What if I said 80 divided by 2 isn’t 40 and it’s 18?
**disclaimer: I don’t study math in my course of study and my math is 👎🏻, pls just read for fun. Thanks you.
If a person lives till 80, then 40 is the midpoint of their life right? But this statement is only half true. From a calendar perspective, yes it is true. However, the time perceived by humans is not linear.Under the logarithmic perception of time model, 18 years old is already the midpoint of one's subjective life experience.
There’s Weber's Law which tells us that human perception of change depends on relative change. Integrating this formula further gives us Fechner's Law.This indicates that human subjective perception is proportional to the logarithm of the objective stimulus.Just imagine during the holiday, ur teacher assigns you 5 exam papers, and then suddenly adds 5 more at the last minute, you would complain. But if they assigned 100 papers and added 5 more, you wouldn't complain as much.In fact, earthquake magnitudes, decibels of sound, and pH levels are all based on logarithmic models.If we apply logarithmic perception to the lifespan, we can model it like this, let’s assume the subjective length of each year is roughly equal to 1 divided by your current age (1/t).
One year at age 5 accounts for (1/5) of your total life experience. Whereas one year at age 50 is only (1/50). Therefore, the accumulated subjective time can be written as this integral formula:
S(t) = ∫ (1/x) dx = ln(t)
Assuming stable memories begin at age 4 and life ends at age 80, we find the half-point and substitute it into the logarithmic formula. After rearranging, we take the exponential of both sides.Thus, the subjective midpoint of life under the logarithmic time perception model can be defined by this result:
t = √(t₀ × T)
As you can see, the subjective midpoint is not the arithmetic mean, but the geometric mean. Substituting the ages, it comes out to 17.9 years old. So, if time is perceived proportionally, then out of a lifespan from age 4 to 80, half of your subjective life has already passed by around age 18.This is also why we always feel that the older we get, the faster time flies. A year during childhood represents a massive proportional change, whereas a year after growing up is just a tiny increment within a long reservoir of experience.
What we are truly losing is not time itself, but our capacity for time to leave distinct markers in our memory.Therefore, what I just wanna say is I hope everyone can courageously try new things. The length of a life does not just depend on how long you live, but on how many moments are truly remembered by you.