I was talking with my grandmother the other day, who is 94 years old. She said something to the effect of "It's just like I eat breakfast and then it's time for bed." My theory on this phenomenon is that one's memory is like a slide projector, fillled with snapshots of images, sounds, feelings. As an infant, the mind is filling itself with as much information as possible, in order to learn and adapt to a new environment. So the mind takes 10,000 "memory snapshots" in ten minutes, making time appear to go very slow for a child. As we age, less and less of the information our senses process is neccessary for survival, (and we probably have less room for memories or something like that) and so our mind takes fewer snapshots... thus making time appear to go faster. It's like the difference between watching a movie in slow-motion or all speed-ed up: the only difference is the amount of information that the camera recorded.

A few more thoughts:

  1. The brain only thinks when it has to This is why we can, for instance, touch type very fast. The brain doesn't consciously figure out what buttons to push, or where they are, so it doesn't remember it.

    When you are old, you don't have to think as hard to get through the day - it's mostly routine. Therefore, you don't remember it, and the day seems to fly by.

  2. The brain likes to optimize things Although this is somewhat anthropomorphic (Can you be anthropomorphic with the brain?), it is also true. If you do a certain task a lot, the brain will optimize things so that you can do it without conscious thought. Touch typing is one example of this. I don't have to think to type. I just focus on what keys/letters I want pressed.

The brain is weird.

I've realised lately that every year of my life seems to go by faster than the year before. Then it hit me....

Imagine you are a four year old. Relatively speaking, what fraction of your lifetime does one year account for? A whopping one quarter. Now, if you are a 25, a year amounts to an insignificant 4% of your lifetime, and this percentage decreases with age...

The point is that as we get older, we tend to think of our lifetime, that is, the years that have already passed us as a constant period. This can be perhaps because the amount of things we remember is pretty much the same throughout. (ie. memories get archived into the back of your mind)

To make things worse, the more boring and repetitive your life becomes the more "constant" your previous experience seems to be (i.e. nothing changed) and thus the years zoom by even quicker and become more and more insignificant.

Maybe this perception of time also stems from the fact that in the first decade of your life you learn much more than in the following decades. This makes your first years much more "dense" than the rest, also giving you the impression that time went by slower in the beginning.

I've always thought that one's perception of the speed of time is directly proportional to how much life experience one can remember.

Look at it this way: when you're six years old, you can't remember much more than the last couple of years, if that. So one year of school is equivalent to half your (remembered) lifetime, which seems like forever. On the other hand, once you're twenty-six years old, two years is just a fraction of your remembered lifetime, so it seems to go by much more quickly.

It also depends on how much you're living your life, of course. When you're busy with an interesting career, a tour of Europe, or an active social life, time seems to go by a lot faster than if you're living alone on Social Security. But that is an independent phenomenon which even Albert Einstein commented on:

When you are courting a nice girl, an hour seems like a second. When you sit on a red-hot cinder, a second seems like an hour. That's relativity.

In a groundbreaking article, T. L. Freeman discusses the relationship between actual age and effective age1. His conclusion is that the passing of the years goes faster as we grow older. This makes sense; for instance when you are 10 years of age, a year represents 10% of your life, and seems like a very long time. However, when you are 50 years old, one year has reduced to only 2% of your life, and hence seems only one-fifth as long.

Summarizing this work, Freeman comes to the conclusion that the actual age (AA) needs to be corrected for the apparent length of a year (AY). The apparent length of a year is inversely proportional to one person's actual age:

          AY= α/AA

The constant of proportionality α is rather loosely defined by Freeman as the age at which a year really seems to last a year, and it was arbitrarily set at 20 years (α=20).

Now Freeman determines the concept of Effective age, which is simply the integral over time of the Apparent Year from age 1 to the actual age (AA) of interest:

               AA            AA
          EA =  ∫ AY d(AA) =  ∫ 20/AA d(AA) = 20 ln(AA)
                1             1
Although this formula results in some interesting conclusions, there are several flaws with this concept. As mentioned above, the choice of the proportionality constant is rather arbitrary. There is no rational justification for the choice of this age, but it was solely chosen based on Freeman's own perception of (the passing of) time. Next, the evaluation of the integral seems incorrect, since its lower limit was set at 1, and not at 0. Obviously, the choice of zero as lower integration boundary yields can not be evaluated due to the logarithmic term in the expression. Because of the obvious problems with Freeman's concept of time perception, it is necessary to redefine the Effective Age on a sounder basis.

In the traditional concept of time perception, one person's Actual Age is proportional to the passing of time (t).

          AA = βt + γ

Note the occurrence of two parameters β and γ that are traditionally set to one and zero, respectively. However, each has a clear (though usually underappreciated) function in time perception. The β-parameter describes the rate at which one person ages; some persons remain annoying little crybabies during their life, while others become boring old farts at 20. The γ-parameter describes the origin of one person's time perception. Did you ever meet those proud parents boasting about their little one who is only x months old, and already walks, writes obfuscated C, or recently sold his first dot.com? No, these youngsters aren't bright for their age; they simply have a high γ-factor.

It is clear that with this definition, one person's Actual Age may already be non-synchronous with time. However, analogous to Freeman's work, the apparent length of a year (AY) is not constant:

          AY= α/AA = α/(βt + γ)
We can remove one of the parameters by defining two parameters δ and ε.
          AY= α/(βt + γ) = (α/β)/(t + γ/β) = δ/(t + ε)
The actual values of δ and ε will become clear from the boundary conditions.

In order to obtain the Effective Age, the integral of AY is evaluated. Note that the integral is evaluated over time, and not over Actual Age, since AA is a function of time:

               t           t
          EA = ∫ AY d(t) = ∫ δ/(t + ε) d(t)
               0           0

          EA = δ ln(t + ε) - δ ln(ε)

The lower boundary condition (t=0) should yield an Effective Age of zero years (EA=0). Therefore ε = 1.

The upper boundary is less apparent. It should be chosen so that at t=tmax, EA = t. At death, the Effective Age and real time are again equal. However, no person knows for sure his or her personal life expectancy. This is clearly an issue for molecular biologists to address. However, if we assume for a person a life expectancy of 80 years (t=80, EA=80), we obtain:

          δ = 80/ln(81)

               80 ln(t + 1)
          EA = ----------
This formula can now be used to calculate the Effective Age (and the Effective percentage Completion of Life) as a function of time. This is shown in the following table:
time (yrs.)  EA (yrs.)  Life%
0            0.0      0
1           12.6      16
2           20.0      25
3           25.2      32
4           29.3      37
5           32.6      41
10          43.7      55
15          50.5      63
20          55.4      69
30          62.5      78
40          67.6      85
50          71.6      89
60          74.8      94
70          77.6      97
80          80.0      100

And thus, the bold statement in the title is justified. Life is half over at age ten, and three quarters over at age thirty. Note the rapid increase at very young ages: in the initial stages of life, life itself makes big strides forward. For instance, consider the concepts of speech, eating and walking; skills that are learned at a young age and are carried on throughout a person's life.

Another interesting observation that we can make is the age at which one year really seems to last one year. This can be calculated quite easily from the derivation above. For a life expectancy of 80 years, it is equal to 80/ ln(81) - 1 = 17.2 years. Quite close to Freeman's original assumption of 20 years.


The concept of Effective Age has far stretching implications. Some of these I have summarized below:
  • "Summer vacations lasted almost forever when I was in grammar school":
    True, they did. In fact, when you were six years old, an Apparent Year would be close to three years. That would make a three week summer vacation feel like almost nine weeks!
  • "Now that I am older, I can communicate better with my parents"
    Right. As you can see, you're catching up with them! Closing the "generation gap", so to speak.
  • "Life starts after 65"
    The credo of many people close to their pension age. Wrong: at 65, you only have about 5% of your Effective Age left. Choose your time wisely; start working late, and retire early.
  • "Old people are slow"
    That is such an insensitive comment. Old people aren't slow at all, they simply have a different time perception.
  • "Those annoying birthdays seem to roll around faster every year
    True, they do. Better start celebrating your Effective Age.

T. L. Freeman, Why it's later than you think, J. Irr. Res., 1983.

... and yet we do more in each passing minute.

I remember Sundays just a few years ago, when the day took forever, and all we did was make love, read the paper and find some food.

A Sunday now starts early, with fresh-brewed coffee, making breakfast for the children, shopping, washing, cleaning, church, chatting, helping out the school parents’ association, balancing budgets, noding, taking the children to a party or a class, My goodness, it’s 2pm and we haven’t even had lunch and cooking and eating and helping with homework and mowing the lawn and trimming the fruit trees and mending the lawnmower and fixing the shelves in the bathroom and now its time to get the children ready for bed and cleaning their teeth and reading to them and ‘Dad can I have a glass of water?’ and paying the bills and noding and good grief, bedtime already? Where did the day go?

Sleep. Blessed sleep. And suddenly we are going on a summer break, but surely Christmas was only last week, and in that time we have planned and built a kitchen extension, found a new school for our younger child, run a couple of events for the school, written and edited a magazine for my alma mater, watched the Brownie promise and helped on school trips and visited half a dozen countries, and written a few nodes and upvoted and paid the credit cards and eaten meals and cooked barbeques and attended concerts and visited family and friends and hosted them back and gone to funerals and comforted ageing relatives and fixed a million minor problems and fought the local council over parking and bought presents for a hundred people and sent cards and done the charity bit and fixed the computer and the freezer which broke at a bad time and serviced the car and cleared out the loft and filled it again and sold the baby things and re-surfaced the driveway and researched some life insurance and WTF? Another year gone?

It’s my life. Mundane. Of this world. All those things take up time and more time, and suddenly all that time we once had for doing cool things gets swamped by the stuff we have to do and the stuff we choose to do. It just means getting up earlier, and going to bed later, and never quite stopping.

That is where the minutes, hours, days and years go. And if a year seems to pass quicker than a wink, console yourself with the thought that you are doing more than you ever imagined possible when every minute seemed like a year.

There is a simple scientific explanation for the common observation that time appears to pass more quickly as we get older, which is this: Time really is flowing at an ever-increasing pace.

This is a natural result of the expansion of the universe: In accordance with Einstein's Theory of Relativity, as space gets stretched out time is correspondingly compressed. So if the minutes seem to be flying by far faster than they did when you were young, console yourself with the thought that it's not because you are now old - it's just that time is flowing faster than it used to.

N.B. This is clearly wrong, but I still think it's a great explanation.

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