Logarithmic Years
Humans tend to perceive differences logarithmically. The difference between the amount of light from one lightbulb compared to two appears much greater than between ninety-nine lightbulbs compared to a hundred, even though the absolute difference in brightness is the same. Especially when quantities span many orders of magnitude, scientists and engineers often express quantities as a logarithm of the actual physical quantity.
A familiar example of a logarithmic unit is the decibel, commonly used to measure the loudness of sound. It is found by taking the base-10 logarithm of a quantity, then multiplying by 10. Thus, compared to a 50 dB noise, a 53 dB noise is approximately twice as loud, and a 60 dB noise is ten times as loud.
Age is an example of a quantity which we often perceive logarithmically. Time appears to pass more quickly as we age, and the difference in maturity and development between a 14 years of age and a 18 years of age is much greater than the difference between a 34 years of age and a 38 years of age, despite both having a 4-year span. Although human age does not span multiple orders of magnitude, measuring age logarithmically may be a more accurate representation of how we perceive time.
One method of doing this could be to take the base-10 logarithm of your age in years, multiply by 10, then optionally round to the nearest integer. We can call this “decibel-years”, or dbY.
Observations
The useful range of dbY appears to be around from 0 dbY (~1 year) to 20 dbY (~100 years).
| dbY | Age |
|---|---|
| 10 | 8 |
| 11 | 11 |
| 12 | 14 |
| 13 | 18 |
| 14 | 22 |
| 15 | 28 |
| 16 | 35 |
| 17 | 45 |
| 18 | 56 |
| 19 | 71 |
| 20 | 89 |
| 21 | 112 |
The year shown on the right is the approximately the earliest age at which one's dbY, rounded to the nearest integer, would be the dbY on the left.
The integer dbYs correspond pretty well to age groups. In the United States, 11 dbY (11–14 years) are middle schoolers, 12 dbY (14–18 years) are high schoolers, and 13 dbY (18–22 years) are college students; 14 dbY is roughly the “twenties”, and the remaining age groups seem pretty reasonable as well.
Taking the difference of ages in dbY rather than years also seems to allow for better comparisons between ages. For instance, the difference between an 18 years of age and a 14 years of age would be 1.09 dbY, and the difference between a 38 years of age and a 34 years of age would be 0.48 dbY, showing there is indeed more of a difference in the former than the latter.
Calculators
Below are a few calculators you can use to play around with dbY. All processing is done in JavaScript on your machine; no data leaves your device.
Calculate your age in dbY:
Calculate the difference between two ages in dbY: