Andrew Zhu

On the Passage of Time


I had been recuperating from a pulmonary infection in the spring which had left me abed for a tricky two weeks. Perhaps a touch of memento mori crossed my mind that led me to ponder on how time passes onwards for us all, whether we like it or not.

On the Passage of Time

There exists a notion: time passes faster with age. Or, to restate, that we experience time not as a constant rate defined by the ticking and tolling of the clock, but rather as a rate proportionally inverse to our biological age, so that a year for a one-year old ‘feels’ equivalent to a decade for a ten-year old. To further elaborate, we can express the passage of time mathematically. Declaring a variable ‘passage’ as equivalent to the sensation of the length of time passed, we can define this term with the expression passage (time) = 1/time, and then integrate over a given period of time to obtain a value that, once normalized to one’s lifespan, crudely characterizes the fraction of a lifespan’s time ‘felt.’ The resultant integral, ln(time), is undefined for when time is a non-positive value. Of course, from a metaphysical perspective, the sensation of time before our birth is impossible to quantify or even qualify, for by definition one is yet to even exist.


So, what shall we use for our bounds? I posit that a lower bound of three years is a reasonable approximation, for there exists an infantile amnesia such that one does not recall the events that occurred when one was a baby or even a young toddler; those anecdotal claims of recalling the monstrous headache arising upon passage of one’s body and head through the birth canal are surely apocryphal. The upper bound of our integral is straightforward – we will simply approximate the length of a natural lifespan as seventy-five years, a duration that is more or less consistent, give or take a few years, throughout the developed world.


With this equation and these bounds now in mind, we can calculate forthwith the fraction of lifespan’s time for certain milestones. In this exercise, for each age range, let us define the lower age bound as one’s reaching that age and the upper age bound as one’s last day being that age:


Ages three to fourteen: a period corresponding with the halcyon days of childhood, carefree and blissful, until the realities of the real world (i.e. high school) set in.

50.0%, 50.0% elapsed


Ages fifteen to eighteen: a period corresponding with the high stress of high school, itself filled with periods of class and periods of other types. Ew, yuck, ur disgusting! Worst. Analogy. Ever. Period.
7.3%, 57.3% elapsed


Ages nineteen to twenty-nine: a period corresponding to that of the young adult, their wings spread wide before taking off and gazing down upon the earth and its vast oceans of opportunity.
14.2%, 71.5% elapsed


Ages thirty to forty-four: a period corresponding to a sprouting of new branches upon the genealogical tree, as two becomes three or four or more.
12.6%, 84.1% elapsed


Ages forty-five to sixty-four: a period of middle age, as the forest leaves – a multi-hued panoply of greens and yellows and browns and blacks – begin their tumble downwards to settle upon the forest floor.
11.4%, 95.6% elapsed


Ages sixty-five to seventy-four: a period of retirement, for the passing of knowledge to the younger generations, for the reflection over a lifetime of memories, for the settling of affairs, one last time.
4.4%, 100% elapsed 



Well, that was a fun thought experiment, wasn’t it? Fifty percent of life passage by the time of one’s fifteenth birthday! For those twenty-odd year-olds in the audience – hope I didn’t preempt a mid-life (or sixty-five percent) crisis! If you are forty and looking in anticipation of celebrating your mid-life crisis… well, I’m afraid you’ll have to make do with twenty percent of time passage remaining. Sorry!

But for those unfortunate souls who wish they had had a ‘better childhood’ or those ‘scientifically-based’ chaps who scoff at the modeling of subjective experiences based off a sham statement with a spurious mathematical equation (these two groups that are very much non-disjoint, if I may judge), please keep in mind another complementing notion: having fun passes time faster.

Now, how do we reconcile that?



I wrote this piece quickly in the span of a couple of hours in June of 2020 – it was quite cathartic. When I first started typing, I planned to actually expand out the shower thought out from a personal perspective with recollections from my childhood and early adult life, but I eventually decided to forego that route and condense the thought into a page or so of text.


This is also the first writing piece that I have posted to the interwebs – I am not a great writer by any means, but I do strive for improvement. Please share comments and critique in the Contact page.