The Times Of Non-Linearity

by | Dec 19, 2017

I don’t think cat videos represent the funniest aspects of the internet. Let’s be honest here. It has more to do with how seamlessly you can transition from Donald Trump to Donald Duck and watch two whole episodes of Uncle Scrooge before you ask yourself, “what am I doing with my life!” One such highly predictable set of events later, I found myself staring at an article on the Harvard Business Review talking about non-linear thinking. I’ll start by reproducing an example cited there.

Imagine you’re responsible for your company’s car fleet. You manage two models, an SUV that gets 10 miles to the gallon and a Sedan that gets 20. The fleet has equal numbers of each, and all the cars travel 10,000 miles a year. You have enough capital to replace one model with more-fuel-efficient vehicles to lower operational costs and help meet sustainability goals. Which upgrade is better?

  1. Replacing the 10 MPG vehicles with 20 MPG vehicles (MPG – Miles per Gallon)
  2. Replacing the 20 MPG vehicles with 50 MPG vehicles

Intuitively, option B seems more impressive-an increase of 30 MPG is a lot larger than a 10 MPG one. And the percentage increase is greater, too. But B is not the better deal. In fact, it’s not even close. Let’s compare.

A.1,000 (@10 MPG)500 (@20 MPG)500
B.500 (@20 MPG)200 (@50 MPG)300

Highly counter-intuitive, isn’t it? We assume the higher the mileage, the higher will be the savings i.e. they are proportional. In other terms, linear. However, the dependency between these two are quite non-linear and the graph below (Taken from the article in reference 1) indicates how this effect manifests itself leading to the clear conclusion why option A is the natural choice.


A similar example of linear thinking has to do with the idea that increasing our driving speed is going to proportionally decrease the time taken to reach a certain distance. Increasing the speed from, say, 45 to 60 Kmph is going to save you more time than increasing from 75 to 90 Kmph for the same distance, although the increase in speed is the same for both cases. This is so counterintuitive that even the math doesn’t convince people easily.

This bias towards linearity is a very dominant trait in humans. We are driven towards connecting the dots by a straight line only and although it serves us well in daily life, it might create a teensy bit of trouble when dealing with problems on a larger scale.

A classic example of this would be the United States pulling off from the Paris Climate Accords. To give a bit of perspective, this was the first time in history that almost every country in the world unanimously agreed that climate change is happening and taking positive steps towards reducing anthropogenic Carbon dioxide (CO2) emissions was of paramount importance. As one of the two leading CO2 emitters, the onus was on the US to take up the mantle and tackle the issue in an exemplary manner. Climate change, as a problem, is as complex as it gets and inherently non-linear. Global warming trends are non-linear, greenhouse gas accumulation is non-linear. Hell, even economic growth is a non-linear function of mean global temperature. So what does USA do? It pulls out of the accord, courtesy of their ‘visionary’ leader, citing unfair economic disadvantages to the country. This very linear approach to such a complex issue is disheartening. Its childlike to the point of “I’m  not eating till I get the Captain America action figure!”

The reason why I wanted to highlight non-linearity is because the development sector is full of them. The problems that are being tackled are not simple. Yet the interventions for a majority of the cases seem to be highly linear in their approach. For example if you are focusing on capacity building of a community, just forcing trainings and exposure visits to model villages on the villagers is at best a single-layered approach. The trainings often span the whole day and you can notice their lack of interest in the proceedings once lunch is over. The harvesting seasons are worse because no one wants to lose out on earning money by working in the fields by spending a day in training. Also since women’s participation in these trainings are substantially low, it puts a huge question mark on the outcome of the process.

True, it is way easier to quantify capacity building by the total attendance of villagers in training events. And that is exactly my point. I shall elaborate. In a community facing crop losses due to scarcity of water, interventions are needed to create awareness about less water intensive cropping techniques. The more sustainable solution seems to lie in helping the farmers learn to  share the available water so as to minimize the crop loss scenario. However, such an approach is quite difficult to model, implement and whose impact assessment becomes a herculean task. It is easier to just build water harvesting structures for them and quantify the intervention by the amount of water saved per year. The question is how far does it address the problem at hand?

In the development sector, the scenario is further complicated by a game of incentives. The funders are interested in project outcomes which are quantifiable and look good on paper and the NGOs, despite having the expertise to tackle complex social issues, often resort to the linear approaches to align with the outlook of the funders. And let’s face it, this is necessary to ensure the influx of funds and secure their continued functioning. The saddest part is that there is hardly any incentive to anyone to go and ask the community what they think that their problems are and what they need help in.

A justified argument to this is that doing something is better than doing nothing. And I am not denying that for a second. Any intervention is better than no intervention at all. But to be guided by the principle of Occam’s razor that the simplest solution is the correct one might be a bit misleading. While we may proclaim ourselves as harbingers of change, let’s take a step back and re-evaluate if the standard of that change should be set as low as ‘just doing something’.

Link to the article on Harvard Business Review here.


  1. Bart de Langhe, Stefano Puntoni and Richard Larrick, Linear Thinking in a Non Linear World, Harvard Business Review, May-June 2017.
  2. Burke M, Hsiang SM, Miguel E. Global non-linear effect of temperature on economic production. Nature. 2015 Nov 12;527(7577):235-9.
  3. Sterner T. Economics: higher costs of climate change. Nature. 2015 Nov 12;527(7577):177-8.
  4. Franzke CL. Warming trends: nonlinear climate change. Nature Climate Change. 2014 Jun 1;4(6):423-4.
  5. Friedrich T, Timmermann A, Tigchelaar M, Timm OE, Ganopolski A. Nonlinear climate sensitivity and its implications for future greenhouse warming. Science Advances. 2016 Nov 1;2(11):e1501923

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  1. Sandeep

    Hey man, this is probably one of the best articles I had read so far. It definitely opened my eyes…

  2. raviteja

    Never saw the linearity through this lens. Great piece saumyadeb.

  3. Amruta Huddar

    Loved this !


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