## Logarithmic Time Perception

**Have you ever wondered why it seems as though the older we get, the quicker we perceive the years to go by?**

**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. While yes, every year is the same amount of time, humans perceive this time differently as we age. For example, when a 10-year-old is going through fifth grade, they may complain about how long it feels, how slow time seems to be passing. Yet, an 80-year-old feels as though her 79th year passed by very quickly.**

**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 perceived shrinkage of our years as we age strongly suggest a logarithmic scale: stretched out at the low end and compressed at the high end.**Consider this graph of y=logx to have an x-axis representing age. From ages 5-6, time seems to be going quite slow because there is a relatively large change from log(5) to log(6)...log(6)-log(5)=.079

Since there is a relatively large change from log(5) to log(6), this is as if humans are perceiving a "lot of time" in just this one year interval from 5-6. Hence, time seems to move slow. However, consider from ages 50-51. Time seems to move very quickly from 50-51 because there is such a slight change from log(50) to log(51)....log(51)-log(50)=.0086. Since there is only a slight change from log(50) to log (51), this is as if humans are perceiving "a little time" in this one year interval from 50-51. Hence, time seems to move quickly. Notice that the log(6)-log(5)=.079 and log(51)-log(50)=.0086 and .079/.0086=14.139 so if humans do really perceive time logarithmically, one could say that ages 5-6 move about 14.139 times slower than ages 50-51. Cool, right?

Since there is a relatively large change from log(5) to log(6), this is as if humans are perceiving a "lot of time" in just this one year interval from 5-6. Hence, time seems to move slow. However, consider from ages 50-51. Time seems to move very quickly from 50-51 because there is such a slight change from log(50) to log(51)....log(51)-log(50)=.0086. Since there is only a slight change from log(50) to log (51), this is as if humans are perceiving "a little time" in this one year interval from 50-51. Hence, time seems to move quickly. Notice that the log(6)-log(5)=.079 and log(51)-log(50)=.0086 and .079/.0086=14.139 so if humans do really perceive time logarithmically, one could say that ages 5-6 move about 14.139 times slower than ages 50-51. Cool, right?