So I guess it’s not just me. This is a topic I’ve been obsessing over since I was about two years old.
Logtime is the cognitive hypothesis that our age is our basis for estimating time intervals, resulting in a perceived shrinking of our years as we grow older.
Another way of looking at it:
It will be convenient, though perhaps depressing, to define equally perceived units of time to replace the decades we conventionally use to pace our lives. 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, using the simplest ratio, 2: 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. The starting age is arbitrary: 8 to 16, 16 to 32, and 32 to 64 are also of equal subjective duration, and are all perceived as being the same as 10 to 20!
It’s an awful lot like music:
The term commonly applied to ratios of 2 is the musical one of “octave” (ignoring its Latin root meaning “8”). (Our perceptions of the pitch and amplitude of musical tones are logarithmic; so, apparently, is our perception of time.) The octave is the most obvious Logtime replacement for the decade, although it has no fixed connection to our base-10 number system. All octaves are equally spaced on a log scale, just as decades are equally spaced on a linear scale.
Going back in time, the octaves from ages 4 to 8, 2 to 4, and 1 to 2, etc., should have seemed equally long, although the logarithmic description may no longer be a good approximation near birth, and can certainly not be quantified by observation!