[dryrun]

Funnily enough, I have the opposite view: given the amount of stars and of earth like planets in the universe, probabilistically speaking there is bound to be a random chance where two instances of life have the same DNA without ever being in contact.

Disclaimer: I'm bad at maths and good at dreaming.

[anonymouskimmer]

:D Yes, you are. :)

The bare simplest genomes are viral genomes about 1000 bases long. These can only operate in environments created by more complex genomes. But even taking them, the theoretical diversity in a genome 1000 bases long, using the 4 canonical nucleic acids, is 4^1000. The number of atoms in the entire universe is around 10^80 (https://educationblog.oup.com/secondary/maths/numbers-of-ato... ).

There's a lot of complexity here: other life may use other nucleotides; those atoms and bases are constantly being rearranged; many base changes are relatively silent - they don't materially matter; etcetera.

I don't know how to calculate all of the rest of these factors, but I think the odds are more than astronomical.

[borissk]

>> The number of atoms in the entire universe is around 10^80

This is incorrect. It's an unsolved question in modern physics if the universe is finite or infinite. Even if it's finite most theoretical physicists believe that visible universe (94 billion light years across) is only a small piece of a far larger universe - so there are probably far more atoms.

If the universe is infinite it may be that there are infinite number of copies of every living organism on Earth out there.

[anonymouskimmer]

At that point aren't we getting into the idea of a multiverse, and not a universe anymore? We have no non-hypothetical knowledge of what exists beyond the limits of the universe as it descended from what we can still see of the radiation shortly after the Big Bang. However, from that radiation, can't we get a ballpark figure for the atomic limits of the Big-Bang-Universe?

[borissk]

No, the different multiverse hypotheses are something different. The size of "our" universe is unknown, we can can see a sphere with a diameter of 94 billion light years. How much is there beyond that sphere is a research topic. No light from beyond the sphere has reached us during the lifetime of the universe.

[anonymouskimmer]

This is about inflation, right? We don't know how much the universe inflated after the big bang, just that it did.

[_Microft]

> I don't know how to calculate all of the rest of these factors, but I think the odds are more than astronomical.

OK, let's do this then. Here we will approximate the ratio 4^1000/10^80:

x = 4^1000 / 10^80

ln(x) = 1000 * ln(4) - 80 * ln(10) // You know your logarithm calculation rules, right? Right?!

ln(x) = 1386 - 184 // Who needs decimal places anyways? ;)

ln(x) = 1202

x = 10^522

[dryrun]

So you're telling me that there _is_ a chance! ;)

And I'm very sad to (re?)learn this finite number of atoms in the universe, that's quite underwhelming for something expanding all the time.

[anonymouskimmer]

The number only seems small because we use notation to make it seem small.

Most combinations of nucleotides aren't functional, or even capable of being synthesized by natural processes. This limits what can be created quite a bit. The true odds are still extremely high, but not nearly as high as these calculations guess.

[anonymouskimmer]

> You know your logarithm calculation rules, right? Right?!

Eh, at one point I did. I'll take your word for it. It seems familiar.

Now factor in number of rearrangements since the universe started. Or heck, let's keep it simple to the last 4.5 billion years.

I count about 30 atoms in a nucleotide, so X is a bit more than 10^523.

Let's say 2 rearrangements per day (this will vary dramatically, but I have to pull some number out of a hat). Over 4.5 billion years that's on the order of a bit more than 10^12. so X is around 10^511.

Yep, still more than astronomical.