Rate of Change - Perception and Reality

The days lengthen and shorten as the seasons change.  Today is one of the days of the year for the most rapid change in day length.   The rate of change of the day length is related to a sine function for those who have a mathematical interest and can visualize derivatives.   My awareness of the varying rate of day length change is driven by observing the position of a building shadow on a side walk that I take to lunch when I am on campus.   With the sun high in the sky and far to the north in the summer, at high noon I must walk in bright sunshine flooding the sidewalk.  As the summer wanes from the longest day each week I notice the shadow line creeping on to the sidewalk.   Eventually the shadow progresses across the walk and on to the grass on the other side.  Shortly after the longest summer day the week to week change is relatively slow.   However,  now that we are at the equinox the week to week change is very rapid and especially noticeable.   I think ancient civilizations used this method to record the seasons and to provide a calendar for planning their planting, harvest and marking the years.   This is reality that can be observed.   Seasons are cyclical and observable.

The perception of the rate of change of time, however, is another matter.   Often my wife and I remark to each other that it seems like in an instant that the week or day has passed by.   Especially if we have been busy with a multitude of things.   Beyond the daily elapse of time, there are the yearly checkpoints such as marking the new year.   It seems that as one ages each succeeding year elapses faster and faster.    This is where perception must come into play.   The year that passes is some portion of ones length of existence.    So when you are four and and a year elapses it is 20 percent of your lifetime and at nine the year following is 10 percent of your lifetime.  However if you are 79 and a year elapses it is 1.25 percent of lifetime.   No wonder the years seem to go by so fast as we age.  We have all those stored memories and experiences in time that generate our perceptions of rate of time flow.

From my view change adds spice to life.   I am glad to live in a climate of changing seasons both of my physical world and the events of a full and interesting life.