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LessWrongWiki: What the hell are they talking about?

Started by LMNO, August 27, 2013, 04:23:24 PM

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The Good Reverend Roger

Quote from: Bebek Sincap Ratatosk on September 03, 2013, 07:07:21 PM
Quote from: Surprise Happy Endings Whether You Want Them Or Not on September 03, 2013, 05:41:35 PM
Quote from: McGrupp on September 03, 2013, 05:36:45 PM
The conversation here is almost exactly like the conversation in my head when I was trying to figure out the problem. Still makes my head hurt.

My understanding is that the name Florida is meant to be misleading. It could be replaced with Susan, or anything. I think it's just important that we know some type of specific information about one of the girls, I think.

but I'm still missing something.

It sounds like, from the excerpt that Rat posted, the original author of the question was using the name Florida to trigger some kind of discussion of the theoretical economics of the name; it doesn't appear to be a book about statistics, but a book about randomness, and so the question is not meant to be answered literally from a statistical perspective.

Somehow this makes the problem even more interesting in some discordian koan way ;)

Koans are for people who can't think without them.

TGRR,
Doesn't think, EITHER way.  :whack:
" It's just that Depeche Mode were a bunch of optimistic loveburgers."
- TGRR, shaming himself forever, 7/8/2017

"Billy, when I say that ethics is our number one priority and safety is also our number one priority, you should take that to mean exactly what I said. Also quality. That's our number one priority as well. Don't look at me that way, you're in the corporate world now and this is how it works."
- TGRR, raising the bar at work.

Kai

Quote from: LMNO, PhD (life continues) on September 03, 2013, 05:49:14 PM
Ok, I think I'm getting on board, but...
Quote from: Surprise Happy Endings Whether You Want Them Or Not on September 03, 2013, 05:19:28 PM
Once again, think of a fair coin that you have just flipped, and it came up heads. What is the chance that it came up tails? None, because it came up heads.

When you have not yet flipped the coin, it has a 50% chance of coming up heads. So does the second coin. To determine the probability that both will come up heads, you can multiply .50 x .50 and find that the probability is .25, right?

Once it has been flipped, there is no more probability, or, you could state it as the probability that it came up heads is 100%.

The second coin flip still has a 50% probability of coming up heads. 1 x .50 = .50. The probability that both coins will be heads, once the first coin has been flipped and came up heads, is 50%, the same as the probability for a single coin flip.

So, if we real-timed this..

I happen to have a coin.  Before I flip it, what's the probability it will turn up heads twice?  25%.

I flip the coin once, and don't tell you what it was.  Before I flip the second one, what's the probability it will turn up heads twice?  25%.

I flip the coin a second time, and don't tell you what either coin is. What's the probability it will turn up heads twice?  25%.

I turn over one of the coins.  It's heads.  What's the probability it will turn up heads twice?


...oh.


OH.

I turn over one of the coins.  It's heads.  What's the probability the other one is heads?  50%



And if I ask you what were the chances both of them would have come up heads... would you say 25%?

This post is /directly relevant/. http://lesswrong.com/lw/oj/probability_is_in_the_mind/

QuoteProbabilities express uncertainty, and it is only agents who can be uncertain.  A blank map does not correspond to a blank territory.  Ignorance is in the mind.
If there is magic on this planet, it is contained in water. --Loren Eisley, The Immense Journey

Her Royal Majesty's Chief of Insect Genitalia Dissection
Grand Visser of the Six Legged Class
Chanticleer of the Holometabola Clade Church, Diptera Parish

Bebek Sincap Ratatosk

Quote from: Kai on September 03, 2013, 11:12:36 PM
Quote from: LMNO, PhD (life continues) on September 03, 2013, 05:49:14 PM
Ok, I think I'm getting on board, but...
Quote from: Surprise Happy Endings Whether You Want Them Or Not on September 03, 2013, 05:19:28 PM
Once again, think of a fair coin that you have just flipped, and it came up heads. What is the chance that it came up tails? None, because it came up heads.

When you have not yet flipped the coin, it has a 50% chance of coming up heads. So does the second coin. To determine the probability that both will come up heads, you can multiply .50 x .50 and find that the probability is .25, right?

Once it has been flipped, there is no more probability, or, you could state it as the probability that it came up heads is 100%.

The second coin flip still has a 50% probability of coming up heads. 1 x .50 = .50. The probability that both coins will be heads, once the first coin has been flipped and came up heads, is 50%, the same as the probability for a single coin flip.

So, if we real-timed this..

I happen to have a coin.  Before I flip it, what's the probability it will turn up heads twice?  25%.

I flip the coin once, and don't tell you what it was.  Before I flip the second one, what's the probability it will turn up heads twice?  25%.

I flip the coin a second time, and don't tell you what either coin is. What's the probability it will turn up heads twice?  25%.

I turn over one of the coins.  It's heads.  What's the probability it will turn up heads twice?


...oh.


OH.

I turn over one of the coins.  It's heads.  What's the probability the other one is heads?  50%



And if I ask you what were the chances both of them would have come up heads... would you say 25%?

This post is /directly relevant/. http://lesswrong.com/lw/oj/probability_is_in_the_mind/

QuoteProbabilities express uncertainty, and it is only agents who can be uncertain.  A blank map does not correspond to a blank territory.  Ignorance is in the mind.

That post was awesome and I actually understood it!
- I don't see race. I just see cars going around in a circle.

"Back in my day, crazy meant something. Now everyone is crazy" - Charlie Manson

jeffjo

Sorry to resurrect an old thread, but I just found this, and there is a critical point missing.
Quote from: LMNO, PhD (life continues) on September 03, 2013, 05:49:14 PM
So, if we real-timed this..

I happen to have a coin.  Before I flip it, what's the probability it will turn up heads twice?  25%.

I flip the coin once, and don't tell you what it was.  Before I flip the second one, what's the probability it will turn up heads twice?  25%.

I flip the coin a second time, and don't tell you what either coin is. What's the probability it will turn up heads twice?  25%.

I turn over one of the coins.  It's heads.  What's the probability it will turn up heads twice?


...oh.


OH.

I turn over one of the coins.  It's heads.  What's the probability the other one is heads?  50%



And if I ask you what were the chances both of them would have come up heads... would you say 25%?
Let's try it a different way:
  • I happen to have two coins.  Before I flip either, what's the probability they will turn up the same way?  50%.
  • I flip one coin and keep it hidden under a cup.  Before I flip the second one, what's the probability it will turn up the same way as they first?  50%.
  • I flip the second coin, keeping it hidden as well. What's the probability they turned up the same way?  50%.
  • I let you pick a cup, and I reveal its coin.  It's heads.  What's the probability the other is heads?
This is also 50%. If that isn't obvious from the progression, consider what you would have said if it had come up tails. The answer can't be different, so call it X for both questions. And if it is X for both questions, it is X if I just ask you to pick a cup and don't reveal its coin. And that's the same as the previous question.

The temptation to give a different answer is a paradox; and it even has a name. It is known as Bertrand's Box Paradox. The need to get the same answer, when the question is about symmetric options like  heads or tails, forces the answer to be the same as when nothing was revealed.
  • Suppose, instead if you picking a cup, you ask me if either is heads. I look at both, and reveal one, showing that it is heads.  What's the probability the other came up the same way?
If both had been tails, originally a 25% chance, I couldn't have done this. Of the remaining 75%, 25% has two heads and 50% has a heads and a tails. So the answer is 25%/75%, or 33%.

Bertrand's Box Paradox doesn't apply, because the possible answers to your question aren't symmetric. The probability of two of the same result must be 100% if I can't reveal a heads.
  • Suppose, instead of letting you pick anything, I look under both cups and show that one is a heads. What's the probability the other is heads?
This can't be answered without more information. If I decided to show a random coin (say, the left cup), the answer is 50% just like when you picked a cup. If I decided to show a heads if I could, the answer is 33%. And if I decided to show a tails if I could, but found I couldn't so I showed you a heads, the answer is 100%.

So the question is ambiguous. But if you had to pick one of those answers as "best," which would you pick? Can you apply Bertrand's Box Paradox?

The Florida question is essentially the same. The question is ambiguous, but maybe a "best" answer is possible. And it isn't the one usually given.

Reginald Ret

Quote from: Kai on September 03, 2013, 11:12:36 PM
Quote from: LMNO, PhD (life continues) on September 03, 2013, 05:49:14 PM
Ok, I think I'm getting on board, but...
Quote from: Surprise Happy Endings Whether You Want Them Or Not on September 03, 2013, 05:19:28 PM
Once again, think of a fair coin that you have just flipped, and it came up heads. What is the chance that it came up tails? None, because it came up heads.

When you have not yet flipped the coin, it has a 50% chance of coming up heads. So does the second coin. To determine the probability that both will come up heads, you can multiply .50 x .50 and find that the probability is .25, right?

Once it has been flipped, there is no more probability, or, you could state it as the probability that it came up heads is 100%.

The second coin flip still has a 50% probability of coming up heads. 1 x .50 = .50. The probability that both coins will be heads, once the first coin has been flipped and came up heads, is 50%, the same as the probability for a single coin flip.

So, if we real-timed this..

I happen to have a coin.  Before I flip it, what's the probability it will turn up heads twice?  25%.

I flip the coin once, and don't tell you what it was.  Before I flip the second one, what's the probability it will turn up heads twice?  25%.

I flip the coin a second time, and don't tell you what either coin is. What's the probability it will turn up heads twice?  25%.

I turn over one of the coins.  It's heads.  What's the probability it will turn up heads twice?


...oh.


OH.

I turn over one of the coins.  It's heads.  What's the probability the other one is heads?  50%



And if I ask you what were the chances both of them would have come up heads... would you say 25%?

This post is /directly relevant/. http://lesswrong.com/lw/oj/probability_is_in_the_mind/

QuoteProbabilities express uncertainty, and it is only agents who can be uncertain.  A blank map does not correspond to a blank territory.  Ignorance is in the mind.

I'm having trouble understanding that.
That may be because I am trying to be a probabilist.
Is probabilism inherently solipsistic?
If that is true, then why did I not notice that?
Lord Byron: "Those who will not reason, are bigots, those who cannot, are fools, and those who dare not, are slaves."

Nigel saying the wisest words ever uttered: "It's just a suffix."

"The worst forum ever" "The most mediocre forum on the internet" "The dumbest forum on the internet" "The most retarded forum on the internet" "The lamest forum on the internet" "The coolest forum on the internet"

Pæs

Quote from: jeffjo on July 12, 2014, 02:39:44 PM
I happen to have two coins.  Before I flip either, what's the probability they will turn up the same way?  50%.

wat

Mesozoic Mister Nigel

Quote from: Pæs on July 13, 2014, 11:46:11 PM
Quote from: jeffjo on July 12, 2014, 02:39:44 PM
I happen to have two coins.  Before I flip either, what's the probability they will turn up the same way?  50%.

wat

Probability they will both flip to heads is .50 x .50. Probability they will both flip to tails is also .50 x .50. Each probability is .25, both probabilities combined is .50.

Essentially you have four conditions:

1. Coin A is heads and coin B is tails .25
2. Coin A is tails and coin B is heads .25
3. Coin A is heads and coin B is heads. .25
4. Coin A is tails and coin B is tails. .25

So you end up with 50% probability of one of each, and 50% probability of two of one.
"I'm guessing it was January 2007, a meeting in Bethesda, we got a bag of bees and just started smashing them on the desk," Charles Wick said. "It was very complicated."


Pæs

Quote from: The Right Reverend Nigel on July 15, 2014, 05:44:39 AM
Quote from: Pæs on July 13, 2014, 11:46:11 PM
Quote from: jeffjo on July 12, 2014, 02:39:44 PM
I happen to have two coins.  Before I flip either, what's the probability they will turn up the same way?  50%.

wat

Probability they will both flip to heads is .50 x .50. Probability they will both flip to tails is also .50 x .50. Each probability is .25, both probabilities combined is .50.

Essentially you have four conditions:

1. Coin A is heads and coin B is tails .25
2. Coin A is tails and coin B is heads .25
3. Coin A is heads and coin B is heads. .25
4. Coin A is tails and coin B is tails. .25

So you end up with 50% probability of one of each, and 50% probability of two of one.

Oh, the SAME WAY. Reading comprehension issue, don't mind me.

Mesozoic Mister Nigel

"I'm guessing it was January 2007, a meeting in Bethesda, we got a bag of bees and just started smashing them on the desk," Charles Wick said. "It was very complicated."


Reginald Ret

Brainfart: The difference between interchangable and identical becomes important when you deal with quantums: There are no mecha-gazillion protons in the universe, there is only one and it has mecha-gazillion instances of existence.

A proton ain't nothing but an instance of a probabilistic interaction.

Incidentally, the same occurs with theoretical coin-flips.  :horrormirth:
Lord Byron: "Those who will not reason, are bigots, those who cannot, are fools, and those who dare not, are slaves."

Nigel saying the wisest words ever uttered: "It's just a suffix."

"The worst forum ever" "The most mediocre forum on the internet" "The dumbest forum on the internet" "The most retarded forum on the internet" "The lamest forum on the internet" "The coolest forum on the internet"

LMNO

What the hell are you talking about?  Wait.  Is this that "there is only one quanta" bullshit?  Feynman was stoned out of his gourd when he came up with that one.

Reginald Ret

Quote from: LMNO, PhD (life continues) on July 24, 2014, 01:56:15 PM
What the hell are you talking about?  Wait.  Is this that "there is only one quanta" bullshit?  Feynman was stoned out of his gourd when he came up with that one.
I have not read what Feynman said about it, but I don't think that is what i mean.
I mean that things on the level that quantum mechanics deals with are definitively identical, not just interchangable. You can't 'exchange' one electron for another, it is a meaningless concept.
Not so in tires, you can replace one tire with another and the car still works despite having one of its parts changed. The tire has been changed.

With electrons there is no slight difference in functionality, there is no change at all. And I mean that in the absolute way, I'm not just saying that there is no detectable change.
Electrons (and their siblings) don't exist outside of their context: They are patterns of interaction, nothing more. Being patterns they are pure abstraction, unlike the objects on the scale we are used to think on.

Argh. Again, I can't tell if i am communicating effectively.
Lord Byron: "Those who will not reason, are bigots, those who cannot, are fools, and those who dare not, are slaves."

Nigel saying the wisest words ever uttered: "It's just a suffix."

"The worst forum ever" "The most mediocre forum on the internet" "The dumbest forum on the internet" "The most retarded forum on the internet" "The lamest forum on the internet" "The coolest forum on the internet"