Number Systems and Time

I'm not sure that I ever thought about the geometries of time until Jacob asked us last week in the orchard garden. I definitely associated certain months with temperatures due to the varying extremes we had in the weather but I'm not sure that I ever asked the question why things are the way they are. I think humans intrinsically have difficulty letting things be as they are; there is an extreme discomfort in not understanding or making sense out of. This leads me to think, there aren't really twenty-four hours in a day, is there? Just because we say it is so, doesn't make it so - it's just our interpretation of it. We took daylight, tracked it using a sun dial, split the intervals into twelve because it was a duodecimal system at the time, then decided the night also needed to be split into twelve, then realized the inconsistencies between the lengths of the intervals, and then at some point squished and molded everything to fit a nice and perfect equal twenty-four parts and called it a day. I understand the importance of the twenty-four hour day in the current state of the world but I don't consider it's importance in general. In the day time we should handle our business, and at night time we should rest - that seems innate. 

Also, for such a stringent species measuring seconds now by the atomic time it seems odd that we are fine with two months in a row having thirty-one days and then throwing in an extra day to the month with the least amount of days every four years so that we stay accurate to the year actually being 365.25 days. I don't know, seems like we pick and choose when to be straight and narrow (perhaps a larger tell of society as well *cough* *cough*).

*edit*

Technically there are no inconsistencies between the two articles however the article written in Scientific American was much more definitive in its justification for why Babylonian's used base-sixty. The article in University of St. Andrew's Math History is less clear. O'Connor and Robertson list several reasons (including the large number of factors and the ability to count to 60 using knuckles and joints) of why Babylonian's used base-sixty however they do not definitely say which of the reasons it is. It is important to note they list these theories as they have been proposed by others. There are no surprises to me when it comes to the calculation of time but I do wish it wasn't so unnatural. I do find it surprising that the Egyptians decided to split the daylight hours into twelve. I understand why twelve (due to its significance in terms of lunar months, knuckles/joints in one hand, etc.) however I don't understand why they felt the need to split the day at all.