h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

Hi Toxx,

Just to let you know that I'm still getting my head around Hilbert and his big hotel. Hope to report back with an amateur mathematical perspective sometime.


In the meantime here's an unrelated paradox for you to sort out.

Mr A: What's the probability of human life on Mars?
Mr B: I have no information, so I say 50%
Mr A: That's fine, so what's the probability of canine life on Mars?
Mr B: Er, 50%
Mr A: Feline life?
Mr B: 50%
Mr A: Bovine life (repeats for 20 types of life)
Mr B: (repeats 50%)
Mr A: So what's the probability of none of these life forms being on Mars?
Mr B: 0.5 times 0.5 times...(repeats 20 times) ... times 0.5, that's about 0.00000095
Mr A: So what's the probability of any of these life forms on Mars?
Mr B: Ah, that's the negative probability of the above, 1 - 0.00000095, that's 0.999999, i.e. as good as certain.
Mr A, so we've proved life on Mars?


Cheers, Icy

OK then, Icy. If you insist on a reply to this daft conundrum - here ya go. You can't equate 'no information' with a 50% chance of something. That leads to all kinds of paradoxes. The circumstances you describe aren't statistically independent. For example, if there is bovine life, then you can bet there's some kind of plant life. So the probabilities don't add to each other but kinda overlap.

toxx

I don't think the 50% chance for "no information" is a problem. The problem is of course the independence of the individual statistics.

A more interesting argument could be:

Is there life in Galaxy A? ... Is there life in Galaxy B,... etc. These are much less likely to be related, as we believe it would take a very advanced level of intelligent development for life to travel between galaxies. (This level of intelligence we cannot comprehend, and therefore cannot quantify)

Whether you start off with 50%, 1% or 0.001% chance of life in Galaxy A, the astronomic numbers of galaxies would surely make life elsewhere in the universe a certainty, by this argument.

Icy

I think the generally accepted mathematical expression is the 'Drake Equation'. I'll just go and look for it...

... Yes, here we are:



Just that 'L' factor could make a big difference to the result.

toxx

Hmmm, I don't like this equation at all.

Quite apart from all the suspected interdependence of the different elements, factors such as "fl = The fraction of those Earth-like planets where life actually develops" make it completely impractical. I would suggest that there can be no statistical significance to this equation until we know of at least 25 planets where life has developed. We know of one. We may never develop the intelligence to discover another.

You don't have to like it, Icy. I'm just surprised that it seems to be new to you! Anyway, I suspect that fl is about unity, so we can forget it for all practical purposes. Neither do I think that relevant planets need to be all *that* Earthlike. There is plenty of room to speculate about these factors and add/subtract as necessary.

toxx