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A model with any predictions on the probability of abiogenesis (the formation of first life from random chemical processes and then RNA) is, so far, hard to come by. But the consensus is that abiogenesis is extremely improbable, although that's only based on the mechanisms and conditions we could think of.

Let me expand on the numbers. This paper from 2020 gives a really generous goalpost of 40–100 nucleotides for a sequence to be self-replicating.

nature.com/articles/s41598-020

Compare this to the minimal genome - the smallest set of genes for life to exist and propagate. The minimal genome is often considered to be 256 genes. A gene is typically 1000 or more nucleotides long, and there is some space in between, so 256 genes would amount to about 300,000 nucleotides. So the difference in definition is crucial. Not taking any fancy processes into account, just purely statistically, there's "no way" of the minimal genome occuring. The odds are one in 10 to the 90,000 power. I wanted to say, that's like winning a lottery on a cosmic scale - for example, if every solar system in the Universe had humans and everyone bought a ticket, but it's far from that. The probability is so low it's indescribable.

Nevertheless, if we suppose that a self-replicating sequence and an arbitrary amount of time is all we need, we may consider a length of 40–100 nucleotides.

On the cosmological side of calculations, it is easier to have some estimates. Totani argues that while the current number of stars in the observable universe is estimated to be approximately 10 sextillion (or 10^22), the number of stars in a model that accounts for universe inflation may be over 10 googol (or 10^100). "If that is the case, that’s a huge petri dish within which RNA, and life, could form," says an article, but I wouldn't be so optimistic. The cited research author himself says that the sequence length must be shorter than ~20 nucleotides for abiogenesis to occur on a single(!) terrestrial planet, but self-replicating activity is not expected for such a short RNA. Therefore, if extraterrestrial organisms of a different origin from those on Earth are discovered in the future, it would imply an unknown mechanism.

So, for the sake of understanding, there is hope in researching more on the mechanism and chemistry, in a wider set of conditions. But in terms of traveling to see our living brethren, that would never be possible. The theory of relativity forbids us from ever leaving our observable universe anyway.

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