History has proved time and again that mathematical modelling is no substitute for a telescope (or other data collection device). Nonetheless, some theoreticians have recently put forward a statistical analysis which suggests that life is probably very rare in the universe – despite the apparent prevalence of habitable-zone exoplanets, being found by the Kepler mission and other exoplanet search techniques.

You would be right to be skeptical, given the Bayesian analysis undertaken is based on our singular experience of abiogenesis – being the origin of life from non-life, here on Earth. Indeed, the seemingly rapid abiogenesis that occurred on Earth soon after its formation is suggested to be the clinching proof that abiogenesis on habitable-zone exoplanets must be rare. Hmm…

Bayes theorem provides a basis for estimating the likelihood that a prior assumption or hypothesis (e.g. that abiogenesis is common on habitable-zone exoplanets) is correct, using whatever evidence is available. Its usage is nicely demonstrated in solving the Monty Hall problem.

Go here for the detail, but in a nutshell:

There are three doors, one with a car behind it and the other two have goats. You announce which door you will pick – knowing that it carries a 1/3 probability of hiding the car. Then Monty Hall, who knows where the car is, opens another door to reveal a goat. So, now you know that door always had a zero probability of hiding the car. So, the likelihood of the remaining door hiding the car carries the remaining 2/3 probability of the system, since there was always an absolute 1/1 probability that the car was behind one of the three doors. So, it makes more sense for you to open that remaining door, instead of the first one you picked.

In this story, Monty Hall opening the door with a goat represents new data. It doesn’t allow you to definitively determine where the car is, but it does allow you to recalculate the likelihood of your prior hypothesis (that the car is behind the first door you picked) being correct.

Applying Bayesian analysis to the problem of abiogenesis on habitable-zone exoplanets is a bit of a stretch. Speigel and Turner argue that the evidence we have available to us – that life began quite soon after the Earth became habitable – contributes nothing to estimating the likelihood that life arises routinely on habitable-zone exoplanets.

We need to acknowledge the anthropic nature of the observation we are making. We are here after 3.5 billion years of evolution – which has given us the capacity to gather together the evidence that life began here 3.5 billion years ago, shortly after the Earth became habitable. But that is only because this is how things unfolded here on Earth. In the absence of more data, the apparent rapidity of abiogenesis here on Earth could just be a fluke.

This is a fair point, but a largely philosophical one. It informs the subsequent six pages of Spiegel and Turner’s Bayesian analysis, but it is not a conclusion of that analysis.

The authors seek to remind us that interviewing one person and finding that she or he likes baked beans does not allow us to conclude that most people like baked beans. Yes agree, but that’s just statistics – it’s not really Bayesian statistics.

If we are ever able to closely study an exoplanet that has been in a habitable state for 3.5 billion years and discover that either it has life, or that it does not – that will be equivalent to Monty Hall opening another door.

But for now, we might just be a fluke… or we might not be. We need more data.

**Explore further:**
Planet spotting

## jamesrm

Modeling the bleeding obvious isn't noteworthy

## Pyle

Sure it is. The problem here is that nothing was modeled. It is a lot of talk about nothing.

We are here. At least holographically. Maybe. We've never looked anywhere else so we have no data. All we can do is speculate.

I personally hope that Nerlich is right and we have a higher chance of getting a goat than a teapot.

## jsdarkdestruction

http://www.physor...ial.html

## dogbert

Yes, it is. Both threads acknowledge that a single instance of something forms no basis for determining the probability of that thing anywhere else.

The former thread was a better presentation. There is no statistical analysis, Bayesian or otherwise, with only one data point.

## Pyle

But further on that point, both articles are referencing the recently published Spiegel and Turner paper: http://arxiv.org/abs/1107.3835

Yes, one data point with no additional points, positive or negative to add to the population doesn't provide any support for a statistical analysis. I'd argue that we have much more information than one data point, given our knowledge of chemistry, biology, physics, astrophysics, etc. However, I'll concede that any number we throw into the Drake equation for the likelihood of abiogenesis is a guess.

WHAT? Better than the king of wit, Nerlich??? No way. Not a single mention of goats in the previous article. The comments had a head start, so let's wait and see.

## Avitar

## tommytalks77

So, if you interview a random person if he/she likes baked-beans and the answer is positive it doesn't mean most people also like baked-beans, that would be an absurd presumption but you can most certainly count on finding out that at least SOME other human beings would posses the same chemistry in their gustative glands that would make them recognize the same pleasure in the taste of such baked beans.

Nobody ever said that life must have arisen in most places of the universe... it only takes a tiny, very very ultra tiny percentage of places in the universe that have seen life originating itself in order for us not to be (I feel ridiculous even saying that) alone in the universe...

I mean, how obvious is that?

## tkjtkj

I thought this 'abiogenesis' relative to earth was a near-dead concept.

## Ricochet

Now, there was another more scientific approach applied to the uniqueness of our planet's situation in this universe involving our moon. The fact that it's larger than (supposedly) most other h-zone planets along with its proximity and origin, suggests that it's because of its role in the stabilization of our axis that makes it unlikely to happen in other places around the universe. Yes, it can drive the likelihood of other planets containing sustained life down quite a bit, but there should be other planets out there with a stable axis, whether naturally or stablized by another body. It lowes the likelihood, but doesn't kill it. If nothing else, it can help focus our efforts.

## deepsand

Poppycock.

Knowing that Door #3 is the wrong one simply leaves Doors #1 & #2 with a 50% probability each.

Nothing is gained by changing your choice.

## Pyle

No. If you picked door #1 there is a 2/3 chance the prize is behind doors 2 or 3. If Monty opens one of those doors, there is still a 2/3 chance you are wrong.

## deepsand

Knowing that a particular door is the wrong one does not make the odds of your original pick being any the worse, as was stated by the article.

And, after the one door is opened, the 50% probability is, not the original probability, but that relative to the newly created case of 2 closed doors.

I.e., contrary to the article, opening a door does not provide any new information that would make your changing your choice beneficial.

## Excalibur

Once Door 1 is opened, and found to be empty, there is now a 100% chance the prize is behind doors 2 or 3, each with an equal 50% chance of being the right one.

This is different from the initial probabilities involving 3 doors as it is now a different situation, with a different number of doors.

While it does not change the fact that you still had a 1 in 3 chance of picking the right door - 50% of 2/3 = 1/3 - it is also the case that the article, as written, wrongly claimed that the new knowledge somehow made it more likely that your original choice was the less likely, as pointed out by Deepsand.

## Eoprime

## Pyle

Kind of. The odds of your original pick doesn't get any worse. You still have a 1/3 chance of winning if you don't switch from door 1.

There was a 2/3 chance that 2 or 3 held the car after you picked and BEFORE Monty picked. Monty ALWAYS picks a goat. This provides information about what is behind doors 2 and 3, but nothing about what is behind door 1. After Monty opens a door your selection is still a 1/3 chance of being the car. The unopened door remaining, however, has 2/3 chance of winning.

@Excalibur:

The article is correct. Originally all three doors had equal chance of being the car. After your selection and the subsequent revealing the probabilities shifted and your selection is now less likely than the other remaining door.

## Pyle

Three of you owe me apologies. It isn't nice to downrate somebody when they are right. Especially since I didn't insult or ridicule anybody. Which is quite out of character for me I might add.

Anyway, Nerlich is pretty much dead on that Bayesian analysis is useless for evaluation of the abiogenesis term in Drake's equation. That makes the whole conversation about nothing really, but at least everybody got a statistics lesson.

## hush1

Probability assumes an independent event.

Not sure we can satisfy that form of absolutism yet.

We need more data.

## ccr5Delta32

It could be set up as a simple computer model

Generate a random number 1 .2 or 3 ,, assign C G G

repeat for choice : Enter Monty

compare statistical results for change or not

## FrankHerbert

"After the Monty Hall problem appeared in Parade, approximately 10,000 readers, including nearly 1,000 with PhDs, wrote to the magazine claiming that vos Savant was wrong. Even when given explanations, simulations, and formal mathematical proofs, many people still do not accept that switching is the best strategy."

It's not hard to get, just counter-intuitive. Any of the doubters could make a program himself to test it. The program could probably fit in one of these posts.

Pyle is certainly right, and I agree he's owed an apology.

Also you'll notice on the new Let's Make a Deal with Wayne Brady, contestants ARE NOT offered the opportunity to switch doors once the first one is revealed. This is precisely because the problem has become so well known.

## brianweymes

Already been done. Pyle is correct. If you don't believe him or the logic, run the experiment yourself or check out the wikipedia page. I admit it's counter-intuitive at first.

To make it more intuitive imagine there are 1,000,000 doors. You pick one. The chance of being correct is 1/1,000,000. The host opens 999,998 doors with goats behind them and then offers to switch. In this case, if you switch the probability of that other door the host didn't open being the car door is 999,999/1,000,000.

## ccr5Delta32

## Ricochet

I think Monty let someone do that when they brought him back for an anniversary episode.

## ccr5Delta32

I could argue from a historical bases as that we've being very wrong in the past .This is a trait in us that is not likely to be discontinued any time soon . We hold on to this "special" lable and it injects a bias ,life may indeed be inevitable .Do we have any good reason to believe it's not ?

## deepsand

Nope.

Regardless of whether you stand or switch, the odds remain the same.

## FrankHerbert

I actually went through the trouble of writing such a program for you. The code is pretty sloppy but I'm pretty sure it accurately encapsulates the problem. It's in QBASIC.

(cont.)

## FrankHerbert

I've ran the simulation several dozen times (each time performing the problem 1,000,000 times). The win percentage has never strayed beyond 1% of 50%. Please download QBASIC and run the program if you are still skeptical.

5th line from bottom should read WINS = WINS 1

## FrankHerbert

The line that reads "WINS = WINS 1" should have a plus sign between WINS and 1.

## bluehigh

Maybe I missed it in the code but do you ensure that the revealed door always has a goat and then exclude that door from the simulation. (because if the revealed door has the prize then no amount of choice change affects the outcome).

Monty knows which door(s) to reveal (1 of 2 have goats) so the expression REVEALED_DOOR = INT(RND * 3) is incorrect. Monty can only choose between 1 of 2 doors of which he knows have Goats.

Perhaps you could retry your simulation by selecting the revealed door from one of only 2 known doors that contain goats. Then exclude that door from the simulation because it is no longer an available choice.

## brianweymes

Thinking more about it I don't know what this has to do with astronomy and the probability of aliens. Seems a misapplication of the idea.

## deepsand

1/3 chance 1st choice correct x 0% chance correct if switch = 0 payoff.

2/3 chance 1st choice incorrect x 50% chance correct if switch = 1/3 payoff.

Total payoff = 0 1/3 = 1/3.

## deepsand

"Total payoff = 0 plus 1/3 = 1/3."

## brianweymes

## FrankHerbert

I attempted to do this but it seems like I goofed somewhere. I had some odd glitch which led to some odd code which led to an odd result. Anyway, it still achieves a probability of 50% and there's no cheating. If anything the glitch is handicapping it. I'm sure someone around here could do a better job but it seems like deepsand will not be convinced.

@deepsand

No actually, it's your position that is of "the subtlety overlooked by many" variety.

## ccr5Delta32

http://rosettacod..._problem

## deepsand

While trying in vain for sleep, it came to me that my most recent post was in error, that the 2nd line should have read as follows:

(1/3 chance 1st choice correct) x (0% chance correct if switch) = 0 payoff.

(2/3 chance 1st choice incorrect) x (100% chance correct if switch) = 2/3 payoff.

Total payoff = 0 plus 2/3 = 2/3.

The chance of winning if switch are actually TWICE that of not switching.

Both my original contention that it remains at 1/3, and the one offered by others that it becomes 1/2 are in error.

I was initially led astray by having erroneously conflated the situation with a similar 3-card game that I played many years ago, one in which I made even odds bets on what were actually 2:1 odds.

## bluehigh

I tend to agree.

## brianweymes

## FrankHerbert

## bluehigh

The error is in believing that switching alters the probability. When one door is eliminated then two doors remain. At that point you can cease to consider the eliminated door. Two doors then exist of which one has the prize. 50/50 chance. Same with coins, just remember to put the revealed coin aside then choose 1 of 2.

Frank well done, at least you make an effort.

In any case even if the chances of finding life are 1 in a billion planets that probably leaves hundreds of billions of planets with life and perhaps even some goats.

## Gawad

The way this has been presented in this thread so far has been in terms of "changing" or altering probabilities. Maybe that's not the most intuitive way to put it after all. In a sense, you are right that the probablities don't "change" and yet that's actually why you're better off switching.

Thing of it this way: Monty will never open the door you pick or the one with the car (if you picked the car, those two happen to be the same door). He will always open only doors with goats. This is true even in "extended" versions of the game with 100 or 1 000 000 doors.

Say there are 100 doors. You pick ONE. There is a 1% chance you picked the car and a 99% chance the car is behind another door. Monty opens all the doors except the one you picked and ONE other door. There is still a 1% chance you originally pick the car, and a 99% chance the car was behind one of the other doors.

Now...your door is still closed and so is that last one Monty didn't open. WOULD YOU SWITCH?

## Pyle

Oh well. Make a note not to bother entering an intelligent conversation with bluehigh and deepsand to the list that already includes paul and doggie and kevin and o'my tumor and ...

## Pyle

## hush1

Our conclusion five years ago to the three doors problem?

After two hours of discussion we unanimously agreed that switching is the best strategy. The thread let me relive and rehash the past. Many thks to all around. Memory lane.

## bluehigh

Such arrogance from a dimwit. When their are only two doors remaining and you have to choose one then quite clearly its a 50/50 bet. To rely on an urban myth propagated by unqualified contributors to that deposit of popular opinion called wikipedia is astounding! Shame on you for bringing logic and the scientific method into disrepute.

## bluehigh

your last comment is reasoned argument and i appreciate you maintaining patience without resorting to abuse. sometimes it is better to agree to disagree and move forward.

Whats incorrect about Avitar comment that we are down to the odds of 1 in 9 for planetary life based on our solar system being an example? Seems like valid data to me.

## Gawad

I think that's a little unfair. The latter characters are, IMO, ill willed, not the former.

Bluehigh's and Deepsand's (initial) reaction are actually normal. I.e., they are the common, instinctive reactions to this problem, even from highly educated people without a math background, esp. in stats and probability. I'm not sure why, but would really like to know! It's almost as if the doors opening "resets" the probabilities for them given the opportunity to "switch" (to choose again); as if they recalculate their probability of having chosen the car based on the number of doors that are still closed after N-2 doors open and they throw out the past probability distribution they actually had to work with. As if they forget that when they picked a door they "locked in" *its* probability because Monty can't open that one.

## Gawad

## Gawad

I know you would be correct in reassigning a 50/50 prob distribution if Monty could open your door at RANDOM to give you a fresh pick from two remaining doors (one with the car and one with a goat). Is you conclusion based on the idea that Monty is offering you a fresh random choice? He's actually not, but it certinaly seems that you're basing yourself on that idea when you write:

The problem is not just that Monty is opening a door or doors, but rather that he can't open the 1 you picked (or the car's).

## Gawad

## Gawad

Well, for one thing, what's he basing the 9 on? Is he including Pluto? If so than that's 2 of 9.

But even then, this is one factor among many and it ASSUMES that complex life (maybe it doesn't even have to BE multicellular) is more probable if a planet's axis is very stable. Or that planets without large moons can't be. Venus's axis appears to be stable, if odd. And, as a case in point, if an atmosphere is thick enough to stabilize temps, even a wandering axis may not be such a big deal.

I.e., while it's not a bad point, we simply don't know enough about extra-solar systems to know what is really common and how "unique" or "special" we are. Or not. Or under what particular conditions life is favoured (within limits, obviously).

## Pyle

To the intelligent conversation point. My observation of this thread has been that lots of intelligent points have been made on both sides. At the point I made that comment I felt that the continued unrelenting behavior of bluehigh (again, oops on deepsand) showed that he wasn't listening to the arguments against his position. You can't have an intelligent conversation if one side is dismissing the other's position without consideration.

Gawad, bravo to you for your reasoned discourse. Shame on me for being the troll, this time anyway. I may not be the brightest bulb in the box, but I have my wits about me, mostly, at least when it comes to first year undergrad statistics.

## Gawad

And though it is a 2nd data point for THAT, it may not be relevant after all as it's probably not doing much for life out in the Kuiper Belt.

I wasn't crusing for a pat on the back really, it's just the sense I got from Bluehigh was that he was growing increasingly frustrated at not connecting with arguments from you, Frank and Brian (or afterwards probably mine for that matter). I guess it helps that I know his conclusions are absolutely the norm. I'll give folks a lot of leeway unless I think they really are being mischievious, and I wasn't getting that here.

## bluehigh

Ah ha ... I see the light. Now I understand. This is not a new discussion for me I have always remained puzzled how people could think other than its a 50/50 chance and now I understand. Thank you.

@Pyle

I get annoyed when the comments descend into slanging matches or negativity without good argument and on this occasion I stepped into the gutter myself. Indeed I was frustrated not being able to understand how it could not be a 50/50 chance and now with that added info I am once again a happy camper.

## deepsand

No problem; unintended stuff happens.

And, the nature of this site, with thread posts compressed into a half-screen, quotes not attributed to the member being quoted, a tiny little 6 lines viewable box for entering posts, etal., makes it all too easy to lose track of who said what when and where, with the result that frustration abounds.