Astronomy without a telescope: The unlikeliness of being

The question is who didn't already know this?

Modeling the bleeding obvious isn't noteworthy

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.

This thread is awfully similar to this one.
http://www.physor...ial.html

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.

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.

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.

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?

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.

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.

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.

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.

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.

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.

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.

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.

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.

We need more data.

Probability assumes an independent event.
Not sure we can satisfy that form of absolutism yet.
We need more data.

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

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.

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.

Thanks guys .I'll check em out

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.

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 ?

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.

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.)

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

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.

@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.

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.

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.

Final sentence in above should read
"Total payoff = 0 plus 1/3 = 1/3."

Why are you multiplying it by 50%? You're arguing switching doesn't change probabilities?

@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.

@ FrankHerbert Here's a selection in various script styles for comparison
http://rosettacod..._problem

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.

@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.

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.

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.

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.

@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?

Gawad: You can't say we didn't try. On both threads.

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 ...

Oops. Sorry deepsand. I read your last post and forgot about it before my last comment.

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.

@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.

@Gawad

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.

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.

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.

@Gawad

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).

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.

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).

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.

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.

@Gawad

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.

Oops. Sorry deepsand. I read your last post and forgot about it before my last comment.

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.