Strange Attractors on My Walk to Work

As I discussed last time, seemingly discrete events in the macroscopic world (like my possible walks to work) seem to “collapse” themselves into fewer possible outcomes based on intervening events. A large set of initial states result in a single end state, and overall, the total number of initial states gets winnowed down into a much smaller number of final states.

Additionally, at many (if not most) points along the spectrum of starting states, a little variation one way or another doesn’t mean much for the outcome – the system is resilient to small changes. However, there are certain points (“inflection” or  “tipping” points, one might say), where the outcome changes drastically based on a small change in initial conditions.

All of this might sound familiar if you’ve read much about chaos theory and strange attractors. Consider that my walk to work is a dynamical system, evolving over time based on a set of constraints, the most significant of which are the red lights. The possible arrival scenarios are attractors – the system tends to evolve towards those points from a large set of initial conditions (the basin of attraction).

Note that there are thousands, if not millions, of other events along my walk to work that affect the timing of my walk to work. This is what makes the system chaotic, and the attractors strange. The sequence of my steps, whether I’m tired or well-rested, the other people walking around me, the prevailing winds, and many other variables affect my speed and my arrival time. However, the red lights have, by far, the most significant effect on my arrival time. That’s why I was able to draw the diagrams I did in the previous post to show how the red lights affect my arrival times at work.

In fact, my exact arrival time may vary by fractions of a second one way or another because of these other, more minor effects. But in analyzing my arrival at work, those miliseconds don’t matter nearly as much as the multi-second (or even multi-minute) swings caused by the red lights.

(Similarly, one might say that in analyzing my entire day, the difference between arriving at work one minute earlier or later doesn’t mean very much, unless, for example, I miss breakfast. Further, one might say that in analyzing my career, my arrival at work on one day doesn’t have much effect, unless, for example, I miss an important meeting and get fired as a result. This points to another interesting bit, which is that a similar analysis of the attractors in a system is valid at many different scales, but that’s a whole other blog post…)

Many systems in the world display truly chaotic behavior, wherein small changes to the initial conditions creating vast differences in the outcomes. On the other hand, many have very stable attractors like those described above, where one can discard most of the external factors affecting them in favor of a much smaller number that have the largest effects on the outcome.

Next time: rampant speculation on how these attractors relate to how we perceive the world…

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