The Universal Language of Math

At the very beginning of our education on math we are all taught through word problems as to how things in our physical world can be represented by equations. Over time we progress into geometry, lines and figures begin to be understood through math and our one dimensional world progresses into two, three and even four dimensions as a time element is introduced. Before long, movement, kinematics, thermodynamics and everything imaginable is realized in math before our eyes. Possibly the most important aspect of modeling is the realization that most everything can be thought of in a set of equations. The beauty of modeling is that getting those equations to play off of one another gives us an incredibly deep understanding of our world. A great example of this is in the modern world of drug development. Every drug has what is called its MoA (Mechanism of Action) which can be represented in a set of equations. In parallel, our bodies have receptive tissues that receive those drugs which can also be represented in a set of equations. Scientists today benefit from mathematical models that allow them to see how exactly the body is expected to react to a drug even before you subject it to cells in a Petri dish or mice. As they study the results of the mice and eventually people in clinical trials against the initial math and its coefficients can be tweaked and equations refined to get an even better representation. One can imagine how this simple example can be scaled against many tissues, organs and systems in the body as we progress to someday having a true digital twin of a human and how we can best effect healthy living.

The rhythm of life’s behaviors

Life is full of rhythms and depends on the synchronicity. The simplest of which to understand is our circadian rhythm. Everyone knows that if they break their habit or rhythm of getting up and going to bed at certain times that their life feels out of balance. But have you considered how many other rhythms are present in life? There is the timing of eating, hydrating, activity, socialization and light exposure just to name a few. When you consider how many rhythms are present in our lives you soon realize that life is not like a single spinning top but instead like a troop of acrobats spinning plates while doing tricks. One plate starting to wobble can drive catastrophic consequences as the others begin to wobble consequently. This is indeed a metaphor for life. We need to keep many spinning plates in balance and if we do not, we wobble. This comparison is powerful when we consider the potential to model behaviors, habits and motivations that drive health. The frequency and magnitude of our actions keep the spinning and inertia of life going and can are profound as we examine and intervene to drive better health.

All models are wrong

British statistician George Box rather notoriously stated in 1976 that, “All models are wrong, some are useful.” For almost 50 years now these words have both haunted and challenged model builders. While it is factually true that it is almost impossible for a model to be 100% correct all the time, especially complex ones such as those endeavoring to capture the nuances of aerospace or drug delivery, there is a much more important point to be made about his usefulness comment. Models can be wonderful tools to explore choices, aid decisions and even avoiding disasters. Early in a modeler’s career they are exposed to the power of a model’s ability to perform a sensitivity analysis. As opposed to a simple equation where inputs and outputs are rather well inferred, in complex systems one does not know what a small change to an input might mean to an output. Often more importantly, models tell us where a system is most reactionary to small inputs and where even large inputs potentially cause little or no output change. This zone of critical operability is essential to things like systems design, urban planning and health management. Sensitivity analysis is extremely useful and even in models that might not exactly hit the mark in terms of predicting the future, they can help us navigate it much more effectively.

Modeling and photography

In a world where everyone seems to be now focused on video, there is something to the lost art of stop action photography. Photographs allow us to freeze the world in a moment of time and examine it. A bird in flight, a car in motion, the biomechanics of a bicyclist in a race. There is so much to be seen that is often missed without the beauty of a photograph.

Similarly, models allow scientists to fly a plan, fast forward weather patterns and even analyze financial markets. Similar to a photograph, a model’s output can be frozen in time. In the example of a financial market, otherwise imperceptible forces at play can be examined at their tipping points and exploitive actions can be taken.

To best understand the potential of a model, one needs to look no further than a simple photograph and to ask themselves, “What do I see here that I otherwise would have missed in real time?”