The Mathematical Significance of Wisdom Over Time

My oldest daughter Maya turned 15 yesterday, Aug 21, 2022. I took some time and went to see her at the end of her special day. Amongst other things, we were discussing wisdom, and how we mature over time. Indeed, a natural process for all of us. I was telling Maya that as she grows older, she will learn things. She will learn things in school, and she will learn things in life. Perhaps more in life than in school.

Then we caught ourselves discussing a more numerical type of analysis (Maya has always been amazing with numbers). We realized that, when she was at her year zero (of course, this is a figure of speech) I was 30. She was a baby whom only knew how to cry for food while I knew a little bit about life and things. Now she is 15, she knows a little bit more than what she knew when she was 0, or 5, or 10. I'm 45, I also know a little bit more than what I knew when I was 30 (or 0, or 5, or 10).

We decided to graph the data, looking into the "wisdom rate of growth" over the years (note: of course, I could be 80 and know nothing, and Maya could be 10 and know a lot, but as the old statistical condition ceteris paribus state, all other things remaining constant, we all somehow learn, grow, and mature over the years). Here's what we built and what we learned together from this analysis.

As the years go by, Maya's wisdom in comparison to mine grows ratio-wise. When Maya is 0 and I'm 30, she mathematically knows very little, almost nothing numerically speaking (she only knows how to cry for food and to express pain) - she's roughly at 0% wisdom when compared to her Dad's life experiences. At 15, she's caught up to 33.3%. At 30, she will reach 50% of her potential wisdom when compared to her Dad, given that she will experience the same amount of opportunities (ceteris paribus) that I have experienced. At 45, she's now at 60% and at 60 she's at 66.7% of "wisdom level" when compared to myself. And so on.

The math behind this is very simple: as our age numbers get bigger, the constant difference of 30 years between Maya and I become less relevant, numerically that is. For example, if I were to live 1,000 years and Maya 970, the difference between her wisdom growth rate and mine would have been only 3% (1 - (970/1,000)*100). Maya's wisdom level at this point would have been 97% of mine. You can actually see how the graph is starting to plateau at our "stretch ages", that is because the "incremental knowledge" gest more and more dissolved over time (again considering the constant difference of 30 years between us).

But is this true, besides the fun mathematical model above? Consider Maya's sister Juliette. They are only two years apart, and that constant difference, being much smaller than 30 years, becomes "irrelevant" quicker. For example, when Maya was already walking Juliette was still trying to hold her own head up. When Maya was leaving the dolls' phase behind, Juliette was still playing with them. Maya is now in high school, and her sister in grade 8 (a huge difference in terms of school dynamics, peer pressure, etc.). But by the time Maya is 25 and Juliette is 23, or say, 40 and 42 respectively, their life experiences and "wisdom level" (given roughly the same experiences of life) could be pretty close.

Seeing this maturing in wisdom in a fun numerical way helped Maya and I understand the process of growing older a little better. If anything, now we both know a little more.