[_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.