Analyzing Motivation Quantitatively

Maslow Pyramid
Motivational theorists are figuring out how to use applied math to quantify motivation. Image by JK Jeffrey/Shutterstock

18 September 2019 – The following essay is taken verbatim from a posting I made to the discussion forum for a class in my Doctor of Business Administration program at Keiser University.

For those who were disappointed by my not posting to this blog last week, I apologize. Doctoral programs are very intensive and I’ve found myself overloaded with work. I’ve had to prioritize, and regular postings to this blog are one of the things I’ve had to cut back. When something crosses my desk that I think readers of this blog might find particularly interesting, I’ll try to take time to post it here and let folks know about it through my Linkedin and Facebook accounts.

In the essay below I suggest an extension to a method for understanding human motivation using applied mathematics techniques. What, you didn’t think that was possible? Read on!

Almost at random, I happened to pick up Chung’s (1969) paper from this week’s reading list first. Since it discussed an approach to questions of motivation that I find particularly interesting, I was inspired to jump in and discuss my reaction to it immediately.

The approach Chung took was to use applied mathematics (AM) techniques for analyzing motivation. Anyone not steeped in AM methods could be excused for being surprised that the field could have anything to say about motivation. On the surface, motivation might seem completely qualitative, so how could mathematical techniques be at all useful for analyzing it?

In fact, quantification of anything that you can rank is possible. For example, Zheng & Jiang, (2017) discussed methods of quantifying species diversity in ecosystems. The fact that you can say this ecosystem is more diverse than that ecosystem means that ecosystem diversity is quantifiable.

Similarly, the fact that you can say that such-and-such a person is more motivated to do something than some other person indicates that motivation is quantifiable as well. Before proposing his Markov-chain model, Chung (1969) discussed five other analytical methods for studying motivation based on Maslow’s hierarchy, all of which descriptions he started by describing some method of quantifying motivation.

It happens that I am quite familiar with the mathematics Chung (1969) used. It is called linear algebra, and is a staple technique for analyzing theoretical physics problems. I started my career as an astrophysicist, so Chung’s paper is right in my intellectual wheelhouse. Reading it stimulated me to think: “Yeah, but what about …?”

What Chung’s analysis left out was how human motivation is subject to chaotic exogenous forces. I’ve more than once used the following thought experiment to illustrate this phenomenon. Imagine Albert Einstein scratching away at General Relativity Theory on the blackboard in his office. I mention Einstein particularly because he was known to be fond of thought experiments, so including him in this one seems appropriate. So, Einstein is totally absorbed in his work puzzling out GRT. Maslow would say that he is motivated at the “self-actualization” level. Suddenly, our hero realizes that it’s lunch time because his body signals a physiological need for a ham sandwich. An exogenous event (lunchtime) has modified Einstein’s needs state.

In Chung’s (1969) analysis, Einstein’s transition matrix P has suddenly switched from having element values that cause Einstein’s needs vector N to remain stable at Maslow’s level five to values that cause his needs to switch to level one at the next transition. At that point, Einstein puts down his chalk and roots around in his briefcase for the ham sandwich he knows his wife put in there this morning.

So, how would we handle this situation from a linear algebra standpoint? Using Chung’s (1969) notation, the transition from the ith state to the (i+1)th state is given by Equation 1:

Ni+1 = Ni P (1)

I’ve modified the notation slightly by writing vectors in regular italic typeface and matrices in bold italic typeface. That satisfies my need to have vectors and matrices sybolized in different typefaces. It’s a stability thing for me, so it’s down at Maslow’s level two (Chung, 1969) in my personal hierarchy of needs.

What we need now is to modify the transition matrix by applying another matrix that isolates the effect of the exogenous event. If we add a subscript 0 to specify the original transition matrix, and multiply it by a new matrix X that accounts specifically for the exogenous event, we get a new transition matrix given by Equation 2:

P = P0 X (2)

Finally, Equation 1 becomes Equation 3.

Ni+1 = Ni P0 X (3)

What is left to do is to develop methods of determining numerical values for the elements of these vectors and matrices in specific situations. This addition shows how to extend Chung’s (1969) Markov-chain model to situations where life events modify an individual’s motivational outlook. Such events can be anything from time reaching the lunch hour to the individual becoming a parent.


Chung, K. H. (1969). A Markov Chain Model of Human Needs: An Extension of Maslow’s Need Theory. Academy of Management Journal, 12(2), 223–234.

Zheng, L. & Jiang, J. (2017) A New Diversity Estimator. Journal of Statistical Distributions and Applications, 4(1), 1-13.