How mathematics and economics have formalised my life lessons

By Koo Ii (21S05A)

Equilibrium can be fleeting. Revisiting RI 3 years after my graduation was another reminder of that: the Popular bookshop had become Casco, the cRIb no longer houses Teddy nor the lockers, and the canteen was devoid of the transparent acrylic safe-distancing screens (COVID-19 batches would understand). 

Yet, ceteris paribus: all else can be taken as constant. I still remembered exactly the way to the Wishing Well from the main gate, where my homeroom used to be – my class’, 21S05A, was near the mirrors – and of course, I would never forget my teachers.

I am stuck between these two extremes. I did have to ponder what value that anything I share in this op-ed could bring to my juniors still in JC. This probably stems from how I still bear a tiny hope that I’m not too far-removed from my JC days. My past few years of university suggest otherwise, and it is from these years that I have gleaned both academic and personal insights. 

These insights certainly aren’t too original – there are others like me who study economics (I think I’ve done enough subtle foreshadowing by this point) or study abroad. 

What I will do is to communicate my two cents’ worth in a way that puts my JC “hybrid” subject combination to good use. Using equal parts math and language, here are two lessons I’ve learnt since graduating from JC. (I suppose they are each worth one cent?)

1. Dynamic optimisation

You might not know it yet, but chances are, the most transferable competency from JC is dynamic optimisation, in my humble opinion. 

I don’t just mean it in terms of the ‘A’ level syllabus. Indeed, in maths or the sciences, solving for stationary points and setting your first derivatives to equal zero to find the maximum or minimum point of some function is definitely an example of static optimisation. That means that you’re solving for the best at a given point in time. 

The same concept also applies when optimising multiple things at once, such as the utility (read: happiness level) you get from CCA and the utility you get from homework. 

Now, introduce some constraints. Something is stopping you from achieving the ideal, so make do with the best you can do, under these restrictions… like the fact that we only have 24 hours in a day.  

Being from a “rojak” class where nearly everyone had a different subject combination, my JC timetable was filled with breaks dotted throughout the day. I used to compartmentalise the hours of the day using my timetable as the constraint. 

Then, when self-study break came around, this optimisation took on a different form. Suddenly, I had whole days or even weeks to myself for revision. Then, I learnt how to practise dynamic optimisation.

Dynamic optimisation refers to how the process of optimisation is done across a time horizon. I didn’t know it then, but JC challenged me to optimise my time day by day, then week by week or term by term, and ultimately, across the entire 2 years. 

Learning about dynamic optimisation in university formalised and validated my understanding that what’s best right now, may not be the best for the long run on a whole, and vice versa. 

Some days, you should just indulge and recharge by taking time for your hobbies or for hanging out with friends. Other days, you need to “lock in” and prioritise schoolwork. 

I know, this doesn’t sound mind-blowing. The importance of balance and time management is almost a cliché. 

What I appreciate from dynamic optimisation is that element of the time horizon: how much do you value the future? When you only consider your utility day by day and prioritise current utility the most, your choices are going to be very different from if you had considered your utility across years.

In fact, the time horizon itself is a personal choice, and only you can choose what is most suitable for yourself to optimise under constraints over time. 

2. Exogenous shocks and hysteresis

Here is where I take a reality check, and remove my rose-tinted glasses for a second. Earlier, I had been tacitly assuming an ideal world with perfect foresight, as if we all are omniscient agents. 

Alas we are not. When curveballs come our way, how are we to react?

In economics, these curveballs are termed “exogenous shocks”, because they come from outside of a given system. Depending on whether we make decisions before or after these shocks are realised and whether we can accurately anticipate such shocks, the choices we make will be different. 

The best example of such a shock to my JC journey is – you would never guess! – the pandemic. However, shocks can also sometimes be positive, like if your pet topic comes out for an examination… 

It is precisely the exogenous nature of these shocks that suggests we cannot control the shocks themselves, but we can certainly control how we respond to them or prepare for them. 

If, after a shock, we are unable to recalibrate ourselves and start afresh, there will be hysteresis effects. It is a fancy way to say there is persistence or even permanence in the effects of such shocks. 

Usually, we’d describe macroeconomic outcomes using these terms, for example when a Central Bank makes decisions following shocks, thus impacting unemployment levels. Nonetheless, here I apply this concept on a personal level.

Indeed, when we get let down or pleasantly surprised, we require some dexterity in adapting to the situation, rather than let the situation scar us for time to come even after the shocks have long passed. 

I internalised this lesson of mine while on holiday with friends. An impending tropical storm was about to upend our ambitious road trip plans on the West Coast of the US. We had 24 hours to decide what to do next: do we cancel our car rental and give up? (Yes, I wasn’t about to risk my life by staying at the eye of the storm.) Then, do we fly home early or do we go somewhere else? 

We decided to take our road trip up north to the Canadian Rockies in British Columbia, and the rest is history – one that is full of memories made even more unforgettable and poignant. Imagine what we would have missed out on in that summer if we hadn’t pivoted and adapted! 

At the risk of sounding like I’m preaching truisms, I just want to highlight these shocks are outside of our control – there is simply nothing we can do to stop them or induce them. Yet, we can only respond appropriately. Perhaps we cannot act as if the shock had not occurred, but we can minimise its lasting impact on us. 

My two cents’ worth (or three cents’, adjusting for inflation)

There is something humbling about applying cold, hard maths or sterile economic models to the intricacies and nuances of fragile human life. 

Don’t get me wrong: I am not trying to reduce complex lived experiences to mere digits. I don’t think I can. Surely, not all the necessary assumptions hold in reality and not all models are necessarily applicable. 

But these models are sufficient – enough to glean insights from. 

Just like how I probably didn’t retain all of my knowledge from JC, I know I have internalised the skills and universal truths JC has instilled in me, which my university education has formalised (albeit in academic rather than personal contexts) and has given me even more opportunities to practise.

It is my hope that my two cents’ worth of little epiphanies can be invested to compound into a larger sum of realisations for those who resonate with them, for the JC context and beyond.