Author Topic: Episode #709  (Read 4081 times)

0 Members and 1 Guest are viewing this topic.

Offline arthwollipot

  • Reef Tank Owner
  • *********
  • Posts: 8875
  • Observer of Phenomena
Re: Episode #709
« Reply #30 on: February 11, 2019, 12:45:46 AM »
I haven't listened to this episode yet (it's at the top of my queue), but I'd like to address a pet peeve of mine that I'm absolutely sure will annoy the crap out of me when I get to the segment.

I, and every Australian and British person I know, understand that Robin Hood has two names. First name Robin, surname Hood. Robin Hood. Americans, however, in almost all cases, pronounce it as though it is only one name: Robinhood. With the emphasis on the first syllable.

The weird thing is that Americans don't do that with other names with the same syllable count. Charlie Brown, for example, is not pronounced Charliebrown. Donald Trump is not Donaldtrump.

Okay, carry on. I might have more to say when I've listened to the episode.
Self-described nerd. Pronouns: He/Him.

Tarvek: There's more to being an evil despot than getting cake whenever you want it.
Agatha: If that's what you think, then you're DOING IT WRONG!

Offline bachfiend

  • Not Any Kind of Moderator
  • Well Established
  • *****
  • Posts: 1796
Re: Episode #709
« Reply #31 on: February 11, 2019, 12:50:31 AM »
So after all the hand-waving about why the letter-writer was wrong about probability calculations, they never did answer her direct question, which was, “What is the formula?”

If I'm remembering my statistics correctly, it's:

 

In other words, it's

1 - 365/365 * 364/365 * 363/365 * ... * (365-n)/365

I figured it would be something along those lines, which would have taken about half a minute for them to say on the show. Hey, if they’re going to read a letter that asks for a formula, they should state the formula. They didn’t even give a particularly good general description.

But it’s not often that in my opinion they fail so badly at a segment.

It would have taken considerably longer than half a minute to explain.  It’s just the formula of my explanation, which would take a few minutes to explain. 

I thought the later suggested method of calculation to be neater - with 23 people there’s 23 x 22/2 pairs of people ie 253 pairs. 

Why 23 x 22/2?  With the first person, there’s 22 pairs possible, with the 2nd person there’s 21 pairs, not already considered, possible, right down to the second last person for whom there’s only one possible pair not already mentioned, meaning there’s 22 + 21 + 20 + ...  + 1 pairs, or rearranging the numbers (22 + 1) + (21 + 2) + (20 + 3) + ... + (12 + 11).  In other ‘words’ 23 x 11 or 23 x 22/2. 

There’s a 364/365 chance one pair won’t share a birthday, so the chance of none of the pairs sharing a birthday is (364/365)253, which equals 0.49952284596342 (roughly).  So the chance of at least one of the pairs sharing a birthday (there could be more) is 0.50047715403658 (again roughly).

Neat isn’t it?  I love numbers.  It must appeal to my inner Asperger’s.

I think your explanation has an error. You can't simply multiply probabilities unless they are independent events (and in this case, the events of different pairs not sharing birthdays are not independent). You should note that your expression for the solution does not match the formula quoted above. It is a very, very close approximation, though. I've posted a graph here: https://www.scribd.com/document/399355955/Birthday
I am not smart enough to figure out how to embed the pdf  :D

Why aren’t the birthdays independent events?  I suppose there’s a possibility that births might be distributed non-uniformly throughout the calendar year with increased numbers of births 9 months after very cold weather.
Gebt ihr ihr ihr Buch zurück?

Offline bachfiend

  • Not Any Kind of Moderator
  • Well Established
  • *****
  • Posts: 1796
Re: Episode #709
« Reply #32 on: February 11, 2019, 01:02:24 AM »
I haven't listened to this episode yet (it's at the top of my queue), but I'd like to address a pet peeve of mine that I'm absolutely sure will annoy the crap out of me when I get to the segment.

I, and every Australian and British person I know, understand that Robin Hood has two names. First name Robin, surname Hood. Robin Hood. Americans, however, in almost all cases, pronounce it as though it is only one name: Robinhood. With the emphasis on the first syllable.

The weird thing is that Americans don't do that with other names with the same syllable count. Charlie Brown, for example, is not pronounced Charliebrown. Donald Trump is not Donaldtrump.

Okay, carry on. I might have more to say when I've listened to the episode.

We Australians do the same thing with names such as Jobson Growth.’
Gebt ihr ihr ihr Buch zurück?

Offline fuzzyMarmot

  • Seasoned Contributor
  • ****
  • Posts: 673
Re: Episode #709
« Reply #33 on: February 11, 2019, 01:37:05 AM »
So after all the hand-waving about why the letter-writer was wrong about probability calculations, they never did answer her direct question, which was, “What is the formula?”

If I'm remembering my statistics correctly, it's:

 

In other words, it's

1 - 365/365 * 364/365 * 363/365 * ... * (365-n)/365

I figured it would be something along those lines, which would have taken about half a minute for them to say on the show. Hey, if they’re going to read a letter that asks for a formula, they should state the formula. They didn’t even give a particularly good general description.

But it’s not often that in my opinion they fail so badly at a segment.

It would have taken considerably longer than half a minute to explain.  It’s just the formula of my explanation, which would take a few minutes to explain. 

I thought the later suggested method of calculation to be neater - with 23 people there’s 23 x 22/2 pairs of people ie 253 pairs. 

Why 23 x 22/2?  With the first person, there’s 22 pairs possible, with the 2nd person there’s 21 pairs, not already considered, possible, right down to the second last person for whom there’s only one possible pair not already mentioned, meaning there’s 22 + 21 + 20 + ...  + 1 pairs, or rearranging the numbers (22 + 1) + (21 + 2) + (20 + 3) + ... + (12 + 11).  In other ‘words’ 23 x 11 or 23 x 22/2. 

There’s a 364/365 chance one pair won’t share a birthday, so the chance of none of the pairs sharing a birthday is (364/365)253, which equals 0.49952284596342 (roughly).  So the chance of at least one of the pairs sharing a birthday (there could be more) is 0.50047715403658 (again roughly).

Neat isn’t it?  I love numbers.  It must appeal to my inner Asperger’s.

I think your explanation has an error. You can't simply multiply probabilities unless they are independent events (and in this case, the events of different pairs not sharing birthdays are not independent). You should note that your expression for the solution does not match the formula quoted above. It is a very, very close approximation, though. I've posted a graph here: https://www.scribd.com/document/399355955/Birthday
I am not smart enough to figure out how to embed the pdf  :D

Why aren’t the birthdays independent events?  I suppose there’s a possibility that births might be distributed non-uniformly throughout the calendar year with increased numbers of births 9 months after very cold weather.
In this case, the "events" are pairs not sharing birthdays. The dependence of these events does not have anything to do with non-uniformity of births.
Consider the following:
Event A: Fred does not share a birthday with Carla.
Event B: Lonzo does not share a birthday with Carla.
Event C: Fred does not share a birthday with Lonzo.
Info on events A and B impacts the probability of event C.
https://en.wikipedia.org/wiki/Independence_(probability_theory)

Offline fuzzyMarmot

  • Seasoned Contributor
  • ****
  • Posts: 673
Re: Episode #709
« Reply #34 on: February 11, 2019, 03:18:01 AM »
To see this more easily, consider a planet where there are only three days per year, and try to find the probability that, in a group of three people, at least two people will share a birthday.

bachfiend's reasoning would lead to a result of 1-(2/3)^3=19/27.

The correct answer is 1-(2/3)*(1/3)=7/9.

The key error is the following: Just because there are three pairs, and a pair has probability 2/3 of not sharing a birthday, it doesn't mean you get to say that the probability of all three pairs not sharing birthdays is (2/3)^3. That multiplicative property of probabilities is only valid for independent events.

Offline arthwollipot

  • Reef Tank Owner
  • *********
  • Posts: 8875
  • Observer of Phenomena
Re: Episode #709
« Reply #35 on: February 11, 2019, 04:28:35 AM »
I haven't listened to this episode yet (it's at the top of my queue), but I'd like to address a pet peeve of mine that I'm absolutely sure will annoy the crap out of me when I get to the segment.

I, and every Australian and British person I know, understand that Robin Hood has two names. First name Robin, surname Hood. Robin Hood. Americans, however, in almost all cases, pronounce it as though it is only one name: Robinhood. With the emphasis on the first syllable.

The weird thing is that Americans don't do that with other names with the same syllable count. Charlie Brown, for example, is not pronounced Charliebrown. Donald Trump is not Donaldtrump.

Okay, carry on. I might have more to say when I've listened to the episode.

Okay, so I've listened to the segment (though not the entire episode yet - my commute isn't that long) and yes, as I predicted, not one of the rogues failed to pronounce the name as Robinhood, and yes, as I predicted, it annoyed the crap out of me. But as I am a listener to both Myths and Legends and GM Word of the Week (which covered the origin of the word "hood" very thoroughly in this episode), I know a fair bit more about the folklore than many and this was not surprising. I've had a bit more of a think about it and I think I've come up with the answer.

I think it's Disney's fault.

The clue came when they said Littlejohn, but not Friartuck. They said Friar Tuck. And a song jumped into my head.

RO-bin-hood-and-LIT-tle-john-WALK-ing-through-the-FO-rest.

It's been a VERY long time since I watched the movie, but I think that in actual dialogue, the other characters refer to him as just "Robin", so it doesn't come up. But it comes up in that song. I could be wrong about that though.

An entire generation grew up knowing THIS as the only version of the Robin Hood story that they knew, and that song is pretty damn catchy. I think it's a plausible explanation.
Self-described nerd. Pronouns: He/Him.

Tarvek: There's more to being an evil despot than getting cake whenever you want it.
Agatha: If that's what you think, then you're DOING IT WRONG!

Offline bachfiend

  • Not Any Kind of Moderator
  • Well Established
  • *****
  • Posts: 1796
Re: Episode #709
« Reply #36 on: February 11, 2019, 05:55:01 AM »
To see this more easily, consider a planet where there are only three days per year, and try to find the probability that, in a group of three people, at least two people will share a birthday.

bachfiend's reasoning would lead to a result of 1-(2/3)^3=19/27.

The correct answer is 1-(2/3)*(1/3)=7/9.

The key error is the following: Just because there are three pairs, and a pair has probability 2/3 of not sharing a birthday, it doesn't mean you get to say that the probability of all three pairs not sharing birthdays is (2/3)^3. That multiplicative property of probabilities is only valid for independent events.

No, it wouldn’t.  My reasoning would go along the line that if there’s three people One, Two and Three, and that if there’s only three days in the year, then One could have a birthday on any of the three days, and the chance is therefore 3/3, Two could have a birthday on either of the other two days, so as to not share a birthday, so the chance is therefore 2/3, and Three must have a birthday on the remaining, again not to share a birthday with One and Two, with a chance of 1/3.  So the odds are 3/3 x 2/3 x 1/3 or 6/27 or 2/9.  And hence the chance of at least two sharing a birthday
is 1 - 2/9 ie 7/9.  Which is the answer I’m supposed to have got.

Oh, wait.  I now see it.  My original explanation was apparently the correct one - it’s the product of 364/365, 363/365, ...  I shouldn’t have taken any notice of the simplified method of calculation.
Gebt ihr ihr ihr Buch zurück?

Offline DevoutCatalyst

  • Well Established
  • *****
  • Posts: 1549
Re: Episode #709
« Reply #37 on: February 11, 2019, 07:24:38 AM »
I think it's a plausible explanation.

ALSO, SKEPTICS ARE PEEVISH ABOUT ODD THINGS.

Offline bachfiend

  • Not Any Kind of Moderator
  • Well Established
  • *****
  • Posts: 1796
Re: Episode #709
« Reply #38 on: February 11, 2019, 11:30:19 AM »
I think it's a plausible explanation.

ALSO, SKEPTICS ARE PEEVISH ABOUT ODD THINGS.

It’s not just sceptics (as an Australian, I get peeved (?), peevish - I think ‘peeved’ sounds better - at the American spelling ‘skeptics’) who are peevish about odd things.  Bart Ehrman got rather peevish in one of his books at some Christians who think that the parents of Jesus Christ were Mr and Mrs Christ (although ‘Mr Christ’ was not actually the biological father of Jesus, allegedly, and Matthew and Luke in listing Jesus’ male ancestral line - different in the two accounts - was irrelevant.  Although one listed Adam as the son of God).

Like everyone, sceptics do get ‘bees in the bonnet’ about the oddest things, which are inexplicable to sensible people.  I wonder about the origin of ‘bees in the bonnet.’  I love bees.  They’re my favourite invertebrate, after spiders.  And perhaps octopuses.  I’d love to have a bee on my headwear.
Gebt ihr ihr ihr Buch zurück?

Offline The Latinist

  • Cyber Greasemonkey
  • Technical Administrator
  • Too Much Spare Time
  • *****
  • Posts: 7775
Re: Episode #709
« Reply #39 on: February 11, 2019, 11:34:06 AM »
It’s not just sceptics (as an Australian, I get peeved (?), peevish - I think ‘peeved’ sounds better - at the American spelling ‘skeptics’) who are peevish about odd things.

That's a silly thing to be peeved about, especially given the etymology of the word.
I would like to propose...that...it is undesirable to believe in a proposition when there is no ground whatever for supposing it true. — Bertrand Russell

Offline bachfiend

  • Not Any Kind of Moderator
  • Well Established
  • *****
  • Posts: 1796
Re: Episode #709
« Reply #40 on: February 11, 2019, 12:02:13 PM »
Where I am, it’s now February 12.  I want to be the first, hopefully, to wish everyone a Happy Darwin Day ( or a Happy Lincoln Day if you’ll prefer).
Gebt ihr ihr ihr Buch zurück?

Offline daniel1948

  • Isn’t a
  • Reef Tank Owner
  • *********
  • Posts: 8609
  • I'd rather be paddling
Re: Episode #709
« Reply #41 on: February 11, 2019, 12:17:10 PM »
The trolley would run over the fat man and continue on and kill the others, too. Congratulations, hero. 

This is basically what I said when I first heard this version of the trolley problem. Except I was a bit less certain. I said: “How do you know the fat man will stop the trolley? Maybe he misses the tracks, and is killed to no purpose. Or is crippled for life, also to no purpose.” But basically all versions of the trolley problem suffer from the same uncertainty: How do you ever know that your action will have the expected effect?
Daniel
----------------
"Anyone who has ever looked into the glazed eyes of a soldier dying on the battlefield will think long and hard before starting a war."
-- Otto von Bismarck

Offline Quetzalcoatl

  • Stopped Going Outside
  • *******
  • Posts: 5028
Re: Episode #709
« Reply #42 on: February 11, 2019, 12:18:50 PM »
Where I am, it’s now February 12.  I want to be the first, hopefully, to wish everyone a Happy Darwin Day ( or a Happy Lincoln Day if you’ll prefer).

Happy Darwin Day! I've got almost 6 hours left to the 12th.
"I’m a member of no party. I have no ideology. I’m a rationalist. I do what I can in the international struggle between science and reason and the barbarism, superstition and stupidity that’s all around us." - Christopher Hitchens

Offline daniel1948

  • Isn’t a
  • Reef Tank Owner
  • *********
  • Posts: 8609
  • I'd rather be paddling
Re: Episode #709
« Reply #43 on: February 11, 2019, 12:23:29 PM »
I can’t quite work out how the trolley problem could be reworked to the medical setting. 

You are in a Saw movie. The bad guy has infected 50 people with a virulent disease. He will give you the cure for 49 of them, on condition that you first inject one person of your choice with a poison that causes an agonizing death.

That’s how you turn the trolley problem into a medical one. And given how unrealistic and arbitrary the trolley problems are, I think the above fits in well enough.
Daniel
----------------
"Anyone who has ever looked into the glazed eyes of a soldier dying on the battlefield will think long and hard before starting a war."
-- Otto von Bismarck

Offline daniel1948

  • Isn’t a
  • Reef Tank Owner
  • *********
  • Posts: 8609
  • I'd rather be paddling
Re: Episode #709
« Reply #44 on: February 11, 2019, 12:34:17 PM »
I haven't listened to this episode yet (it's at the top of my queue), but I'd like to address a pet peeve of mine that I'm absolutely sure will annoy the crap out of me when I get to the segment.

I, and every Australian and British person I know, understand that Robin Hood has two names. First name Robin, surname Hood. Robin Hood. Americans, however, in almost all cases, pronounce it as though it is only one name: Robinhood. With the emphasis on the first syllable.

The weird thing is that Americans don't do that with other names with the same syllable count. Charlie Brown, for example, is not pronounced Charliebrown. Donald Trump is not Donaldtrump.

Okay, carry on. I might have more to say when I've listened to the episode.

From the Wikipedia entry on Robin Hood, under “Early References” comes this quote:

Quote
From 1261 onward, the names 'Robinhood', 'Robehod' or 'Robbehod' occur in the rolls of several English Justices as nicknames or descriptions of malefactors.

So there is some precedent for Robinhood as a single name.
Daniel
----------------
"Anyone who has ever looked into the glazed eyes of a soldier dying on the battlefield will think long and hard before starting a war."
-- Otto von Bismarck

 

personate-rain
personate-rain