All of William_Kasper's Comments + Replies

"Your dirty lying teachers use only the midnight to midnight 1 day (ignoring 3 other days) Time to not foul (already wrong) bible time."

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Mr. Bonaccorsi:

Here are two links to classic posts by Eliezer Yudkowsky that you may find pertinent to the second dialog from your last comment. I hope you enjoy them.

How to Convince Me That 2 + 2 = 3

The Simple Truth

2JohnBonaccorsi
Thank you for those links, Mr. Kasper. In taking a quick first look at the two pieces, I've noticed passages with which I'm familiar, so I must have encountered those posts as I made my initial reconnaissance, so to speak, of this very-interesting website. Now that you've directed my attention to those posts in particular, I'll be able to read them with real attention.

Let's establish some notation first:

P(H): My prior probability that the coin came up heads. Because we're assuming that the coin is fair before you present any evidence, I assume a 50% chance that the coin came up heads.

P(H|E): My posterior probability that the coin came up heads, or the probability that the coin came up heads, given the evidence that you have provided.

P(E|H): The probability of observing what we have, given the coin in question coming up heads.

P(E&H): The probability of you observing the evidence and the coin in question coming up hea... (read more)

5JohnBonaccorsi
Thank you, Mr. Kasper, for your thorough reply. Because all of this is new to me, I feel rather as I did the time I spent an hour on a tennis court with a friend who had won a tennis scholarship to college. Having no real tennis ability myself, I felt I was wasting his time; I appreciated that he’d agreed to play with me for that hour. As I began to grasp the reasoning, I decided that each time you state the chance that the coin is heads, you are stating a fact. I asked myself what that means. I imagined the following: I encounter you after you’ve spent two months traveling the world. You address me as follows: “During my first month, I happened upon one hundred men who told me—each of them—that he had just flipped a coin twice. In each case, I asked, ‘Was at least one of the results heads?’ Each man said yes, and I knew that, in each case, the probability was 1/3 that both flips had been heads. “In my second month, I again happened upon one hundred men who told me—each of them—that he had just flipped a coin twice. Each added, ‘One of the results was heads; I don’t remember what the other was.’ I knew that, in each case, the probability was 1/2 that both flips had been heads. “Just as I was about to return home, I was approached by a man who had video recordings of the coin flips that those two hundred men had mentioned. In watching the recordings, I learned that both flips had been heads in fifty of the first one hundred cases and that, likewise, both flips had been heads in fifty of the second one hundred cases.” In considering that, Mr. Kasper, I imagined the following exchange, which you may imagine as taking place between you and me. I speak first. “My dog is in that box.” “Is that a fact?” “Yes.” “In saying it’s a fact, you mean what?” “I mean I regard it as true.” “Which means what?” “Which means I can imagine events that culminate in my saying, ‘I seem to have been mistaken; my dog wasn’t in that box.’” “For example.” “You walk over to the bo

No, the chance that the kidnapped child is a boy is 1/2.

In the correct version of this story, the mathematician says "I have two children", and you ask, "Is at least one a boy?", and she answers "Yes". Then the probability is 1/3 that they are both boys.

In the correct version of the story, you do not gain access to any information that allows you to differentiate between the mathematician's two children and identify a specific child as a boy.

A woman says, "I have two children." You respond, "What are thei

... (read more)
0JohnBonaccorsi
Thank you for the reply, Mr. Kasper. Let me try this. You come upon a man who, as you watch, flips a 50-50 coin. He catches and covers it; that is, the result of the flip is not known. I, who have been standing there, present you the following question: "What is the chance the coin is heads?" That's Question A. What is your answer? The next day, you come upon a different man, who, as you watch, flips a 50-50 coin. Again, he catches it; again, the result is not revealed. I, who have been standing there, address you as follows: "Just before you arrived, that man flipped that same coin; it came up heads. What is the chance it is now heads?" That's Question B. What is your answer? If you and I were having this discussion in person, I would pause here, to allow you to answer Questions A and B. Because this is the internet, where I don't know how many opportunities you'll have to reply to me, I'll continue. You come upon a man who is holding a 50-50 coin. I am with him. There is the following exchange: I (to you, re the man with the coin): This man has just flipped this coin two times. You: What were the results? I: One of the results was heads. I don’t remember what the other was. Question C: What is the chance the other was heads? Let’s step over Question C (though I'll appreciate your answering it). After I tell you that one of the results was heads but that I don't remember what the other was, you say: "Which do you remember, the first or the second?" I reply, "I don’t remember that either." Question D: What is the chance the other was heads?

But why is the goal of voting an example important? For me, what matters is creating your own example, and helping those who put theirs.

I agree with you. Receiving votes on our posts and comments is only an instrument to help us build better content. The content and how people use it is what matters.

Although the karma voting system provides imperfect information, it provides cheap imperfect information. Separating the question and answer seems like an easy way to make better use of the information that the votes provide. One benefit that I see from the ... (read more)

Or you could put your answer in the body as an example, explaining that you've also posted the answer as a comment. Then people can vote on your answer independently from your question, and you can establish the expected form before people begin reading other people's comments.

1diegocaleiro
Then that I will try on next time. Just one thing: both you and gwillen mentioned "voting on your example" I didn't think the point of giving an example was to allow for it being voted. An example is an example. Sure, one may like or dislike it, and think it more or less good. But why is the goal of voting an example important? For me, what matters is creating your own example, and helping those who put theirs. Advice is 99,9% of time not a 1 bit thing that can be summarized in thumbs down or up.

rstarkov wrote a nice discussion piece on the two envelopes problem: Solving the two envelopes problem. thomblake commented that the error most people make with this problem is treating the amounts of money in the envelopes as fixed values when calculating the expectation.

Here's a solution to a more general version of the problem:

Let's say that the red envelope contains N times as much money as the blue envelope with probability p, and the blue envelope contains N times as much money as the red envelope with probability (1 - p).

Without loss of generality, N is at least 1.

If N = 1, both envelopes contain the same amount, and there is no point in switching.

If N > 1, let the variable s represent the smaller amount of money between the amounts of the two envelopes. So one envelope contains s, and the other envelope contain... (read more)

[Political "gaffe" stories] are completely information-free news events, and they absolutely dominate political news coverage and analysis. It's like asking your doctor if the X-rays show a tumor, and all he'll talk about is how stupid the radiologist's haircut looks. . . . ["Blast"] stories are. . . just as content-free as the "gaffe" stories. But they are popular for the same reason: There's a petty, tribal satisfaction in seeing a member of our team really put the other team in their place. And there's a rush of outrage ad

... (read more)

I am consistently impressed by the quality of the writing that comes out of Cracked, especially relative to what one might expect given its appearance.

instead of covering pending legislation or the impact it could have on your life

If "impact on your life" is the relevant criterion, then it seems to me Wong should be focusing on the broader mistake of watching the news in the first place. If the average American spent ten minutes caring about e.g. the Trayvon Martin case, then by my calculations that represents roughly a hundred lifetimes lost.

It's weird how proud people are of not learning math when the same arguments apply to learning to play music, cook, or speak a foreign language.

http://xkcd.com/1050/

2A1987dM
Not many people are required to take cooking classes, hardly any goes through 20 years after graduating without ever needing to cook, and there are lots people “proud” of not learning foreign languages. And playing music is higher-status than doing maths.

I think that the relevant distinction is "is it really horribly unpleasant and I make no progress no matter how long I spend and I don't find correct output aesthetically pleasing."

"Weird" is a statement about your understanding of people's pride, not a statement about people's pride.

Please correct me if any of my assumptions are innacurate, and I apologize if this comment comes off as completely tautological.

Expected utility is explicity defined as the statistic

U(x)})

where X is the set of all possible outcomes associated with a particular gamble, p(x) is the proportion of times that outcome x occurs within the gamble, and U(x) is the utility of outcome x, a function that must be strictly increasing with respect to the monetary value of outcome x.

To reduce ambiguity:

  • 1A, 1B, 2A, and 2B are instances of gambles.

  • For 1B, the possible o

... (read more)
0thomblake
That all seems pretty uncontroversial.

Hello. I'm William. I am a thirty year-old undergraduate student in the University of Wisconsin--Madison's Industrial and Systems Engineering department, with some additional study in Computer Science.

The study of logic and rational thought have always been hobbies of mine. My interest in mathematical optimization techniques has also been developing for decades, but this interest in these dark arts started taking steroids when I realized simple ways to apply the techniques to video games and Poker.

I originally stumbled upon this site two years ago, while ... (read more)

0orthonormal
There's a good regular meetup here in Madison; you should check it out! And yeah, the Allais paradox was one of the biggest "wow" moments for me with the original sequences, too.