Why does increasing the flickering speed of a light have a dimming effect? I'm setting up one of my first circuits. I have a knob to increase the flickering speed of a led. When I increase the flickering speed up to a certain point I am not able anymore to perceive it is flickering. When I increase the flickering speed even more the led dims. 
Why? Some sort of wave interference effect?
 A: Educated guess:
The LED can't turn on and off instantaneously so your LED isn't operating as a perfect square-wave. There is some curvature at the edges. When you flicker too fast, the LED can't turn itself on fast enough.
Example with numbers: Say it takes 1 ms for the LED to go from dark to light or vice-versa. If you're telling it to flicker with a period (off to on to off) of 1 ms, your LED will never reach peak brightness. It will look more like a series of hills. As you flicker even faster, the hills will shrink further.
A: Human eye takes 24 frame per second, approximately 70GB data. If you blink LED above some frequency, you may not see the off state of LED. You see LED is on continuously. For more info: Persistence of vision.
But high speed cameras capture it, it actually blinks. There are some videos on youtube.
There is a method called LED matrix which takes advantage of this. LEDs are turned on and off at high speed and user see all of them on. This method requires less control pin and gives expected result.
Why we see it dimmed instead of on or off states? I think it's also sensitivity of human eye. You may not see darkness right after the lightness. Luminosity function.
Power consumption of blinking system with clock (square wave) is almost half of the power consumption system with stable signal. But when you increase frequency, you see the LED more bright. And I think, lifetime of LED may be doubled because of use time...
A: This is the result of simple averaging. 
At low rates you eye separately measures and reports the intensity during the bright period and the intensity during the dark period. When the rate exceeds the response time of the eye, the report is effectively the average brightness which is necessarily less than the brightness of the bright periods.
