We are so bad at understanding exponential growth.
For instance, imagine a water lily on a lake that can give birth to a baby daily. Let’s pretend the newborns can do the same right away. So each new plant will produce another one the next day.
We know that after 30 days, there is no more room in the lake, which means all water lilies will die from lack of space. How many days do you think it will take for the water lilies to cover half the lake?
It’s not 15 or 20 buts 29.
The forest ranger would have to be very reactive to avoid the tragedy. Indeed, at the end of the 24th day, 97% of the lake surface was still available.
But let’s admit he decided to act on the 27th day.
The man chose to quadruple the lake’s surface to have some respite until he could find another solution. Workers arrive the next day and managed to dig and fill the new lake space in two days. We are now on the 30th day, and the first quarter of the lake is no longer available. The man uses the weekend to deal with the issue. He plans something, but when he arrives on Monday…
On the 32nd day of growth, the entire new lake is invaded. It took two days to fulfill four times what had taken a month.
But julien, where are you taking us with all this?
My Graduation Day
Do you remember when you were six in primary school? Fourteen in high school? These times you look at the upper years with admiration. They were tall, competent, and fun. They seemed far from where you were, and you were full of admiration and jealousy for them.
You probably didn’t regard yourself this way once in their shoes. You did not feel that tall, skilled, or fun.
I recently experienced the same feeling.
As I write this, there is one week left before the day of my graduation, which will be the final point of 5 years of study.
I used to dream about being an engineer. Now that I’m one, it’s no more a dream. It’s normal.
Our school organizes a graduation ceremony, a dinner, and a gala. I was rather indifferent to this event. But as we got closer. And as I received congratulations from my loved ones. I began to wonder; Why am I the only one who is not excited!?
Then, I understood. Like the little Julien looking at the big kids at school, they were looking at the engineer of the family.
I didn’t find school terrible. You wake up, sit down on a chair, try to focus a bit, and that’s all. Some projects need more time, and you must lock yourself to learn the lesson one week before the test. But it didn’t seem exceptional. All the more that I was surrounded by dozens of people in the same position.
I completely minimized the years of consistent work to get to this level.
Learning Isn’t Linear
On the one hand, the school gives a framework for education. It includes gradual levels, dedicated time for learning, and tests to assess our knowledge. But more importantly, it forces us to be consistent and disciplined.
On the other hand, new ideas confront old ones, which make them grow or shrink. And from this interaction will rise a new knowledge that will take its place in what we know so far.
The learning process is not linear, like the water lilies’ reproduction. That’s why we struggle so much in understanding its growth.
So It’s the non-linearity of learning and the consistency — provided by the school — that fools us.
Everyone sees this huge mountain that is, let’s say, an engineering degree. And it’s like you came one day to tell them: “You see this mountain? I’ve moved it over there alone.”
Of course, they are impressed by the achievement. While you. You don’t understand what is unbelievable in carrying rocks of 1 kilogram. Sure, you’ve done it long enough to make a pile that looks like a mountain. But it’s just 1 kilogram.
People will see the achievements rather than the process. And you will see the process rather than the achievements. So you will envy the achievements of others and neglect your own, which is very toxic.
No matter how old you are, you will always struggle to grasp the amount of work to get to this or that position. One thing remains certain. The importance isn’t in the weight of the rock you can carry at once. It’s how long you can regularly move that damn 1-kilogram rock.
“The greatest weakness of the human species comes from its inability to understand the exponential function” — Albert Bartlett