It seems likely to me that the way we come to think about time as children stays with us all through our lives, even if we later encounter other models for envisioning a year, or a season, or a month, or an hour. From my own childhood, my way of envisioning a year was really two semi-circles. Starting on the x-axis (not that I would have known anything about an x-axis at that age!), we are at the start of the spring. The direction of travel around the circle is clockwise. In the "height of summer" - a phrase I learned from a young age - we find ourselves at the top of the first semi-circle. From there back to the x-axis is the movement towards the fall. From fall, the journey through winter takes us along the "negative side" of the circle, with the "lowest" point of the circle falling somewhere around Christmas-January.
As it turns out, the circle was how I thought about everything to do with time. No doubt I was influenced (and my parents and teachers were influenced) by the circular clock and traditional watch faces. While I cannot think of any geometry I associated with individual seasons, the way I conceived of the months and days and hours was all the same: everything was a circle. That the months were also circles is interesting and perhaps is owing to the fact that my parents had a unique kind of calendar in our home that displayed each month in a circular way! So finding the 15th of the month always meant looking basically at the bottom of the circle to me (it was slightly different for 28, 29, 30, and 31 days, but it was always right around the bottom of the month).
As I reflect on this conception of time in circular ways, I am struck that, as Lombardi explains, the Egyptians too developed their conception of time from circles. According to Lombardi, the Egyptians had a base 12 number system (a fact that contradicts O'Conner and Robertson's claim that "no major civilisation seems to have come up with [a base 12 system]"!) and so used a sundial (the circle!) divided into 12 parts to divide the interval between sunrise and sunset. But even in dividing the time of the night into 12 parts, as Lombardi explains, the Egyptians followed the movement of the stars in a "semicircular" way through the sky.
Though circles seem to connect both the Eygptian and Babylonian contributions to our timekeeping conventions, it is a blending of the base 12 and base 60 systems that give us the full picture. I find it intriguing that all we have are theories for why these bases were developed, but I appreciate O'Conner and Robertson's proposal that the Sumerians (who preceded the Babylonians and developed the base 60 system) came about through a mixing of two peoples having 10 and 6 as their number bases. As they point out, this would account for the use of the "10 unit" in the Babylonian system as a remnant of the earlier decimal system.
Two things I learned in reading the Lombardi article are: (1) that the meaning of the "hour" was not commonly understood to be a duration of 60 minutes for many centuries - "until the first mechanical clocks that displayed minutes appeared near the end of the 16th century, and (2) that the division of the circle of the clock into 60 "minutes" was originally terminology taken from the division by Greek astronomers of the 360 degrees of latitude and longitude into "minutes" and "second minutes," or "seconds."
Finally, I find myself reflecting on the significance of the circle as a way of conceiving of the passing of time. In my faith tradition of Christianity (not something I knew as a young child but came to later in life), the Celtic cross has always intrigued me: it is a traditional cross that features a circular ring intersecting the arms of the cross (it was developed in the 8th-9th centuries in Ireland and Britain). As I understand it, the vertical and horizontal components of the cross came to be understood as the intersection of the human and divine realms. But what fascinates me is that intersection is itself contained within the circle, likely a symbol of the sun, which itself represented the passing of time. For me, it is a reminder to me that we all seek to form our understanding of our place in the universe within the same "circle" of time.
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