Uniform Distribution Puzzle/Breaking Sticks

[pzhon]

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Hey, guys, I was kidding the first time about being mean. Now you both seem really mad. You shouldn't be. No fraud or slander is intended.

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Now you are trying to say this is just a big joke, and it is our fault if we are upset. You're way out of line, whether you choose to acknowledge it or not. An apology is in order, not just to us, but to other readers of this forum.

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When someone asks a puzzle for which they already know the answer, I give an answer and as much or little explanation as I care to.

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In mathematics, the problem normally includes both finding the answer and justifying it. (I usually add a third part, communicating to others.)

If you hadn't posted the technobabble about the continued fraction, I wouldn't be upset. However, you posted it after I posted a proof, and you said, "As to showing my work..." as though the continued fraction has something to do with a proof.

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If I have a clever approach ...
If I slogged through it by brute force...
You may not like those kinds of answers, might I suggest the obvious solution is not to read them?


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In what context do you think it is appropriate to post something misleading in order to pretend you have solved a problem which you have not?

Do you understand what you were claiming? If you have a connection between this problem and a continued fraction expansion for ln(2), this may be the simplest justification for the continued fraction expansion for ln(2), and it would be publishable.

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phzon, I was not "asked to show my work."


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WTF? You were asked to show your work with the sentence, "Show your work." You didn't overlook this, since you later said, "as to showing my work..."

Is there some reason you have such difficulty copying 5 letters in order, even if you can't figure out what they mean? Is garbling my name every time supposed to be witty?

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I was told I got "0 points" and accused of getting it by simulation. I generally respond straightforwardly to requests, but tease in response to accusations.


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You are trying to rationalize your behavior, but you have the order wrong. You posted the misleading claim about the continued fraction before I asked whether that came from a simulation. You can't justify "teasing" us with a flagrantly unethical post by pointing to the response "accusations."

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I am now told "my bluff has been called" (without, I notice, any money being put up by the alleged caller),

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In case you hadn't noticed, your credibility is on the line. This is not a zero-sum game, and there was very little to gain from bluffing into a dry sidepot as you did. Most mathematicians would not have been able to tell that the statement about the continued fraction was misleading technobabble, but they probably would have ignored it.

I offered (and offer) to bet money in case losing the respect you have earned is not enough for you.

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No one has to read posts they don't like. There are no rules about using simulation, or fraud, or teasing.

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You violated the ethics of mathematics. You abused the trust you had built up. You still don't have the guts to apologize or admit that it's inappropriate to mislead people intentionally in a mathematical discussion. Nothing is wrong with using a simulation (or even a joke), if you identify it, rather than suggesting that you have a logical argument.

ln(2) is not [0;1,2,3,4,5,...] and you have given no logical connection between this problem and either this continued fraction or a continued fraction expansion for ln(2).

[pzhon]

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I'm beginning to see the problem here. You want to see [img]/images/graemlins/smile.gif[/img] icons near jokes, I assume you also like people to say "here comes a joke" before saying anything not meant to be taken literally.

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No. If you read my past posts, you will find plenty of jokes I have made without inserting a smilie, and they are not necessary when there is a reasonable expectation that the audience can tell you are joking.

Stating that you have done something mathematically that you have not in a way that 99% of the forum readers will be unable to detect is not a joke. It is unethical.

Of those who understand what "recall that ln(2) = 1/(1 + 1/(2 + 1/(3 + . . ." means, how many did you think would see it as a joke? How many would think it means the false statement ln(2) = [0;1,2,3,4,5...]? How many would think it means that you have established a connection between a continued fraction and this problem?

I don't want yet more nonsense from you. I want an admission that this was at best a horribly botched joke for which you should apologize, because it came out as a lie, not a joke.

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I've been waiting for someone to ask me how to solve the problem,


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"Show your work."

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I'm a "magic word" kind of guy.

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I'm an honest kind of guy. You're being an [censored].

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Here is my peace offering. I allege that I have put a simple, clear analytic solution to the problem in white below. I apologize for teasing Jason1990 and phzon. In return, I ask both those gentlemen to post, before they read my alleged solution, what they will do if it is simple, clear and correct.

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In your peace offering, you still can't copy the 5 letters of "pzhon" in order?

I have not yet read your solution. My response depends on whether your solution is original and involves the continued fraction you posted. If so, I will post that I am impressed, and I will offer to help you to publish it in a respected mathematics journal, if possible. If it appears that you have found a connection to the continued fraction, but that this is not original, I'll post that I'm impressed. If it has nothing to do with the continued fraction, I will again request an explanation for and retraction of what appears to be a flagrantly unethical intentional misstatement.

[AaronBrown]

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Now you are trying to say this is just a big joke, and it is our fault if we are upset. You're way out of line, whether you choose to acknowledge it or not. An apology is in order, not just to us, but to other readers of this forum.

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I take it you reject my peace offering. I don't know what more I can do. I'm not saying it was all a big joke, all the math I posted was sincere and correct, including the continued fraction and the other two solutions. Only the last one was meant to be complete and clear.

I agree that you have only yourself to blame for being upset. You have assumed you were lied to without evidence as far as I can see, you haven't asked me to explain, and you keep reading posts that make you mad. Who else is to blame? I also agree that apologies are in order. I have made mine.

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If you hadn't posted the technobabble about the continued fraction, I wouldn't be upset. However, you posted it after I posted a proof.

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But you're only upset because you think the continued fraction is technobabble. Why do you think that? I'm sorry I missed your proof, but I don't see why I shouldn't post my answer after yours.

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In what context do you think it is appropriate to post something misleading in order to pretend you have solved a problem which you have not?

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In a joking context. However, that's not what I did. I stand by all the math I've posted. I did solve the problem. I think I offered you a fair opportunity to verify or disprove that. You haven't taken it.

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Do you understand what you were claiming? If you have a connection between this problem and a continued fraction expansion for ln(2), this may be the simplest justification for the continued fraction expansion for ln(2), and it would be publishable.

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I think I see some of your confusion. The continued fraction expansion of ln(2) is not unique.

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WTF? You were asked to show your work with the sentence, "Show your work."[/url]

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Sorry, I meant "ask" as in "a sentence ending with a question mark." I won't hold out for "often preceded by 'please'."

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You can't justify "teasing" us with a flagrantly unethical post by pointing to the response "accusations."

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I just don't see the ethics here. I posted work I think it correct, I admit it is not complete and not a proof. I'm not submitting it for publication, or to get money from anyone. The first post that annoyed me was the "0 points" one, so I posted a teasing (but not fraudulent or unethical, whatever that means in this context) one. It was teasing only in that it hinted at the solution without showing all the steps. Then came the accusation of simulation and guessing, which prompted another tease. Then I figured out the two of you were really mad, after which I have stopped teasing. It was never meant to upset you.

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In case you hadn't noticed, your credibility is on the line.

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I hadn't noticed. I didn't have any in the first place with you, as you have called me a liar, and worse, without asking whether I can back up my statements, or reading the clear, simple solution I claimed to have. Perhaps it is on the line from others, if so, let's hear from them.

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I offered (and offer) to bet money in case losing the respect you have earned is not enough for you.

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All you have to do is post "I will donate $100 to charity if Aaron's white font explanation is clear and correct," and I will donate $100 to charity if you think it is not clear and correct. If you want to bet, bet. No one's holding you back.

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You violated the ethics of mathematics.

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I don't know what the ethics of mathematics are, nor the mathematics of ethics. But you seem sure. Anyway, I stand by all the mathematics I've posted here; and I think all the other stuff conforms to the ethics of message boards.

[pzhon]

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If it has nothing to do with the continued fraction, I will again request an explanation for and retraction of what appears to be a flagrantly unethical intentional misstatement.

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Your solution appears to be correct. However, it has nothing to do with a continued fraction expansion for ln(2). So, I repeat my request for an explanation/retraction of your statement, "As to showing my work for the ln(2) answer, recall that ln(2) = 1/(1 + 1/(2 + 1/(3 + . . .".

[img]/images/graemlins/diamond.gif[/img] This is at best highly misleading. The normal interpretation of "ln(2) = 1/(1 + 1/(2 + 1/(3 + . . ." is false.

[img]/images/graemlins/diamond.gif[/img] This has nothing to do with the work you just showed.

[jason1990]

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I'm beginning to see the problem here. You want to see [img]/images/graemlins/smile.gif[/img] icons near jokes, I assume you also like people to say "here comes a joke" before saying anything not meant to be taken literally.

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Man, what's wrong with you? You said, "Boy, that's mean" and "More mean stuff." Then later you say, "Hey, guys, I was kidding the first time about being mean." How about if I tell you you're a jerk? I'll come back tomorrow and tell you I was kidding. Then I'll ridicule you for not being able to figure it out without an emoticon. Really, what's wrong with you? You're like a split personality. One of them is BruceZ. The other is a Troll.

You can rest assured you won't get an apology from me, no matter what you've typed in white. Correct or not, you've wasted enough of my time with your crappy "jokes" and your coy games.

[jason1990]

Well, I just read your solution. It is now indisputable. You truly are a jerk. This is a lie:

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As to showing my work for the ln(2) answer, recall that ln(2) = 1/(1 + 1/(2 + 1/(3 + . . .

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This is a lie:

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Now compute the probability of losing the reduced game:

[Integral from 0 to 0.5]{[Integral from 0.5 to 1] 4*x/(1-x) dy} dx
=[Integral from 0 to 0.5]{[Integral from 0.5 to 1] [4/(1-x) - 4] dy} dx
= [Integral from 0 to 0.5]{2/(1-x) - 2} dx
=-2*ln(1-x) - 2*x from 0 to 0.5
= -2*ln(0.5) - 2
= 2*ln(2) - 1

0.5 plus half of that is 0.5 + ln(2) - 0.5 = ln(2), the chance of losing.

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You intentionally posted nonsense in order to waste everybody's (or just my?) time. I wonder why. Ah! I think I see...

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The first post that annoyed me was the "0 points" one...

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Man, you need to grow up. (Not to mention you need to stop starting fights in bars.) I see from your webpage that you claim to be appearing at the Courant Institute's Mathematical Finance Seminar this year. I do not, however, see you on the schedule at Courant's webpage. But if you do ever make it on the seminar calendar, I'm tempted to fly out there and say hi. Maybe we could go to a bar together.

[AaronBrown]

I see you both ignored my request and read the solution without putting up anything for bets. Oh, well. I also think you both admit that I did have an analytic solution, but don't feel the need to retract or apologize for repeatedly saying that I didn't. Oh, well again.

Now you both seem to be shifting ground to claim my hints were misleading (in order to keep the volume down, I'll omit the words you do use). Both hints were intended to be hints, that is things that might help someone see the solution, but also give room for people to mislead themselves. Neither of you has asked for explanations of the hints.

You both took the bait on the continued fraction hint to assume that the next term was 1/4. I posted only the first three terms. You both took the bait on the second hint to assume the bounds of the integrals were the points of first and last break. Both hints are completely correct, and both lead to correct answers, but both were written to include bait.

I'm genuinely sorry that I made both of you mad. I think I've been civil, that all my math has been correct, and that my hints were entirely in the spirit of a discussion of a puzzle. I haven't called either of you worse than "mean," which was intended in fun, and I immediately retracted when you took it seriously. I've apologized for posting the hints before the analytic solution, and for getting annoyed at the accusations so that I made the hints trickier than either of you like.

If there's anything else I can do to cheer either of you up, please let me know. I don't promise to do it, but if it's reasonable and within my power, I'll consider it seriously. I'm really not trying to do any of the bad things you guys think I did.

[jason1990]

Look BruceZ/Troll, this is what happened. I pissed you off by "giving you a zero." You reacted by posting intentionally misleading material aimed at wasting people's time. It was a childish and petty thing to do, and you realized that. So now you're trying to play it off like that's not what happened. What would cheer me up is if you got out of my thread.

Now, would anyone other than BZT like to take a stab at the prisoner puzzle?

[PairTheBoard]

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I ask both those gentlemen to post, before they read my alleged solution, what they will do if it is simple, clear and correct. It could be apologize for doubting me, give $100 to charity, kiss the next person they see, be tolerant of the next person who tries to tease them

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Although I was not in on the bet, after reading your solution I immediately went next door and gave my neighbor a nice juicy open mouth kiss. Unfortunately she called the police and is having a restraining order issued against me.

If it's a formal request you need, I for one would like to see your thinking behind the continued fraction and double integral. There are nearly 400 views of this thread and I doubt the 4 of us have looked at it 100 times apiece. So there are probably quite a few others who would like to see your other 2 solutions as well. I'll even say please.

fwiw, I thought the solution you gave was pretty slick. I'm sure pzhon and jason's were good too but I gave up reading them when I saw differential equations and Taylor Series expansions. [img]/images/graemlins/shocked.gif[/img]

PairTheBoard

[AaronBrown]

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What would cheer me up is if you got out of my thread.


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Fair enough, I'll do that. I realize I'm violating it by posting this, but it's intended to reassure you rather than irritate you. I won't post or read further here.

To respect PairTheBoard's request, I'll start a new thread explaining the continued fraction and reduced problem hints. I might suggest that anyone who got mad at my posts on this thread, stay away from the new one. I'm not trying to tell anyone what to do, just keep the peace.