This is the sort of result you get when you start playing with infinities.
It’s not just impossible it’s INFINITELY impossible! If an atom can’t survive these ages, and even black holes evaporate in time, I can’t see the odds of something intelligent assembling itself before all the particles are too far apart. Iron? Is there a stable element at all? Hydrogen? Perhaps, though even that may decay into pions and positrons… Lead? We don’t have a half-life figure for that, but it must be capable of decay by tunnelling too. Here’s a trick question: what is the heaviest stable element? Not bismuth-209 – that has a half-life of about a billion times the age of the universe. But once it is out, the chance that it, or some other particle will ever get back into the nucleus becomes tiny. If you have anything complex, such as an atom, there is always a finite chance that it will decay as one of the nuclear particles tunnels out of the nuclear energy well. The trouble with all these calculations involving random events over long timescales is that the universe is expanding and so the odds that any two particles are going to be within any given range is dropping all the time.
