I have a little battery powered handheld fan by my computer. If I turn it on and hold it in front of on my computer screen, it appears the blades slow down. Depending how close I hold the fan to the screen the blades will continue to slow down, stop, reverse direction. Why is this?
I think it is because the moniter does not give off a constant light but instead flashes really fast, creating a strobe effect.
But why does distance from the screen matter?
It’s got to be a perspective effect, the closer the fan is to your eye the more screen is seen behind it.
As the amount of covered screen changes, the mis-match between the fan rotation and screen raster changes giving the odd strobe effect.
Bit like car wheels on a movie screen.
milk milk lemonade, is your name a reference to the saying:
milk, milk, lemonade, the other side is where fudge is made?
Is it possible that you have fluorescent lights that alter the stroboscopic effect according to distance to the computer monitor?
Does the effect of apparent change of rate only occur when you are moving the fan to and fro? - if it does, then it is probably caused by the fan slowing down when you move it toward you (it is travelling upwind) and going faster when you move it away (travelling downwind)
The monitor is indeed a rapidly flashing light source, like a strobescope. If it flashes 80 times a second and your fan is rotating at 80 rotations per second, it will appear to stop. If it’s 90 rotations/sec then it appears to be rotating very slowly (10 rotations/sec). If it’s an integer multiple or division of that number (say 10 rotations/sec) similar things happen.
But as for it slowing down as you bring it closer, that can’t be explained by strobescopic effect. I think the fan is actually slowing down because of the back pressure from the screen surface.
The light dot that draws the picture flies from the top left to the bottom right of a TV screen 50 times a second in the UK or 60 in the USA.
The hand held fan spins at some fixed rate, say 200rpm, although I imagine it slows down microscopically as the batteries run down.
The TV screen is literally flickering many times a second and illuminating the fan as a strobe light would. This gives the odd stops/goes backwards effect.
So you’ve got 2 things to consider - the screen refresh rate and the fan spin speed. As you move the fan towards your eye you are exposing it to more passes of the raster per rotation of the fan, giving you a different strobe effect.
Just hoding it stationary would probably give you a periodic back/still/forward impression as well as the two rates of change go in and out of phase (and as the battery runs down).
PS: Where I live we say “round the corner chocolate’s made” 
No.
The effect seems stronger in the middle of the screen, meaning if the fan in the middle of the screen (same distance from the screen) it will either appear slower or if the dirrection has reveresed it appears faster. In fact, I can’t get it to appear to stop at the outer parts of the screen. I am not sure how this affects your hypothesis.
It is not a flat screen and I am wearing glasses.