It doesn't matter
Throughout the vast, vast, vast majority of human history, we neither cared nor noticed that day length varied in the context you're describing.
We cared that it varied throughout a year (i.e., depending on your latitude, the length of the day was longer in the summer than in the winter), and it could be said that it's unfortunate that at the poles day length tends to vary on the order of months, but again, that appears to be outside the context of your question.
OK, maybe it matters
For the vast, vast, vast majority of humans today we still don't care. Well, we care a little bit. We care enough to implement annoying things like Daylight Savings Time.1 But it should be noted that we were somewhat forced into caring by, among other things, train schedules. Which want to be predictable (even immutable) despite the later advent of busses that can't keep to the schedule to save their proverbial souls in heaven. And the problem with that predictability is the planet's annoying habit of slowing down, perceptually "adding time" to the schedule and apparently requiring all trains to freeze in position somewhere around midnight for just a moment to let the predictable schedules catch up to reality. (Maybe that's why the busses are always late... as a city cost-saving feature they don't freeze at midnight....)2
Which seems to suggest that things in motion tend to stay in motion until acted upon by Man's inability to account for all of the infinite variables that affect the precise measurement of time.3
Rats... apparently it matters
Now, honestly, all of this wouldn't matter at all were it not becoming more apparent that somehow I'm being left behind in the Information Age because my bedside clock cannot talk to my refridgerator to obtain the correct time.4 Despite advancing confidently from sundials and water clocks (which were more than enough for my honorable ancestors) to digital clocks,5 we humans have determined that it isn't enough. I mean, after all, navigators during the Age of Sail could always use a more accurate clock to figure out where they were on the open sea.6 So, apparently, we do need to care about just how long a day is.
Stop babbling and tell me why!
Back in the days when our day started sometime after the sun came up and ended eventually after the sun went down (or after we drank enough mead...) and spent most of our time gathering food and having the ability to actually move when our neighbors got too close to us, it didn't matter at all that the length of a day was predictably unpredictable.
But as we evolved into a species that trained its young in advanced planetary zombie/alien defense (which depends on the mod you're using), allowing for friendships to flourish across oceans, we discovered that it's actually a bit of a trick for everyone to stop doing what they're doing at midnight and hold their breath the requisite time to ensure the next day was really 24 hours long. ...ish. The more we humans must synchronize and coordinate our time, the more important knowing just how long a day is, is.7
So, whether it's ocean navigation, train schedules or the latest incarnation of Half-Life, it's unfortunately true that more than just Java developers have to and do care about the measurement of a day's length.
Because time waits for no teenager8
1 Thanks to the movie National Treasure, it is popularly believed in the U.S. that Benjamin Franklin is the father of Daylight Savings Time. What he actually proposed in an anonymous letter to a French newspaper was to use cannon to wake the Parisians at sunrise as a method of saving candles — infering, perhaps with reasonable credulity, that the French really enjoy their nightlife. Whether or not this letter constitutes a rational proposal for re-aligning the calendaring process during the course of a year to better distribute available photons for public use is still being debated.
2 It's a really good thing the Earth isn't speeding up because asking a train to freeze is a LOT simpler than asking it to momentarily accelerate to the speed of light to compensate for a shorter day....
3 My sincere thanks to Sir Isaac Newton for not climbing out of his grave to slap me with his dislocated left arm for so abusing his otherwise excellent First Law.
4 I've had that clock for years and it kept perfectly good time for all that time before my fridge could contact a server farm in India to schedule a time for its own repairs. But now, for some reason, it no longer keeps accurate enough time. Stupid fridge. Time to upgrade my timepiece....
5 A 26"x44" version being on sale right now for only $350 USD! The pretty girl looking coyly at me from the depths of my monitor was the final decision maker for me. Oddly, it's lacking the wireless network connection my refridgerator needs to ensure it keeps the correct time. Apparently the folks at Big Time Clocks aren't Java developers.
6 And they didn't apparently care when the sun rose or set (other than as a means of avoiding cannon fire). They cared about noon — because if you don't know exactly when noon be, one beint unawarez of where Tortuga and all da rum be! Aaaargh!
7 I've waited my whole life to use a double-is like that... really!
8 A reasonable PhD thesis could be written on the number of people each individual in the U.S. depends on during the course of a single day — each doing his or her job in a reasonable period of time. And that requires us to care about the precise length of a day to such a degree that it causes concern among Java developers. Think about the precision we'd need if people had to actually do their jobs to the second! It's enough to make a
civet's Java developer's head explode just thinking about it. I loved NullPointer's answer, BTW. I upvoted it and you should, too.