The interplay of uncertainty and knowledge on our lives is a common theme of philosophy which appears across time and culture. In western philosophy, one of the most vivid allegories of this theme are opposing female characters of Fortuna and Sapientia, who also provide an insightful metaphor for mathematical modeling. This article explores how these philosophical figures symbolize the balance between the unpredictable and the methodical approaches in groundwater modeling.
The Whims of Fortuna and the Wisdom of Sapientia
The concept of Fortuna and Sapientia isn’t a singular, well-defined myth like those of Zeus or Hercules but rather a conceptual pairing often explored in medieval and Renaissance literature and art. The two figures represent contrasting aspects of human life and destiny: Fortuna embodies uncertainty, luck, and the capricious nature of fate, while Sapientia represents wisdom, knowledge, and reasoned decision-making.
In various literary and philosophical works, these two entities are depicted in dialogue or in
opposition to illustrate moral and existential debates. For instance, the interplay between the unpredictability of fortune and the steadiness of wisdom is a common theme used to discuss the nature of human success and happiness, and how much of it is due to luck versus personal effort and prudence. In art, they may be represented in allegorical forms, with Fortuna often shown with a wheel that she turns arbitrarily and Sapientia sometimes depicted with a book or other symbol of knowledge. For hundreds of years the conceptual pairing of Fortuna and Sapientia has encouraged contemplation on how one should live knowing that life is both unpredictable and yet can be guided by wisdom and rational choices.
Whims and Wisdom in groundwater modeling
Groundwater modeling is commonly perceived as a purely rational and scientific endeavor, heavily reliant on the principles embodied by Sapientia—wisdom, knowledge, and reason. This perspective emphasizes the application of hydrological data, mathematical formulas, and computer simulations to predict and manage groundwater resources with expectations of ‘precision’ and ‘accuracy’. However, this view often underestimates or even overlooks the significant role played by Fortuna—the uncertainty that inherently exists within environmental systems. In reality, the success and reliability of our groundwater models hinge on various factors such as spatial variability in geological formations, incomplete data, subjective interpretations, values-based assumptions and unexpected conditions. These factors can dramatically alter the outcomes of models, suggesting that Fortuna’s hand is often more in control than we assume or acknowledge. Recognizing this balance between the known and the uncertain, between Sapientia’s guidance and Fortuna’s whims, is crucial for developing more resilient and adaptive groundwater management strategies.
Accepting the Whims
The first step to creating useful models is accepting the fact that Fortuna is hiding amongst the facts and figures. Moreover, she is very good at hiding and most of us are mediocre at seeking. As such the best we can do is be aware that uncertainty enters the modeling process many times, beginning the moment we attempt to observe and measure the real world, to last iteration of the mathematical calculation. Of course, it’s our job to try and find all her hiding places but frustratingly there is no algorithm that can either fully identify or quantify the uncertainty of our models. As such, we need to simply accept that there is uncertainty in all our models and then figure out how to proceed given the uncertainty. If you are stuck on accepting these facts, then try asking yourself: How much of my own money am I willing to bet that this model is absolutely correct?
Applying more Wisdom
To enhance Sapientia’s influence over the groundwater modeling process, it is essential to design models that are not only reasonable approximations of the real world but also quick to build, easy to understand, and readily adaptable to new information. This can be achieved by simplifying model structures where possible, and choosing modeling methods which are flexible enough to allow you to update the model as you go.
Maxim: It is wise to start simple, add complexity incrementally thereby allowing uncertainty to reveal itself (at least some of it!).
Emphasizing transparency in the modeling process is also crucial to reducing uncertainty. Most importantly, this involves clear communication of the model’s objectives. This is because all our models involve some level of subjectivity, and this subjectivity limits how the model can be used. For example, on a given project, a Geotech engineer is likely to be concerned with affects of groundwater on slope stability. On the same project a hydrologist will likely be concerned with changes to stream flow. As such, these two professionals are likely to perceive the presence or absence of groundwater very differently and may even have opposing project objectives. Accordingly, the engineer and hydrologist will likely address uncertainty from their specific perspective and consequently each can make very different ‘conservative’ assumptions about the exact same real-world system.
Maxim: It is wise to know a model’s objectives, assumptions, and limits.
Finally, create models with adaptive management practices in mind from the outset. Effectively this means creating more than one model so that you can consider alternative possible futures. Having a plan for when things go wrong before they go wrong is extremely valuable (see Terzaghi’s ‘Observational Method’). Of course, building more models of possible futures is always easier and cheaper to do if you are following the first suggestion noted above.
Maxim: It is wise to have a back up plan because the real world has a charming way of not doing what your model says it should.
Back to Work
The metaphor of Fortuna and Sapientia provides a compelling lens through which to view the practice of groundwater modeling. It reminds us that our models are subject to uncertainty, but we can navigate that uncertainty with experience and reason. By starting with simple models, using methods that allow rapid updates, maintaining clear objectives and by planning for adaptation, we can simultaneously accept Fortuna’s presence and encourage Sapientia’s favour.