Bill P. Godfrey et al

Thursday, May 18, 2006

Happy log(birthday)!

How old are you? I'm in my early thirties.

Ask a child, and you'll probably get an get an answer accurate to nearest month.
I'm six and nine months!
-- A hypothetical 6 year old.
And nine months!
-- A hypothetical 6¾ year old. (Sorry)
To a six year old, those nine months are a ninth of that person's life. Yet as adults, we cheerfully mush our ages into broad periods covering many years. At the other end of the scale, ask a parent the age of a new born and your answer will probably be in the order of days.

So goes the idea that a person's age is on a logarithmic scale, even if we use the linear "years old" scale in everyday life.

A quick aside for those of us who don't know a logarithm from an exponent. The log function can take a linear value (such as the number of years) and turn it into the base 10 logarithmic equivilent. You can experiment with the log function using Google's calculator function.
Notice that log(x) can be reversed with 10x. So to find log(x)=3, we calculate 103, which is 1000.

We also see this idea at work when talking about age differences in relationships. A ten year difference for someone over 40 is unremarkable, but a 20 year old might say "That's would be like me dating a ten year old!" But its not really like that at all.

(When dealing with human relationships, I found that the calculations make more sense if we start at puberty, which I arbitarily fixed at exactly 13 years old. If you are y years old, we should use x=log(y-13) and y=(10x)+13 in this context.)

To calculate the age difference in post-puberty-log-years of our 40 and 30 year old couple, we calculate;
0.200914843 log-years

To find the equivilent younger partner for our 20 year old, we find that person's age in post-puberty-log-years, subtract 0.2 log-years, finally converting that back into regular years.

10(log(20-13)-0.200914843)+13 = 17 (ish) years old

This article started out as discussion of the mathematics of reporting financial news and making investment decisions. Its a funny old world. (And don't worry about age differences so much.)


  • 49. 50 in Feb.

    Damn, it hurts to say that.

    By Anonymous Rori, At 1:45 AM, May 21, 2006  

  • I think you've independently discovered the "half your age plus seven" rule, but you would add 6½ years instead. (Half of 13)

    By Anonymous Anonymous, At 1:20 PM, May 21, 2006  

  • That all sounds good, but my brain hurts.

    I'm 32 years and 337 days old... and I have a problem. [oh, wait, wrong room]

    By Blogger M., At 2:27 PM, May 23, 2006  

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