This is a test question I have never forgotten.
Question:
An algae doubles in size every day. If it takes 30 days for the algae to completely cover a pond, how many days will it take to cover half the pond?
It’s more fun if you pause to think about it before looking at the answer.
Solution:
The algae doubles in size daily, meaning that on the 30th day, it covers the entire pond.
If it doubles each day, then on the 29th day, the algae must have covered half the pond (since doubling half the pond on the next day results in the full pond being covered).
Exponential growth is almost always surprising.
I used to think that a software engineer was one of the most reliable, high-paying jobs in the country, with plenty of upside.
During my twenties as a banker, I probably thought a million times: “Should I learn to code?”
I never did because it did not seem suited to my personality, I was doing well as a banker, and there are other ways to make money.
Well, fast forward and it looks like I was wrong about the reliability part. Many software engineers are nervous about Artificial Intelligence taking their jobs. Mark Zuckerberg just told Joe Rogan that Meta is going to replace mid-level engineers…this year.
What about our jobs?
I’d be nervous if you gave me $3 million, but told me AI took my job permanently.
Economists say when people lose their jobs, they can get trained to do other jobs. Sure, maybe, for a lot less money. So, yes there will always be new jobs, but I’m skeptical. If AI eats 100 jobs, will there be 100 new jobs? 120 new jobs? Or 20 new jobs? What happens to the other 80 people?
If you use ChatGPT, you have noticed that it has become extremely good. I use it daily and each day, it amazes me.
Before posting this, I asked it to create the image above and for the solution to the test question. I also was going to make an analogy about how exponential growth is like getting the flu and linear decline is recovering from the flu. I asked ChatGPT if that was a fair comparison (if you do not use ChatGPT, scroll to the bottom for its response).
So, the point is I looked right about the software engineers for 15 years, and then all of a sudden, I looked wrong.
If you and I were watching the pond in the test question, as the algae grew and took other jobs, by the 29th day, seeing that it’s only covered half the pond, we may think have plenty of time before it is fully covered.
See also:
- Why Good People Are Divided by Politics & Religion (10/30/22)
- Who to Marry, Work With, & Befriend (6/6/22)
- Designing Your Life (8/10/17)
ChatGPT Prompt: Is it a fair comparison to say exponential growth is getting the flu and linear decline is recovering from the flu?
ChatGPT Answer
This is a fair and insightful analogy, but it has limitations that are worth discussing. Here’s how the comparison works and where it might fall short:
How the Comparison Works:
- Exponential Growth (Getting the Flu):
- When you catch the flu, the virus multiplies rapidly in your body, which is analogous to exponential growth. Each virus particle replicates, leading to a sharp increase in viral load over a short period.
- Exponential growth is often characterized by fast and accelerating change, similar to how symptoms can worsen quickly when the flu takes hold.
- Linear Decline (Recovering from the Flu):
- Recovery tends to follow a slower, more steady process. Your immune system gradually clears the virus, and symptoms subside incrementally, resembling a more linear pattern.
- This matches the idea that undoing damage or reversing processes often takes longer than the initial impact (e.g., building immunity, repairing tissue).
Where the Comparison Falls Short:
- Recovery is Rarely Linear:
- Recovery from the flu is often more irregular than a smooth linear decline. There may be periods of faster improvement followed by plateaus or slight regressions, making it more akin to a complex curve than a straight line.
- Complexity of Systems:
- Exponential growth and linear decline oversimplify the dynamics of both the flu and broader systems. Biological processes, like viral replication and immune response, involve feedback loops and thresholds, which may not strictly align with these mathematical patterns.
- Time Scales Differ:
- Exponential growth often happens quickly, while recovery (even linear) can take a significantly longer period. The mismatch in time scales highlights the inherent asymmetry in growth and recovery processes.
Conclusion:
The analogy effectively highlights the asymmetry between rapid growth (or damage) and slower recovery. However, it’s an oversimplification, especially when applied to complex biological or systemic processes. For a nuanced understanding, it might be better to think of recovery as involving dynamic, nonlinear processes rather than strictly linear decline.
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