
Implicitly, we think about the years of our lives in a linear fashion, e.g. in terms of decades: our twenties, thirties, etc. In this linear view, all our years are equal and time moves at a uniform pace.
This simple picture, however, doesn’t quite fit with our perceptions as we age: Where are the long, leisurely summers we knew as children? If it seemed forever to get through the fifth grade, what happened to last year?
The ‘logtime’ hypothesis is that we use our age to estimate the passage of time, resulting in a perceived shrinking of our years as we grow older, and giving a subjective scale of life very different from that of the calendar: In this view, the older we become, the faster we seem to age or, conversely, the shorter the years seem to be. Mathematically, this relationship is said to be either logarithmic or exponential, depending on which variable is used as the reference.
Starting with the premise that the human mind judges the length of a long period of time by comparing it with current age, the logarithmic nature subjective human temporal experiences can be easily rationalized: Hence a year adds 10% to the life of a ten-year-old, but only 5% to that of a twenty-year-old. For the twenty-year-old, two years are required to add 10%.
A consequence of the logarithmic function is that it is the ratio of the years defining an interval of time that we use to judge the duration of that interval, not the absolute magnitudes of those years. For example, the years from ages 10 to 20 seem to pass at the same rate as the years from 20 to 40, or 40 to 80 – they are all of equal subjective duration.

A logarithmic scale: stretched out at the low end and compressed at the high end.
However, the changing nature of our lives when we are young tends to obscure the shrinking years: the twenty-year-old rarely thinks about how life was at age 10; life at 20 is filled with different activities and concerns, and it is the future that dominates reverie.
It is only after life becomes more settled and routine that we become more retrospective, and only then do we have an easier basis for comparing the years.
This sense of elapsed time, narrowly dependent on memory, is also heavily reliant on psychological factors: Intervals of time may be judged differently in retrospect than while being experienced; they may seem longer if you feel you have accomplished much or had a memorable experience.
In great part at least, the foreshortening of the years as we grow older is due to the monotony of memory’s content and the consequent simplification of the backward-glancing view. In youth, new experiences are pretty common and regular, apprehension is vivid, and our recollections of that time, like those of a time spent in rapid and interesting travel, are of something intricate, multitudinous, and long-drawn-out. But as each passing year converts some of this experience into automatic routine which we hardly note at all, the days and the weeks smooth themselves out in recollection to contentless units, and the years grow hollow and collapse.
William James (1890): The Principles of Psychology. New York: Henry Holt.
Link to the original article on Logtime by James Main Kenney