[wahern]

Nobody can tell you without pulling numbers out of thin air. That's the point. The only thing that can be said is that the probability of intelligent life arising is greater than 0, which follows from our own existence. Beyond that, any claims about the likelihood of intelligent life are just 20th and 21st century versions of "there must be a God because the universe couldn't have arisen by chance."

[omnicognate]

Strictly speaking our own existence doesn't even tell us the probability is greater than zero. For an event to have probability zero doesn't imply it can't occur. If a number is chosen from a uniform distribution on the reals between zero and one, whatever the result is the probability of that exact result occurring was zero.

[dotancohen]

  > For an event to have probability zero doesn't imply it can't occur.

The distinction in meaningless. We exist, ergo intelligent life can develop in this universe.

[omnicognate]

> The distinction in meaningless. We exist, ergo intelligent life can develop in this universe.

I didn't say anything contrary to this. I was just pointing out an interesting detail about probability theory.

It's impolite to edit your comment in such a way as to turn its existing replies into non-sequiturs. For the record, this comment initially cast doubt on the claim about zero probability events, hence the reply saying it was correct.

[danbruc]

It is correct, if you split 100% across infinitely many possible outcomes, each outcome will have probability zero, still one of the possible outcomes will occur.

[rsj_hn]

Doesn't this require a continuum? I don't think you get there with a measure on a countable set. That would make this an unphysical argument, IMO.

[omnicognate]

Yes, it requires uncountability. It could be that physics is ultimately best modelled with countable sets, but that hasn't been established and our current best physical theories are certainly full of uncountability.

The distinction between "surely" and "almost surely" [1] is "just" a curiosity about probability theory though, albeit a rather fundamental one, and I only brought it up as such. It's interesting to think about, and if you do so it quickly brings you up against deep philosophical questions about what probability means.

[1] https://en.m.wikipedia.org/wiki/Almost_surely

[danbruc]

Just out of curiosity, is there are short answer why it requires uncountability? Naively something like pick a random natural number would also seem to lead to probability zero. I can see that pick a random natural number might be problematic, how would you do this? Pick on digit and then with some probability either stop or continue and pick another digit, but it is at the very least not obvious that one could make this work without larger numbers just having smaller and smaller probabilities and there might also be issues with termination. On the other hand it is not obvious to me why one could not work with uniform distributions over the set [0, n) and then look at the limit as n goes to infinity.

[rsj_hn]

> It could be that physics is ultimately best modelled with countable sets

That's not my argument. The issue isn't whether physics requires a continuum to model reality -- I'm certain it does. But just because a continuum is required to model the universe doesn't mean that the observables in the universe actually form a continuum. For that, I am certain that they don't.

[mensetmanusman]

Infinity times zero might be meaningless in a quantized reality

[mensetmanusman]

The universe became conscious in the form of man and asked ‘who made me’ so it’s the universe arguing with the universe about a creator :)