When updates automatically arrive, I dutifully install them. Sometimes, when they take a longish time, I start to worry if this is the end of my Mac's life as I know it. But the computer (not to mention all of those brilliant geeks out in Cupertino) is much smarter than I am. Everything always comes out all right in the end. At least it has so far.
This morning I was notified that my "Time Machine" backup hadn't backed up in a week! Disaster! I clicked on the TM icon to back up and received info that (a) it wasn't backing up and (b) I needed to install new items including the latest OS X update. I dutifully installed all updates. Having been warned that it would take some time, I waited patiently. When it took a really long time, I began to wonder. I know that the Blue Screen of Death is primarily the prerogative of P.C. users, but when my screen turned an unusual shade of bright blue I began to tremble. Not to worry, the "regular" blue finally appeared and then—sigh of relief—the comforting old Aurora Borealis screen saver appeared with all of my friendly old icons. Whew! At this moment, Time Machine is still backing up, not that there was anything really important to back up. My great unwritten American novel takes up no space at all.
As far as Time Machine not backing up for a week, I tried the commonest, and least practiced, DIY routine. I unplugged it and plugged it in again. Success! Its little blue light went on, and all is serene once again. At least for a while.