Avoiding False Dynamism
What random walks can teach us about living a dynamic life
Avoiding False Dynamism
In probability the most basic event is the coin flip. Half the time you get heads and half the time you get tails. In technical terms this is a "Bernoulli Process"1.
Observing a Bernoulli process can give us an intuition for how the world operates and what this means for the kind of things we should pursue. To do this we can consider a random walk. To generate a simple random walk, imagine a system of a single variable starting at 0. Flip a coin. If you get heads heads you will add one (+1) to the variable if tails you will take away one (-1). Your variable now has the value 1 or -1. Repeat the process taking the output following the first coin flip as the new value for your variable. Flip a coin again and either add one or take away one. This will give you a new value for the variable (in this case: 2, 0 or -2) which can in turn be plugged into the following coin flip.
As this process goes on and you take more steps the system will move ("walk") randomly through time. You can plot this on a chart as a line. When you do this for multiple random walks you can start to get a sense for how the process operates. No two walks are ever exactly alike. Each generates peaks and valleys that appear like the complex arcs of a unique trajectory.
We can learn something from this about our own lives and ventures. We always experience some amount of random change. Staying our current course our stove will break and need to be replaced, our tastes will change and we begin a new diet, our company's core product may be discovered by a new demographic boosting sales or there could be a shift in public mood and new regulations come in that harm our profits.
In aggregate these occurrences can feel like a wild roller coaster of change. However, if we are not paying attention it may be that these are the result of a simple random walk. None of us whether in our personal lives or with our ventures wishes to be a pawn of fate in this way. Instead we want to chart truly dynamic paths. To get there we need to seek out brand new possibilities. Rather than allowing our current situation to unfold we should look for opportunities to change the underlying process.
Bernoulli processess and their derivatives underlie many areas of statistical thinking including things like randomised controlled trials and A/B testing. When you think about whether or not a drug treatment worked you are essentially asking the same question as whether the coin you are flipping is fair.