4-digit 7-segment indicator on Multi-function shield

ShermanP:
The sweeping is called multiplexing.

Well, yes and no.

Multiplexing means time-sharing a single data channel to transfer multiple streams of data. The 4-digit indicator of the MF shield does use multiplexing to transfer data for each digit, no argument here.

However, this has nothing to do with the need to constantly "sweep" the image on the display. The MF shield could, for example, implement simple latches for each segment in each digit to make it stay on by itself once it is lit (i.e. add internal "memory" for each segment). This would eliminate the need to constantly "sweep" the display. The display would simply hold its last set state for all its segments. Of course, such display would cost quite a bit more.

Note that we would still have to use miltiplexing to update the state of each digit when necessary, but we would not have to constantly "sweep" the display anymore.

So, sweeping and multiplexing are two completely independent/orthogonal principles here. Multiplexing is how we transfer data. Sweeping is how we create the optical illusion of all 4 digits being lit up simultaneously.

ShermanP:
And as PaulRB says, if you light up one digit all the time it will be a lot brighter than if it were ON only 1/4 of the time.

Yes, I know that.

Again, the question is: do the segments get damaged by 100% duty cycle? Are they normally designed for 100% duty cycle? Or do they need 25% duty cycle to have time to "rest" and "cool down"?