The Vienna clock museum follow naturally from the globe museum. On some deep level the two museums are the two sides of the same temporal, geographic coin. As with globes, we take for granted how clocks determine our thinking about time. It feels to us like this absolute notion. As part of my work I regularly handle integer values that mark the number of seconds since January 1st 1970, the Unix epoch, which as far as a command line wizard is concerned, marks the true Common Era. I imagine you have to do a lot of astrophysics subject to effects of relativity to shake this absolute thinking.
The key scientific innovation in pendulum clocks is isochronism. First observed by Galileo, this means that the period of a pendulum — that is to say the time it takes to swing back and forth — doesn’t depend on the how big the swing of the pendulum is. So when you set a pendulum swinging, the first period takes the same amount of time as the hundredth, even though the pendulum by this point isn’t swinging as far. (Wikipedia tells me that this property is only approximately true). Thus regular increments of time can be measured out. Fortunately our days and calendar events happen with sufficient periodicity that they can be broken down in measurable fashion.
Also, I learned that people used to put working clocks into paintings to be hung with the dual painting/clock functionality.