First: Huey Lewis.

And, you’re welcome. That’s my my-birthday present to you!

For it is indeed my birthday. Even better, it’s my 36th birthday, which is a perfect square, which got me thinking about those as interesting markers of time in a life: ages 1, 4, 9, 16, 25, 36, 49, 64, 81, and 100. More interesting than decades to me, for reasons of both math and psychology.*

So, my reflective exercise** for the day has been to spend some time in the Land of Old Photos, and to pull out the ones that are a) from those perfectly square ages (I think!) and b) that I recognize myself in…meaning not that I look especially similar to my now-self, but that I see my then-self experiencing life in a way I recognize.

So! Between 25 and now has been a beautiful 30.5% of my life, and if blogs are still a thing in 13 years, maybe I’ll let you know how the next 26.5% is.

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***Math:** this also got me thinking about the intervals between these numbers, which are 3, 4, 7, 9, 11, 13, 15, 17, and 19. And thus, why the interval increases by 2 each time. And I got to do the fun thing where you discover math for your own self…something that you could just look up, but because it’s math, you can figure it out! So: given the function (x+1)²-x²… use your FOIL from 7th grade…(x+1)(x+1)-x²…then x²+2x +1 -x², and you end up with a simplified f(2x+1) as the interval between x² and x²+1. Right so for “5”–2(5)+1=11. And indeed: (5+1)² -5²=6²-5²=36-25=11! So I was all excited about that. But then I also wanted it to make more intuitive sense to me, and so I visualized: given x=4, I now know that the interval between 16 and the next perfect square will be 9. And if I visualize 4² as 4 4s, and then 5² as 5 5s, I can add a little +1 to each of the 4s to get to 5 (okay so that’s 4 of the 9 I need), and then of course there’s one more 4+1 because there’re 5 5’s, not 4, and voila! 4+4+1. And given that the next jump would be 5+5+1, I can see easily that 5+5+1 is 2 more than 4+4+1. BOOM.

**Psychology (and more math)**: It also seems significant that as we age, space between these markers represent different percentages of the years we’ve experienced. When you are 10 years old, one year feels like forever because indeed any given year represents 10% of *your whole life* thus far! As we age, any given year represents such a smaller percentage (down to 2.7% for me now), but the same *amount of things* probably happen, let’s say 100 interesting-enough-to-call-a-friend-about things. So that’s weird, because 10% used to = 100 things and now 2% = 100 things and that’s maybe why we are often surprised by our relationship with time and its passing. Anyway though: I like thinking of perfect squares (rather than decades) as milestones because it honors all this time weirdness:if we think of “time since last marker” as something we’d attend to (and it is, duh…when you are 30, everyone want to talk about what you’ve done since 20, what you expect before 40, etc) :

With perfect squares: **at 9, time since 4 is 5 years, 55% of life so far**; at 16, time since 9 is 7 years, 43% of life; at 25, time since 16 is 9 years, 36% of life; at 36, time since 25 is 11 years, 30.5% of life; at 49, time since 35 is 13 years, 26.5% of life; **at 64, time since 49 is 15 years, 23.4% of life**.

With decades**: At 10, time since 0 is 100% of life so far**; at 20, time since 10 is 10 years, 50% of life; at 30, time since 20 is 10 years, 33.3% of life; at 40, time since 30 is 10 years, 25% of life; at 50, time since 40 is 10 years, 20% of life; **at 60, time since 50 is 10 years, 16.6% of life**. Anyway, perfect squares by no means make it so the intervals between markers represent the same percentage of total life each time, but my god it’s much gentler of a change from ages 9-65 (55-23.4%) than from ages 10-60 (100-16.6%).

**reflexercise!

Love these pictures of your perfect squares – they are all indeed so clearly YOU!

Happy Birthday, Dearest Sarah Renaissance Woman of word etymology, social justice, crossword radicalism, visual journaling, educational wizardry and now MATH!!!…Is there no territory you cannot travel with mischief and delight?

My visual of the the interval between the squares was simply to picture a square set of tiles (I actually pictured laying tile from one corner of a room) 2×2, then 3×3 then 4×4, adding an L-shaped layer of tiles each time the square grew. The L-shape gets bigger by one tile at each end every time the whole square expands, thus adding two tiles to the new layer, which is yet another way to explain why the interval grows by two between each perfect square….such fun!

I think my favorite birthday was 11 – prime AND palindromic…no other like it!

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YES–I love your visual. I often feel mad I learned math in a way so divorced from how things actually take up space…so when I “visualize” I’m still visualizing equations. And thank you for these sweet words!

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Great reflection, though admit I skimmed over some of those initial equations like I skim over especially extended biblical genealogies; yet the perfectly square practice of working out math in a blog balances out the well rounded art of your life-marker-photos and poetic writing–a nice literary mandala for us to enjoy on your birthday! Here’s to the high quality quantitative reflection you bring to life! Happy birthday and Thank you!

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James, I think we need to get you a guest post on inter ruralia one of these days.

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