Open Thread Posted by christian h., 12 Apr 2007 07:29 pm

Weird Mathematics & Open Thread

We have all heard of the famous Monty Hall problem, and only the most stubborn
still disbelieve the solution - you gotta switch!

In this spirit, here’s another one. Let’s say you have a choice of two envelopes containing money, one of them twice as much as the other. You are not, however, told how much money. You select one envelope; a person opens the envelope you chose and gives you the opportunity to change your choice to the other envelope. What should you do? Is there a paradox here, and if so, how is it resolved?

We accept all answers - mathematical, poetic, political,…

Also, this is an Open Thread.

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Responses to “Weird Mathematics & Open Thread”

  1. on 13 Apr 2007 at 8:03 am 1. JP Stormcrow said …

    I am probably off base here because for some reason I think that this may be my unlucky day.

    At first blush, this seemed to be either trivial or I need more information (the person to tell me how much money was in there.) But just as I was about to launch into basically writing WTF on that, I think I see why it might be “paradoxical” - my restatement:

    I do not know the amount of cash in the opened envelope, but call it X. Now it appears that I should always switch, because at worst I “lose” 1/2x from my current position, while I stand to gain x. But lets say after I switch to the 2nd one the same offer is made again, the logic is the same and I should switch back. (And potentially so on ad infinitum…. - and yet in fact I am no better off than when I started.)

    So I believe that I have framed it, but have not thought through any potential resolution.

    I simultaneously love and hate this type of stuff.
    In the spirit of an Acrostic poem I posted over at James Killus site let me just say:

    For poor confused, enfeebled man
    Understanding such a devilish test
    Cannot have been dreamt of in God’s great plan.
    Keep them to yourself please, and let us rest

  2. on 13 Apr 2007 at 8:12 am 2. JP Stormcrow said …

    Here is the poem I mentioned:
    From John Bishop Peale - who as far as I know generally played it straight. (he was the model for a character in Ths Side of Paradise)

    .. remember, I am not cursing at you, I’m cursing with you.

    Famously she descended, her red hair
    Unbound and bronzed by sea-reflections, caught
    Crinkled with sea-pearls. The fine slender taut
    Knees that let down her feet upon the air,
    Young breasts, slim flanks and golden quarries were
    Odder than when the young distraught
    Unknown Venetian, painting her portrait, thought
    He’d not imagined what he painted there.

    And I too commerced with that golden cloud:
    Lipped her delicious hands and had my ease
    Faring fantastically, perversely proud.

    All loveliness demands our courtesies.
    Since she was dead I praised her as I could
    Silently, among the Barberini bees.

  3. on 13 Apr 2007 at 9:22 am 3. peter ramus said …

    I’m going for the Gordian Knotism of taking whatever envelope is lying loose and being on my way. Any more money than I currently have is fine by me.

    From a purely rational perspective the problem might result in and endless loop of re-choosings based on the probability that the other envelope might well make me even richer than the one I’m holding, so I’ll exchange it for the one I’m holding, and on and on.

    Let’s look at it from a non-rational perspective, though. Here we need to answer the question, “Are you feeling lucky, punk? Well, are you?”

    Hey, it’s Friday the Thirteenth over here, man, hallowed home of unluck. So the obvious non-rational solution is to decide which envelope you want, and then, assuming unluck, take the other one, the one you don’t want to take.

  4. on 13 Apr 2007 at 12:57 pm 4. James Killus said …

    I would take the unopened envelope, because, God knows, you can’t trust anyone and the bastard probably palmed some of the money that was in it. Then, as he turned to walk away, I would coldcock him and take the opened envelope.

    Then, if the two envelopes didn’t have exactly 1/2 difference between them, I’d kick him on my way out, and maybe steal his watch and wallet. I mean, you can’t trust anybody.

  5. on 13 Apr 2007 at 1:15 pm 5. JP Stormcrow said …

    I mean, you can’t trust anybody.

    Agree, that is why I always try for the exit row on airplanes. Would not want to have to wait behind some big, slow, old guy with a bad knee who might happen to be sitting there.

  6. on 13 Apr 2007 at 1:18 pm 6. Oaktown Girl said …

    James -
    See? This is why I love you. There’s a place for you on the Ministry of Justice. We’ll talk soon.

    Radical change of topic - open thread style:

    New Loyal Party Patriot “Seattle”, knowing that I am a huge classical music fan, thoughtfully sent me a link to this article. By happenstance, I had already seen it, but could not get through it all because I found the writing to be, “sooooo incredibly gratuitous and obnoxiously self-aware, and not just a little condescending.”

    My question is this: is my critique too harsh? Is my opinion overly skewed by the fact that I’m not a classical music novice? Do you think most people might have found this article purely delightful? I’m really curious. Thanks.

    For the record and if it helps with perspective for my question, I’m not classical music snob. In fact, I’m an activist anti-snob for classical music.

  7. on 13 Apr 2007 at 1:41 pm 7. JP Stormcrow said …

    Oaktown,

    You have a lot of company, that article got pretty much slammed in a lot of places in the blogosphere (I recall Kevin Drum and a few others.)

    It all seemed like a set up to prove that Americans are so boorish when it comes to culture. (We probably are .. but this article does not necessarily show it.)

  8. on 13 Apr 2007 at 1:46 pm 8. Seattle said …

    Ok, about the guy with the money in the envelopes…look him in the eye, give him a big smile, and turn around and walk away. I can’t think of any better way to mess with his head.

    About the article-when you’re done reading it in an hour or so, I think the test was flawed. They should have tried on different days at different times to get a better sample of passers-by reactions. My argument is that our society is so time/timeliness conscious that it’s unfair to put people in the position of deciding whether to listen to the world class violinist or get where they’ve committed to going on a given work commute morning.

  9. on 13 Apr 2007 at 2:11 pm 9. Jams said …

    Paradox?

    The situation is a paradox because the most valuable information cannot be attained until it is too late to make use of that information. The paradox can only be resolved by choosing.

    What I’d do.

    If the first envelope had an odd amount of money in it, I would guess that it wasn’t the envelope with twice as much. Especially if the envelopes didn’t seem to be holding change.

    Failing that, if the first envelope was an amount of money I wasn’t prepared to lose, I would stay with it, but if it was an amount of money I wouldn’t feel bad about losing, I would opt for the second envelope.

    If possible, I would take the second envelope and place it in the first open envelope and say “I think… I’ll stay with this first envelope”.

  10. on 13 Apr 2007 at 2:13 pm 10. Oaktown Girl said …

    Thanks for the feedback, JP. Since virtually all my blog time is doing admin here, I’m really out of the loop.

    Seattle, you make some very good points. Regarding people needing to get to work, those were my thoughts exactly, especially in a climate where people are so fearful for their jobs. Why the hell not do it on a weekend when you can have a better sampling of folks who have to opportunity to actually stop an listen if they choose to?

  11. on 13 Apr 2007 at 2:15 pm 11. spyder said …

    The envelope problem, is combined with the Monty Hall problem on Deal or No Deal. I heard, but have not see, that there is a mathematical analysis of the choosing the best probabilities in terms of when to take the Deal. But it seems that one must assume that the “banker” knows what values are in each of the cases, has a print-out of computed odds and equivalent monetary values to offer, and utilizes his direct communication with the host and more importantly to the producers and directors to facilitate an entertaining episode.
    Of course, there is nothing requiring the banker to be honest or truthful in determining the amount of the deal as it relates to the remaining cases. It is television afterall.

    The same holds true for that show about being smarter than a fifth grader. One might assume that if the show was honest and forthright, it would be easy to start with the highest grade-level questions (when one has the full compliment of cheats) and use the lower grade level questions to achieve the greatest amounts of value. But there is nothing that would keep the producers from changing the questions degrees of difficulties disregarding whatever grade level was intended. Therein lies the lie so to speak.

  12. on 13 Apr 2007 at 2:23 pm 12. christian h. said …

    Intercession from the guy at the airport:

    Oaktown Girl - that article was elitist in the worst way.

    Sigh. I see the Cubs are loosing after being up 5-0 on the Reds. The Cubs could choose any envelope - their preformance is not related to payroll, apparently.

  13. on 13 Apr 2007 at 2:45 pm 13. JP Stormcrow said …

    Yet another OT …. wait a minute, just realized:
    Off Topic = OT =Open Thread. (or is this like Kanga + Roo = Kangaroo, everyone else got it years ago?)

    I highly recommend Chris Clarke’s very provacative post: How not to be an asshole: a guide for men over at Pandagon. Great stuff for guys and gals both.

  14. on 13 Apr 2007 at 3:03 pm 14. black dog barking said …

    re: envelopes. Not much info to work from so we have to fill in context in order to answer the question. Which hints we’re dealing with a logical Rorschach test. A person (stranger?) is offering us a choice (advice?)(bluff?).

    I’d politely take the opened envelope. If the rest of the game is random it won’t matter. If the person examining its contents has knowledge and there is purpose behind the offer to switch I’d go with that purpose not being my best interest. (Is offering the choice mandatory?) Nothing against strangers, cash is a ethics corrosion accelerant.

    Apropos the Monty Hall problem, one of the biographies (?? My Brain is Open ??) tells of Paul Erdos having more than a little trouble seeing the logic of accepting Monty’s offer to switch. It took quite a bit of patience and persuasion to bring him around.

    Apropos blog-whoring (must one have a blog to blog-whore?) a Javascript simulation of the Monty Hall Problem and a followup Cheating the Sim with an unusual consequence.

  15. on 13 Apr 2007 at 3:34 pm 15. Oaktown Girl said …

    Oaktown Girl - that article was elitist in the worst way.

    Thank you, Airport Guy. I really didn’t know if my opinion was too tainted by stress and fatigue when I read it. And incidentally, reading only added to my stress and fatigue (”what the fuck is this?”).

    If I wasn’t at work, I’d write a nice little vignette of JP Stormcrow on an airplane, grabbing both envelopes, and trampling elderly people and children on his way to the emergency exit because he couldn’t get a seat in the exit row. Maybe someone else can do that since I’m still stuck in the office and need to get off the blog before I get in serious trouble.

  16. on 13 Apr 2007 at 3:55 pm 16. Seattle said …

    “I highly recommend Chris Clarke’s very provacative post: How not to be an asshole: a guide for men over at Pandagon. Great stuff for guys and gals both.”

    Read it. Wondered why it only matters when a guy says it.

  17. on 13 Apr 2007 at 3:59 pm 17. jimmiraybob said …

    Oaktown Girl,

    In the second video, there’s a little girl in a pink coat and hat that seems fixated on the music even as dad scoots her through the door - I would like to think that means something good.

    Is there a paradox here…?

    Maybe, but there’s definitely a para envelopes…badda bing! Whew, now that I got that out of my system. I’d stick with the first choice. Just because.

  18. on 13 Apr 2007 at 4:11 pm 18. Oaktown Girl said …

    Is there a paradox here…?

    Maybe, but there’s definitely a para envelopes…badda bing!

    Thank you very much, Ladies and Germs. jimmyraybob will be here all weekend. Please don’t forget to tip your servers generously.

  19. on 13 Apr 2007 at 4:20 pm 19. spyder said …

    Please don’t forget to tip your servers generously.

    Then why are they adding that 15% gratuity directly into the bill???? Ugh?? What gives here, a tip to the cleaning staff??? And this on a day when a scientific report is released that links T-Rex to chickens; and now we know why the T-Rex crossed the road.

    Meanwhile i will take case number 23, 17, 19, 11, and 13 please Howie. I am sure these are lucky numbers although they rarely appear as lottey winners.

  20. on 13 Apr 2007 at 4:36 pm 20. Oaktown Girl said …

    spyder’s right. We need to add the phrase “Deal? Or no deal?” to the envelope scenario.

    Oh, and JP also tramples the shit out of Howie Mandel in my little vignette. And kidnaps a 5th grader.

  21. on 13 Apr 2007 at 7:44 pm 21. Oaktown Girl said …

    From the Black Commentator on the Imus aftermath: some deep, deep truths from Rev. Irene Monroe:

    Imus’ humor about the Rutgers athletes was inexcusable. Why? Because jokes framed around distorted concepts of race and gender invalidates the behavior, culture and accomplishments of the group. The jeering and ridiculing of the women’s physical features suggest a norm of beauty, femininity and class, in both Imus’ and the show producer Bernard McGuirk’s minds, these women do not possess.

    And this:

    These women’s strength is to be lauded. However, African American women’s strength for beating the odds or being strong in the face of adversity is either demonized as being emasculating of black men, or seems impervious to stereotypes that obfuscate our real countenances. When a disparaging comment such as Imus’ is accepted as a joke or brushed aside as distasteful humor and not acknowledged for what it is - hate speech, it closes the window of opportunity to educate.

    The Black Commentator is a very important progressive voice and needs your support. Read always, donate what you can.

  22. on 13 Apr 2007 at 10:47 pm 22. JP Stormcrow said …

    To continue with the profane art that I started this thread with, commemorate the Friday the 13th after Good Friday, and celebrate my driving-4-hours-after-work-to-yet-another-state-running-out-of-gas-on-the-interstate-up-at-dark-thirty-tomorow-to-visit-another-fricking-campus-kind-of-night:

  23. on 13 Apr 2007 at 10:56 pm 23. JP Stormcrow said …

    Oh, and JP also tramples the shit out of Howie Mandel in my little vignette. And kidnaps a 5th grader.

    Actually I ripped the idea off J.P. Donleavy in The Unexpurgated Code (Miss Manners’ evil twin.) After a long discussion on whether one should bring a parachute on board (answer: regrettably no), he launches into proper seating:

    Would you mind awfully, my good chap, If I sat here next to the emergency exit. I tend to gouge people’s eyes out if they get in front of me.

  24. on 14 Apr 2007 at 9:25 am 24. hi ho, hi ho said …

    I don’t think the Washington Post article establishes much of anything at all. If they’d done the experiment in New York I bet more people would have stopped. Why? Because New York has a well-established tradition of people performing in the subway — there’s even an official program for doing so. Which means that people in NYC are used to and expect performers — of all kinds.

    As I recall, the article mentioned that all the kids were interested in the music, even if they weren’t allowed to stop and listen.

  25. on 14 Apr 2007 at 10:58 pm 25. JP Stormcrow said …

    Spyder
    I went ahead and embedded the YouTube in your comment.

    I think Tom Lehrer should pretty much be given an honorary membership for his overall body of work including:

    Once the rockets go up, who cares where they come down, that’s not my department says Werner Von Braun.

    So Long Mom, I’m off to drop the bomb, so don’t wait up for me ….. I’ll look for you when the war is over, an hour and-a-half from now.

    First we got the bomb and that was good,
    ‘Cause we love peace and motherhood.
    Then Russia got the bomb, but that’s o.k.,
    ‘Cause the balance of power’s maintained that way!
    Who’s next?

  26. on 15 Apr 2007 at 12:57 am 26. The Constructivist said …

    Back to math, I’d have the person looking at the envelope look at both while in one a them brain scanning machines and have a team of neurologists tell me which envelope to take (promising them a small cut). How to get them to foot the costs of the scanning and consultation? Well, that’s the same problem as with ethanol for cars, right?

  27. on 15 Apr 2007 at 8:52 am 27. christian h. said …

    Somebody broke the tubes! I’m sitting at the airport and listening to… Richard fucking Perle. What I’m learning: Perle thinks he can tell that talking to Iran won’t work.. because he was totally right before. He says that invading Iraq was “like buying insurance”, so criticising the invasion is like saying “we shouldn’t have bought insurance” just because your house didn’t burn down. He claims that there clearly were connections between Iraq and Al Qaeda. There was great deal of planning for the post-war period. Etc. pp. Who do you think should be put to a wall first: Perle - or Blitzer for actually letting him talk bs on his show again?

  28. on 15 Apr 2007 at 9:24 am 28. Porlock Junior said …

    Almost-black type on a dark gray background? Gimme a break! WHY do people think it clever to do funny innovative color schemes that might or might not be readable on various machines other people use? (My weirdly unorthodox ill-designed machine: MacBook Pro, late-model. And why does Apple want their machines to sound like hamburgers and MacMansions and MacPaper and all those insults?)

    Posting this mainly to see whether this blog will accept comments, unlike a couple on which I’ve recently wasted some real good typing on the assumption that giving the right answer to the Turing test would get the comment in.

  29. on 15 Apr 2007 at 9:55 am 29. peter ramus said …

    Porlock Junior, last I heard this blog accepts comments. This blog approves of comments. This blog cries out for comments.

    As for the background, it’s pretty darn white on my my MBP. Hit Reload a couple of times and pause while your Turing test is graded by the MOJ. Maybe that will clear thing up.

  30. on 15 Apr 2007 at 10:20 am 30. jimmiraybob said …

    Who do you think should be put to a wall first: Perle - or Blitzer…

    On the one hand Bush/Cheney have already set a precedent - let them go together (I know it was only super secret unsworn testimony but the buddy system can at least be economical in this case). On the other hand I’d defer to whatever the Hague feels is appropriate…….after a fair trial of course.

  31. on 15 Apr 2007 at 10:28 am 31. Oaktown Girl said …

    A MESSAGE FROM THE MINISTER OF JUSTICE

    I don’t know what the hell happened, but I deleted spyder’s comment and it seemed to fix the massive FUBAR problem we were experiencing on this thread.
    No more YouTubes in the comments except from the MOJ and Cabinet Officers until further notice, please.

    Porlock Junior - please try to comment again now that the problem is fixed.

  32. on 15 Apr 2007 at 10:39 am 32. hi ho, hi ho said …

    Hmmm . . . . must have been a machine or OS-specific FUBAR since it wasn’t happening on my machine. Or maybe it was an outbreak of Rove rays and Norquist particles. Or perhaps some Gonzales Gremlins have escaped from the missing RNC emails and are loose in the Tubes.

  33. on 15 Apr 2007 at 11:06 am 33. spyder said …

    The comment and site worked fine without the embed of the vid clip.. damn now i have to recreate that comment from so many many hours ago.

    So i will reiterate that Tom Lehrer’s vision of our GNF future requires our allegiance through his mastery of teh English to describe how we all need to feel about the great glorious Giant Nuclear Fireball.

  34. on 15 Apr 2007 at 11:45 am 34. JP Stormcrow said …

    …except from the MOJ and Cabinet Officers until further notice, please.

    The comment and site worked fine without the embed of the vid clip.. damn now i have to recreate that comment from so many many hours ago.

    MEA CULPA

    This all comes down to me, since I added the embed via editing that comment. So:
    1) Apologies to spyder - will not do that again. Will add as a next comment if I think it adds something.
    2) So not sure anyone putting an embed in right off the bat is an issue. or instead I screwed up the edit.
    3) What were the symptoms? Looked OK for me - and I think Porlock was referring to not being able to comment on other blogs. OS specific?

  35. on 15 Apr 2007 at 3:52 pm 35. Oaktown Girl said …

    OK, I’m back.
    So sorry I had to delete your comment spyder - there was nothing else I could do. The whole thread was completely ruined…on certain operating systems, anyway. Looked like some web designer gone completely berserk. Porlock Junior tried to describe the look of it here:

    Almost-black type on a dark gray background? Gimme a break! WHY do people think it clever to do funny innovative color schemes that might or might not be readable on various machines other people use?

    but he’s being very generous. Margins were completely blown-out, type face all over the place, the colors were so dark it made it virtually unreadable.

    Whatever you did, JP, gotta hand it to you - you did a hell of a job! You know what football coaches say: if you’re gonna make a mistake, make a BIG one (i.e. if you’re gonna jump offsides, at least knock the shit out of the other guy when you do it!).
    Outstanding!

  36. on 15 Apr 2007 at 4:18 pm 36. Oaktown Girl said …

    I went to the movies yesterday and saw The Lives of Others. Really liked it a lot.
    I was interested in seeing it not just because of the good reviews and Oscar win, but because I’m so concerned (understatement) about what’s going on in our country with ever-growing surveillance by our government.

  37. on 15 Apr 2007 at 5:04 pm 37. peter ramus said …

    A friend who spent a lot of time in Berlin said that The Lives of Others felt exactly like those times in Germany, and she was amazed that the director, too young to have lived through it, could portray it so well.

    In spite of my misgivings about the likelihood of the transformation experienced by the main character, I suppose this may be exactly the sort of healing story unified Germany needs to tell itself these days. In the history of oppression, it’s almost universally the case that those engaged in that line of work rationalize — no, valorize — their behavior, rather than recognize and revolt against their own terrible dehumanization. Today Germany needs at least the possibility of this sort of story.

    So, the exception proving the rule, maybe, but ending the film with the long, long coda saluting the fellow’s good deed leeched a lot of the power from the movie for me. If it had ended on the street outside the writer’s house it would have been perfect.

  38. on 15 Apr 2007 at 6:15 pm 38. Porlock Junior said …

    Yeah, it was a double problem that hit me when in a nice mood after losing comments to a couple of other blogs. (Real nice when, as in those two cases, there’s no email address to send a bug report to.)

    The screen really was nearly unreadable, and that’s fixed. Thanks. And obviously the test comment went up on the site after a due time.
    Now perhaps I’ll remember the comment that I wanted to post in the first place…

  39. on 15 Apr 2007 at 6:28 pm 39. The Constructivist said …

    Hey, as this is an open thread, I’ll ask any Party members or lurkers who happened to watch the last 2 holes of the Ginn Open give me their own play-by-playa nd color commentary at Mostly Harmless. The final group was six-over on the last hole alone and spyder claims the conditions were unplayable (as evidence by the PGA cancelling the day’s event–wusses). What say the GNF death-cultists and -voyeurs?

  40. on 15 Apr 2007 at 8:22 pm 40. Oaktown Girl said …

    peter -
    I agree absolutely with you about the ending to Other People’s Lives. The only reason I didn’t say anything about it in my commment above is because I didn’t have time to give a full movie review, and to have my only comment regarding the details of the film be a complaint about the ending didn’t seem exactly fair, esp. since I liked the rest of the movie so much. And as every Loyal Party Patriot knows, the Minister of Justice is nothing if not fair.

    In the history of oppression, it’s almost universally the case that those engaged in that line of work rationalize — no, valorize — their behavior, rather than recognize and revolt against their own terrible dehumanization.

    Brilliantly stated!

  41. on 15 Apr 2007 at 8:54 pm 41. christian h. said …

    The director definitely couldn’t have lived through Stasi oppression, if only because he’s West German. (That’s not a criticism of the film - which I haven’t seen, since I’m waiting to watch it without those annoying subtitles.)

  42. on 15 Apr 2007 at 8:56 pm 42. JP Stormcrow said …

    Back to the Pair of Docks, the distraction of which has caused me to:
    Not check my gas gauge with predictable results.
    Blaspheme on this thread.
    Contemplate the trampling of children.
    Wreck the Internets.
    Insult the good folks at the college we were at by referring to the growing pile of crap they have sent us.(It is a pile of crap, but no end was served by voicing it under the circumstances.)
    Put off doing my %&%??$@&^@)$@#+# taxes! (Let me say right here that the PA. Dept. of Revenue can bite me.)

    Ignoring the human factors involved and sticking with just the “dry” mathematics, I can say that it is quite the doozy. I finally broke down and looked it up on teh ‘Tubes, but I can say I am deepy unsatisfied, i want something I can intuitively understand and this one still eludes me.
    I did come up with a sequence of problems that I think highlights the issues involved.

    1) You have $10 - someone offers to trade you an envelope that has a 50% chance of having $5 and 50% chance of having $20. I think this is not paradoxical, you should make the trade assuming trust, etc. for E(x) = $12.50.

    2) You do your problem, but the person tells you there is $10 after they open it. This seems like 1) and you should switch - but I think suffers the paradox (but without the infinite regress), I think the problem with it involves the prior probability of getting $10.

    3) Problem as you stated it. You do not know the actual value.

    Formulation #2 is the one I am trying to get straight first - it seems like #1, but I think in fact you have two different “worlds” and really cannot calculate E(x) across them.

  43. on 15 Apr 2007 at 9:01 pm 43. christian h. said …

    JP, I am deeply sorry if I ruined your weekend. I have to admit that my statement of the problem is deliberately vague.

  44. on 15 Apr 2007 at 9:14 pm 44. The Constructivist said …

    Evil! I knew it! What would the squirrel lady’s poetry teacher say about such a mathematician?

  45. on 15 Apr 2007 at 9:21 pm 45. Oaktown Girl said …

    (That’s not a criticism of the film - which I haven’t seen, since I’m waiting to watch it without those annoying subtitles.)

    Oh thanks, Christian. That’s just great.
    And after I spent the day today telling folks about our blog and how one of the reasons it’s so great is because there’s no snobs.

    And come to think of it, your Open Thread question is snobby too. Why you gotta be deliberately vague? See, if math major JP was having trouble, then I know it’s bad.

    JP - tax empathies. And you are completely off the hook for breaking the blog earlier today, which caused me undue stress because this morning not only did I wake up to a broken blog, I had to fix my taxes (which I got notified this morning needed correcting per the State of CA). Plus I had an appointment to get to, AND we had an unhappy new potential WAAGNFNP member because Christian made you break the blog. So yeah. Christian’s fault, totally. He’ll be spending a night in the Box at the Ministry of Justice’s Re-Education Center.

  46. on 15 Apr 2007 at 9:28 pm 46. JP Stormcrow said …

    JP, I am deeply sorry if I ruined your weekend. I have to admit that my statement of the problem is deliberately vague.

    Not to worry. You certainly did not! I am perfectly capable of all those behaviors without help, and worse even! But it was fun to blame it on your problem. You know, just like rappers caused Imus to say “hos”.

    I liked the vagueness, I enjoy that type of crap (better than “our college pwns!” crap). I also like thinking through the Bayesian approaches, but it is a hard thing to wrap my head around. Here is an interesting site to check out that tries to develop an intuitive understanding of Bayes.

  47. on 16 Apr 2007 at 4:10 am 47. christian h. said …

    What a night in that box. I’m not a snob, though - German just happens to be my native language.

    And the weird thing with subtitles is - maybe it’s just me being fixated on anything readable (now I’m a snob) - but if they’re on, half the time, I’m following the subtitles (along with the pictures, of course) instead of listening to the actors speak (I enjoy subtitled films, but translated and abbreviated is not quite the same).

  48. on 16 Apr 2007 at 7:18 am 48. Oaktown Girl said …

    I’m not a snob, though - German just happens to be my native language.

    Vat? Vee haf a slow lerrner. Back in the Box until your humor returns!

    Oh wait, you’re German. Nevermind.

  49. on 16 Apr 2007 at 10:53 pm 49. Zeus said …

    It seems to me from the excellent and informative wikipedia explanation their are at least three common (excluding the quantum event) event “influences”, all of which act on different planes. There is one where an “actor” (the guy who presents you the money or the doors with goats behind them) merely chooses blindly (randomness).

    There is the one where the “actor” knows what is behind the doors (and/or envelopes) and chooses a particular kind of door or envelope (i.e. goat or more/less money) and lets you make your own choice (omniscience).

    And there is the one in which the “actor” knows but is trying to influence your choice, perhaps and he works for the show, and thinks winking and giving you a chance to change to the “big prize” will increase ratings or is trying to feather his own nest and keep the car for himself trying to tempt you to “blow it” (motivation).

    The first strikes me as what we may call either “emptiness” or “entropy” depending upon how we are disposed, the cold, and pitiless, mechanism of universe.

    The second strikes me as what some people think as God.

    And the third strikes me as entirely human.

    Each “modulates” probability. There is a reason why good poker players have to be able to read the card probabilities as well as the other players’ behaviors in order to win fairly consistently, as well as get other players to misread them (i.e. bluffing). Add to that the increased bullying power that can come with a pile of chips.

    Just a couple of thoughts,
    Zeus

  50. on 22 Apr 2007 at 7:44 pm 50. john said …

    To elaborate on JP Stormcrow’s argument #1 from comment 42 (which I didn’t see until I previewed), the concept of expected value tells you to switch.

    Let’s say the first envelope contains $100. The other envelope either contains half as much, or twice as much; it’s a fifty percent chance at $200, and a fifty percent chance at $50.

    Expected value equals the probability of an outcome multiplied by its value. The expected value of standing pat is 100% of $100, or $100. The expected value of switching is the sum of the expected value of the two possibilities involved:

    .5($50) + .5($200) = $125.

    So, if you’re a rational self-maximizer (the big if of undergrad econ) you switch, as you expect to gain $25, probabilistically speaking, by switching.

  51. on 23 Apr 2007 at 8:04 am 51. JP Stormcrow said …

    To elaborate on JP Stormcrow’s argument #1 from comment 42

    #1 was not so much an “argument” as a restatement of a related, but slightly diferent problem. And yes for that problem, I agree that the expected value argument is a valid one for switching. But #2 & #3 (the original problem), it is not so simple - in fact for #3 that argument would lead to infinite switching each time with a 25% gain in expected value, which is clearly nonsensical.

    So the magic is in examining what goes “wrong” in moving from 1->2->3.