Topical Guide 627
Mark Dorset
Rambling
Randomness
Where Do You Stop? Chapter 29:
I was annoyed by articles without cross-references. I doubted that one little article could be all there was to say on a subject. Could this really be the last word? Was there nothing else related to this topic? At first, I tried getting out of these dead ends by backing up. I’d retreat an article or two along the irregular path I’d been following until I came to a cross-reference I hadn’t chosen. Then I’d take that route instead of the one I’d followed originally and hope that it would put me on a longer trail, but I didn’t care for that technique. […]
Sometimes I got out of cross-referential dead ends by simply jumping to the next article, or to another on the same page, or flipping the pages until something else caught my eye, but this felt wrong, like leaping a fence into some stranger’s yard and dashing through to the next street, or leaping like Ping-Pong balls from mousetrap to mousetrap across a tabletop. It was a short, easy way out of the cul-de-sac, but taking the easy way out was ignoble. The noble thing to do, it seemed to me, was to swallow your pride, retrace your steps, and find out how things were connected, and when there were no paths provided, cut your own, so that you could, and eventually would, get everywhere, know everything.
Michael Sutton, “Random and Brownian Motion and Fractal Analyses”:
Brownian motion describes the apparently random motion of particles suspended in a fluid, named for Scottish botanist Robert Brown, who first observed through a microscope pollen particles moving erratically on the surface of otherwise still water. On an atomic level, such motion is due to collisions with the molecules comprising the suspending fluid, but due to the frequency and unpredictable nature of these collisions, on a macroscopic level we observe essentially random motion. There are many useful applications in the study of such motion, from stock market models to foraging animal paths, and entire fields of study in particle science; the mathematics behind Brownian motion apply in analysis of nearly all things apparently random. […]
Conceptually simpler than Brownian motion, Random Walks are a good place to start when examining more complex random motion. Also called a “Drunkard’s Walk,” Random Walks are a series of discrete steps taken on a d-Dimensional lattice. There are interesting probabilistic conclusions that can be drawn dependent on number of paths and the dimension the motion takes place in. […]
As the step size approaches zero and the number of steps increases to infinity, random walks begin to approximate Brownian motion. […]
On a one dimensional lattice, the distance from the origin takes a Gaussian distribution when considered as a random variable, so this gives us the idea that in lower dimensions Random Walks will tend toward their origin, […]
A two-dimensional simulation of a random walk (adapted from SoHu:
Have you missed an episode or two or several?
You can begin reading at the beginning or you can catch up by visiting the archive or consulting the index to the Topical Guide. The Substack serialization of Little Follies begins here; Herb ’n’ Lorna begins here; Reservations Recommended begins here; Where Do You Stop? begins here.
You can listen to the episodes on the Personal History podcast. Begin at the beginning or scroll through the episodes to find what you’ve missed. The Substack podcast reading of Little Follies begins here; Herb ’n’ Lorna begins here; Reservations Recommended begins here; Where Do You Stop? begins here.
You can listen to “My Mother Takes a Tumble” and “Do Clams Bite?” complete and uninterrupted as audiobooks through YouTube.
You can ensure that you never miss a future issue by getting a free subscription. (You can help support the work by choosing a paid subscription instead.)
At Apple Books you can download free eBooks of Little Follies, Herb ’n’ Lorna, and Reservations Recommended.
You’ll find overviews of the entire work in An Introduction to The Personal History, Adventures, Experiences & Observations of Peter Leroy (a pdf document), The Origin Story (here on substack), Between the Lines (a video, here on Substack), and at Encyclopedia.com.