I think of mathematics as if it were a real world. You open the door to your house, walk down the path to the road and head off into “Mathlandia” taking any direction you choose. Unfortunately for me, my journey into this world begins and ends just beyond my front door. From there I observe the vast universe of mathematics, impressed with its scope and power. Then I pick up the morning paper and go back inside to see what odd foibles we have been up to whilst I was sleeping.
It is from this lofty perch as math observer that I thought about the concept of
“random walk”. Imagine a drunk as a skunk party goer clinging precariously to a lamppost. It is late and he must get home but seems to have lost his way, if in fact he ever had a way to begin with. Nonetheless he departs the safety of the lamppost and embarks on a series of short staggering journeys which take him hither and yon in a chaotic pattern. Our good friends at MIT made this little graphic of not one, but seven such wandering souls.
After a series of “N” random lurches of average distance “r” you can approximate how far from the lamppost our brave explorer has gone. And this is where math goes from merely interesting to way cool, bro. This little mental exercise in drunken hijinks has practical application in myriad fields, including gas diffusion, bacterial colony growth, financial market behavior, and even baseball!
Under our seemingly chaotic world a structure exists — awaiting discovery – out there in Mathlandia. Get out there!
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