Jamie Thingelstad's personal website

Fractions and Life

Every year just seems to go by faster, doesn’t it? How many times have you said that to yourself? Well, I’m here to tell you that not only does it feel that way but that mathematically it is the simple truth!

You see, I figured this out a while ago. When you are a kid it seems like the summers lasted forever. Winter was months of playtime. As an adult it seems that the weeks are days and the seasons fly by in a blink. Winter is no sooner here than it is spring and you are looking forward to summer. This all comes down to math and how you perceive time.

Here is my theory. Let’s take a look at the math. When you are 4 and then you turn 5, you are 1 year older right? When you are 9 and then turn 10, again, you are one year older. So the time from 4 to 5 is the same as the time from 9 to 10. Actually, no, it isn’t. You see, as you experience it the time from 4 to 5, when you turn 5, represents 20% of your life experience. In fact, it really even represents more since you don’t remember the time very, very early on, but we’ll leave that for another discussion. When you turn 10 years old the year that just preceded you is 1/10th of your life or 10%. As a result, the time from your 4th to your 5th birthday is twice as much experintially as the time from your 9th to your 10th birthday.

You can extend this easily and see that as you get older each passing year represents a smaller and smaller portion of your life. The entire decade that you spend from your 40th to your 50th birthday represents the same as that one year of fun from your 4th to your 5th birthday. They both represent 20% of your experience. As a result, it is absolutely true that time, or at least the perception of time, just goes faster.

There is an interesting by product of this which is the time before your first birthday. Technically that would be something over nothing, n/0. You cannot divide by zero but in essence this represents infinity. So that first year, if only you could remember it, was infinitely long. We could apply some limit theorem here (and you are welcome to give it a whirl) that that first second of your life was a breakthrough moment. It’s somewhat depressing to compare the infinity of your first second of life to the infinitely small percentage, like %0.000000001 of your life, for that last second.


  1. But towards the end, when you can’t remember anything, you get back to the infinite beginning. If you can’t remember anything from, say, longer than 10 days in the past, then every day is 10% of your total life experience.

    So it is only really fast in the middle. Particularly in the middle where you are, pal. ; >

  2. Jamie,
    I believe that I read on slashdot not too long ago ( Within the last six months, which isn’t that long to us grey beards ) that this is precisely the case. Some cognative researcher had your same thought, got funding somehow and verified the theory. I don’t remember the study details though. Might be worth it to check it out.
    Don’t know about the newborn part of it though. Maybe that explains why kids learn as much as they do. They have plenty of relative time to let it sink in.


  3. what are you doing out there? Freaking out on the new idea of being a Dad or something, gads the things your trying to figure out, you need Tammy to help again, with the let’s have some fun time! OK, now that I’ve razzed you a bit, interesting concept. Keep thinkin’

  4. Finally found the link I was referring to. Interesting article.

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