One of my all time favourite travel books is Broke Through Britain by Peter Mortimer. He walks from London to Edinburgh with no money. No cash, no credit cards, nada. He has to scrounge for every meal, and beg for a place to sleep. The result is a very fun and unpredictable book.
Can't say I'd want to do it myself, but it's fun to read about.
Yikes!
I just thought it was a mildly diverting way to show that age and appearance have a complicated relationship.
Also, thanks for the clarification on the BBC and Channel Four. I don't live in Britain -- I bet you couldn't tell, eh?
BlueHorse, many sympathies!
A bit of advice: as soon as you can, get yourself to a sports injury doctor. Regular doctors will deal with the immediate problem -- sticking your various broken bits back together. But in my experience they are completely useless at the recovery side of things.
A sports injury doctor will be focused on issues like getting you back on your feet again sooner, ensuring you maintain full range of motion, etc. That can literally take months off the recovery process.
Also, DO YOUR PHSYIO! Even if it hurts. Especially if it hurts. And if you haven't connected with a physiotherapist yet, go to the sports doctor and get his/her opinion about when you should start. They can also refer you to a decent physio practioner.
(If you're not sure where to find a good sports doctor, most university campuses have sports medicine clinics.)
Remember, too, that every sports injury, however miserable, is also an opportunity to learn about your body and your spirit. Don't miss that chance. (Here's an article you might find interesting, too.)
Good luck.
On the weekend I witnessed a car accident. For real.
A teenaged girl stepped out from behind a city bus, and basically just walked right in front of an oncoming car. Luckly it wasn't going very fast. The girl bounced off the front grill, landed on the pavement, got up on one elbow for a few seconds, then collapsed in a heap.
Cars stopped everywhere -- we were on a busy, four lane road -- cell phones flashed out and the cops & paramedics were there in literally a minute or two. From what I could see, it looked like the girl was going to be ok.
The car that hit her was green.
I had a delicious steak dinner with my lovely wife last night, had a couple glasses of good red wine, took the dog out for a walk in the brisk November evening air, and the penny dropped.
It's true that in any individual case the witness will be 80% likely to be correct. But the wrinkle is: exactly how many opportunities do you have to be correct?
When the witness says "blue", there are only 2 possibilities:
1. Correct, the taxi is blue, or
2. Wrong, the taxi is really green.
So, how big is the correct pile? How many yes's can there be? Out of every hundred taxis, we know 15 are blue, and with an 80% accuracy rate, that means the correct pile will be 12 taxis.
How big is the wrong pile? How many no's can there be? If the witness always identifies 80% as correct, she'll identify 67 taxis as green. That leaves 17 green taxis, 20%, improperly identified as blue.
Do the math and you get the 59% likelihood that the witness will be wrong.
On the one hand, I find this counterintutive to the point of loveliness. It is true that the witness will always identify any specific taxi 4 times out of 5. It is true that this 4/5 success rate always stays the same no matter what the ratio of green to blue taxis. But at the same time it's equally true that altering the ratio of blue to green can make it probable that the witness will be wrong when she says "blue". That's very cool.
But on the other hand, it now seems pretty obvious that 80% of 15 is smaller than 20% of 85.
Go figure.
Thanks everybody for a most enjoyable discussion.
Help me out, Xerxexrex.
I agree that...
We're trying to find the probability that the car is actually blue given that the witness saw blue.
But if it's given that the witness says "blue" I don't get how it can be among the possiblities that "C. it was green and you identified it as green".
If it's a given that the witness says "blue", how can you assign a probability to the chance that the witness says "green"? It's a 100% certainty the witness said blue.
And as for you, Rhomboid, I forgive you for your uncouth words.
Imagine setting up an experiment where our guy watches a computer animation of the hit and run accident many, many times - 15% blue taxi animations and 85% green taxi animations. Which is going to happen more often...that he gets the color wrong, or that the color is blue? Since he kind of sucks at seeing blue stuff, it's going to be the former, so the probability you're looking for has to be more than 50%.
Over many, many accident simulations, there will be a total universe of n accidents of which 15% will be blue and 85% will be green. And the 80-20 right-wrong ratio will sort itself out as Rhomboid described.
But in each individual case, the odds are always 80-20.
This is perfectly consistent with Rhomboid's numbers:
A. It was actually blue, and you identified it correctly as blue; 0.15 * 0.80 = 0.12
B. It was actually blue, but you misidentified it as green; 0.15 * 0.20 = 0.03
C. It was actually green, and you identified it correctly as green; 0.85 * 0.80 = 0.68
D. It was actually green, but you misidentified it as blue; 0.85 * 0.20 = 0.17
0.12 + 0.03 + 0.68 + 0.17 = 1.00
Over many, many sightings, when you look in the 80% pile, you'll see a ratio of 68 green and 12 blue (17 to 3).
But for any specific sighting -- whether it's blue or green -- the ratio of right to wrong answers will always be the same: 4 out of 5 times (80%). If the witness says a specific taxi is blue, Rhomboid's numbers say that in 12 out of 15 times (80%), that will be correct. If the witness says it's green, his numbers say that will be correct 68 out of 85 times (80%).
Whatever the proportion of taxis on the road, you can count on the witness to correctly identify them 4 out of 5 times.
That's a good question, StoryBored: Is she 80% sure she saw the hit and run taxi? Or is she 100% sure she saw it, but only 80% sure of what colour it is?
I thought the latter. But the former would make much more sense.
Wen righting, klaritee and persision r aul.
Think of it this way...
I see somebody steal candy from a baby. He's wearing a baseball cap and a gorilla suit.
I'm a pretty observant guy. I can spot caps and gorilla suits equally well -- 90% of the time.
45% of the population of my city wear baseball caps. .00001% of the population of my city wear gorilla suits.
At the trial, should you treat my evidence about the gorilla suit as less persuasive than the evidence about the baseball cap? Am I more likely to be wrong about the gorilla suit just because it's unusual?
Roryk -- Agreed, when you shift around the total blue and green taxi ratio, the ratio of blue to green in the 80% correct bunch will shift. And, of course, the ratio of blue to green in the 20% error group will shift as well.
But for each individual instance, the success rate still sits at 80%, whatever the actual colour of the taxi.
The decision of the taxi dispatcher to send out a bunch of green taxis one night doesn't suddenly drop my reliability as a witness from 80% to 59%.
Even on a night when greens greatly outnumber blue, I can still properly identify blue 80% of the time.
One of these identifications is wrong, according to the tests of the witness's ability.
Wouldn't there be a 33% chance that the witness has it right?...
1st event -- 80% chance correct
2nd event -- .8 x .8 = 64% chance correct
3rd event -- .8 x .8 x .8 = 51%
4th event -- .8 x .8 x .8 x .8 = 41%
5th event -- .8 x .8 x .8 x .8 x .8 = 33%
What are the odds it would happen at the YWCA?
posted by Torluath 17 years ago
In "37 fads that swept the U.S."
No internet?
posted by Torluath 17 years ago
In "Curious Hiking George."
One of my all time favourite travel books is Broke Through Britain by Peter Mortimer. He walks from London to Edinburgh with no money. No cash, no credit cards, nada. He has to scrounge for every meal, and beg for a place to sleep. The result is a very fun and unpredictable book. Can't say I'd want to do it myself, but it's fun to read about.
posted by Torluath 17 years ago
In "Happy MLK Day"
Good God, azpenguin, that never even crossed my mind!
posted by Torluath 17 years ago
In "What Makes a Cartoon New Yorker-Worthy? Draw Your Own Conclusion."
Excellent post. Muchos bananas! ))))
posted by Torluath 17 years ago
In "What does 200 calories look like?"
But how much beer is 200 calories?
posted by Torluath 17 years ago
In "Global warming 'past the point of no return'"
Green arctic summers as early as 2040.
posted by Torluath 17 years ago
In "Some people look clapped out at 25..."
Yikes! I just thought it was a mildly diverting way to show that age and appearance have a complicated relationship. Also, thanks for the clarification on the BBC and Channel Four. I don't live in Britain -- I bet you couldn't tell, eh?
posted by Torluath 17 years ago
In "Curi-ouch! George"
BlueHorse, many sympathies! A bit of advice: as soon as you can, get yourself to a sports injury doctor. Regular doctors will deal with the immediate problem -- sticking your various broken bits back together. But in my experience they are completely useless at the recovery side of things. A sports injury doctor will be focused on issues like getting you back on your feet again sooner, ensuring you maintain full range of motion, etc. That can literally take months off the recovery process. Also, DO YOUR PHSYIO! Even if it hurts. Especially if it hurts. And if you haven't connected with a physiotherapist yet, go to the sports doctor and get his/her opinion about when you should start. They can also refer you to a decent physio practioner. (If you're not sure where to find a good sports doctor, most university campuses have sports medicine clinics.) Remember, too, that every sports injury, however miserable, is also an opportunity to learn about your body and your spirit. Don't miss that chance. (Here's an article you might find interesting, too.) Good luck.
posted by Torluath 17 years ago
In "Confused George: Probability Problem"
Come to think of it, my car's green, too. Move along, move along, nothing to see here...
posted by Torluath 17 years ago
On the weekend I witnessed a car accident. For real. A teenaged girl stepped out from behind a city bus, and basically just walked right in front of an oncoming car. Luckly it wasn't going very fast. The girl bounced off the front grill, landed on the pavement, got up on one elbow for a few seconds, then collapsed in a heap. Cars stopped everywhere -- we were on a busy, four lane road -- cell phones flashed out and the cops & paramedics were there in literally a minute or two. From what I could see, it looked like the girl was going to be ok. The car that hit her was green.
posted by Torluath 17 years ago
Ur, gosh. Thanks.
posted by Torluath 17 years ago
In "Eroica!"
)))))!!! Amazing. Thanks.
posted by Torluath 17 years ago
In "Confused George: Probability Problem"
I had a delicious steak dinner with my lovely wife last night, had a couple glasses of good red wine, took the dog out for a walk in the brisk November evening air, and the penny dropped. It's true that in any individual case the witness will be 80% likely to be correct. But the wrinkle is: exactly how many opportunities do you have to be correct? When the witness says "blue", there are only 2 possibilities: 1. Correct, the taxi is blue, or 2. Wrong, the taxi is really green. So, how big is the correct pile? How many yes's can there be? Out of every hundred taxis, we know 15 are blue, and with an 80% accuracy rate, that means the correct pile will be 12 taxis. How big is the wrong pile? How many no's can there be? If the witness always identifies 80% as correct, she'll identify 67 taxis as green. That leaves 17 green taxis, 20%, improperly identified as blue. Do the math and you get the 59% likelihood that the witness will be wrong. On the one hand, I find this counterintutive to the point of loveliness. It is true that the witness will always identify any specific taxi 4 times out of 5. It is true that this 4/5 success rate always stays the same no matter what the ratio of green to blue taxis. But at the same time it's equally true that altering the ratio of blue to green can make it probable that the witness will be wrong when she says "blue". That's very cool. But on the other hand, it now seems pretty obvious that 80% of 15 is smaller than 20% of 85. Go figure. Thanks everybody for a most enjoyable discussion.
posted by Torluath 17 years ago
Help me out, Xerxexrex. I agree that... We're trying to find the probability that the car is actually blue given that the witness saw blue. But if it's given that the witness says "blue" I don't get how it can be among the possiblities that "C. it was green and you identified it as green". If it's a given that the witness says "blue", how can you assign a probability to the chance that the witness says "green"? It's a 100% certainty the witness said blue. And as for you, Rhomboid, I forgive you for your uncouth words.
posted by Torluath 17 years ago
Imagine setting up an experiment where our guy watches a computer animation of the hit and run accident many, many times - 15% blue taxi animations and 85% green taxi animations. Which is going to happen more often...that he gets the color wrong, or that the color is blue? Since he kind of sucks at seeing blue stuff, it's going to be the former, so the probability you're looking for has to be more than 50%. Over many, many accident simulations, there will be a total universe of n accidents of which 15% will be blue and 85% will be green. And the 80-20 right-wrong ratio will sort itself out as Rhomboid described. But in each individual case, the odds are always 80-20. This is perfectly consistent with Rhomboid's numbers: A. It was actually blue, and you identified it correctly as blue; 0.15 * 0.80 = 0.12 B. It was actually blue, but you misidentified it as green; 0.15 * 0.20 = 0.03 C. It was actually green, and you identified it correctly as green; 0.85 * 0.80 = 0.68 D. It was actually green, but you misidentified it as blue; 0.85 * 0.20 = 0.17 0.12 + 0.03 + 0.68 + 0.17 = 1.00 Over many, many sightings, when you look in the 80% pile, you'll see a ratio of 68 green and 12 blue (17 to 3). But for any specific sighting -- whether it's blue or green -- the ratio of right to wrong answers will always be the same: 4 out of 5 times (80%). If the witness says a specific taxi is blue, Rhomboid's numbers say that in 12 out of 15 times (80%), that will be correct. If the witness says it's green, his numbers say that will be correct 68 out of 85 times (80%). Whatever the proportion of taxis on the road, you can count on the witness to correctly identify them 4 out of 5 times.
posted by Torluath 17 years ago
That's a good question, StoryBored: Is she 80% sure she saw the hit and run taxi? Or is she 100% sure she saw it, but only 80% sure of what colour it is? I thought the latter. But the former would make much more sense. Wen righting, klaritee and persision r aul.
posted by Torluath 17 years ago
Think of it this way... I see somebody steal candy from a baby. He's wearing a baseball cap and a gorilla suit. I'm a pretty observant guy. I can spot caps and gorilla suits equally well -- 90% of the time. 45% of the population of my city wear baseball caps. .00001% of the population of my city wear gorilla suits. At the trial, should you treat my evidence about the gorilla suit as less persuasive than the evidence about the baseball cap? Am I more likely to be wrong about the gorilla suit just because it's unusual?
posted by Torluath 17 years ago
Roryk -- Agreed, when you shift around the total blue and green taxi ratio, the ratio of blue to green in the 80% correct bunch will shift. And, of course, the ratio of blue to green in the 20% error group will shift as well. But for each individual instance, the success rate still sits at 80%, whatever the actual colour of the taxi. The decision of the taxi dispatcher to send out a bunch of green taxis one night doesn't suddenly drop my reliability as a witness from 80% to 59%. Even on a night when greens greatly outnumber blue, I can still properly identify blue 80% of the time.
posted by Torluath 17 years ago
One of these identifications is wrong, according to the tests of the witness's ability. Wouldn't there be a 33% chance that the witness has it right?... 1st event -- 80% chance correct 2nd event -- .8 x .8 = 64% chance correct 3rd event -- .8 x .8 x .8 = 51% 4th event -- .8 x .8 x .8 x .8 = 41% 5th event -- .8 x .8 x .8 x .8 x .8 = 33%
posted by Torluath 17 years ago
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