Astronomy without a telescope: The unlikeliness of being

August 1, 2011 By Steve Nerlich

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

Related Stories

Planet spotting

May 9, 2011

The Extrasolar Planets Encyclopedia counted 548 confirmed extrasolar planets at 6 May 2011, while the NASA Star and Exoplanet Database (updated weekly) was today reporting 535. These are confirmed findings and the counts ...

3 Questions: Sara Seager on discovering a trove of new planets

February 4, 2011

NASA’s Kepler -- an orbiting, planet-finding telescope launched in 2009 -- has dramatically increased the discovery rate of planets around stars other than the sun, known as exoplanets. Before Kepler, there were a total ...

Astrophysicists apply new logic to downplay the probability of extraterrestrial life

July 27, 2011

David Spiegel and Edwin Turner of Princeton University have submitted a paper to arXiv that turns the Drake equation on its head. Instead of assuming that life would naturally evolve if conditions were similar to that found ...

Habitable planets and white dwarfs

March 22, 2011

(PhysOrg.com) -- The search for habitable planets similar to Earth has routinely focused around active nuclear burning stars. However, in a recently published paper by Eric Agol from the University of Washington, the idea ...

Weird orbits of neighbors can make 'habitable' planets not so habitable

May 24, 2010

Astronomers hunting for planets orbiting nearby stars similar to the sun are looking for signs of rocky, Earth-like planets in a "habitable" zone, where conditions such as temperature and liquid water remain stable enough ...

Exomoons could be excellent incubators

June 20, 2011

With the arrival of the Cassini–Huygens mission in 2004 to Saturn’s satellite Titan, we terrestrials became acutely aware that similar moons could be orbiting similarly large planets in other solar systems besides ...

Recommended for you

Research offers clues about the timing of Jupiter's formation

December 9, 2016

A peculiar class of meteorites has offered scientists new clues about when the planet Jupiter took shape and wandered through the solar system.

Hubble catches a transformation in the Virgo constellation

December 9, 2016

The constellation of Virgo (The Virgin) is especially rich in galaxies, due in part to the presence of a massive and gravitationally-bound collection of over 1300 galaxies called the Virgo Cluster. One particular member of ...

Khatyrka meteorite found to have third quasicrystal

December 9, 2016

(Phys.org)—A small team of researchers from the U.S. and Italy has found evidence of a naturally formed quasicrystal in a sample obtained from the Khatyrka meteorite. In their paper published in the journal Scientific Reports, ...

Scientists sweep stodgy stature from Saturn's C ring

December 9, 2016

As a cosmic dust magnet, Saturn's C ring gives away its youth. Once thought formed in an older, primordial era, the ring may be but a mere babe – less than 100 million years old, according to Cornell-led astronomers in ...

SOFIA sees super-heated gas streams churning up possible storm of new stars

December 9, 2016

Scientists on board NASA's flying telescope, the Stratospheric Observatory for Infrared Astronomy, or SOFIA, caught sight of roiling material streaming from a newly formed star, which could spark the birth of a new generation ...

Under construction: Distant galaxy churning out stars at remarkable rate

December 8, 2016

Astronomers have used NASA's Chandra X-ray Observatory and other telescopes to show that a recently-discovered galaxy is undergoing an extraordinary boom of stellar construction. The galaxy is 12.7 billion light years from ...

jamesrm
1.6 / 5 (8) Aug 01, 2011
The question is who didn't already know this?

Modeling the bleeding obvious isn't noteworthy
Pyle
1 / 5 (1) Aug 01, 2011
Modeling the bleeding obvious isn't noteworthy

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
3 / 5 (4) Aug 01, 2011
This thread is awfully similar to this one.
http://www.physor...ial.html
dogbert
2.2 / 5 (10) Aug 01, 2011
This thread is awfully similar to this one.

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
3 / 5 (4) Aug 01, 2011
Speaking of goats...

This thread is awfully similar to this one.
Yes, it is.

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

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

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.

The former thread was a better presentation.
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
1.7 / 5 (7) Aug 02, 2011
The modeling that needs to be done is what is the likelyhood of a planet in the habitable zone of tilting on its axis so it pionts directly at its sun. This wooble will limit muticellure life and if it happens frequently low the probability of the development of radio using life. Our one big moon is not a single data point but one example among nine planets. If that is what it takes to creat a stable planet then we are already down to one of nine.
tommytalks77
5 / 5 (2) Aug 02, 2011
Look, I got to point out to this rather obvious question that the authors of such statistical analyses seem to be so embarrassingly not considering:

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
not rated yet Aug 02, 2011
Abiogenesis?? really! What i see in this story could be that even ONE instance of life originating abiogeneticly could *guarantee* that life exists in many places! .. We know that a meteor's internal environment is not such that it would sterilize itself as meteor becomes meteorite.
I thought this 'abiogenesis' relative to earth was a near-dead concept.
Ricochet
not rated yet Aug 02, 2011
So, if life on this planet was the result of playing Let's Make A Deal, can we say definitively that we were the car, or were we the Zonk?

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
2.4 / 5 (17) Aug 02, 2011
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 doesnt 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.

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
2.4 / 5 (9) Aug 03, 2011
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.

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
2.4 / 5 (17) Aug 03, 2011
You missed the point.

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
2.8 / 5 (14) Aug 03, 2011
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.

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.

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
5 / 5 (4) Aug 03, 2011
The Problem is that with your first guess you get a 2/3 chance for a goat, If you guess on one of the two goats and Monty opens the other Goatdoor, the remaining door MUST be the car. Thats why the probability is better for a change but every door got an equal chance. counterintuitive.

Pyle
3 / 5 (8) Aug 03, 2011
You missed the point.
Nope. You're just wrong.
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.
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
3.5 / 5 (8) Aug 03, 2011
btw,
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
1 / 5 (1) Aug 06, 2011
We need more data.

Probability assumes an independent event.
Not sure we can satisfy that form of absolutism yet.
We need more data.
ccr5Delta32
not rated yet Aug 06, 2011
And there's a 50% chance that Monty only has one choice
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
1 / 5 (52) Aug 06, 2011
It's been done ccr5Delta32. http://en.wikiped...mulation

"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
5 / 5 (4) Aug 06, 2011
And there's a 50% chance that Monty only has one choice
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

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
not rated yet Aug 06, 2011
Thanks guys .I'll check em out
Ricochet
not rated yet Aug 06, 2011
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.

I think Monty let someone do that when they brought him back for an anniversary episode.
ccr5Delta32
not rated yet Aug 06, 2011
If I'm wrong I'll have a lot of goats .On to the emphasis of the article ," life form non life " and not 1/4 life 1/2 life .Without some path at least one theorized or a well defined definition of what life is .It seems a little frivolous to use probability statistics on a data set of one without including the possible paths or even an understanding of a destination not so well defined, as it where
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
2.3 / 5 (19) Aug 06, 2011
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.
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.

Nope.

Regardless of whether you stand or switch, the odds remain the same.
FrankHerbert
0.9 / 5 (51) Aug 07, 2011
You are wrong deepsand. Please refer to wikipedia or any number of websites that deal with the issue. Better yet, learn a programming language and make a program that demonstrates the problem. Will you be convinced if you see the simulation with your own eyes?

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.

CLS

RANDOMIZE TIMER

TRIES = 1000000
WINS = 0
PRIZE_DOOR = 0
CHOICE_DOOR = 0
REVEALED_DOOR = 0

FOR A = 1 TO TRIES

PRIZE_DOOR = INT(RND * 3)
CHOICE_DOOR = INT(RND * 3)

REDO:
REVEALED_DOOR = INT(RND * 3)

DO WHILE REVEALED_DOOR = (PRIZE_DOOR OR CHOICE_DOOR)
REVEALED_DOOR = INT(RND * 3)
LOOP

(cont.)
FrankHerbert
0.9 / 5 (51) Aug 07, 2011

IF REVEALED_DOOR = PRIZE_DOOR GOTO REDO
IF REVEALED_DOOR = CHOICE_DOOR GOTO REDO

IF REVEALED_DOOR = 0 THEN
IF CHOICE_DOOR = 1 THEN CHOICE_DOOR = 2
IF CHOICE_DOOR = 2 THEN CHOICE_DOOR = 1
GOTO SKIP
END IF

IF REVEALED_DOOR = 1 THEN
IF CHOICE_DOOR = 0 THEN CHOICE_DOOR = 2
IF CHOICE_DOOR = 2 THEN CHOICE_DOOR = 0
GOTO SKIP
END IF

IF REVEALED_DOOR = 2 THEN
IF CHOICE_DOOR = 0 THEN CHOICE_DOOR = 1
IF CHOICE_DOOR = 1 THEN CHOICE_DOOR = 0
GOTO SKIP
END IF

SKIP:

IF PRIZE_DOOR = CHOICE_DOOR THEN
WINS = WINS 1
END IF

NEXT A

PRINT WINS; " OUT OF "; TRIES
PRINT WINS / TRIES * 100; "% WIN RATE"

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
0.9 / 5 (51) Aug 07, 2011
Evidentially, Physorg does not allow plus signs in posts.

The line that reads "WINS = WINS 1" should have a plus sign between WINS and 1.
bluehigh
1.4 / 5 (11) Aug 07, 2011
@FrankHerbert

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
5 / 5 (2) Aug 07, 2011
He doesn't even need knowledge of programming, all he needs is a friend. You can do it with cards, coins, colored pieces of paper... Have the friend randomly mix up three cards and designate one as the 'car' card. Pick one, your friend should know which is which, so then they pick one of the other cards which is a 'goat' card and offer the switch. Do this twenty times. More convincing yet, use 10 cards, 9 'goat' and 1 'car'. You'd see the effect of switching even faster.

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
2.4 / 5 (14) Aug 07, 2011
The subtlety overlooked by many is that, if your 1st choice is the correct one, there a 2 empty doors to be revealed; if your 1st choice is wrong, only 1 empty door can be revealed.

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
2.5 / 5 (13) Aug 07, 2011
Final sentence in above should read
"Total payoff = 0 plus 1/3 = 1/3."
brianweymes
not rated yet Aug 07, 2011
Why are you multiplying it by 50%? You're arguing switching doesn't change probabilities?
FrankHerbert
1 / 5 (53) Aug 07, 2011
@bluehigh,

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

The subtlety overlooked by many is that

No actually, it's your position that is of "the subtlety overlooked by many" variety.
ccr5Delta32
not rated yet Aug 07, 2011
@ FrankHerbert Here's a selection in various script styles for comparison
http://rosettacod..._problem
deepsand
3.3 / 5 (14) Aug 07, 2011
With very little sleep over the past week, and none of it quality, been suffering severe sleep deprivation. And, ongoing problems with this site not promptly rendering posts with the Edit function active have made for frustration with mistakes going uncorrected.

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
1 / 5 (3) Aug 07, 2011
@Avitar

If that is what it takes to create a stable planet then we are already down to one of nine.

I tend to agree.
brianweymes
5 / 5 (2) Aug 07, 2011
Right, one's chances of success after switching go up to 2/3. I don't know what to make of the programs giving 50% results, something is in error. That would happen if you switched half the time, but not all the time.
FrankHerbert
0.8 / 5 (51) Aug 07, 2011
Yeah brianweymes, my program is faulty. Every so often "monty" reveals the "door" with the "prize" behind it rendering winning impossible in the scenario. I wasn't able to fix this as I had to go to sleep and my knowledge of QBASIC is rusty.
bluehigh
1 / 5 (4) Aug 08, 2011
I don't know what to make of the programs giving 50% results, something is in error.

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.

4.2 / 5 (5) Aug 09, 2011
@Bluehigh:
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
5 / 5 (4) Aug 09, 2011

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
4.2 / 5 (5) Aug 09, 2011
hush1
4 / 5 (4) Aug 09, 2011
The thread commentary is astronomical. I had an opportunity to discuss this (the doors) five years ago with a professional card player - the best in his field and his country. He gave up a mathematician's career to turned to professional card playing.
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
1 / 5 (5) Aug 10, 2011
@Pyle

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
1.4 / 5 (9) Aug 10, 2011

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.
4.4 / 5 (7) Aug 10, 2011
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...

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.
4.4 / 5 (7) Aug 10, 2011
Such arrogance from a dimwit.
You know, I'm certainly not above lobbing insults at those who've clearly earned it, but I have to say: this SUCKS because, IMO, it's bleedingly obvious that niether of you are dimwits or incabable of intelligent conversation.
When their are only two doors remaining and you have to choose one then quite clearly its a 50/50 bet.
Ah ha! But you *LOCKED IN* the 1/x probability of the car being behind one of the doors when you picked that door because Monty CAN'T open THAT ONE. Thus, you're performing an unwarranted reasignement of probs based solely on dividing 100% by the number of doors left closed after Monty opens the remaining doors. The reaming doors DON'T have to have equal probability. That's the counterintuitive crux of it.
To rely on an urban myth propagated by...wikipedia is astounding!
Bluehigh, no one has to rely on anything: you can try this yourself. Use a friend and full deck of cards with, say, the ace of spades as the car.
4.4 / 5 (7) Aug 10, 2011

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.
Thanks, and yes, sometimes it is. But I really would like to understand the source of your conclusion because it is so common! So forgive me for not letting you off the hook so easily :)

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:
When their are only two doors remaining and you have to choose one then quite clearly its a 50/50 bet.

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).
4 / 5 (4) Aug 10, 2011
The reaming doors DON'T have to have equal probability.
Reaming doors! That actually sounded like an inslut (insult!). Was *supposed* to be "remaining" doors.
4.3 / 5 (6) Aug 10, 2011
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.

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
4.3 / 5 (6) Aug 10, 2011
Well, for one thing, what's he basing the 9 on? Is he including Pluto? If so than that's 2 of 9.
Gawad, did you find life on Pluto and not tell us? Or did your 2 have to do with axis tilt?

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.

4.3 / 5 (6) Aug 10, 2011
Gawad, did you find life on Pluto and not tell us?
Shuuussh! We're not ready to publish yet!
Or did your 2 have to do with axis tilt?
O.k., yeah, it was about planets needing large Moons to stabilize their axial tilt. Yeah, yeah, that's it! ;)

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
1.4 / 5 (10) Aug 10, 2011

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).

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
3.6 / 5 (14) Aug 14, 2011