Home > Challenge, Probability > Random Walks (and Bike Rides)

## Random Walks (and Bike Rides)

For the second consecutive day, I unexpectedly crossed paths with an acquaintance.  In both cases, the encounter occured outside my daily routines, the person was someone I know only minimally, and we were both en route to different destinations when we happened to notice each other.

There are a lot of interesting results associated with objects moving around randomly in a given space, but as is usually the case with mathematics, the situations are idealized to eliminate some of the complicating real-world issues.  Imagine a dot moving back and forth on the number line, or randomly around the Cartesian plane, for example.

I’m not really sure how unlikely it is for me to have two serendipitous encounters on back-to-back days, but the following questions are probably significant:  how dense is the population?  How many people do I know?  How attentive am I?  How popular is my destination?  There are probably many more other important and complicating factors.

In any event, it’s certainly unlikely that it will happen again today.

www.mrhonner.com

1. August 4, 2010 at 4:35 pm

For the record, it did not.

2. August 26, 2010 at 2:35 pm

I think the attentiveness piece is key. I often wonder how many times I have passed someone I know but didn’t realize it. More often, less often, or equal to the number of times I notice?

3. August 26, 2010 at 6:24 pm

Yes, and some people are more attentive than others. I wonder how that could be quantified.

4. September 28, 2010 at 7:46 pm

could this be an example of a Markov chain? because it really doesn’t matter how you got to the meeting place, it just matters that you did at some point go there and so on.. i think.