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rubysue
Skeptic Friend
USA
199 Posts |
 Posted - 08/29/2001 : 20:46:29 [Permalink]
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I must confess that I bought five quick picks for that last Powerball drawing (our state just joined the Powerball lottery). Although I had better odds of being hit by lightning at precisely the same time I was deflecting a meteorite with one hand and battling a rattlesnake with the other, I figured what the hell... If I won, that $5 investment was certainly worth it (no, I don't play very often and I get VERY bored with regular casino gambling, unless it's a $2 Blackjack table).
Now, having said that, mathematical incompetency and probability theory imbecility are, unfortunately, quite the norm in this country. As Zandermann so elegantly put it:
quote:
Always amazes me that the same people who will plunk down $$$ they can't afford on the opportunity to participate in a millions-to-one chance, are also the people who are shocked/stunned by the likelihood that any group of 25 or so people will include 2 with the same birthday.
Both are examples of probability...simple multiplication.
Have you ever noticed that when an improbable event occurs (e.g., one with a very low, but slightly greater than zero probability of occurrence), it is invariably labeled a "miracle", if the outcome is good? Last week, an Air Transit Airbus A330 flying from Canada to Portugal lost both engines over the Atlantic. The pilots guided the powerless aircraft to a small island in the Azores with only minor injuries and no fatalities (the aircraft, with more than 300 on board, actually glided for more than 18 minutes). Naturally, this has now been called a "miracle" in the media and articles across the Internet talk about how hard people were praying and that god answered their prayers. Perhaps these survivors should be reminded that the good folks on EgyptAir Flight 990 and Swissair Flight 111 probably also prayed very hard before they died in an absolutely horrifying way. Many of the other fine folks on TWA flight 800 and the Concorde were also probably god-fearing, but they didn't even have time to pray. In a probabilistic analysis of unlikely events, it is a possible outcome that a crippled aircraft will land safely. It is also a possible outcome (probably equally likely, given that each outcome has a very low probability) that Air Transit could have cartwheeled into the ocean, instantly killing all on board. No miracles were involved, only possible outcomes in a probabilistic series.
This basic lack of understanding explains why the average citizen is convinced they will win Powerball (at 1 in 80 million odds) but prevents many of them from driving defensely or safely (a FATAL auto accident has odds of 1 in about 15,000!).
Sorry for the long post - this is an interesting topic.
Thoughts?
rubysue
If your head is wax, don't walk in the sun.
Edited by - rubysue on 08/29/2001 21:03:55
Edited by - rubysue on 08/30/2001 16:36:01 |
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Trish
SFN Addict
USA
2102 Posts |
Posted - 08/30/2001 : 19:48:15 [Permalink]
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quote:
Last week, an Air Transit Airbus A330 flying from Canada to Portugal lost both engines over the Atlantic. The pilots guided the powerless aircraft to a small island in the Azores with only minor injuries and no fatalities (the aircraft, with more than 300 on board, actually glided for more than 18 minutes).
I'd like to know what altitude they were at when they lost engines and the glide ratio of that particular aircraft, not being familiar with it. These would go a long way toward explaining how the craft stayed in the air without engines. Also, pilot experience has a lot to do with keeping the bird in the air.
He's YOUR god, they're YOUR rules, YOU burn in hell! |
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PhDreamer
SFN Regular
USA
925 Posts |
Posted - 08/30/2001 : 20:33:05 [Permalink]
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quote:
This basic lack of understanding explains why the average citizen is convinced they will win Powerball (at 1 in 80 million odds) but prevents many of them from driving defensely or safely (a FATAL auto accident has odds of 1 in about 15,000!).
Sorry for the long post - this is an interesting topic.
Thoughts?
I hereby propose: Rubysue's fallacy of positive outcomes. The more positive the outcome, actual or perceived, the more likely an individual is to ignore the odds.
Very entertaining post.
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Torsten
New Member
Canada
16 Posts |
Posted - 08/30/2001 : 22:04:46 [Permalink]
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Trish asked
quote:
"I'd like to know what altitude they were at when they lost engines and the glide ratio of that particular aircraft, not being familiar with it.
32,000 feet and 100 or so miles for a glide ratio better than 16:1.
From a Canadian news source:
"5:25 a.m. (local time 5 hrs ahead of EDT) Flight 236 reports a fuel leak at 39,000 ft, and diverts its flight path to the closest airstrip at Azores, 300 nautical miles away
5:48 a.m. Crew declares emergency.
6:13 a.m. Right-side engine fails due to fuel starvation
6:26 a.m. At 32,000 feet the left engine fails, still 100 miles from the airstrip. The crew reports they may have to ditch at sea.
6:46 a.m. After a dead-stick glide, the plane lands at Lajes with only minor passenger injuries."
I don't know what it is with Canadian airliners running out of fuel, but back in July 1983, an Air Canada Being 767 ran out of fuel and the crew safely landed it on an old runway-come-dragstrip in Gimli, Manitoba.
The Gimli Glider:
http://www.frontier.net/~wadenelson/successstories/gimli.html
That one flamed out at 41,000 feet and went about 100 miles for a glide ratio of about 13:1. (the crew estimated 11:1 after a couple of minutes of descent, and quickly calculated they wouldn't get to Winnipeg, so they went for this little field (sorta keeping with the math theme here, heh heh).
(I remember Gimli because on my private pilot written exam back in 1977, the navigation exercise involved a flight to Gimli, with a re-route to Winnipeg due to weather - weird)
I once owned a floatplane and occasionally practiced power-off landings. With all that gear hanging off of it, the glide ratio was about 7.5:1 -- quite steep. The airliners do well by comparison. But I never ran out of fuel.
TK
huh? |
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rubysue
Skeptic Friend
USA
199 Posts |
Posted - 08/31/2001 : 05:39:53 [Permalink]
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quote:
I'd like to know what altitude they were at when they lost engines and the glide ratio of that particular aircraft, not being familiar with it. These would go a long way toward explaining how the craft stayed in the air without engines. Also, pilot experience has a lot to do with keeping the bird in the air.
Trish, maybe you missed my point. Although the specific reasons for why this aircraft was able to dead-stick its way to a landing are probably quite interesting, that really wasn't why I brought it up. I was using this example of a "miracle" (as dubbed by the media and many of the survivors) to demonstrate that there is more than one possible outcome in a improbable event. If this plane had been further away or at a lower altitude, then the end result would have been totally different and the relatives and friends of the passengers and crew would be attending huge funerals and questioning why these things happen. In either case, there is no "divine intervention" in the outcome. However, the lack of understanding by the general public of even simple probability theory serves to perpetuate beliefs in "higher powers" that apparently intervene in our lives at random times.
Another example: A child falls into a well and is trapped. The nation is riveted while rescuers work around the clock to save her. She's finally pulled from the well, alive but quite hungry and dirty, and everyone immediately calls this a "miracle" of God. Another child falls into another well somewhere else, and the outcome is different (her lifeless body is brought back up by distraught rescue workers). Where's the "miracle" in this case? Why was one child rescued alive and another had to die? Because these are merely two possible outcomes in an event that is improbable, e.g., the event has a low but positive probability of occurrence with one or more possible outcomes. Probability theory is a roll of the dice.
quote:
I hereby propose: Rubysue's fallacy of positive outcomes. The more positive the outcome, actual or perceived, the more likely an individual is to ignore the odds.
I like it!!!!!
rubysue
If your head is wax, don't walk in the sun.
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Garrette
SFN Regular
USA
562 Posts |
Posted - 08/31/2001 : 05:59:42 [Permalink]
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Having a complete lack of knowledge in regard to aeronautics, please answer a question of curiosity?
Is a higher glide ratio better or worse? Is 16:1 better than 13:1?
My kids still love me. |
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Valiant Dancer
Forum Goalie
USA
4826 Posts |
Posted - 08/31/2001 : 08:16:10 [Permalink]
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quote:
Having a complete lack of knowledge in regard to aeronautics, please answer a question of curiosity?
Is a higher glide ratio better or worse? Is 16:1 better than 13:1?
My kids still love me.
From Howstuffworks.com
quote:
The way you measure the performance of a glider is by its glide ratio. This ratio tells you how much horizontal distance a glider can travel compared to the altitude it has to drop. Modern gliders can have glide ratios better than 60:1. This means they can glide for 60 miles if they start at an altitude of one mile. For comparison, a commercial jetliner might have glide ratios somewhere around 17:1.
If the glide ratio were the only factor involved, gliders would not be able to stay in the air nearly as long as they do. So how do they do it?
The higher the number, the better the aircraft glides. Hope this helps.
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Trish
SFN Addict
USA
2102 Posts |
Posted - 08/31/2001 : 08:35:35 [Permalink]
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quote:
If the glide ratio were the only factor involved, gliders would not be able to stay in the air nearly as long as they do. So how do they do it?
Thermals maybe? Updrafts? There's a lot that will keep the things up after they're released. But they will eventually come down. Same concept as keeping a hangglider in the air.
quote:
Trish, maybe you missed my point. Although the specific reasons for why this aircraft was able to dead-stick its way to a landing are probably quite interesting, that really wasn't why I brought it up. I was using this example of a "miracle" (as dubbed by the media and many of the survivors) to demonstrate that there is more than one possible outcome in a improbable event. If this plane had been further away or at a lower altitude, then the end result would have been totally different and the relatives and friends of the passengers and crew would be attending huge funerals and questioning why these things happen. In either case, there is no "divine intervention" in the outcome. However, the lack of understanding by the general public of even simple probability theory serves to perpetuate beliefs in "higher powers" that apparently intervene in our lives at random times.
Not really rubysue at least I don't think I did. I was really thinking of the questions I would ask when presented with the situation. When you consider the glide ratio and altitude and distance to air strip there really isn't any miracle involved. It's a matter of math at that point. Pilot skill is the only real variable factor after that point and your probability, as a matter of course.
He's YOUR god, they're YOUR rules, YOU burn in hell!
Edited by - Trish on 08/31/2001 08:36:50 |
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Valiant Dancer
Forum Goalie
USA
4826 Posts |
Posted - 08/31/2001 : 09:37:12 [Permalink]
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quote:
quote:
If the glide ratio were the only factor involved, gliders would not be able to stay in the air nearly as long as they do. So how do they do it?
Thermals maybe? Updrafts? There's a lot that will keep the things up after they're released. But they will eventually come down. Same concept as keeping a hangglider in the air.
Clipped too much of the article on gliders. Sorry.
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Torsten
New Member
Canada
16 Posts |
Posted - 08/31/2001 : 10:48:53 [Permalink]
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rubysue said: quote:
Where's the "miracle" in this case? Why was one child rescued alive and another had to die? Because these are merely two possible outcomes in an event that is improbable, e.g., the event has a low but positive probability of occurrence with one or more possible outcomes. Probability theory is a roll of the dice.
Much of what I'm about to write here is going strictly from memory, so there may be errors in detail, but the gist is not affected. Your example reminds me of the people who travel to Portugal to be saved by "Our Lady of Fatima". When I was a kid, a catholic friend of mine gave me a book that described the story of the three kids who had apparently met an apparition of Mary at this place in Portugal. The book described a number of ensuing miracles. I thought it sounded like a lot of hokum. Years later I read Sagan's Demon Haunted World, and I believe it's in this book that he addresses this very topic. The point he made was that of the many people who travel to the site each year looking for a cure for say, their cancer, a number will go into remission and claim that it was a miracle brought about as a result of their pilgrimage. It turns out that the proportion who experience a remission of their disease is about equal to the rate of spontaneous remission in the larger population.
I'd like to think that if we consider the remission to be a mundane event, then we can possibly look for and find reasons it happened, and maybe cure a lot of other people.
Similarly with these airliner examples. Accident investigations point to causes, crews subsequently are trained better, organizations adopt appropriate procedures, and we get airliners safely landed more often. No miracles required.
TK
huh? |
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Snake
SFN Addict
USA
2511 Posts |
Posted - 08/31/2001 : 23:33:13 [Permalink]
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I've been wanting to say this since the 1st time I saw the topic.
People Who Can't Do Math, are probably NOT Chinese.
Rap Crap is to music what Paint by Numbers is to art. |
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rubysue
Skeptic Friend
USA
199 Posts |
Posted - 09/01/2001 : 11:17:19 [Permalink]
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quote:
I'd like to think that if we consider the remission to be a mundane event, then we can possibly look for and find reasons it happened, and maybe cure a lot of other people.
Similarly with these airliner examples. Accident investigations point to causes, crews subsequently are trained better, organizations adopt appropriate procedures, and we get airliners safely landed more often. No miracles required.
I agree! I had planned on also using the disease remission case in my earlier post, but I've been having problems where something "times out" on the board when I'm writing a post and I lose everything I've written. If we could examine those outcomes that are improbable (or, in the case of a distribution of data, reside at 6 sigma (or 6 standard deviations) or greater from the population mean), then perhaps we can derive meaningful data for the rest of the population, e.g., disease remission causes or airplane crash causes or airplane crash avoidance causes (both of the latter reside at significant standard deviation points from the population mean because airline flights are overwhelmingly successful).
The disease remission case is another good example of how people overlook statistical data and probability theory and decide that an event must be miraculous. The "miraculous" can be easily disproven if you examine a total family of data. For the sake of the argument, say you have a population of 20,000 people suffering from a serious disease (e.g., pancreatic cancer). Plotting the various outcomes after diagnosis leads to the following groupings:
8,000 die within one year after diagnosis
5,000 die within two years
4,000 die within three years
2,000 die within four years
900 die within five years
95 go five years without the the disease but now the disease has returned
5 have complete remission of the disease and it have never returned
Out of the total population, the odds of a complete remission are 5/20000 or 0.03%, a very small number (and equating to a little less than 6 sigma away from the population mean, if plotted) but it is still a possible outcome. Rather than assessing this as "miraculous", this outcome should be carefully tested to determine why it occurred in this very small subset of a total population. Unfortunately, because it is such a rare outcome, it is easier to ascribe it to divine intervention. One or more of these remissions may occur due the fact that the victim is extremely religious (since religious belief is pervasive), so the cause is naturally attributed to that belief, without examining the complete population of data and the probabilities of outcomes.
[Trish - Sorry about that earlier response. It looks like you were agreeing with my point.]
So, how do we educate the masses about probability and statistical populations or is it a lost cause? Is it easier to blame or thank god when improbable events occur?
Sorry to go on and on about this subject - I find it absolutely fascinating. Sagan's examples in the "Demon Haunted World" are excellent; Richard Dawkins has also written about ignorance of probability and statistics when examining coincidences and improbable events.
rubysue
If your head is wax, don't walk in the sun.
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Trish
SFN Addict
USA
2102 Posts |
Posted - 09/01/2001 : 15:34:29 [Permalink]
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quote:
[Trish - Sorry about that earlier response. It looks like you were agreeing with my point.]
Not a problem. Just I am familiar with jets, having worked on a particular model with the glide ratio of a rock. However, the A-6 did do something that the math said shouldn't happen. It maintained an inverted flat spin with out going into a spiral. Both the pilot and B/N ejected and were recovered safely off the coast of Okinawa.
There was quite a lot of guessing going on as to why it stayed in the air. Neither the pilot or B/N attributed it to god - just that they were just damned lucky.
He's YOUR god, they're YOUR rules, YOU burn in hell! |
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PhDreamer
SFN Regular
USA
925 Posts |
Posted - 09/01/2001 : 21:41:59 [Permalink]
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quote:
I've been wanting to say this since the 1st time I saw the topic.
People Who Can't Do Math, are probably NOT Chinese.
Although I might suggest to them a university course: Population Density 101.
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ljbrs
SFN Regular
USA
842 Posts |
Posted - 09/03/2001 : 13:42:11 [Permalink]
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My idea of *HELL* would consist of being stuck in a casino without the chance to leave (or stuck at a race track, or stuck in a lottery line, or you name it).
However, I am not against legalized gambling (with the state coming in the winner), because otherwise the poor people would find their local mobster willing to fleece them instead. I would rather have that money going into state coffers than to have the same amount of money going to the mob.
People are never going to stop gambling. The poor look at it as the fleeting promise for getting out of poverty. Of course, it seldom works, but with hope, it might keep them happy instead of always miserable.
To each his/her own. Many things in life are gambles. The stock market is a huge casino (unless it is used wisely). People can throw away more money simultaneously on the stock market than they possibly can lose playing the lottery/lotto.
ljbrs  
Perfection Is a State of Growth...
Edited by - ljbrs on 09/03/2001 13:46:05 |
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