- Suppose a person can improve by 1 time (100%) compared to last year after one year of effort. The ability value changes from 1 to 2 after one year.
- If broken down into two half-years, each half-year improves by \frac{1}{2} times compared to the past, then after one year it becomes \left(1 + \frac{1}{2}\right)^{2} , and the ability value changes from 1 to 2.25.
- If further broken down into twelve months, each month improves by \frac{1}{12} times compared to the past, then after one year it becomes \left(1 + \frac{1}{12}\right)^{12} , and the ability value changes from 1 to 2.613.
Abstracting the formula: \left(1 + \frac{1}{n}\right)^{n} , its maximum value is the natural constant e ≈ 2.718.
Even if a person divides their time into countless parts and uses each part to the limit, the maximum outcome they can achieve is 2.718 times.
This is the constraint that the natural constant e imposes on everyone. So, don’t think that just by working harder once more you can create a miracle. In this marathon called life, even if you exhaust yourself, you cannot break through this limit.
It is better to maintain a good pace, sustain a 2.2 annual growth rate, work from age 20 to retirement at 60, working for 40 years, the harvest would be
2.2^{40} = 49763077761695
If you force yourself to have a 2.718 annual growth rate, working from age 20 to 40, you would collapse halfway, working for 20 years, the harvest would be
e^{20} = 485165195
Which do you choose?
Supplement
But honestly, I feel I can’t even improve by one time in a year, haha.
So, I want to add that this assumed 1-time annual growth rate is not absolute, but varies from person to person and is unique to each individual.
- He can sustain studying 12 hours every day for 365 days a year, and his 1 looks like this.
- I can’t. My 1 is only studying 2 hours every day.