Ever since I read James Gleick's "Faster", I have been aware of the possibility of being a time nut, a person overly concerned with time accuracy. The other day, I visited the current web page at time.gov
I am intrigued by trying to be more accurate in reporting the time but for no good reason, just interest. The webpage at the link tells me how far off the current exact time where I am, my computer clock is. I have never seen an estimate like that before.
I am aware of the difficulty of knowing the time. I don't think being a little off matters. The most dramatic situation I can think of is when the sound booth man gives the signal for the beginning of a broadcast to start NOW. It is a surprise to me how much trouble it is to capture when the signal was given and then to check how correctly timed it was.
We don't have too much trouble knowing the day of the week, or of the month but we know that is a somewhat crude measure, mostly easily tracked. I use a mnemonic of 'small time' to remind myself that when I or my relatives and friends try to be super accurate in calling or arriving, we are going to run into the accuracy of clocks problem. The book "Longitude" by Dava Sobel is excellent at explaining how being able to tell time accurately mattered in a life and death way to ocean-sailing ships in the modern age. Read that and you can marvel all the more at Polynesians traveling on rafts and navigating by stars.
You can get all nervous about the tick of your clock realizing that each tick is one more step toward the end of your life, but I recommend you don't. We saw an old clock in London that has no face and no hands that chimed every quarter hour. Our ancestors did without second hands and stopwatches for millenia and we can work at being relaxed about what time it is? Remember Yogi Berra: "Yogi, what time is it?" "You mean, now?"