Is a year really 1/50th of your life at 50? Testing a formula from 1877

“Let any one remember his last eight or ten school years: it is the space of a century.” William James quoted that line in 1890, in the chapter on time in The Principles of Psychology, and he put next to it the arithmetic that came with it: a child of 10 feels a year as a tenth of his whole life, a man of 50 as a fiftieth.

The arithmetic belongs to Paul Janet, a French philosopher who published it in 1877 in the Revue philosophique under the title “Une illusion d’optique interne.” It explains why the complaint has the shape it does, but James doubted it was the cause. Which of them is closer to your own life is something you can check in ten minutes with a grid of 52 boxes.

What did Janet’s formula claim?

That a stretch of time feels as long as it is large compared with everything you have lived so far. One year at 10 is 10% of your life, and the same year at 60 is under 2%.

Age	One year as a share of life so far	Share of an 80-year life’s felt length used up
10	10%	53%
20	5%	68%
40	2.5%	84%
60	1.7%	93%

The third column is my arithmetic from Janet’s rule (each year weighted at 1/age, counting from age 1), not a published finding. It shows why the formula is quoted so often: on its terms you are over half done at ten.

Why did James refuse to call it a law?

He accepted that the formula roughly fits and denied that it was a basic law of the mind. His own explanation was about what gets stored. In youth, he wrote, we may have “an absolutely new experience, subjective or objective, every hour of the day.” Each passing year then converts some of that into “automatic routine which we hardly note at all,” and so “the days and the weeks smooth themselves out in recollection to contentless units, and the years grow hollow and collapse.”

The two accounts disagree in a way that can be tested. Janet’s rule discounts a year by your age whatever filled it. James’s predicts that a year at 40 holding forty datable episodes should feel longer in retrospect than a year at 40 holding four. Modern work leans toward James’s side for stretches of time: Avni-Babad and Ritov (Journal of Experimental Psychology: General, 2003) found routine-filled periods remembered as shorter, a result unpacked in this post on a week away versus a month at home. Those were controlled tasks, though, and nobody has run a randomised trial of whether adding episodes lengthens a remembered year.

How do you test it on your own year?

The 52-box test counts the weeks you can still tell apart, which is the quantity James cared about.

1. Draw 52 small boxes, one per week of the last 12 months.
2. From memory alone, fill a box if you can name something in that week your usual schedule would not have predicted.
3. Count the filled boxes. That unaided number is the result.
4. Then open your calendar and camera roll and fill in any further weeks they can place. The gap between the two counts is what you had stored but could not reach.
5. Put at least three datable things into the next four weeks. They can be small: a street you have never walked, a first lesson, a dinner with someone you see once a year.
6. In a month, recount the four new weeks unaided and compare the fill rate.

There is no benchmark for a good score. A grid with 11 filled boxes at age 45 is a fact about your recall, and Janet’s formula says nothing about it either way. The test only shows whether a change in what you put into weeks changes what comes out.

What if the grid comes back nearly empty?

Then the problem may be upstream of novelty. A year that went to getting through, with nothing left over, produces blank boxes for reasons unrelated to routine, and the sorting method in a triage log for a life that fell apart is a better first move than a hobby. If the blanks look more like sleepwalking, the autopilot problem describes how routine gets automatic enough that you stop noting it, which is James’s mechanism in modern clothes.

Where company is available, use it for the weekly item. Plans with another person get a date and a retelling afterwards, and scheduling fun like a meeting is a low-effort way to make sure the box gets filled. That part is my reasoning from how memory is cued, not a measured result.

Where does the start of the day come in?

Days that begin by drifting have no edge in recollection, and days with an edge are easier to separate from yesterday. That is a guess in James’s spirit, not a finding. One cheap way to give a morning an edge is to have it start at a fixed, clear moment, and DontSnooze does that by asking for a short video within 30 seconds of the alarm.

Frequently asked questions

Was it Paul Janet or Pierre Janet who proposed this?

Paul Janet (1823 to 1899), a philosophy professor at the Sorbonne. Pierre Janet, the psychologist known for work on dissociation, was his nephew and was born in 1859, so he was 18 when the 1877 article appeared. The two names are often swapped in popular retellings.

At what age is half of a life’s felt length gone, if Janet’s rule is right?

For an 80-year life, counting from age 1 and weighting each year at 1/age, the midpoint falls near age 9, because it is the square root of 80. That arithmetic is mine, built on Janet’s rule, and it is why the formula is said to put most of ‘felt’ life behind you in childhood.

Can I use my camera roll to run the year test?

As the aided step, yes. Scroll the library week by week and mark any week containing a photo from somewhere or someone out of the ordinary. It is a rough stand-in for what memory could have retrieved, since many people photograph routine too, so treat the aided count as a ceiling.

Does the ratio hold for short spans like a week?

Not in the survey data. Wittmann and Lehnhoff (2005, Psychological Reports, 499 people aged 14 to 94) found that ratings of how fast the last hour, week or month passed did not change with age, while ratings for the last decade did.