The stars are still there in the daytime, but then you don't see them because the sky is then so brightly blue (at least, if it isn't cloudy). The blue of the sky is light that comes from the Sun at that was on its way to a different place from where you are, but that hit an air particle along the way and then came to you after all. Scientists call this "scattering of light". Such collisions go easiest with blue light, and that's why the sky is blue. The sky is much less bright than the Sun itself, but is yet much brighter than the stars, and that's why you can't see any stars during the day.
It does not help if you reduce the amount of sky that you see, for example by looking up a smoke stack, because that does not reduce the brightness of the sky next to the star nor increase the brightness of the star, so it does not make the star more visible by comparison.
You could see the star only if you reduced the amount of sky so much that you could not tell anymore where the sky begins and the star ends, but then there'd be a very good chance that no bright star at all would happen to pass through the tiny window when you were looking, and it would take a star only a second or two to pass through that window. It seems hardly worth the effort to go to all that trouble.
But there is a better way. You can reduce the apparent brightness of the sky by looking at it through a magnifying optical instrument, such as a telescope. If you look at the sky through a telescope, then a particular patch of sky looks bigger, so its brightness seems to be spread over a larger amount of sky and is lower. A star still looks like a point, so its brightness is not spread out. So, if you look at the sky with magnification, then the sky looks less bright compared to the stars. If the magnification is large enough, then you can see stars during mid-day.
I don't know off-hand how large a magnification you need, but it can't be all that large, because it seems that you can sometimes see Venus (at magnitude −4) at midday even without magnification, if you know where to look.
It does not help if you reduce the amount of sky that you see, for example by looking up a smoke stack, because that does not reduce the brightness of the sky next to the star nor increase the brightness of the star, so it does not make the star more visible by comparison.
You could see the star only if you reduced the amount of sky so much that you could not tell anymore where the sky begins and the star ends, but then there'd be a very good chance that no bright star at all would happen to pass through the tiny window when you were looking, and it would take a star only a second or two to pass through that window. It seems hardly worth the effort to go to all that trouble.
But there is a better way. You can reduce the apparent brightness of the sky by looking at it through a magnifying optical instrument, such as a telescope. If you look at the sky through a telescope, then a particular patch of sky looks bigger, so its brightness seems to be spread over a larger amount of sky and is lower. A star still looks like a point, so its brightness is not spread out. So, if you look at the sky with magnification, then the sky looks less bright compared to the stars. If the magnification is large enough, then you can see stars during mid-day.
I don't know off-hand how large a magnification you need, but it can't be all that large, because it seems that you can sometimes see Venus (at magnitude −4) at midday even without magnification, if you know where to look.
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