Reflecting on Stochasticity

By Donovan Makus




For most of us, this word has many meanings. These can range from the positive, such as receiving an unexpected gift, to the negative, such as an unexpectedly poor test result. However, we typically tend to value predictability, be it in life or grades. This value ascribed to predictability extends to the modern sciences, which are inherently deterministic, striving to connect variables to results. Scientific models strive to accurately represent the outcome of changing variables, yet these models are limited both in their ability to predict far into the future and in their accuracy in the first place. This can be attested to by anyone who has ever planned a weekend event, such as an outing on a lake; you anticipate good weather based on weather reports a week or two from the event, only to find the day of that the weather is miserable. These limitations reflect the scientific principle of stochasticity, one with implications for scientific study, and our lives in general.


For most of our everyday activities, we can see cause and effect relationships. A lack of sleep will translate to sluggishness the next day. An essay written with little thought or concern will typically yield a low mark. While it would be pleasant to find a poor night’s sleep or hastily written essay leading to more positive outcome, it’s not expected. The consistency of these patterns allow us to plan around them. We know that if we want to be in peak shape for a midterm, we need to spend time studying and resting properly. A good mark on an essay can only be expected after hours of deliberate drafting and the creation of polished prose.


Modern science follows this same principle of consistency. For science to “work,” there must be a pattern or relationship between variables. The entire foundation of modern science rests upon being able to predict outcomes using past knowledge and models in the creation of hypotheses. Yet the natural world is inherently variable, with even tightly controlled experiments demonstrating some variability, typically measured using the concept of standard deviation. For the natural world, variability is even greater where stochasticity combines with all the other variables that contribute to differences between samples. Without an understanding of stochasticity, this can be quite confusing. Any student who has ever completed outdoor sampling can attest to this; even with the known variables controlled, there is still variability inherent to the natural system. This challenges the ability of models to approach 100% accuracy all of the time, but can be accounted for and controlled in modeling.  


This concept of stochasticity is not restricted only to biological systems starting at the level of the individual organism, it can be seen at the very foundations of all matter. At the beginning of the 20th century, models such as the Bohr atom model held that electrons exhibited consistent patterns, following what could be visualized as tracks around the central nucleus. However, the model was limited and unable to explain many experimentally-determined findings. Quantum theory changed this by introducing probability clouds related to stochasticity, where instead of an electron sticking to a defined track around the atom, it instead exists in a probability cloud of likely places it could be found. While research in physics continues, quantum theory was revolutionary in introducing the language of randomness, or stochasticity, into what was previously thought to be a field firmly ground in models that did not leave significant room for variation.


The concept of stochasticity does not mean that the scientific models are invalid nor that we should merely give up trying to predict and model our world. Instead, it should help us better explain our surroundings. Stochasticity is limited depending on the system, to some extent; while it expands the range of values we can expect to observe, it doesn’t do so infinitely. Models that fail to account for stochasticity provide reasonable approximations in many scientific disciplines, and considering the contradiction of predicting randomness in a model, we’re left with few options for a 100% accurate model. However, this realization should not cause us to reject scientific models, but instead offers us a valuable life lesson.


Scientific models are undeniably important, but we can easily go our whole lives failing to understand the concept of stochasticity and live fulfilled lives, which begs the question, why does reflecting on stochasticity matter? There is intrinsic value to knowledge, such as understanding stochasticity, but knowledge that can be applied is often seen as having greater value. For stochasticity, it provides us with an broader life lesson, and that is the importance of adaptability. We may try to plan our lives perfectly–yet, in the same way that long-term weather forecasts often fail to reflect reality, long-term plans may also fail us and require us to adapt to new challenges or opportunities.  For stochasticity, this applied knowledge can be seen in systems that are built to accept randomness and unanticipated future uses and continue operating.


Most systems, be they cars or our own bodies, have a set operating envelope inside of which they function at their best. Some systems, like our bodies, are incredibly resilient, and can accept a wide variety of conditions. Other systems, like a car or a precision laboratory instrument, require careful use to prevent damage. Engineers and designers can take into account the principles of randomness behind stochasticity in their design by building “flex” into their systems, and in the same way, we too can take this into account in our lives. As students, we’re busy; we have classes and lives to balance, and it can be easy to try and stack activities together without any space between them. This may be fine while everything is inside this tightly-operating envelope, but unforeseen events pop up, colds are caught, and new opportunities present themselves. If we don’t build “flex” into our lives, our operating envelope can turn from a comfortable range of values into a cage that restrains our options. Factoring in stochasticity, in the same way that it is taken into account by designers of physical machines, gives us some much-needed latitude. Perhaps, instead of ensuring that every moment of each day is accounted for with a punishing schedule that allows no opportunity for stochasticity, you might pencil in optional activities with the understanding that these are actually flex-times. No matter what kind of person you are, we can all learn to embrace randomness and seek out experiences where every day would be different.


While stochasticity is an admittedly complex topic, it has wide applications into our everyday lives beyond places where we’d expect to see it such as the weather, to the very core of how we live our lives. While embracing and planning for randomness may seem like a strange move at first, it can provide us with the space and ability to function better in our ever-changing world.

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