# Difference between revisions of "Talk:1159: Countdown"

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::{{w|Benford's law}} is about the probability of certain first digit(s). Sebastian --[[Special:Contributions/178.26.121.97|178.26.121.97]] 22:34, 11 January 2013 (UTC) | ::{{w|Benford's law}} is about the probability of certain first digit(s). Sebastian --[[Special:Contributions/178.26.121.97|178.26.121.97]] 22:34, 11 January 2013 (UTC) | ||

:::Hmm... "Benford's law also concerns the expected distribution for digits beyond the first, which approach a uniform distribution". I missed that the first time I read the article. Okay, that covers the essential parts of the argument. - [[User:Frankie|Frankie]] ([[User talk:Frankie|talk]]) 19:43, 12 January 2013 (UTC) | :::Hmm... "Benford's law also concerns the expected distribution for digits beyond the first, which approach a uniform distribution". I missed that the first time I read the article. Okay, that covers the essential parts of the argument. - [[User:Frankie|Frankie]] ([[User talk:Frankie|talk]]) 19:43, 12 January 2013 (UTC) | ||

− | ::::Come on now Frankie, I'm doing my best. I was just too quick to think that the claim was just another of these casual confusions about probability that non-math people have from time to time. (You know, I haven't rolled a 6 for some time, so now the chances must be pretty high...) I hadn't heard about this very counter-intuitive Benson-principle before, but found | + | ::::Come on now Frankie, I'm doing my best. I was just too quick to think that the claim was just another of these casual confusions about probability that non-math people have from time to time. (You know, I haven't rolled a 6 for some time, so now the chances must be pretty high...) I hadn't heard about this very counter-intuitive Benson-principle before, but found [http://plus.maths.org/content/looking-out-number-one this page] helpfylly explanatory. |

::::So, I trust you on this. What I don't understand is, how do we know that Benfords law can be applied to this particular 14 digit number? The time left to an eruption? Also, how could a calculation of the actual probabiliy of the preciding digits being zero or anything else be made? – [[User:St.nerol|St.nerol]] ([[User talk:St.nerol|talk]]) 22:52, 12 January 2013 (UTC) | ::::So, I trust you on this. What I don't understand is, how do we know that Benfords law can be applied to this particular 14 digit number? The time left to an eruption? Also, how could a calculation of the actual probabiliy of the preciding digits being zero or anything else be made? – [[User:St.nerol|St.nerol]] ([[User talk:St.nerol|talk]]) 22:52, 12 January 2013 (UTC) | ||

:::::What is more important for this comic than the Benford's law itself, is its underlying condition that many naturally existing numbers are lognormally distributed. And not uniformally distributed. Under that premise we can try do hypothesize about the odds of leading zeroes. Sebastian --[[Special:Contributions/178.26.121.97|178.26.121.97]] 00:28, 13 January 2013 (UTC) | :::::What is more important for this comic than the Benford's law itself, is its underlying condition that many naturally existing numbers are lognormally distributed. And not uniformally distributed. Under that premise we can try do hypothesize about the odds of leading zeroes. Sebastian --[[Special:Contributions/178.26.121.97|178.26.121.97]] 00:28, 13 January 2013 (UTC) |

## Revision as of 01:33, 14 January 2013

If you assume (with nothing else known), that large numbers have a probability about reciprocal to themselves to ensure a sum/integral of 1, the digits not being zeroes is extremely unlikely.

Whether black hat guy thinks a supervolcanoe eruption is a favourable event or being spared from one is not made entirely clear. Sebastian --178.26.121.97 08:56, 11 January 2013 (UTC)

- I warmly recommend the article harmonic series (mathematics). ;-) --131.152.41.173 13:30, 11 January 2013 (UTC)
- You are right, the harmonic series is divergent. However, the maximal number of digits - which can be possibly displayed - is finite. Which distribution would you suggest? Sebastian --178.26.121.97 19:35, 11 January 2013 (UTC)

- Sebastian, do you know the specific name of the statistical principle you're invoking? I agree, but St.nerol does not, and he has a quick tendency to remove things. One part of it is that you don't know the magnitude of a number, exponential distribution is a more appropriate model than linear. Another part is about the unlikelihood of the middle digits being zero. - Frankie (talk) 21:37, 11 January 2013 (UTC)
- Benford's law is about the probability of certain first digit(s). Sebastian --178.26.121.97 22:34, 11 January 2013 (UTC)
- Hmm... "Benford's law also concerns the expected distribution for digits beyond the first, which approach a uniform distribution". I missed that the first time I read the article. Okay, that covers the essential parts of the argument. - Frankie (talk) 19:43, 12 January 2013 (UTC)
- Come on now Frankie, I'm doing my best. I was just too quick to think that the claim was just another of these casual confusions about probability that non-math people have from time to time. (You know, I haven't rolled a 6 for some time, so now the chances must be pretty high...) I hadn't heard about this very counter-intuitive Benson-principle before, but found this page helpfylly explanatory.
- So, I trust you on this. What I don't understand is, how do we know that Benfords law can be applied to this particular 14 digit number? The time left to an eruption? Also, how could a calculation of the actual probabiliy of the preciding digits being zero or anything else be made? – St.nerol (talk) 22:52, 12 January 2013 (UTC)
- What is more important for this comic than the Benford's law itself, is its underlying condition that many naturally existing numbers are lognormally distributed. And not uniformally distributed. Under that premise we can try do hypothesize about the odds of leading zeroes. Sebastian --178.26.121.97 00:28, 13 January 2013 (UTC)
- The initial timer is a physical quantity, therefore scale invariant, and created by a lognormal distribution (first random experiment). Now there are two possibilities: -- a) BHG specifically got a 14-digit display for the countdown (with the first digit according to Benford's law of course) and the initial timer 14 digits wide. b) The initial timer value possibly was much smaller and it could have been any number which fit on the display. -- Cueball comes in. The shown timer is uniformally distributed within the range below the initial timer (second random experiment). Because of the visible zeroes a) does not seem to be likely and b) would be true, specifically b) with the hidden digits being zero, as the shown zeroes are very unprobable with all large timer values, and the short timer actually is quite probable (lognormal distribution). Is this a valid way to argue for probabilities? Sebastian --178.26.121.97 00:55, 13 January 2013 (UTC)
- It seems legit, but I can't tell, really. But we have no concrete estimation yet (maybe that's too hard). Do you
*really*think that this phenomenon is so strong so that (from the 1 in 30000) it makes the probability for four zeroes*higher*than for all the other 29999 possibilities together? –St.nerol (talk) 08:45, 13 January 2013 (UTC)- Another effect is that if the initial counter was small to begin with, it is quite unprobable (with only one supervolcanoe eruption) that Cueball comes in during the run of the counter. I will try to do a calculation example to compare the possibilities with reasonable assumptions. Sebastian --178.26.121.97 08:52, 13 January 2013 (UTC)

- It seems legit, but I can't tell, really. But we have no concrete estimation yet (maybe that's too hard). Do you

- Hmm... "Benford's law also concerns the expected distribution for digits beyond the first, which approach a uniform distribution". I missed that the first time I read the article. Okay, that covers the essential parts of the argument. - Frankie (talk) 19:43, 12 January 2013 (UTC)
- This is a wholly inappropriate accusation to make here. If you have a problem, please put it through appropriate channels. No editor has a perfect score, we all slip up because we're all human. lcarsos_a (talk) 23:49, 12 January 2013 (UTC)

- Benford's law is about the probability of certain first digit(s). Sebastian --178.26.121.97 22:34, 11 January 2013 (UTC)

"I forget which one" may be a reference to the 7 known supervolcanoes, or it might be to a list published by the Guardian in 2005 of the top 10 existential threats to life on Earth, which went briefly viral. It included a supervolcano eruption, as well as viral pandemic, meteorite strike, greenhouse gases, superintelligent robots, nuclear war, cosmic rays, terrorism, black holes, and telomere erosion [1]

I understand how the hidden numbers could mean that a volcano could either erupt very soon or a very long time. But I don't get why this is a joke. Is there something funnny that I am missing? -- 72.38.90.50 (talk) *(please sign your comments with ~~~~)*

- It's a joke, because a supervolcano eruption would have a major impact on the earth, and Black Hat has a timer that will tell him when one will occur, but he is too lazy to see whether it will happen soon. -- 76.14.25.84 (talk)
*(please sign your comments with ~~~~)*

The title-text may be a reference to the line "May the odds be ever in your favor!" in *The Hunger Games*. I wonder if this might also be a commentary on the foolishness of assuming that a rare event won't happen anytime soon. gijobarts (talk) 19:54, 12 January 2013 (UTC)

The picture could be somewhat symbolic. It could be a sunset or sunrise, like the would could be about to end or not. 67.194.183.127 06:19, 13 January 2013 (UTC)