On the Potentiality of a [Mathematical] Model for Social Value

Haley Beer & Kélig Aujogue

Quantifying and discovering mathematical models has long been part of human understanding and progression. Whether it is applied to scientific, technological or social matters a mathematical model can help us to comprehend, predict, and compare important phenomenon, and their influences, in our environment.

“By curious skill they could number the stars and the sand, and measure the starry heavens, and track the courses of the planets. For with their understanding and wit, which Thou bestowedst on them, they search out these things; and much have they found out; and foretold, many years before… But they knew not the way, Thy Word, by Whom Thou madest these things which they number, and themselves who number, and the sense whereby they perceive what they number, and the understanding, out of which they number; or that of Thy wisdom there is no number.” - Saint Augustine

Typically, the use of mathematical models follows a pattern: it is developed within the sciences to describe natural phenomenon and/or laws and then diffused towards other applied subjects.  For instance, partial differential equations utilized for centuries in physics to describe continuous medium are now applied to understand financial values; as in the Black-Scholes equation being used to predict the price of European options. Similarly, the Fourier Transform, a mathematical tool discovered nearly 200 years ago that projects a continuous timeline of events into a series of frequencies, is now used in signal processing devices (vocal, optical…) around the world.

Justly, the influence of many mathematical models has expanded away from their original applications in sciences and one could legitimately wonder: Can we model and predict social values with such tools? Probably. If we are interested in modelling a social value such as happiness and make the assumption that it reacts as a fluid, we could use the Navier-Stokes equation. The advection in time or the rate of Happiness would then be described as the sum of external forces (e.g., relationships, satisfaction with job, personal resources, opportunities for expression, etc.) and the diffusivity of happiness.  We could then write in terms of mathematical formalism that:

where VHappiness is the value of Happiness at a given position in space and in time, Fexterior corresponds to the external constraints (positive or negative) influencing the happiness and v a “viscous” coefficient of happiness. This last term could thereby be interpreted as some capacity of the happiness holder to share or influence their environment.

However, as much as this model shines a different light on the notion of Happiness and is a good starting point, it is conceivably not fully satisfactory for modelling social values. Natural science models are founded in the belief that phenomenon exist 'out there' and are independent from humans; but, arguably social value such as happiness reside 'inside', or at the very least are interpreted individually interiorly, so somehow motions to be known in a different way.

By using a model to derive a figure for social value, whichever way we choose to define it using present mathematical models, we largely overlook the interior process of coming to know such value (whether that is the process of interpretation of an external social value or the nurturing of personal social value understanding and expression).

Just because I am capable of describing Happiness in a model does not necessarily translate into the generation of more (or less) Happiness for others or myself. That is, mathematical models as they are used today encourage us to ‘know’ something as external to us, to identify things in the physical realm, but not necessarily to understand what they mean for us as individual people, or how to change such things (e.g., how am I affected by knowing the phenomenon Happiness exists and what does it mean for how I conduct myself or my organization?). We may have developed models which help us predict Earthquakes and Solar Flares, but is there anything we can actually do to stop/transform them? No. Though, do we have some sway over our levels of happiness? By all means yes.

Likely for a veracious modelling of social value we will eventually need to come up with new 'models' that stretch our current conceptions of 'coming to know' something. That is, because the point is to lend ontological (or a part of reality) credence that in the past was not considered (at least not very much in institutional and organizational settings), we arguably need new epistemologies (ways of knowing that reality). While the natural science models might bring us a first way to measure for social value, and thereby discuss its potential and usefulness at organizational, institutional, national and international levels, due to its intersubjective nature, we think the way of measuring for social value should itself evolve to enable different kinds of knowing. Why only use models to predict and compare levels of Happiness when there is a seeming opportunity to personally foster, understand, and express it more meaningfully?

Atlas Coelestis – The Copernican System - 1660

In practice also, mathematically such equations as the Happiness one needs boundary conditions to be solved. These conditions are properties at the end of the studied domain that are not well defined in the known reality of social values. What are the limits or boundaries to social values anyway? And should there even be any placed? Besides, can we really limit the movement of social values to an advection/diffusion process? Maybe for some of them but it seems that there are insufficiencies for most social values.

Taking an example such as freedom, we have to admit that even if we could find some ground to justify the advection it would be harder to explain the diffusion. Certainly, freedom is something that is owned by its holder and sometimes can be given by its holder. These points highlight only the tip of the iceberg for the complexity of human relations and modelling social values. Perhaps the measuring rate in the world of social values can be approached through a different formalism such as Network Theory or Thermodynamics. Nonetheless, humans’ capacity to experience, generate, express and share social value is arguably one of the most under appreciated resources in our present use of mathematical models.

In other words, these existing mathematical models might help us bridge the initial gap between this so far much neglected interior realm of our universe and our obsession with objectivity since the Enlightenment, but once we become more comfortable talking about and ‘modelling’ social value, then we bet we can also come up with original ways of knowing, discussing, and/or generating it. However, in the meantime, using a host of mathematical models from the natural sciences to begin exploring how to integrate social value into economic and organizational discourse is helpful as it stimulates interest in and energies towards social value- and this is ultimately a first step towards discovering its potentiality!  

“Spirale” by Michelle Gouin