com> wrote:
Don't know what it says about me, but the placement of the line-break in Allan's email (right after the word "Fifty") made me imagine a book by Mosteller called "Fifty Shades of Probability".
On Fri, May 19, 2017 at 3:58 PM, Allan Wechsler <acwacw@gmail.com>
wrote:
A little Googling reveals that Mosteller's book is called "Fifty Challenging Problems in Probability with Solutions", and it was first published in 1965. Dover reprinted it at some point. The problem in question is #12, and is called "Quo Vadis?"
I am somewhat annoyed by the problem statement. This is not Dan's
problem;
he remembered the relevant circumstances well enough. But the poser clearly expects us to generate our own "rules of the game", and it's not clear what's on the table and what's not. How many "locations" are there in New York City? How long does it take to check one to see if it contains your friend? Does the "structure" of New York City (other than it being a set of possible locations) matter? If the New York City of the problem has a "geometry", how fast can one move through it?
On Fri, May 19, 2017 at 2:29 PM, Dan Asimov <asimov@msri.org> wrote:
This reminds me of the very first rendezvous problem I heard, in a little book on probability by Frederick Mosteller (et al.?) from the 1960s:
----- You have agreed to a rare meeting in New York City with an old friend at a date and time both of you will have no trouble remembering. When the arrangement was made, however, the location of the was to be determined, and now that the date and time are upon you, you realize that a) no place was ever set for the meeting and b) you have no way of communicating with your friend now that you are both somewhere in New York City unbeknownst to the other.
Problem: What do you do to maximize the chance of meeting the other person at the appointed time? -----
—Dan ———— Note: Wording of problem is my own, as I don't know which book I saw it in.
On May 17, 2017, at 10:58 PM, Dave Dyer <ddyer@real-me.net> wrote:
My ultimate rendezvous problem:
You and your partner are located at separate locations somewhere in the milky way galaxy. You have a ship capable of acceleration to light speed in negligible subjective time, and a beacon that can be detected over any distance its light reaches.
Rendezvous for a victory drink before either of you dies of old age.
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Sure [HINT WARNING], to meet the friend you both need to think of someplace that is not only unique, but in some sense is the most prominent unique-type place. —Dan
On May 19, 2017, at 1:51 PM, Allan Wechsler <acwacw@gmail.com> wrote:
Dan, when you say, "Many people can solve it in the way the poser intended," I feel a little sad because I'm not one of them. Is there *anything* you can say about this obvious-to-some interpretation that will shed some light on it for me? At the moment, I haven't a clue. I have a vague model of people trying places sequentially, where there are N places, and so each trial gives a probability of N^(-2) of success. I am guessing that there is some intended trick that allows one to do better than that.
On Fri, May 19, 2017 at 4:39 PM, Dan Asimov <dasimov@earthlink.net> wrote:
Pavlov had some stuff to say about that sort of thing.
—Dan
On May 19, 2017, at 1:20 PM, James Propp <jamespropp@gmail.com> wrote:
Don't know what it says about me, but the placement of the line-break in Allan's email (right after the word "Fifty") made me imagine a book by Mosteller called "Fifty Shades of Probability".
On Fri, May 19, 2017 at 3:58 PM, Allan Wechsler <acwacw@gmail.com>
wrote:
A little Googling reveals that Mosteller's book is called "Fifty Challenging Problems in Probability with Solutions", and it was first published in 1965. Dover reprinted it at some point. The problem in question is #12, and is called "Quo Vadis?"
I am somewhat annoyed by the problem statement. This is not Dan's
problem;
he remembered the relevant circumstances well enough. But the poser clearly expects us to generate our own "rules of the game", and it's not clear what's on the table and what's not. How many "locations" are there in New York City? How long does it take to check one to see if it contains your friend? Does the "structure" of New York City (other than it being a set of possible locations) matter? If the New York City of the problem has a "geometry", how fast can one move through it?
On Fri, May 19, 2017 at 2:29 PM, Dan Asimov <asimov@msri.org> wrote:
This reminds me of the very first rendezvous problem I heard, in a little book on probability by Frederick Mosteller (et al.?) from the 1960s:
----- You have agreed to a rare meeting in New York City with an old friend at a date and time both of you will have no trouble remembering. When the arrangement was made, however, the location of the was to be determined, and now that the date and time are upon you, you realize that a) no place was ever set for the meeting and b) you have no way of communicating with your friend now that you are both somewhere in New York City unbeknownst to the other.
Problem: What do you do to maximize the chance of meeting the other person at the appointed time? -----
—Dan ———— Note: Wording of problem is my own, as I don't know which book I saw it in.
On May 17, 2017, at 10:58 PM, Dave Dyer <ddyer@real-me.net> wrote:
My ultimate rendezvous problem:
You and your partner are located at separate locations somewhere in the milky way galaxy. You have a ship capable of acceleration to light speed in negligible subjective time, and a beacon that can be detected over any distance its light reaches.
Rendezvous for a victory drink before either of you dies of old age.
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Wait a second! I was talking about the Mosteller problem, not the one posed by Cris Moore. (Or am I misunderstanding?) —Dan
On May 19, 2017, at 1:51 PM, Allan Wechsler <acwacw@gmail.com> wrote:
Dan, when you say, "Many people can solve it in the way the poser intended," I feel a little sad because I'm not one of them. Is there *anything* you can say about this obvious-to-some interpretation that will shed some light on it for me? At the moment, I haven't a clue. I have a vague model of people trying places sequentially, where there are N places, and so each trial gives a probability of N^(-2) of success. I am guessing that there is some intended trick that allows one to do better than that.
Sounds like a psychology problem: What's the first place you think of when you hear "New York City". So you go to Times Square. Of course it's and old friend you're to meet, you might recall a place in NYC you met before. Brent On 5/19/2017 11:29 AM, Dan Asimov wrote:
This reminds me of the very first rendezvous problem I heard, in a little book on probability by Frederick Mosteller (et al.?) from the 1960s:
----- You have agreed to a rare meeting in New York City with an old friend at a date and time both of you will have no trouble remembering. When the arrangement was made, however, the location of the was to be determined, and now that the date and time are upon you, you realize that a) no place was ever set for the meeting and b) you have no way of communicating with your friend now that you are both somewhere in New York City unbeknownst to the other.
Problem: What do you do to maximize the chance of meeting the other person at the appointed time? -----
—Dan ———— Note: Wording of problem is my own, as I don't know which book I saw it in.
On May 17, 2017, at 10:58 PM, Dave Dyer <ddyer@real-me.net> wrote:
My ultimate rendezvous problem:
You and your partner are located at separate locations somewhere in the milky way galaxy. You have a ship capable of acceleration to light speed in negligible subjective time, and a beacon that can be detected over any distance its light reaches.
Rendezvous for a victory drink before either of you dies of old age.
math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
On 19/05/2017 21:31, Brent Meeker wrote:
Sounds like a psychology problem: What's the first place you think of when you hear "New York City". So you go to Times Square. Of course it's and old friend you're to meet, you might recall a place in NYC you met before.
I'm sure this is essentially the intended solution. However, introspect as I may I cannot with confidence identify the single most obvious place in NYC. Times Square? Empire State Building? Central Park? Grand Central Terminal? It doesn't help that some of these are pretty big. (For what it's worth, Mosteller ends up going for the top of the Empire State Building, precisely because Times Square is big.) So I think what I would actually do is this: on arrival in NYC, start buttonholing people and asking where is the single most famous place in NYC. (Perhaps even explain to them that I'm trying to meet someone but we failed to agree where.) Once I'm in (say) Times Square, continue: "what's the obvious place in Times Square to meet someone?". With a bit of luck, my counterpart will do the same thing too, but even if s/he doesn't I think this approach will have more chance of choosing the same place as s/he did than just picking the most salient place in NYC for *me*. -- g
Larry Niven constantly has his characters doing the moral equivalent ... going somewhere they think is obvious, or doing something they think their separated colleagues will notice. I have to say I was skeptical of this as a plot device, too. The chances that I would end up on the Empire State Building while my friend loiters around the Statue of Liberty, or the like, seem very large. On Fri, May 19, 2017 at 8:20 PM, Gareth McCaughan < gareth.mccaughan@pobox.com> wrote:
On 19/05/2017 21:31, Brent Meeker wrote:
Sounds like a psychology problem: What's the first place you think of
when you hear "New York City". So you go to Times Square. Of course it's and old friend you're to meet, you might recall a place in NYC you met before.
I'm sure this is essentially the intended solution. However, introspect as I may I cannot with confidence identify the single most obvious place in NYC. Times Square? Empire State Building? Central Park? Grand Central Terminal? It doesn't help that some of these are pretty big. (For what it's worth, Mosteller ends up going for the top of the Empire State Building, precisely because Times Square is big.)
So I think what I would actually do is this: on arrival in NYC, start buttonholing people and asking where is the single most famous place in NYC. (Perhaps even explain to them that I'm trying to meet someone but we failed to agree where.) Once I'm in (say) Times Square, continue: "what's the obvious place in Times Square to meet someone?".
With a bit of luck, my counterpart will do the same thing too, but even if s/he doesn't I think this approach will have more chance of choosing the same place as s/he did than just picking the most salient place in NYC for *me*.
-- g
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On 20/05/2017 01:34, Allan Wechsler wrote:
Larry Niven constantly has his characters doing the moral equivalent ... going somewhere they think is obvious, or doing something they think their separated colleagues will notice. I have to say I was skeptical of this as a plot device, too. The chances that I would end up on the Empire State Building while my friend loiters around the Statue of Liberty, or the like, seem very large.
On that specific example, Mosteller remarks that the SoL is likely to stop looking like a plausible candidate as soon as one discovers how difficult it is to get to. (I know that's changed since Mosteller wrote his book, but not exactly how.) -- g
Incidentally, this makes a pretty good party game: The "moderator" picks a category, and everyone else writes on their own piece of paper what thing in that category is most likely to be written down by the other people. The person with plurality is the next moderator. (Scoring, schmoring.) —Dan
On May 19, 2017, at 5:20 PM, Gareth McCaughan <gareth.mccaughan@pobox.com> wrote:
On 19/05/2017 21:31, Brent Meeker wrote:
Sounds like a psychology problem: What's the first place you think of when you hear "New York City". So you go to Times Square. Of course it's and old friend you're to meet, you might recall a place in NYC you met before.
I'm sure this is essentially the intended solution. However, introspect as I may I cannot with confidence identify the single most obvious place in NYC. Times Square? Empire State Building? Central Park? Grand Central Terminal? It doesn't help that some of these are pretty big. (For what it's worth, Mosteller ends up going for the top of the Empire State Building, precisely because Times Square is big.)
So I think what I would actually do is this: on arrival in NYC, start buttonholing people and asking where is the single most famous place in NYC. (Perhaps even explain to them that I'm trying to meet someone but we failed to agree where.) Once I'm in (say) Times Square, continue: "what's the obvious place in Times Square to meet someone?".
With a bit of luck, my counterpart will do the same thing too, but even if s/he doesn't I think this approach will have more chance of choosing the same place as s/he did than just picking the most salient place in NYC for *me*.
Sounds a bit like "Family Feud", the game show. Though the "Newlywed Game" also did something similar, but with just two people. --ms On 2017-05-19 20:43, Dan Asimov wrote:
Incidentally, this makes a pretty good party game:
The "moderator" picks a category, and everyone else writes on their own piece of paper what thing in that category is most likely to be written down by the other people. The person with plurality is the next moderator. (Scoring, schmoring.)
—Dan
On May 19, 2017, at 5:20 PM, Gareth McCaughan <gareth.mccaughan@pobox.com> wrote:
On 19/05/2017 21:31, Brent Meeker wrote:
Sounds like a psychology problem: What's the first place you think of when you hear "New York City". So you go to Times Square. Of course it's and old friend you're to meet, you might recall a place in NYC you met before. I'm sure this is essentially the intended solution. However, introspect as I may I cannot with confidence identify the single most obvious place in NYC. Times Square? Empire State Building? Central Park? Grand Central Terminal? It doesn't help that some of these are pretty big. (For what it's worth, Mosteller ends up going for the top of the Empire State Building, precisely because Times Square is big.)
So I think what I would actually do is this: on arrival in NYC, start buttonholing people and asking where is the single most famous place in NYC. (Perhaps even explain to them that I'm trying to meet someone but we failed to agree where.) Once I'm in (say) Times Square, continue: "what's the obvious place in Times Square to meet someone?".
With a bit of luck, my counterpart will do the same thing too, but even if s/he doesn't I think this approach will have more chance of choosing the same place as s/he did than just picking the most salient place in NYC for *me*.
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On May 19, 2017, at 5:20 PM, Gareth McCaughan <gareth.mccaughan@pobox.com> wrote:
. . .
(For what it's worth, Mosteller ends up going for the top of the Empire State Building, precisely because Times Square is big.) . . .
I happen to believe that, of all the obvious places, the Empire State Bldg. is the most obvious. Especially if you consider the New York City of the 1960s, when it actually still was the tallest building in the city — for that matter, in the world. The top of the building is, or at least was, the unique highest place you could go in the city. Which imho supersedes a debate about which is the most famous. —Dan
There is a variant where you have agreed to meet a friend in Vienna, at the Cafe Mozart. You arrive in the city, and find to your horror that there are N cafes called Cafe Mozart. Each day, you and your friend each go to one of these cafes at noon, hoping to see each other. How can you minimize the expected number of days before you meet? This problem is fairly easy if you and your friend agree on your roles in advance. For instance, one of you can go to the same cafe every day, while the other goes through all N in random order, then the expected time is N/2. It gets more interesting if you don’t have such a prior agreement, so that you and your friend have to follow the same randomized strategy. In that symmetric case, can you achieve an average less than N? [Spoiler] here is a recent paper on this topic: https://arxiv.org/abs/1609.01582 - Cris
On May 19, 2017, at 12:29 PM, Dan Asimov <asimov@msri.org> wrote:
This reminds me of the very first rendezvous problem I heard, in a little book on probability by Frederick Mosteller (et al.?) from the 1960s:
----- You have agreed to a rare meeting in New York City with an old friend at a date and time both of you will have no trouble remembering. When the arrangement was made, however, the location of the was to be determined, and now that the date and time are upon you, you realize that a) no place was ever set for the meeting and b) you have no way of communicating with your friend now that you are both somewhere in New York City unbeknownst to the other.
Problem: What do you do to maximize the chance of meeting the other person at the appointed time? -----
—Dan ———— Note: Wording of problem is my own, as I don't know which book I saw it in.
On May 17, 2017, at 10:58 PM, Dave Dyer <ddyer@real-me.net> wrote:
My ultimate rendezvous problem:
You and your partner are located at separate locations somewhere in the milky way galaxy. You have a ship capable of acceleration to light speed in negligible subjective time, and a beacon that can be detected over any distance its light reaches.
Rendezvous for a victory drink before either of you dies of old age.
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I'd like to think about and even discuss this ultra-fascinating question — *without* knowing the answer (or hints) — with others in the same boat. So, would it be OK if anyone posting a spoiler about this adds the word SPOILER to the subject line? If that wouldn't screw up threading or anything too badly. —Dan
On May 19, 2017, at 1:36 PM, Cris Moore <moore@santafe.edu> wrote:
There is a variant where you have agreed to meet a friend in Vienna, at the Cafe Mozart. You arrive in the city, and find to your horror that there are N cafes called Cafe Mozart. Each day, you and your friend each go to one of these cafes at noon, hoping to see each other. How can you minimize the expected number of days before you meet?
This problem is fairly easy if you and your friend agree on your roles in advance. For instance, one of you can go to the same cafe every day, while the other goes through all N in random order, then the expected time is N/2.
It gets more interesting if you don’t have such a prior agreement, so that you and your friend have to follow the same randomized strategy. In that symmetric case, can you achieve an average less than N?
[Spoiler]
At this point, regarding the Mosteller problem, Dan's hint is something that I thought of for about ten seconds, and dismissed it because I was thinking of it as a math problem. Two people sitting separately, trying to decide what is the most salient point in NYC, didn't seem very mathematical to me. Isn't this Brent's "psychology problem"? I'm going to be very skeptical if it turns out that the answer is "Go to Times Square and wait.". Especially since finding somebody in Times Square isn't trivial! How many "most salient points" are there in NYC? All this does is reduce N, maybe by a lot, but not enough. I'm going to be *somewhere* at the moment specified; the chance that we have both picked the same somewhere is 1/N. On Fri, May 19, 2017 at 5:01 PM, Dan Asimov <asimov@msri.org> wrote:
I'd like to think about and even discuss this ultra-fascinating question — *without* knowing the answer (or hints) — with others in the same boat.
So, would it be OK if anyone posting a spoiler about this adds the word
SPOILER
to the subject line? If that wouldn't screw up threading or anything too badly.
—Dan
On May 19, 2017, at 1:36 PM, Cris Moore <moore@santafe.edu> wrote:
There is a variant where you have agreed to meet a friend in Vienna, at the Cafe Mozart. You arrive in the city, and find to your horror that there are N cafes called Cafe Mozart. Each day, you and your friend each go to one of these cafes at noon, hoping to see each other. How can you minimize the expected number of days before you meet?
This problem is fairly easy if you and your friend agree on your roles in advance. For instance, one of you can go to the same cafe every day, while the other goes through all N in random order, then the expected time is N/2.
It gets more interesting if you don’t have such a prior agreement, so that you and your friend have to follow the same randomized strategy. In that symmetric case, can you achieve an average less than N?
[Spoiler]
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The 21st century solution to this problem is to contact the other person on your cell phone. -- Gene On Friday, May 19, 2017, 2:10:43 PM PDT, Allan Wechsler <acwacw@gmail.com> wrote:At this point, regarding the Mosteller problem, Dan's hint is something that I thought of for about ten seconds, and dismissed it because I was thinking of it as a math problem. Two people sitting separately, trying to decide what is the most salient point in NYC, didn't seem very mathematical to me. Isn't this Brent's "psychology problem"? I'm going to be very skeptical if it turns out that the answer is "Go to Times Square and wait.". Especially since finding somebody in Times Square isn't trivial! How many "most salient points" are there in NYC? All this does is reduce N, maybe by a lot, but not enough. I'm going to be *somewhere* at the moment specified; the chance that we have both picked the same somewhere is 1/N. On Fri, May 19, 2017 at 5:01 PM, Dan Asimov <asimov@msri.org> wrote:
I'd like to think about and even discuss this ultra-fascinating question — *without* knowing the answer (or hints) — with others in the same boat.
So, would it be OK if anyone posting a spoiler about this adds the word
SPOILER
to the subject line? If that wouldn't screw up threading or anything too badly.
—Dan
On May 19, 2017, at 1:36 PM, Cris Moore <moore@santafe.edu> wrote:
There is a variant where you have agreed to meet a friend in Vienna, at the Cafe Mozart. You arrive in the city, and find to your horror that there are N cafes called Cafe Mozart. Each day, you and your friend each go to one of these cafes at noon, hoping to see each other. How can you minimize the expected number of days before you meet?
This problem is fairly easy if you and your friend agree on your roles in advance. For instance, one of you can go to the same cafe every day, while the other goes through all N in random order, then the expected time is N/2.
It gets more interesting if you don’t have such a prior agreement, so that you and your friend have to follow the same randomized strategy. In that symmetric case, can you achieve an average less than N?
[Spoiler]
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The psychological approach is easily extended. Yeah, Times Square is big and there are a lot of people in it; so where's a unique place in it: The Official NYC Information Center, which is right there at the intersection of 7th and Broadway where the New Year's Eve TV shows are televised. Brent On 5/19/2017 2:10 PM, Allan Wechsler wrote:
At this point, regarding the Mosteller problem, Dan's hint is something that I thought of for about ten seconds, and dismissed it because I was thinking of it as a math problem. Two people sitting separately, trying to decide what is the most salient point in NYC, didn't seem very mathematical to me. Isn't this Brent's "psychology problem"? I'm going to be very skeptical if it turns out that the answer is "Go to Times Square and wait.". Especially since finding somebody in Times Square isn't trivial!
How many "most salient points" are there in NYC? All this does is reduce N, maybe by a lot, but not enough. I'm going to be *somewhere* at the moment specified; the chance that we have both picked the same somewhere is 1/N.
On Fri, May 19, 2017 at 5:01 PM, Dan Asimov <asimov@msri.org> wrote:
I'd like to think about and even discuss this ultra-fascinating question — *without* knowing the answer (or hints) — with others in the same boat.
So, would it be OK if anyone posting a spoiler about this adds the word
SPOILER
to the subject line? If that wouldn't screw up threading or anything too badly.
—Dan
On May 19, 2017, at 1:36 PM, Cris Moore <moore@santafe.edu> wrote:
There is a variant where you have agreed to meet a friend in Vienna, at the Cafe Mozart. You arrive in the city, and find to your horror that there are N cafes called Cafe Mozart. Each day, you and your friend each go to one of these cafes at noon, hoping to see each other. How can you minimize the expected number of days before you meet? This problem is fairly easy if you and your friend agree on your roles in advance. For instance, one of you can go to the same cafe every day, while the other goes through all N in random order, then the expected time is N/2. It gets more interesting if you don’t have such a prior agreement, so that you and your friend have to follow the same randomized strategy. In that symmetric case, can you achieve an average less than N? [Spoiler]
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I don't know the answer, so I don't think that the following discussion can count as a spoiler. I highly suspect that my three proppsed answers are all wrong! But anyway: given that Mosteller is a probabilist, perhaps his idea of the canonical meeting place would be the centroid of Manhattan? (It's the unique location P that minimized expected squared distance between P and a point chosen uniformly at random in Manhattan.) Or maybe it should be the expected location of a randomly-chosen New Yorker, i.e. the population-weighted centroid? Or maybe we should assign more weight to people who weigh more? Jim Propp On Friday, May 19, 2017, Dan Asimov <asimov@msri.org> wrote:
I'd like to think about and even discuss this ultra-fascinating question — *without* knowing the answer (or hints) — with others in the same boat.
So, would it be OK if anyone posting a spoiler about this adds the word
SPOILER
to the subject line? If that wouldn't screw up threading or anything too badly.
—Dan
On May 19, 2017, at 1:36 PM, Cris Moore <moore@santafe.edu <javascript:;>> wrote:
There is a variant where you have agreed to meet a friend in Vienna, at the Cafe Mozart. You arrive in the city, and find to your horror that there are N cafes called Cafe Mozart. Each day, you and your friend each go to one of these cafes at noon, hoping to see each other. How can you minimize the expected number of days before you meet?
This problem is fairly easy if you and your friend agree on your roles in advance. For instance, one of you can go to the same cafe every day, while the other goes through all N in random order, then the expected time is N/2.
It gets more interesting if you don’t have such a prior agreement, so that you and your friend have to follow the same randomized strategy. In that symmetric case, can you achieve an average less than N?
[Spoiler]
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My ultimate rendezvous problem: You and your partner are located at separate locations somewhere in the milky way galaxy. You have a ship capable of acceleration to light speed in negligible subjective time, and a beacon that can be detected over any distance its light reaches. Rendezvous for a victory drink before either of you dies of old age.
participants (12)
-
Allan Wechsler -
Brent Meeker -
Cris Moore -
Dan Asimov -
Dan Asimov -
Dave Dyer -
Eugene Salamin -
Gareth McCaughan -
Henry Baker -
James Propp -
Keith F. Lynch -
Mike Speciner