Posted on 03/21/2008 11:46:03 AM PDT by Squidpup
A mathematical mystery that has baffled top minds in the field of symbolic dynamics for nearly four decades was cracked last year by a 63-year-old former Israeli security guard.
Avraham Trakhtman, a mathematician who worked as a laborer after immigrating to Israel from Russia, succeeded in solving the elusive Road Coloring Problem. The conjecture assumes that it is possible to create a universal map that would direct people to arrive at a certain destination, at the same time, regardless of their original location. Experts say this proposition, which seems to defy logic, could actually have real-life applications in the fields of mapping and computer science.
"In math circles, we talk about beautiful results. This is beautiful and it is unexpected. Even in layman's terms it is completely counterintuitive, but somehow it works," said Stuart Margolis, a colleague who recruited Trakhtman to Bar Ilan University near Tel Aviv.
"The first time I met him he was wearing a night watchman's uniform," said Margolis.
The Road Coloring Problem was first posed in 1970 by Benjamin Weiss, an Israeli-American mathematician, and a colleague, Roy Adler, who worked at IBM at the time.
Weiss said he believed that given a finite number of roads, one should be able to draw up a map, coded in various colors, that would lead to a certain destination regardless of the point of origin.
.....snip.....
Margolis says the solution could have many applications.
"Say you've lost an e-mail and you want to get it back - it would be guaranteed," he said. "Let's say you are lost in a town you have never been in before and you have to get to a friend's house and there are no street signs - the directions will work no matter what," he said.
(Excerpt) Read more at haaretz.com ...
There is hope for finding all of those lost socks
So if I am in LA and need to attend a meeting monday morning at 10:00 AM and need to leave my house and drive down the street park and arrive.
Assuming my meeting is with someone from London he would have to fly over at an earlier date, get a hotel and leave and arrive at the 1000 AM meeting with me.
Who knew the guy from London would have to leave earlier to meet me here.
Well, you ARE in LA, so he wouldn’t have to leave that much earlier than you. /semi-sarc
It’s difficult for me to understand the implications of the solution if I don’t understand the problem.
Luuuuuuucy, ‘splain this to me.
“Weiss said he believed that given a finite number of roads, one should be able to draw up a map, coded in various colors, that would lead to a certain destination regardless of the point of origin.”
All roads lead to Rome.
“”Let’s say you are lost in a town you have never been in before and you have to get to a friend’s house and there are no street signs - ...
Ask your girlfriend for directions.
(Yes, just kidding.)
Good one!!!
That’s nothing! There was this kid from Southie who was a janitor at MIT who ... oh, wait. Nevermind.
“The conjecture assumes that it is possible to create a universal map that would direct people to arrive at a certain destination, at the same time, regardless of their original location...”
That would be quite useful if you’re bombing a country...like maybe, Iran?
You could converge all the aircraft to reach the target, coming from different directions, at the same time.
It would appear (from the info in the article) to be like a dis...
If we color code all the highways, and you as in Las Vegas, and I am in New York, then we each get a set of UNO cards that tell us what highways to take, so we can meet in Texas.
It might not be the shortest ‘route’, but the numeric value of the colors is equal for both of our decks.
somehow, I think that specific information is not being given in the article to allow us to understand the ‘problem’ or ‘solution’.
Or I iz just dumm as hell.
“Trakhtman’s solution is available for viewing on the Internet and will soon be published in the Israel Journal of Mathematics.”
My luck.
I want the problem and all they got is the answer.
ping
Is this from graph theory? That is very intense and slightly odd.
Here. I found a much more detailed explanation.
http://www.jpost.com/servlet/Satellite?cid=1202246348334&pagename=JPost%2FJPArticle%2FPrinter
And then, the clouds parted.
The sun shone brightly.
And it was all clear.
The Road Map problem. The Road Coloring problem.
Hmmmmm....should resolve our religious differences.... :-)
Thanks for the link.
Uh.... ok. I think I got it.
uh..... The robot guy uses different colored lights to signal to a hot chick robot.
If the chick signals back the same colors, they get synchronized, and the guy robot can make it all the way to home (base).
If something goes amiss, or the guy robot is too fresh, then the chick robot uses her ‘safe word’, and the guy robot’s brain is reset to the last safe checkpoint.
“Is this from graph theory? That is very intense and slightly odd.”
Post #16 is pretty informative. You are correct about it being graph theory. (all this time and we still can’t prove graphs are real?)
Disclaimer: Opinions posted on Free Republic are those of the individual posters and do not necessarily represent the opinion of Free Republic or its management. All materials posted herein are protected by copyright law and the exemption for fair use of copyrighted works.