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Time Perception

Logarithmic Time Distortion

Home | William James's Idea on Time Perception

Time scarcer? Years getting shorter? Want an explanation? Logtime is the the hypothesis that our age is our basis for estimating time intervals, resulting in a perceived shrinking of our years as we grow older. A simple mathematical analysis shows that our time perception should be logarithmic, giving us a subjective scale of life very different from that of the calendar.

We usually think about the years of our lives in terms of decades: our teens, twenties, thirties, etc. This is an implicitly linear view: that all our years are equal; that clock time is our time, through which we move at a uniform pace.

This simple picture, however, doesn't square with our perceptions as we age. By our middle years, at least, most of us have become aware that something is amiss, that a very slow but profound change has been sneaking up on us: the years that formerly crawled are now racing by. 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? Why do we now seem so rushed by life? Where are all the things we wanted to accomplish, but never seemed to find the time for?

There is another clue that our lives are not running in a linear, clocklike fashion: when we try to remember back to the earliest years of our childhood, they seem incredibly distant, like a far horizon that always recedes as we attempt to approach it. Why should we find it so much harder to remember the first few years of life than to remember later years, even after a longer time? And why do parents see their children growing up so much faster than they did?

Since the linear view of time perception seems inadequate, it is reasonable to look for a non-linear alternative. The observations we make about the apparent shrinkage of our years as we age strongly suggest a logarithmic scale: stretched out at the low end and compressed at the high end.

The fundamental importance of the logarithm has suggested the term "Logtime" to succinctly refer to the cognitive hypothesis discussed here.

Another term may usefully be coined here to denote this general field of study: "psychochronometry", the psychology of time estimation. Logtime is a psychochronometric model, i.e., an attempted mathematical simulation of subjective human temporal experiences. The logarithmic scale of time perception presented by this model may be only a rough approximation of actual human perception, but is probably a much closer one than the linear scale usually assumed.

That our time perception should be logarithmic can be easily rationalized (although proving it is a different matter!). The simple premise of Logtime, from which the logarithmic relationship can be derived, is that the human mind judges the length of a long period of time, such as a year, by comparing it with current age. For example, 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%.

The Logtime hypothesis is that it is this percentage that we perceive, not the years themselves: to the twenty-year-old, two years will seem to pass as quickly as one year will seem to the ten-year-old. Similarly, three years to a thirty-year-old and four years to a forty-year-old, etc., will seem to pass equally fast.

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: the length of the years seems to shrink logarithmically if we regard our subjective aging as uniform, while the speed of passage of these years seems to increase exponentially if we regard the years as being of equal length. Using other terminology, our sense of aging follows an arithmetic progression while the corresponding calendar years follow a geometric progression. Either way you can see that as you get older your time perception can be greatly altered.