Menu Bar
Common Sense Is Worthless In Science
Needs Plugin: Flash |
Not Working?
Retweet This
Share on Facebook
Email This
Common sense is lauded as a virtue. But is it really?
Only within the narrow range of experiences we grow up with. It's often more harmful than helpful in the scientific process.
How far should we trust common sense?
When does it steer us wrong?
Why do we find common sense so appealing?
Please feel free to share in the comments your own favorite counter-intuitive scenario that is nevertheless true.
Only within the narrow range of experiences we grow up with. It's often more harmful than helpful in the scientific process.
How far should we trust common sense?
When does it steer us wrong?
Why do we find common sense so appealing?
Please feel free to share in the comments your own favorite counter-intuitive scenario that is nevertheless true.
Aug 31, 2009 2:52 AM
Re: Common Sense Is Worthless In Science
Common sense tells me that this video could not be more boring but then I remembered my high school chemistry class and realized that science could prove otherwise.
By: Chewbot
Re: Common Sense Is Worthless In Science
If the car was really in door number one then common sense is superior to probability bullshit. I can't stand arrogant mathematicians.
By: digitalprime
Re: Common Sense Is Worthless In Science
Ok so if the car was really in door number 2 then you would consider common sense inferior? You know, just using your reasoning. Personally I think neither situation would prove it one way or the other, but that's just me.
It's not bs man, just a little tricky to understand the reasoning if you don't think about it for a bit:
http://mathforum.org/dr.math/faq/faq.monty.hall.html
If there are three doors all with equal chance of having the car. The one you choose has 1/3 chance of being the right door. There is 2/3 chance the car will be in the other two doors. When the guy removes one of the doors from the 2/3 set then the 2/3 is reassigned to the remaining of the two doors. When you say that it's 50:50 you are acting like the 1/3 stat never existed for each door.
Not saying I liked the video though. I think his point was poorly presented.
It's not bs man, just a little tricky to understand the reasoning if you don't think about it for a bit:
http://mathforum.org/dr.math/faq/faq.monty.hall.html
If there are three doors all with equal chance of having the car. The one you choose has 1/3 chance of being the right door. There is 2/3 chance the car will be in the other two doors. When the guy removes one of the doors from the 2/3 set then the 2/3 is reassigned to the remaining of the two doors. When you say that it's 50:50 you are acting like the 1/3 stat never existed for each door.
Not saying I liked the video though. I think his point was poorly presented.
By: gerrywastaken
Re: Common Sense Is Worthless In Science
Oh there was something on that page which I think explains this example a lot better.
====
What if there were 1,000 doors? You would have a 1/1,000 chance of picking the correct door. If Monty opens 998 doors, all of them with goats behind them, the door that you chose first will still have a 1/1,000 chance of being the one that conceals the car, but the other remaining door will have a 999/1,000 probability of being the door that is concealing the car. Here switching sounds like a pretty good idea.
====
To not accept this is to say that simply by opening up 998 of his 999 doors and showing you the result, the changes of your door containing the car changes to 50%. If you did this 20 times then do you think you would pick the right door approximatly 10 of those times? Or is it more accurate to say that each of those 20 times you have a 1/1000 chance of picking the right door no matter how many doors Monty reveals on his side?
====
What if there were 1,000 doors? You would have a 1/1,000 chance of picking the correct door. If Monty opens 998 doors, all of them with goats behind them, the door that you chose first will still have a 1/1,000 chance of being the one that conceals the car, but the other remaining door will have a 999/1,000 probability of being the door that is concealing the car. Here switching sounds like a pretty good idea.
====
To not accept this is to say that simply by opening up 998 of his 999 doors and showing you the result, the changes of your door containing the car changes to 50%. If you did this 20 times then do you think you would pick the right door approximatly 10 of those times? Or is it more accurate to say that each of those 20 times you have a 1/1000 chance of picking the right door no matter how many doors Monty reveals on his side?
By: gerrywastaken
Re: Common Sense Is Worthless In Science
Oh, I understand the science behind it perfectly. The truth is that probability doesn't mean jack-diddly-squat in reality. As the video states, humans have trouble with statistics and the biggest trouble is we read into things incorrectly. There will ALWAYS be a statistic for something, but many times those statistics are meaningless.
Basically, no matter what the probability is it doesn't change where the car is.
I don't entirely agree with this vid in general. There is a time and place for common sense. Ruling out common sense.....just doesn't make sense.
Basically, no matter what the probability is it doesn't change where the car is.
I don't entirely agree with this vid in general. There is a time and place for common sense. Ruling out common sense.....just doesn't make sense.
By: digitalprime
Re: Common Sense Is Worthless In Science
Aarrrrrggghhh, had to run out to work before I could fully elaborate. It's torturous to work a shift knowing I couldn't finish my train of through. Ha ha.
I saw the movie 21 so I'm familiar with this theory. I believe whomever came up with this theory was dead wrong. Here is why:
The probability is LOCKED into place the moment you made your decision. With 3 doors you only eliminate 1 and still have a decision to make. Eliminating 2 doors reveals the answer. So imagine 100 doors and each round a certain number can be open. For each round you must pay an admission to play and can make one guess, but you can choose to join for any round. With 100 doors to open, you would have a 1 in 100 chance of winning. It doesn't matter how many doors are opened after you decided, because the probability is locked into place when you decided. Since you have to pay admission to play it would be wise to wait until more doors are open. Ideally, the best time to play is when there are only 2 doors left. However, the prize may have been won by then. Therefore, you decide upon a threshold for when you will join, perhaps 1 in 20 or 1 in 10 doors.
In Let's Make a Deal, the contestant had a 1 in 3 chance of winning. Since their is no admission to pay, there is no risk to play regardless of the probability. If one door was open, but the person could NOT make another decision, then they would still be locked in that 1 in 3 chance from before. Since they are given another chance to decide, this technically counts as a whole new round and the third door is meaningless. So all those people who said they had a 50/50 chance of winning (you know the ones who relied on common sense and were scoffed at), as it turns out they were right all along. The 3rd door does not affect the remaining two since that was a previous round.
This may sound confusing, but the 3rd door does not affect the chances of winning. It's how many doors that are left closed that count. Yes, opening doors does alter how many are left closed, but they no longer count themselves.
Now you may be thinking that probability worked to the favor of the students in the movie 21, but they didn't play every game. Each game costs money (admission). They counted cards essentially eliminating "doors". They waited until a threshold was met before they joined, and they had a threshold with which to leave the game.
Common sense is sometimes unexplainable or at least very difficult to explain. Sometimes common sense gives us wisdom beyond our own comprehension. There are many occasions were a "gut feeling" proved to be correct. It's amazing that we can be subconsciously aware that something is correct or incorrect. I would say that science is not hindered by common sense, but instead is driven by it. We don't seek to explain that which makes sense, we seek to explain that which doesn't not make sense. It's what keeps us up at night. I think Einstein would agree had he been given a chance.
I think this video is confusing common knowledge with common sense. The difference is that common sense is unique among us all because it incorporates personal experiences in addition to common knowledge. Unfortunately, common sense....is not that common.
I saw the movie 21 so I'm familiar with this theory. I believe whomever came up with this theory was dead wrong. Here is why:
The probability is LOCKED into place the moment you made your decision. With 3 doors you only eliminate 1 and still have a decision to make. Eliminating 2 doors reveals the answer. So imagine 100 doors and each round a certain number can be open. For each round you must pay an admission to play and can make one guess, but you can choose to join for any round. With 100 doors to open, you would have a 1 in 100 chance of winning. It doesn't matter how many doors are opened after you decided, because the probability is locked into place when you decided. Since you have to pay admission to play it would be wise to wait until more doors are open. Ideally, the best time to play is when there are only 2 doors left. However, the prize may have been won by then. Therefore, you decide upon a threshold for when you will join, perhaps 1 in 20 or 1 in 10 doors.
In Let's Make a Deal, the contestant had a 1 in 3 chance of winning. Since their is no admission to pay, there is no risk to play regardless of the probability. If one door was open, but the person could NOT make another decision, then they would still be locked in that 1 in 3 chance from before. Since they are given another chance to decide, this technically counts as a whole new round and the third door is meaningless. So all those people who said they had a 50/50 chance of winning (you know the ones who relied on common sense and were scoffed at), as it turns out they were right all along. The 3rd door does not affect the remaining two since that was a previous round.
This may sound confusing, but the 3rd door does not affect the chances of winning. It's how many doors that are left closed that count. Yes, opening doors does alter how many are left closed, but they no longer count themselves.
Now you may be thinking that probability worked to the favor of the students in the movie 21, but they didn't play every game. Each game costs money (admission). They counted cards essentially eliminating "doors". They waited until a threshold was met before they joined, and they had a threshold with which to leave the game.
Common sense is sometimes unexplainable or at least very difficult to explain. Sometimes common sense gives us wisdom beyond our own comprehension. There are many occasions were a "gut feeling" proved to be correct. It's amazing that we can be subconsciously aware that something is correct or incorrect. I would say that science is not hindered by common sense, but instead is driven by it. We don't seek to explain that which makes sense, we seek to explain that which doesn't not make sense. It's what keeps us up at night. I think Einstein would agree had he been given a chance.
I think this video is confusing common knowledge with common sense. The difference is that common sense is unique among us all because it incorporates personal experiences in addition to common knowledge. Unfortunately, common sense....is not that common.
By: digitalprime
Re: Common Sense Is Worthless In Science
I don't think you read my second post and perhaps not even the first one. There may be a similar situation in the movie 21, I don't know, I was not talking about it.
Do the experiment yourself using 10 items which are all the same except for the 1 winning item. Have your friend conceal them all. Pick one and have your friend eliminate 8 loosing doors from the doors not chosen by you. Now don't swap doors as apparently you now have 50% chance of your existing door being the right one. Run this over and over until you are satisfied that the ratio is 50:50. You will quickly see that the odds are not 50:50 but instead are 1:9. You can even do it with 3 items so that it's just like the example given, although it will probably take more iterations before it becomes obvious to you.
If you are still not convinced then perhaps we should gamble some time. :P
Do the experiment yourself using 10 items which are all the same except for the 1 winning item. Have your friend conceal them all. Pick one and have your friend eliminate 8 loosing doors from the doors not chosen by you. Now don't swap doors as apparently you now have 50% chance of your existing door being the right one. Run this over and over until you are satisfied that the ratio is 50:50. You will quickly see that the odds are not 50:50 but instead are 1:9. You can even do it with 3 items so that it's just like the example given, although it will probably take more iterations before it becomes obvious to you.
If you are still not convinced then perhaps we should gamble some time. :P
By: gerrywastaken
Re: Common Sense Is Worthless In Science
You're wrong. The solution to the Monty Hall Problem has been empirically proven. Do about 100 trials of it with your family and/or friends. You should switch doors, every single time.
By: i8ursandwich
Re: Common Sense Is Worthless In Science
Or if you don't want to bore your acquaintances with esoteric mathematical quandaries, you could always just go here. http://math.ucsd.edu/~crypto/cgi-bin/MontyKnows/monty2?1+12636
By: i8ursandwich
Re: Common Sense Is Worthless In Science
I agree. The probability is ALWAYS 50/50, whether it is 3 or 300 doors, since Monty will only open the doors that do not contain a car. Regardless of how many doors you start with, only one has a car, and there is 100% probability that Monty will not open that one... hence, you will always be down to 2 doors, one which has a car, and one which does not.
I think it is very important to point out that quite a few people seem to overlook the fact that Monty knows where the car is, which directly affects probability. I could be wrong, but none of the explanations have convinced me so far.
I think it is very important to point out that quite a few people seem to overlook the fact that Monty knows where the car is, which directly affects probability. I could be wrong, but none of the explanations have convinced me so far.
By: twent4
Re: Common Sense Is Worthless In Science
I found the flaw in this theory. You only have 2/3 chance of being right if you can open 2 doors at once. As long as you can open only 1 then there is 1/3 + 1/3 + 1/3, not 1/3 and 2/3. If I could open 2 doors instead of 1, I would. I think the person who created this theory missed that point.
By: digitalprime
Re: Common Sense Is Worthless In Science
Now, now, no picking on mathematicians. There is something melodramatic about a life lived in conceptual therms, theories and dreams, especially if every few years theories have to be rewritten. The drama of it all.
As to the video, yawn.... let me guess this is from a person inventing a new way of getting out of the paper bag. Hmm... Maybe they can use the nuclear atom splitter?
As to the video, yawn.... let me guess this is from a person inventing a new way of getting out of the paper bag. Hmm... Maybe they can use the nuclear atom splitter?
By: imkoan
Re: Common Sense Is Worthless In Science
Pet peeve: The audio in these videos always sounds like it was recorded through a drive-thru speaker. If you're planning to make a serious hobby out of making these kinds of videos, drop a little dough on a halfway decent mic & preamp.
By: quisph
Re: Common Sense Is Worthless In Science
Can nobody see the obvious? Probability only really matters if you get to play the game over and over again. That's how it's ultimately proven or disproven. In real life, Monty only lets you play once, where your "chance" (as opposed to theoretical probability) is indeed 50/50. 2 doors - one car.
The title of this particular example should read "Science is worthless in singular games of chance!"
Overall, the author is a bit disengenouos in his presentation. His take on common sense is loosely defined. Sometimes it's assumption. Sometimes it's ignorance. Sometimes its dogma. Ultimately, common sense tells us to embrace that which can be proven, making it invaluable to science, not worthless.
The title of this particular example should read "Science is worthless in singular games of chance!"
Overall, the author is a bit disengenouos in his presentation. His take on common sense is loosely defined. Sometimes it's assumption. Sometimes it's ignorance. Sometimes its dogma. Ultimately, common sense tells us to embrace that which can be proven, making it invaluable to science, not worthless.
By: awfabee
Re: Common Sense Is Worthless In Science
If you've read all my posts, you'll see how I changed my mind over time. Yet, I still didn't feel completely satisfied.
I started thinking about all the people who would switch with a cocky attitude that the odds were in their favor, only to lose. I started thinking that with only 3 doors, probability doesn't matter. If you convert the fraction to a decimal, the numbers are deceivingly blown out of proportion. 50/50 and 33/66 seem far apart, but that percentages messing with your mind and shouldn't be used.
Sometimes in life we need to accept that there are more than one answer. That's why people are divided on this, because BOTH groups are CORRECT. If the number of doors increased to 10, 100, or 1000 then I would say switch every time. With 3 doors it doesn't matter.
Plus, Monty Hall will always open a wrong door and give the person a second chance to choose. Therefore he is eliminating the 1 in 3 chances. What difference does it make if he eliminates the 3rd door immediately and then asks to make a decision? With only 1 chance to guess, it would be 50/50.
So here is a case where both groups are correct in their assumptions. With one chance to guess, and one wrong door always eliminated changes the probability rule. Yet, with more chances to play or more doors then probability counts.
I started thinking about all the people who would switch with a cocky attitude that the odds were in their favor, only to lose. I started thinking that with only 3 doors, probability doesn't matter. If you convert the fraction to a decimal, the numbers are deceivingly blown out of proportion. 50/50 and 33/66 seem far apart, but that percentages messing with your mind and shouldn't be used.
Sometimes in life we need to accept that there are more than one answer. That's why people are divided on this, because BOTH groups are CORRECT. If the number of doors increased to 10, 100, or 1000 then I would say switch every time. With 3 doors it doesn't matter.
Plus, Monty Hall will always open a wrong door and give the person a second chance to choose. Therefore he is eliminating the 1 in 3 chances. What difference does it make if he eliminates the 3rd door immediately and then asks to make a decision? With only 1 chance to guess, it would be 50/50.
So here is a case where both groups are correct in their assumptions. With one chance to guess, and one wrong door always eliminated changes the probability rule. Yet, with more chances to play or more doors then probability counts.
By: digitalprime
Re: Common Sense Is Worthless In Science
Look at it this way digitalprime. The scenario implies you only get to play once. It is a game show, after all. That means what happens every ten time, or a hundred times, etc., is irrelevant. Probability is irrelevant. At the moment of your final choice you are still faced with picking one door with one of two possible items behind it. Even if Monty opens 999,998 of a million doors, your final choice boils down to that fact. And that fact can be represented as a 50/50 chance. The eggheads that disagree are essentially changing the rules in mid-stream - going from playing once to playing numerous times where probability would then come into play. Perhaps this is a case of science being worthless in common sense?
By: awfabee
Re: Common Sense Is Worthless In Science
I'm going to disagree if there were a million doors. If there were a million doors, I would always switch to the door he CHOSE to not open.
The fact that this scenario has 3 doors makes it an exception to the rule. He will always open a wrong door, so whether you choose between two before or after he opens a door is irrelevant. With a million doors, you're chances of guessing the right door with only one chance is so slim that it would be better to switch.
With 3 doors, I could open 1 door and Monty could open 1 door with 1 remaining. That would not work with 4 doors or more. Since Monty will choose a wrong door, it doesn't matter if I choose before or after he opens a wrong door. Probability doesn't work with 3 doors, but does with more doors and/or more chances to play.
The fact that this scenario has 3 doors makes it an exception to the rule. He will always open a wrong door, so whether you choose between two before or after he opens a door is irrelevant. With a million doors, you're chances of guessing the right door with only one chance is so slim that it would be better to switch.
With 3 doors, I could open 1 door and Monty could open 1 door with 1 remaining. That would not work with 4 doors or more. Since Monty will choose a wrong door, it doesn't matter if I choose before or after he opens a wrong door. Probability doesn't work with 3 doors, but does with more doors and/or more chances to play.
By: digitalprime
Re: Common Sense Is Worthless In Science
Don't misunderstand me. I'm switching too!
Theoretically, with a million doors, we can play 999.999 times and initially pick a goat. So when we play just once we can very, very, VERY easily assume that we picked a goat.
But, in the context of the problem, there is no evidence to PROVE we picked a goat, only supposition. Based on the evidence, however, we know for a fact that we still end up having to choosing a door that has one of two outcomes. (And we can still choose wrong!) Our ASSUMED odds may be a 999,999 to one. But our PROVABLE, actual odds are one out of two. I mean, doesn't a scientific claim demand proof?
Theoretically, with a million doors, we can play 999.999 times and initially pick a goat. So when we play just once we can very, very, VERY easily assume that we picked a goat.
But, in the context of the problem, there is no evidence to PROVE we picked a goat, only supposition. Based on the evidence, however, we know for a fact that we still end up having to choosing a door that has one of two outcomes. (And we can still choose wrong!) Our ASSUMED odds may be a 999,999 to one. But our PROVABLE, actual odds are one out of two. I mean, doesn't a scientific claim demand proof?
By: awfabee
