What 'Constant Growth' Really Means

An exploration of the phrase 'constant growth,' dissecting the clash between its everyday meaning and its precise mathematical definition. Using calculus and a Calcutta landmark, this post highlights the importance of clarity when modeling our world.

7/28/2025

It is a peculiar feature of the human mind that it can, without any external prompting, get itself into a frightful muddle over the simplest of things. My own mind, a chuntering and often unreliable apparatus, recently decided to have a rather public argument with itself, an internal schism so profound it had to be committed to paper, resulting in the rather peculiar sketch you see here.

The whole kerfuffle began with two seemingly innocuous words: “constant growth.”

There I was, probably contemplating the heat of a West Bengal afternoon or some other matter of galactic importance, when this phrase popped into my head. “Constant growth,” I thought. “Simple enough.” But it was not. One part of my brain, the practical, everyday part that handles things like remembering to buy milk, immediately pictured a chart going steadily, reassuringly, upwards. The growth of a well-tended sapling, perhaps, or a very successful savings account.

But then, another part of my brain—the pedantic, troublesome part that probably should have been a lawyer—reared its head. “Hold on a tick,” it said. “If something is constant, doesn’t that mean it isn’t changing?”

And thus, the debate began.

As the debate in my sketchbook reveals, our colloquial use of language is a wonderfully slippery thing. When we speak of “growth” in common parlance, we almost universally mean an increase. The economy, our height, the national debt—all things we expect to go up. To say a child has had “no growth” is to say their height has remained stubbornly, worrisomely, the same.

In this linguistic world, “constant growth” is an oxymoron if “constant” means “unchanging.” How can something be unchangingly changing? What we really mean is a constant rate of growth.

But let’s put on our mathematician’s hat for a moment, a piece of headwear that demands precision above all else that most in Bengal are unaccustomed. What if we take the phrase literally? What if the “growth” itself is the thing that is constant?

Consider a state of affairs represented by the variable $y$. This could be anything—the height of a building, the temperature of a room, the amount of existential dread in my soul on a Monday morning. If we plot this value $y$ against time $x$, what does it mean for its growth to be constant?

One perfectly valid, if slightly unsettling, interpretation is that the growth is zero. A constant of zero is still a constant, after all. In this case, the rate of change is nil. For the calculus-inclined among us, that’s a situation where the derivative is zero:

Graphically, this gives us a perfectly flat, horizontal line. The value of $y$ is fixed at some number, let’s call it $c$, for the entire duration we’re observing it. So, we get the simple, unexciting equation:

This, as the right-hand side of my doodle points out, is a state of “no growth.” And this is where the Shaheed Minar in Kolkata wanders into the conversation. Here is a magnificent structure. Whatever its height was yesterday, it is precisely that height today, and we can be reasonably certain it will be that same height tomorrow (barring any seismic or otherwise calamitous event). Within our span of observation, its growth is constant—a constant value of zero. It is the perfect, real-world embodiment of $y=c$.

So, we have a linguistic pickle. “Constant growth” can mean:

In common speech: A steady, non-zero increase (a sloped line).

In literal mathematics: A rate of change that is constant, which could be zero (a horizontal line).

Why does this seemingly trivial distinction matter a jot? Because it sits at the very foundation of how we model the world. Before we can build a fancy equation or run a supercomputer simulation, we must first translate our messy, ambiguous human language into the unforgivingly precise language of mathematics. If you tell a physicist you’re modelling “constant growth” and you mean a sloped line while they assume a flat one, your collaboration will produce nothing but gibberish.

The model is a caricature of reality, and the first important thing to always do is defining your terms very clearly. The universe doesn’t much care for our linguistic shortcuts. It operates on principles, and our job, as curious observers, is to describe those principles with as much clarity as we can muster. It’s a humbling reminder that sometimes the most profound challenges lie not in the complex equations, but in simply agreeing on what our words mean in the first place. And, it’s more important in India where English isn’t the first language or taught very well, or learned very well, or you don’t have enough exposure to the nuances to prepare you for subtle distinctions, which is why every blog post I am writing is an effort to make sure that whoever is reading these posts can see reality clearly, because I’ll be dead soon, and India’s future is in the hands of the people people who can see through the noise.