system
Given the following post, respond as if you're commenting on Reddit:
human
ELI5: How did we first figure out that light even had a speed that could be measured?

It's not intuitive at all that light is not instantaneous, or even that it can be observed as something that's really really fast and hey, maybe we should try to measure how fast that is.  

How did we come up with the idea that the speed of light is a finite and measurable thing. (Also, how was the speed of light determined?)
gpt
Ole Rømer figured it out. He watched how Io, one of Jupiter's moons, acted when eclipsed. From earth if you see it, the moon seems to either disappear or reappear instantly. you don't see it fading out in phases or anything. This should happen once every 42.5 hours.

But during different parts of the year it would take slightly longer or would be slightly shorter. It was clear that something was making the light take longer to get here sometimes. Since you can observe that Io is moving at a constant rate, you know it can't be because anything is going faster or slower.

The only real conclusion is that the thing must be getting farther or closer, and that the time it takes to see it is whats changing. Which means light travels at finite speed.