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        riddles >> hard >> lover random rendezvous
        
(Message started by: ERIC H. ZENGULUS on Jun 28^th, 2004, 9:25am)

Title: lover random rendezvous
Post by ERIC H. ZENGULUS on Jun 28^th, 2004, 9:25am

somewhere there exists another world where the time-space fabric is discrete, and we dont know the space fabric it might be 1D 2D 3D or the space might be curved. two lover breaks at zero point at zero time then start random walk. will they run into each other again and when (probability-wise) ?

if u prefer big bang then:
somewhere there exists another world where the time-space fabric is discrete, and we dont know the space fabric it might be 1D 2D 3D or the space might be curved. at time zero there is big bang which generates equal infinite number of particles and antiparticles. Assume there is no gravity and those particles start random walk then. If any particle meets any anti-particle they both will disapear. How many perentage of them will still alive in the end ?

Title: Re: NEW: HARD: lover random rendezvous
Post by towr on Jun 28^th, 2004, 9:38am

::[hide]
On the line in on the plain they will meet again with probability 1, but it may take an eternity.

You can take either of them as a reference point, and then the other will either move two steps in a direction, or none. So it's equal to a simple random walk where you need to return to the origin.

For 3D the chance they will meet is less than one, there's another thread dealing with a random walk in 3D (which makes it only slightly different from this one). And since it'll take an eternity even in the 1D case, it'll take at least as long here.

As for curved space, if any dimention is infinite it'll take an eternity for them to meet. If the surface is one or two dimensional they are guaranteed to meet, but I'm not sure about the higher dimensions.
If at least 3 dimensions are infinite they'll meet with a probability less than 1.
As for weirder shapes of curvature, I'm not even gonna start on it..[/hide]::

Oh yeah, in higher dimension, is one step taken in all directions (i.e 1 step left/right and 1 up/down), or one step in one of the directions (i.e 1 step left/right/up/down)?

Title: Re: NEW: HARD: lover random rendezvous
Post by towr on Jun 28^th, 2004, 9:50am

on 06/28/04 at 09:25:35, ERIC H. ZENGULUS wrote:

if u prefer big bang then:
somewhere there exists another world where the time-space fabric is discrete, and we dont know the space fabric it might be 1D 2D 3D or the space might be curved. at time zero there is big bang which generates equal infinite number of particles and antiparticles. Assume there is no gravity and those particles start random walk then. If any particle meets any anti-particle they both will disapear. How many perentage of them will still alive in the end ?

Equal fractions go in each direction after the first step, so all particles will have annihilated after the first step.

Title: Re: NEW: HARD: lover random rendezvous
Post by THUDandBLUNDER on Jun 28^th, 2004, 10:15am

Do you think that the two lovers would be happy to be told, "Yes, you will meet again!" but that they must expect to wait an eternity before it happens? Personally, I don't think it leaves much time for starting a family.

Similarly, would a Christian (Muslim, Hindu, etc) be happy to have it somehow confirmed that God exists, while yet being told that he/she can expect to wait an eternity before the many become One? Is this what He meant when he promised Eternity?