Flagship U Academic Calendars and the Golden Ratio

I created the above chart to show the semester start and end dates for the state flagship universities in America (not included: Oregon's trimester and Washington's quarter schedules). The start date is the date which classes began, and the end date is the last possible date of finals that semester.

As you can see, they're all pretty similar except Spring semester at the University of Delaware, which has an insanely late February 11 start date and June 1 end date! The average Fall semester start date is August 24 and its end date average is December 15 (113 days), and for Spring they're January 15 and May 10 (115 days) respectively.

It was interesting trying to put all of their calendars all together in a chart to visually compare them, and I learned a new Google Sheets trick along the way, the SPARKLINE function! But I wasn't initially interested in just comparing their calendars, I started out thinking about something completely else. I started out thinking about a Twitter bot.

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One of the accounts I follow is @year_progress, a bot that simply Tweets a status bar increasing 1% every 3.65 days throughout the year. It's just long enough in between posts that I'm mildly surprised each time I see the percentage increase and just a fun little reminder. 

On a soon-to-be-related note, something I've been slightly obsessed with for a while is the Golden Ratio (0.618 : 1 : 1.618). I'm paraphrasing here but it's basically just a balanced system with the smaller section proportionate to the bigger section as the bigger one is to the whole. Something about this special balance is beautiful to us humans; for thousands of years we have created art and built structures specifically to this ratio. There's a natural beauty as well to it, as evidenced in its fractal symmetry found everywhere in nature. In sum the Golden Ratio just feels right, with everything in balance.

Back to my story, I wondered one day what the Golden Ratio date would be for the year, similar to @year_progress: turns out that 61.8% of the way through the year is August 15. As a lifelong student this date instantly stuck out to me as right around when we normally started the school year.

Wait a sec... could it be that our school year started around then because that date "felt right"? I had always heard that the school year was when it was because of farming back in the day, but a quick search showed that it really had to do with wealthy people wanting to avoid the heat in cities during the summer and a need for standardization. But why were we still using these dates? Just because of the inertia of current processes or because of some other unexplained reason?

Ok then, for my theory of a "right balanced" school year length to be correct, there should be some significance to when we end school too. For it to adhere, the end of the year should be around the other significant percentage of the Golden Ratio, 38.2% (which is 100% - 61.8% OR CONVENIENTLY THE SAME AS 61.8% of 61.8% or 0.618 times 0.618). Well 38.2% of the way through the year is May 19...right around when college normally ends!

So that led me to begin painstakingly collecting all the semester start and end dates from state's flagship universities. Turns out that the average start date for those 48 universities (August 24) is 9 days after the Golden Ratio start date (August 15) and the average end date (May 10) is 9 days before the Golden Ratio end date (May 19). Symmetry is cool.

In the end my theory was close but wrong by a little over a week in both directions. Maybe if I averaged ALL universities in the U.S. instead of just the flagships it'd be closer to my prediction, but ain't nobody got time to do all that. However a new coincidence emerged when looking these date ratios; that I'll dive more into below.

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To reiterate, I originally hypothesized there was some significance in our school year calendar in regards to the Golden Ratio, with us starting the year around when we were about 62% of the way through the year (with the ratio of what was left in the year to what had already passed the same as what had passed to the whole year) and ending around 38% of the way through the next year. This turned out to be close but not exactly correct for flagships.

But in looking at their calendars, I began to wonder if there was any significance to a date within each semester, for the "just right" date feeling to show self-similarity like the Golden Ratio does with fractals in nature. So I began wondering, "What event in a semester signifies that we're as much of the way through a semester as the semester start date does to the year?" I settled on when students can begin registering for the next semester's classes, as that usually signals enough time has passed in the current semester that we should start thinking about the next.

Well guess the fuck what? The average day in Fall 2018 that students could begin registering for the Spring 2019 semester's classes is November 1, or 61% of the way through the Fall semester! The average first registration day in Spring 2019 for Fall 2019 classes is April 1, which is 66% through the Spring semester. Fall's registration is closer to the Golden Ratio than Spring's but the general theory is still relevant.

While each college's academic calendar is different than that of other colleges as well as different from its own year to year, on average our college schedules revolve around dates that "feel right" and are relatively in balance with the Golden Ratio.

1. Fall semester starts about 0.618 of the way through the year --> Aug 15 : Dec 31 :: 0.618 : 1
2. Spring semester ends about 0.618 of the way to the Fall start date --> May 19 : Aug 15 :: 0.382 : 0.618
3. Registration for the next semester starts about 0.618 of the way through that current semester
4. The total number of days (228) college students could be "in school" for the year (113 on avg for Fall and 115 for Spring) is about 0.618 of the year's 365 days [228/365 = 0.624]. Consequently, the average number of days (114) in each half school year -- a semester --  is about 0.618 of the number of days in each half year

Admittedly, I'm showing confirmation bias plus other biases by picking and choosing these similarities but I think the relative nature of the length of time ratios is fascinating. There's a lot that we currently do that we can't really explain why, but I believe we subconsciously set our school calendars relative to dates that "feel right". It's an interesting thought but that's probably as far as it will ever go.

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Here's the flagship date info for anyone interested, I'm sure there are errors in collecting and interpreting these dates from the college's individual websites but some were very easy to find and other registration dates and such were hard to find: