Sunday, August 19, 2012

Why time appears to speed up with age

Interesting article, I've stumbled on this somewhere before, but it's the first time I took the time to read it.

His conclusion is that the passing of the years goes faster as we grow older.
This makes sense; for instance when you are 10 years of age, a year represents 10% of your life, and seems like a very long time.
However, when you are 50 years old, one year has reduced to only 2% of your life, and hence seems only one-fifth as long.
Summarizing this work, Freeman comes to the conclusion that the actual age (AA) needs to be corrected for the apparent length of a year (AY). The apparent length of a year is inversely proportional to one person's actual age
Because of the obvious problems with Freeman's concept of time perception, it is necessary to redefine the Effective Age on a sounder basis.
It is clear that with this definition, one person's Actual Age may already be non-synchronous with time. However, analogous to Freeman's work, the apparent length of a year (AY) is not constant
The lower boundary condition (t=0) should yield an Effective Age of zero years (EA=0). Therefore ε = 1.
The upper boundary is less apparent. It should be chosen so that at t=tmax, EA = t. At death, the Effective Age and real time are again equal. However, no person knows for sure his or her personal life expectancy. This is clearly an issue for molecular biologists to address. However, if we assume for a person alife expectancy of 80 years (t=80, EA=80), we obtain:

  δ = 80/ln(81)

               80 ln(t + 1)
          EA = ----------

This formula can now be used to calculate the Effective Age (and the Effective percentage Completion of Life) as a function of time. This is shown in the following table:

time (yrs.)  EA (yrs.)  Life%
0            0.0      0
1           12.6      16
2           20.0      25
3           25.2      32
4           29.3      37
5           32.6      41
10          43.7      55
15          50.5      63
20          55.4      69
30          62.5      78
40          67.6      85
50          71.6      89
60          74.8      94
70          77.6      97
80          80.0      100

And thus, the bold statement in the title is justified. Life is half over at age ten, and three quarters over at age thirty. Note the rapid increase at very young ages: in the initial stages of life, life itself makes big strides forward. For instance, consider the concepts of speecheating and walking; skills that are learned at a young age and are carried on throughout a person's life.
Another interesting observation that we can make is the age at which one year really seems to last one year. This can be calculated quite easily from the derivation above. For a life expectancy of 80 years, it is equal to 80/ ln(81) - 1 = 17.2 years. Quite close to Freeman's original assumption of 20 years.
The concept of Effective Age has far stretching implications. Some of these I have summarized below:
  • "Summer vacations lasted almost forever when I was in grammar school":
  • True, they did. In fact, when you were six years old, an Apparent Year would be close to three years. That would make a three week summer vacation feel like almost nine weeks!
  • "Now that I am older, I can communicate better with my parents"
  • Right. As you can see, you're catching up with them! Closing the "generation gap", so to speak.
  • "Life starts after 65"
  • The credo of many people close to their pension age. Wrong: at 65, you only have about 5% of your Effective Age left. Choose your time wisely; start working late, and retire early.
  • "Old people are slow"
  • That is such an insensitive comment. Old people aren't slow at all, they simply have a different time perception.
  • "Those annoying birthdays seem to roll around faster every year
  • True, they do. Better start celebrating your Effective Age.

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