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Regarding 20/20. The optician's test image is a Snellen eye chart. At 20/20 the letter "E" has bars 1 arcminute thick and the two gaps between the 3 bars are also 1 arcminute (5 arcminute high total). Also the contrast is good and the background is 100 foot lamberts (i.e. brighter than typical for video projected images and TVs which gives the eye better acuity). However there is more to the story.

First, if the resizing is a weighted blending of the original pixels (bi-linear interpolation), then letters of a 20/20 eye chart would have fuzzy edges (if the displayed pixel overlapped half a dark original pixel and half a light pixel, then the bilinear interpolated output pixel would be gray). Thus 4K resolution projection would suffer only half the degradation that a 2K projector would suffer. In other words, the letters of a 20/100 resolution eye chart will be a little sharper but for the highest displayable resolution eye chart it will be a lot sharper.

Second, the eye has much higher vernier resolution and can discern if a line has a 12 arcsecond step displacement. That means the eye is very sensitive to aliasing artifacts. A 4K display would inherently have only half the angular magnitude line displacement of a 2K display. (Although line displacements will be less, they can still be visible since the displayed pixels are still larger than 12 arcseconds. Antialiasing algorithms hide these artifacts but somewhat blur the image. On a pixel basis, double display resolution allows these artifacts to be hidden with antialiasing pixel processing that is only half as blurry.

Third, if the resolution is twice as high, then motion blurring is twice as noticeable. Thus, if your eye gaze follows numbers across the screen (e.g. football jersey or stock market data scrolling across or film credits scrolling down), then the eye is blurring twice as many pixels together. This means at 4k, 240 Hz motion blur reduction is required to attain the same affect as 120 Hz MBR at 2K resolution. The good news is this is only a fair comparison when the numbers on the 4K display are half the angular size as on the 2K display and you are expecting to see them equally well. If both projectors display the same image of a moving 20/40 Snellen eye chart, then of course the high resolution projector will suffer motion blur no more than the 2K projector even when both are MBR at 120 HZ. However do not expect to then switch the 4K projector video to a 20/20 Eye chart moving at the same angular rate across the screen with the same clarity as the 20/40 video on the 2K projector unless you also run the 4K projector at double the motion blur reduction rate. On a 4K display, when motion blur occurs, the temporary resolution degradation is much more noticeable.