In a groundbreaking article T. L. Freeman discusses the relationship between actual age and effective age. 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:

AY= α /AA

The constant of proportionality α is rather loosely defined by Freeman as the age at which a year really seems to last a year, and it was arbitrarily set at 20 years ( α =20).

Now Freeman determines the concept of Effective age, which is simply the integral over time of the Apparent Year from age 1 to the actual age (AA) of interest:

AA AA EA = ∫ AY d(AA) = ∫ 20/AA d(AA) = 20 ln(AA) 1 1

Although this formula results in some interesting conclusions, there are several flaws with this concept. As mentioned above, the choice of the proportionality constant is rather arbitrary . There is no rational justification for the choice of this age, but it was solely chosen based on Freeman's own perception of (the passing of) time. Next, the evaluation of the integral seems incorrect, since its lower limit was set at 1, and not at 0. Obviously, the choice of zero as lower integration boundary yields can not be evaluated due to the logarithmic term in the expression. Because of the obvious problems with Freeman's concept of time perception , it is necessary to redefine the Effective Age on a sounder basis.

In the traditional concept of time perception, one person's Actual Age is proportional to the passing of time (t).

AA = β t + γ

Note the occurrence of two parameters β and γ that are traditionally set to one and zero, respectively. However, each has a clear (though usually underappreciated) function in time perception. The β -parameter describes the rate at which one person ages; some persons remain annoying little crybabies during their life, while others become boring old farts at 20. The γ -parameter describes the origin of one person's time perception. Did you ever meet those proud parents boasting about their little one who is only x months old, and already walks, writes obfuscated C, or recently sold his first dot.com? No, these youngsters aren't bright for their age; they simply have a high γ -factor.

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:

AY= α /AA = α /( β t + γ )

δ

ε

AY= α /( β t + γ ) = ( α / β )/(t + γ / β ) = δ /(t + ε )

δ

ε

We can remove one of the parameters by defining two parametersandThe actual values ofandwill become clear from the boundary conditions

In order to obtain the Effective Age, the integral of AY is evaluated. Note that the integral is evaluated over time, and not over Actual Age, since AA is a function of time:

t t EA = ∫ AY d(t) = ∫ δ /(t + ε ) d(t) 0 0 EA = δ ln(t + ε ) - δ ln( ε )

ε

The lower boundary condition (t=0) should yield an Effective Age of zero years (EA=0). Therefore= 1.

The upper boundary is less apparent. It should be chosen so that at t=t max , 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 a life expectancy of 80 years (t=80, EA=80), we obtain:

δ = 80/ln(81) 80 ln(t + 1) EA = ---------- ln(81)

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