MATH FOLKS -- explain the flaw in this reasoning (Doomsday Hypothesis)

Discussion in 'Mayberry Lounge' started by Tycho Brah, Jan 9, 2013.

  1. Tycho Brah

    Tycho Brah You drink water, I drink anarchy Platinum Member

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    Okay, the whole set-up of this thing seems irrational to me, but I can't figure out where exactly the problem lies. Apparently the disagreement over that fact is pretty widespread, so I'm not alone. Maybe someone here can shed light on the situation.

    From the article here: http://rationallyspeaking.blogspot.ca/2013/01/its-not-all-doom-and-gloom.html

    This is the original line of reasoning:

    And now (less trivially) applied to a Doomsday scenario:

    So what's the problem here, or is there one at all?
     
  2. Matt4786

    Matt4786 Gold Belt

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    I don't think it's a problem rather an explanation. This is how I saw it: if you are dealing with an ordered list (1,2,3,4,...,n), and you randomly select a single item whose order is given, but do not know how many total items are part of the list, it's much more likely that the total number of items is closer to the lower bound given by the item than a far away number.

    E.g. let's say I have a box of numbered balls, with balls being numbered 1,2,3,4,...,n and I don't know how many total balls there are. I then take a random ball and it's numbered 5. If the total number of balls is n=5, you have a 1 in 5 chance of selecting that ball randomly, which is quite probable. If n=100, then you'd have a 1 in 100 chance of selecting that ball and only a 9 in a 100 chance of even selecting a single digit number. So it seems more probable that the total number of balls is closer to 5 than 100.
     
  3. MortalWombat

    MortalWombat Vombatus Sherdoggus

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    I'm calling biased experiment. P(R<60b|DoomSoon) is actually 1. P(R<60b|DoomLate) = 1. When you're picking blamo's, you know the buggers exist. When you're picking humans, you know they don't.

    If you go with P = 1, then you end up with odds of 1:50 and 50:1, ie your original assumption. That's because your experiment yielded diddley squat.
     
  4. gotBooched

    gotBooched maximus entertainus

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    Get it, boi!
     
  5. MortalWombat

    MortalWombat Vombatus Sherdoggus

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    Is that an upvote or a downvote? I am feeling on very shaky ground having voiced an opinion on something I have very little understanding of. Like that gameshow host thing still does my head in, let alone


    [​IMG]
     
  6. MortalWombat

    MortalWombat Vombatus Sherdoggus

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  7. adam199

    adam199 Purple Belt Platinum Member

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    Pretty interesting to think about. The problem here lies in the fact that outside factors are ignored. You can't predict the doomsday of a species based simply on the number of members that have existed, and the unlikelihood that the total members will be exponentially higher.

    The growth of a species is almost always exponential. two turn into four, four turn into eight, and so on. The first two members of any species never think that there will be billions of their own kind. I'd say it's always safe to assume that any growing, healthy species is closer to zero than their upper-bound, based simply on exponential growth.

    The question here is whether our species is growing healthily. The flaw here is in the fact that this problem only factors the number of members of our species so far. God's not going to hurl an asteroid at Earth just to prove a basic probability question true.
     
    Last edited: Jan 9, 2013
  8. tkotom

    tkotom Fedor belt

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    well the blam o is a bad example since the 112 serial number could refer to the mixture's code, the type of casing or material used or a number of other things.. what's to say that it is number 112 of blam o's
     
  9. def1

    def1 Brown Belt

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    it seems like two different premises to me.

    On one hand you have blamos which have stopped production.

    On the other hand you have people who are still being born (produced).

    But Bayesian statistics is over my head so i dunno
     
  10. Tycho Brah

    Tycho Brah You drink water, I drink anarchy Platinum Member

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    It seems pretty straightforward, I'm not sure why exactly my gut reaction is so against it. I've never been good with probabilities. Maybe it's just because the conclusion is so intuitive: it's less likely that there will be many humans that it is that there will be fewer humans.

    But I'm not really sure why I think that either, besides the typical ecological constraints. Maybe this is the mathematical reason spelled out in plain English.

    Can you explain this a little bit further? I'm not good at this stuff.

    This is from the article as well:

    Will read the link too.
     
  11. Tycho Brah

    Tycho Brah You drink water, I drink anarchy Platinum Member

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    Hmm.. I think we can assume for the sake of the example that the serial number indicates the position of production.

    Yea I dunno either, but here are a couple other critiques that may have something to do with your comment:

     
  12. TheQu**

    TheQu** Brown Belt

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  13. ocean size

    ocean size Black Belt

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    I like the Bayes theorem approach - it is something I think about more and more in my field. I just don't see that it applies here. When you are pulling a random blamo out of a population you know there is some finite number - looking at the number of humans you know we are is not the same thing - we don't know how long all of the given factors will allow ourselves to keep us around. I am not a good enough statistician to know what the problem it is but it seems like a violation of assumptions.

    The blamo thing would be more comparable to picking a human throughout the human-rank of anatomically modern humans and putting odds on what the highest rank is now.

    Think of it this way - Rank a person's days and set odds on how long they will live. Do it in a developed country with a good population growth rate. Say you pick a toddler, and this concept says they will most likely live to 3 or 5 instead of 76 or 90, since they are two now.

    No, bullshit, a whole lot of factors goes into setting how long they can expect to live, which is the 76 to 90.

    I'm linking to three different places:
    Objections to the hypothesis: http://mind.oxfordjournals.org/content/107/426/403.full.pdf
    A refutation of those objections: http://www.anthropic-principle.com/preprints/ali/alive.html
    A more balanced take that says it is sometimes appropriate: http://brian.weatherson.org/doomsday.pdf
     
  14. Tycho Brah

    Tycho Brah You drink water, I drink anarchy Platinum Member

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    Qu to the rescue!

    Although I'll admit that after quickly glancing at the front page I find it more intimidating than the guy in the "you gun get raped" meme.

    Will attempt to understand though.
     
  15. ocean size

    ocean size Black Belt

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    Seems like Bayesian stats can either be very intuitive, or completely counterintuitive... awesome.
    [​IMG]
     
  16. Tycho Brah

    Tycho Brah You drink water, I drink anarchy Platinum Member

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    I want to laugh... I really do. I'm sure it's clever -- whatever it means.

    So... Introductory books on Bayesian stats! More crap to add to the reading list lol
     
  17. PolishHeadlock

    PolishHeadlock Putin Belt Platinum Member

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    Dividedbyzero.jpg
     
  18. ocean size

    ocean size Black Belt

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    No hidden pun, just referring to xkcd's take with the awesome. There is a website that gives a really good introductory explanation -

    edit: ok here's is: http://oscarbonilla.com/2009/05/visualizing-bayes-theorem/ I think the cancer example is a really good one of where answers it gives are surprising compared to what back-of-the-envelope calculations you do in your head, yet strangely intuitive at the same time.

    Here is a quote I read on a slightly unrelated topic that sort of sums up the difference between Bayesian and frequentist stats:

     
    Last edited: Jan 9, 2013
  19. PolishHeadlock

    PolishHeadlock Putin Belt Platinum Member

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    I sent that to my sister who has a Phd in Econ and loves stat.

    I'll let you know later if I loled.
     
  20. MortalWombat

    MortalWombat Vombatus Sherdoggus

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    I have read this paper end to end.


    Here is my considered opinion on the matter, armed with the knowledge in that paper.


    [​IMG]
     

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