How time flies: Predicting when your life shall end

Every summer vacation in primary school was like a never ending holiday, and in my mind, still, the six years in primary school were very long, and definitely much longer than the seven years in secondary school. My memories of the days in the 2000s and 2010s are like yesterday, but those of my primary school days are much older history, disproportionally older! One thing for sure is that the perception of time duration gets shorter as one becomes older! In other words, time moves faster when you get older! So, depending on how old you are, your perception of a 10-year duration can be quite different!

The perceived absolute time also changes as one gets older! When you're young, you felt things that happened 40 years ago were like ancient history! But as you get older, things that happened 40 years ago seemed really not that long ago to you!

You probably still find the music of the 2010s pretty good. Way back, when you're a kid, your perception of the music that your mother loved was like ancient tune! The perception of time clearly changes as you grow older! That seems to be unavoidable, and you can do nothing to revert it. The question is not why, but how fast? Can we possibly work out how fast our perceived time shrinks? If you know the answer, you probably know how rapidly you age and perhaps also when your life shall end (disregarding accidental life-threatening events).

Taking another perspective, if our life ends at the time when our perceived time has shrunk to zero, or in practice shortened to a threshold point that life becomes almost meaningless, then one could possibly predict his own lifespan based on his own perception of time while he still lives and continues to age. This in theory should work!

Suppose your perceived time is Tperception while the actual time is T. A simple first order law that describes how rapidly your perceived time shrinks with time is:

Tperception = T exp( –T / τ )

where the parameter τ determines how fast (by how much) your perception of time would shrink over a fixed time lapse. Experience suggests that time perception shortens by half at the age of 25, around the time when one finishes college and gets to the real world. This means τ is roughly 37, because exp(–25/37) ≈ 0.5.

Hong Kong's average lifespan is 88 for women and 83 for men, say 85 for any average person. Thus, our perceived time has shortened to around 10% of the actual time at the end of our life, since exp(–85/37) = 0.1. We may say that if one perceives time as 90% shorter than it actually is, life is no longer meaningful!

If you know how rapidly your perception of time shortens, i.e., the value of τ, you should theoretically know when your life shall end.

January 16, 2021