Learning analytics and the three-body problem

The three body problem

In 1687, Sir Isaac Newton published his seminal article “Philosophiae Naturalis Principia Mathematica” in which he described the motion of celestial bodies (Newton, 1987). Newton’s theory of gravity provided a means for precisely characterising complex orbital motion by establishing that celestial bodies excerpt force on all other celestial bodies, where the force is inversely proportional to the distance between the bodies (Newton, 1987). Newton’s work, particularly with Principia Mathematica, became a cornerstone to natural philosophy and remains one of the most important scientific works in human history (Smith, 2008). However, for mathematicians in particular, Newtons work in Principia Mathematica created a long-standing problem.

The problem became known as the three-body problem and has been described as the most celebrated of all dynamical problems (Barrow-Green, 1997). The three-body problem can be simply stated:

Three particles move in space under their mutual gravitation attraction; given their initial conditions, determine their subsequent motion

(Barrow-Green, 1997).

The essence of the three-body problem is that even if we know the initial position and momentum for three bodies, we cannot solve for their subsequent motion (except in some highly specific and contrived situations). Between 1750 and 1900, over 800 publications were written related to the three-body problem representing many distinguished mathematicians of that time (Barrow-Green, 1997), with the problem remaining unsolved to this day.

So what has this got to do with learning analytics?

Well, not much really and I’m probably even guilty of committing a logical fallacyreductio ad absurdum. It is also an apples/oranges comparison, but it does help to illustrate a point.

Consider the dominant management model and the dominant approach to technology adoption in our universities: Universities tend to be based on the Newtonian-machine management model where the focus is on hierarchical structures, rules-based culture, command, control and formal relationships (Cenere, Gill, Lewis, & Lawson, 2015; Goldspink, 2007). This mechanical model assumes that goals can be achieved through deliberate action based on knowledge of what has happened previously (Beer & Lawson, 2017). Put simply, we tend to think that a thorough analysis of what has happened previously can help us to predict what will happen next, and so we make our plans and design our systems based on the assumption that the past can inform the future.

Getting back to the three-body problem, we only have three entities, each with its own mass, vector and velocity, and we are still unable to algorithmically characterise their respective positions in the future. If we have a class with only three students, we cannot begin to perceive or quantify the variables that will contribute to their success or otherwise. Even if we had the hypothetical ability to perceive these variables at the outset of their studies, it would have little bearing on the outcome or the journey to the outcome.

My point here is that techno-centric approaches to learning analytics, where the focus of attention is on historical data, are fundamentally flawed. I’m not sure we truly understand this yet as a sector. I’m still seeing people buying into the delusion that says predicting student success is simply a matter of investing in some IT infrastructure and applying some fancy-sounding algorithm. Investment in data infrastructure and exploring these algorithms is something we should be doing, no argument, but what about investing the human side of learning analytics, the non-IT side? Even if we have the most amazing systems and the most amazing algorithms, what can we do about that student who hasn’t logged on for two weeks because they have been busy with their three jobs and complex family challenges? Do our policies and processes allow the flexibility required to respond to the range of situations that will be brought to light by our learning analytics systems? More broadly still, do our systems, processes and policy appropriately represent our specific cohort of students?

I’m a nerd and I get the fascination with IT systems and predictive algorithms with learning analytics, I really do. But we need to think about the assumptions that underpin our investments in learning analytics. Resources are finite, now more than ever, so we need a more balanced approach to how we conceptualise learning analytics in each of our organisations.


Barrow-Green, J. (1997). Poincaré and the three body problem: American Mathematical Soc.

Beer, C., & Lawson, C. (2017). Framing attrition in higher education: A complex problem. Journal of Further and Higher Education, 1-12. doi:10.1080/0309877X.2017.1301402

Cenere, P., Gill, R., Lewis, M., & Lawson, C. (2015). Communication Skills for Business Professionals. Port Melbourne, Victoria, Australia: Cambridge University Press.

Goldspink, C. (2007). Rethinking Educational Reform: A Loosely Coupled and Complex Systems Perspective. Educational Management Administration & Leadership, 35(1), 27-50. http://dx.doi.org/10.1177/1741143207068219

Newton, I. (1987). Philosophiæ naturalis principia mathematica (Mathematical principles of natural philosophy). London (1687), 1687.

Smith, G. (2008). Isaac Newton. https://plato.stanford.edu/archives/fall2008/entries/newton/: Metaphysics Research Lab, Stanford University.


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