[skykooler]

The width of the Sun in the sky is wide enough that it takes about 1 minute and ten seconds to cross its own diameter. So optically speaking, it would be pretty much impossible to have any resolution finer than a minute, no matter how small the holes are.

[Someone]

I cannot see how to do it, but one way to beat that limit might be the use of diffraction gratings. It might be possible to have the light from two opposing edges of the solar disk interfere and produce a darker spot, thus allowing one to draw the time in darker text on a light background.

If that can work, I guess both the design (I can't see how to design one object that shows a number for say 5 seconds; now fit thousands in a single object) and the engineering challenge would be quite a bit higher (at submicrometer scales), and that the resulting contrast of the display would be a lot lower.

[05]

Sun isn't a coherent light source, so no interference of light from different sides..

[Eridrus]

I think it should still be possible, but it will depend a lot on the length of the holes too.

If you imagine a really long tube, any light entering at an angle will eventually hit the side, and if the sides do not reflect any light, nothing will come through the tube.

I don't want to bother doing the math to figure out how big the diameter of the sundial would have to be to have sub-minute accuracy, but I think it is very possible.

[jerf]

skykooler's point is that the Sun is not a point source. I think you may be mentally modeling it as a point source. A point source would make it just a matter of length, but when it's not a point source you can't help but get overlap between two "points" that are close enough together, because they both will be lit up at the same time, no matter how long the tube may be.

[Eridrus]

Ah, I think you're right.

Though the intensity would fade as the sun moves, so maybe you could potentially have some sort of intensity filter?

[grandalf]

Perhaps a nighttime version intended to work with starlight would work. It could be aimed at Polaris and combine the light from all the stars swirling around it to project the digits.

[tzs]

I wonder of you could do some kind of mechanism so that when the leading edge of the sun turns on a pixel, that also warms up something causing expansion which is used to block an earlier pixel that is still on and you want to turn off?

That might not count as a sundial, though.