cosmology - Is observable universe an explanation against Olbers' paradox?

First of all, let me tell you that I'm not a physicist but rather a computer scientist with a mere interest in physics at nowhere near a professional level so feel free to close this question if it doesn't make any sense.

I remember a physicist friend mentioning me about an argument about the finiteness of the universe. I have looked it up and it turned out to be Olbers' Paradox.

We computer scientist like to use astronomical numbers to help us imagine the complexity of an algorithm. One of the most common one is the number of atoms in the Observable Universe (which we take as $10^{80}$) so I have a crude understanding about the observable universe concept.

I had known these two for some time hence I woke up with the dilemma today. So my question is, how come it can be argued that universe is finite just because it is dark if we know that we can only observe a finite portion of it? Can't it be the case that the universe is infinite even if the sky is dark because not all the light from all the stars reach the earth?

I have searched this a little bit but I think I need an explanation in simpler terms (like popular physics). A historical perspective would also be welcomed.

Answer

So my question is, how come it can be argued that universe is finite just because it is dark if we know that we can only observe a finite portion of it?

You are mixing two theories here. Olbers paradox has as a basic theory a static infinite in space and time universe. The dark night sky means that either the universe is not static, or has a beginning, or has a finite extent in space. Or all three.

Can't it be the case that the universe is infinite even if the sky is dark because not all the light from all the stars reach the earth?

A different model than a static infinite in space and time universe is needed in this case, an infinite universe that appeared at a time t=0, for example, so that the light of distant stars would not have reached us by now. But there are more data than the dark night sky to be fitted by a cosmological model and the available data fit the Big Bang model quite well:

the Big Bang occurred approximately 13.75 billion years ago, which is thus considered the age of the Universe. After its initial expansion from a singularity, the Universe cooled sufficiently to allow energy to be converted into various subatomic particles, including protons, neutrons, and electrons.