How do Ethernet controllers show activity with the LED indicator?
How do these controllers convert the extremely fast pulses to something that resembles "activity" to our brains?


That's pretty much up to the controllers. But yeah, you can savely assume that every packet that the MAC layer detects turns on the LED, and just resets a counter to full value, and that this counter is counted down with a fixed clock, and when it turns zero, the LED turns off.

Or some variation thereoff that allows short packets to be seen. 

Maybe throw in a state machine that allows for "blinking" in case of prolonged activity. Just some cheap digital logic in the fabric.