Time Keeps Accelerating

Many people have told me that you can gain everything you want in life, you just can't have it all at the same time. It is said that when you are young you have time and energy but no money, in middle age you have money and energy but no time, and in old age you have money and time but no energy.

This makes me think - how long do I have left on this earth? When are these stages of life?

A simple way of looking at this is by life expectancy. I am 21, and the average Australian life expectancy is 82. Going off this we can conclude that I have lived 1/4 of my life so far. No worries, I have heaps of time left.

But it's not that straight forward. I remember my primary school days, when the days stretched out for eternity and the seasons felt as if they were locked in permanence. I remember when a 2 hour car trip was an unbearable ordeal, but now it goes in the blink of an eye. Perhaps how we perceive time is relative to our age? After all, every year seems to go quicker than the last.

Let's say year 1 is the base unit of time. You have no conception of how long is ahead of you or when a year will end. Year 2 is another measure of year 1, as it is a repeat of that base unit of time. Year 3 however, only feels like half as long as that first year, as it is half the length of time experienced thus far. Year 4 feels like a quarter.

Thus S(N) = 1 + 1 + 1/2 + 1/3 + ... + 1/(n-1) years, where S(N) is how long your life of N years is perceived in terms of your first year of life.

S(82) ~= 4.977. That sounds stupidly small. But it isn't. Do you actually remember your first year of life? If you did, maybe you would remember time moving that creepingly slow for you. However since no-one can remember their first year, it is an impractical measure.

How about measuring against something you can relate to? What about your first 10 years of life?

In that case, S(N) = 1 + 1/10 + 1/11 + ... + 1/(n-1).

So how quickly did the next 10 years of your life, S(20) - S(10), go by? As S(20) = (1 + 1/10 + 1/11 + ... + 1/19) ~= 1.718, therefore (S(20) - S(10))/S(10) ~= 0.718 . Therefore the second decade of your life went by in only 70% of the time of your first decade.

Using the decade (arbitrary decision) as the base perspective of time, how much of my time on this earth have I consumed?

That would be S(21) / S(82) ~= 1.769 / 3.149 = 56%. That is remarkably scary. If time were perceived linearly, that would mean I really only have until I am 38. That is remarkably soon.

But using the first decade is an arbitrary decision. The smaller the period of reference, the less perceived time we have left. As the period of reference approaches 0, so does the perception of any later period relative to it.

The best answer to this issue is to use your current age as the base reference. After all, it has encompassed everything you have perceived thus far. In doing so, S(21) / S(82) = 1 / (1 + 1/21 + 1/22 + ... + 1/81) ~= 42%. That means I have lived 42% of my perceived life.

On an interesting note, if you are expected to live until 82, you have lived half your life at age 30. Must be why no-one wants to turn 30.

Running these sums, the result backs up my own intution on how I perceive time. On the downside, I have less time to do what I want to do. On the plus side, these numbers remind me not to waste what dwindling time I have.