explain xkcd - User contributions [en]

Talk:1159: Countdown

2013-02-03T11:11:34Z

178.26.121.97:

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 --[[Special:Contributions/178.26.121.97|178.26.121.97]] 08:56, 11 January 2013 (UTC)
:I warmly recommend the article {{w|harmonic series (mathematics)}}. ;-) --[[Special:Contributions/131.152.41.173|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 --[[Special:Contributions/178.26.121.97|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 [[User:St.nerol|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. - [[User:Frankie|Frankie]] ([[User talk:Frankie|talk]]) 21:37, 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)
::::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)
:::::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)
:::::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 --[[Special:Contributions/178.26.121.97|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? –[[User:St.nerol|St.nerol]] ([[User talk: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 --[[Special:Contributions/178.26.121.97|178.26.121.97]] 08:52, 13 January 2013 (UTC)
::::::::I restructured the last part somewhat. Hope that I didn't screw anything up, and if so, fix it! And it would be very nice if you could also add some more explanation of the math involved! –[[User:St.nerol|St.nerol]] ([[User talk:St.nerol|talk]]) 19:36, 13 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. [[User:Lcarsos|lcarsos]]_a ([[User talk:Lcarsos|talk]]) 23:49, 12 January 2013 (UTC)
: Assuming that the middle digits are random, the expected value is 1.53 million years. But: If the display is off-the-shelf, it is probably larger than the largest number actually displayed. Maybe the counter started at 1e8, and the next smaller display had only 8 digits. Maybe we should have a look at the statistical distribution of digits in commercially available LED displays ... [[Special:Contributions/77.88.71.157|77.88.71.157]] 08:42, 14 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 [http://www.guardian.co.uk/science/2005/apr/14/research.science2]

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? {{unsigned|72.38.90.50}}

: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. {{unsigned|76.14.25.84}}

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. [[User:gijobarts|gijobarts]] ([[User Talk: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. [[Special:Contributions/67.194.183.127|67.194.183.127]] 06:19, 13 January 2013 (UTC)

Benford's Law has no bearing on what any of the covered digits are except the first, and even then it only weakly applies; it only applies to the FIRST digit of natural numbers, and since we can have leading 0's is really doesn't apply. Furthermore, even if it applied to all the digits, the probability distribution on the covered digits is not affected by the shown digits; that's not how probability works. If I flip a coin 10 times and it's heads all ten times, the probability that the 11th flip is still 50/50. -Mike Powers
:Benford's Law shows that with real-life (physical) numbers you cannot just use a 10% probability for each digit. These numbers are not uniformally, but lognormally distributed. That means, there is a smaller tendency to greater numbers than their possible number space would allow. Benford's Law with its relevancy to the first n digits is not directly applicable here, but its general validity contradicts some of the assumptions normally often made. As you see many zeroes in the middle part, the probability is quite high that also the first digits are zero. Here the length of the number has a normal distribution and a short number is about as probable as a long one. And long ones with zeroes in the middle are seldom so it is probably a short number. This would not be the case, if each digit is randomly selected from 0-9. Then the greater probability of longer numbers would cancel out this effect. Sebastian --[[Special:Contributions/178.26.121.97|178.26.121.97]] 10:07, 3 February 2013 (UTC)
:Regarding the independence of the digits: That is conditional probability. We have a probability distribution for the complete number. In nature this is a lognormal distribution (with suitable parameters regarding the scale; that is why the intention to buy a display with certain width is important). That means zero digits are quite common, as short numbers have much weight. With just creating the digits independently you do not get a lognormal distribution. With four zeroes shown only 1/10.000 of the longer numbers are possible any longer, making them much rarer. To begin with they would need a probability of at least 10.000 as high to counter this effect, but they do not have it (with a uniformal distribution they would have it). Sebastian --[[Special:Contributions/178.26.121.97|178.26.121.97]] 10:25, 3 February 2013 (UTC)
:If we have initially the same probability for numbers of digit length 1-14 (about 7%): After looking we (partly) know that digits 1 till 4 are non-zero and digits 5-8 are zero. Then numbers of digit length 1-3 have 0% probability, numbers with digit length 5-8 have 0% probability. Numbers with digit length 9-14 have a probability of 0.01% each and numbers with length 4 have a probability of 99.94%. The results differ with the logarithmic distribution of number length. E.g. with mu=11 digits and sigma=2 digits, the probability of 4 digits is 85%. With mu=12 digits and sigma=3 digits, the probability of 4 digits is 98.3%. With mu=7.5 digits and sigma=4 digits the probability of 4 digits is 99.95%. With mu=12 digits and sigma=2 digits, the probability of 4 digits is 47.64%. Sebastian --[[Special:Contributions/178.26.121.97|178.26.121.97]] 11:07, 3 February 2013 (UTC)
The 11:59 subtle joke is slightly reinforced as the countdown steps over 2400. Sebastian --[[Special:Contributions/178.26.121.97|178.26.121.97]] 11:11, 3 February 2013 (UTC)

Talk:1159: Countdown

2013-02-03T11:09:09Z

178.26.121.97:

Talk:1159: Countdown

2013-02-03T11:08:11Z

178.26.121.97:

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 --[[Special:Contributions/178.26.121.97|178.26.121.97]] 08:56, 11 January 2013 (UTC)
:I warmly recommend the article {{w|harmonic series (mathematics)}}. ;-) --[[Special:Contributions/131.152.41.173|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 --[[Special:Contributions/178.26.121.97|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 [[User:St.nerol|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. - [[User:Frankie|Frankie]] ([[User talk:Frankie|talk]]) 21:37, 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)
::::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)
:::::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)
:::::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 --[[Special:Contributions/178.26.121.97|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? –[[User:St.nerol|St.nerol]] ([[User talk: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 --[[Special:Contributions/178.26.121.97|178.26.121.97]] 08:52, 13 January 2013 (UTC)
::::::::I restructured the last part somewhat. Hope that I didn't screw anything up, and if so, fix it! And it would be very nice if you could also add some more explanation of the math involved! –[[User:St.nerol|St.nerol]] ([[User talk:St.nerol|talk]]) 19:36, 13 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. [[User:Lcarsos|lcarsos]]_a ([[User talk:Lcarsos|talk]]) 23:49, 12 January 2013 (UTC)
: Assuming that the middle digits are random, the expected value is 1.53 million years. But: If the display is off-the-shelf, it is probably larger than the largest number actually displayed. Maybe the counter started at 1e8, and the next smaller display had only 8 digits. Maybe we should have a look at the statistical distribution of digits in commercially available LED displays ... [[Special:Contributions/77.88.71.157|77.88.71.157]] 08:42, 14 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 [http://www.guardian.co.uk/science/2005/apr/14/research.science2]

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? {{unsigned|72.38.90.50}}

: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. {{unsigned|76.14.25.84}}

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. [[User:gijobarts|gijobarts]] ([[User Talk: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. [[Special:Contributions/67.194.183.127|67.194.183.127]] 06:19, 13 January 2013 (UTC)

Benford's Law has no bearing on what any of the covered digits are except the first, and even then it only weakly applies; it only applies to the FIRST digit of natural numbers, and since we can have leading 0's is really doesn't apply. Furthermore, even if it applied to all the digits, the probability distribution on the covered digits is not affected by the shown digits; that's not how probability works. If I flip a coin 10 times and it's heads all ten times, the probability that the 11th flip is still 50/50. -Mike Powers
:Benford's Law shows that with real-life (physical) numbers you cannot just use a 10% probability for each digit. These numbers are not uniformally, but lognormally distributed. That means, there is a smaller tendency to greater numbers than their possible number space would allow. Benford's Law with its relevancy to the first n digits is not directly applicable here, but its general validity contradicts some of the assumptions normally often made. As you see many zeroes in the middle part, the probability is quite high that also the first digits are zero. Here the length of the number has a normal distribution and a short number is about as probable as a long one. And long ones with zeroes in the middle are seldom so it is probably a short number. This would not be the case, if each digit is randomly selected from 0-9. Then the greater probability of longer numbers would cancel out this effect. Sebastian --[[Special:Contributions/178.26.121.97|178.26.121.97]] 10:07, 3 February 2013 (UTC)
:Regarding the independence of the digits: That is conditional probability. We have a probability distribution for the complete number. In nature this is a lognormal distribution (with suitable parameters regarding the scale; that is why the intention to buy a display with certain width is important). That means zero digits are quite common, as short numbers have much weight. With just creating the digits independently you do not get a lognormal distribution. With four zeroes shown only 1/10.000 of the longer numbers are possible any longer, making them much rarer. To begin with they would need a probability of at least 10.000 as high to counter this effect, but they do not have it (with a uniformal distribution they would have it). Sebastian --[[Special:Contributions/178.26.121.97|178.26.121.97]] 10:25, 3 February 2013 (UTC)
:If we have initially the same probability for numbers of digit length 1-14 (about 7%): After looking we (partly) know that digits 1 till 4 are non-zero and digits 5-8 are zero. Then numbers of digit length 1-3 have 0% probability, numbers with digit length 5-8 have 0% probability. Numbers with digit length 9-14 have a probability of 0.01% each and numbers with length 4 have a probability of 99.94%. The results differ with the logarithmic distribution of number length. E.g. with mu=11 digits and sigma=2 digits, the probability of 4 digits is 85%. With mu=12 digits and sigma=3 digits, the probability of 4 digits is 98.3%. With mu=7.5 digits and sigma=4 digits the probability of 4 digits is 99.95%. With mu=12 digits and sigma=2 digits, the probability of 4 digits is 47,64%. Sebastian --[[Special:Contributions/178.26.121.97|178.26.121.97]] 11:07, 3 February 2013 (UTC)

Talk:1159: Countdown

2013-02-03T11:07:07Z

178.26.121.97:

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 --[[Special:Contributions/178.26.121.97|178.26.121.97]] 08:56, 11 January 2013 (UTC)
:I warmly recommend the article {{w|harmonic series (mathematics)}}. ;-) --[[Special:Contributions/131.152.41.173|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 --[[Special:Contributions/178.26.121.97|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 [[User:St.nerol|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. - [[User:Frankie|Frankie]] ([[User talk:Frankie|talk]]) 21:37, 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)
::::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)
:::::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)
:::::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 --[[Special:Contributions/178.26.121.97|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? –[[User:St.nerol|St.nerol]] ([[User talk: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 --[[Special:Contributions/178.26.121.97|178.26.121.97]] 08:52, 13 January 2013 (UTC)
::::::::I restructured the last part somewhat. Hope that I didn't screw anything up, and if so, fix it! And it would be very nice if you could also add some more explanation of the math involved! –[[User:St.nerol|St.nerol]] ([[User talk:St.nerol|talk]]) 19:36, 13 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. [[User:Lcarsos|lcarsos]]_a ([[User talk:Lcarsos|talk]]) 23:49, 12 January 2013 (UTC)
: Assuming that the middle digits are random, the expected value is 1.53 million years. But: If the display is off-the-shelf, it is probably larger than the largest number actually displayed. Maybe the counter started at 1e8, and the next smaller display had only 8 digits. Maybe we should have a look at the statistical distribution of digits in commercially available LED displays ... [[Special:Contributions/77.88.71.157|77.88.71.157]] 08:42, 14 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 [http://www.guardian.co.uk/science/2005/apr/14/research.science2]

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? {{unsigned|72.38.90.50}}

: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. {{unsigned|76.14.25.84}}

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. [[User:gijobarts|gijobarts]] ([[User Talk: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. [[Special:Contributions/67.194.183.127|67.194.183.127]] 06:19, 13 January 2013 (UTC)

Benford's Law has no bearing on what any of the covered digits are except the first, and even then it only weakly applies; it only applies to the FIRST digit of natural numbers, and since we can have leading 0's is really doesn't apply. Furthermore, even if it applied to all the digits, the probability distribution on the covered digits is not affected by the shown digits; that's not how probability works. If I flip a coin 10 times and it's heads all ten times, the probability that the 11th flip is still 50/50. -Mike Powers
:Benford's Law shows that with real-life (physical) numbers you cannot just use a 10% probability for each digit. These numbers are not uniformally, but lognormally distributed. That means, there is a smaller tendency to greater numbers than their possible number space would allow. Benford's Law with its relevancy to the first n digits is not directly applicable here, but its general validity contradicts some of the assumptions normally often made. As you see many zeroes in the middle part, the probability is quite high that also the first digits are zero. Here the length of the number has a normal distribution and a short number is about as probable as a long one. And long ones with zeroes in the middle are seldom so it is probably a short number. This would not be the case, if each digit is randomly selected from 0-9. Then the greater probability of longer numbers would cancel out this effect. Sebastian --[[Special:Contributions/178.26.121.97|178.26.121.97]] 10:07, 3 February 2013 (UTC)
:Regarding the independence of the digits: That is conditional probability. We have a probability distribution for the complete number. In nature this is a lognormal distribution (with suitable parameters regarding the scale; that is why the intention to buy a display with certain width is important). That means zero digits are quite common, as short numbers have much weight. With just creating the digits independently you do not get a lognormal distribution. With four zeroes shown only 1/10.000 of the longer numbers are possible any longer, making them much rarer. To begin with they would need a probability of at least 10.000 as high to counter this effect, but they do not have it (with a uniformal distribution they would have it). Sebastian --[[Special:Contributions/178.26.121.97|178.26.121.97]] 10:25, 3 February 2013 (UTC)
:If we have initially the same probability for numbers of digit length 1-14 (about 7%): After looking we (partly) know that digits 1 till 4 are non-zero and digits 5-8 are zero. Then numbers of digit length 1-3 have 0% probability, numbers with digit length 5-8 have 0% probability. Numbers with digit length 9-14 have a probability of 0.01% each and numbers with length 4 has a probability of 99.94%. The results differ with the logarithmic distribution of number length. E.g. with mu=11 digits and sigma=2 digits, the probability of 4 digits is 85%. With mu=12 digits and sigma=3 digits, the probability of 4 digits is 98.3%. With mu=7.5 digits and sigma=4 digits the probability of 4 digits is 99.95%. With mu=12 digits and sigma=2 digits, the probability of 4 digits is 47,64%. Sebastian --[[Special:Contributions/178.26.121.97|178.26.121.97]] 11:07, 3 February 2013 (UTC)

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Talk:1168: tar

2013-02-01T07:24:09Z

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I thought the title text would be "tar --help"
[[Special:Contributions/123.202.19.132|123.202.19.132]] 06:59, 1 February 2013 (UTC)

The comic is about the difficulty of the tar program options.

Even if his life depended on it and after years of usage, Bob/Randall could not come up with the right parameters without looking them up. So a situation is shown, where Bob's life depends on coming up with the right parameters:

* It shows an atomic warhead
* It has a user interface, which requests any valid tar command
* If it is not entered on the first try within 10s, the bomb is not disarmed and potentially explodes on the spot

Randall has come up with a situation, where the unix guy Bob can be the hero by knowing tar parameters. This is a pipe dream of a geek; nobody cares IRL, if you know tar parameters on the first try.

It is hilarious, that
* the bomb says in full detail the rules including that you should not cheat and it probably has no means to check whether you cheated. This is no game, but feels like one. In war and love every means is allowed - even cheating; it would also be self-defense for disarming the bomb; Bob and his colleagues are not even considering to cheat.
* the user has root access to the bomb, shown by the bomb as ~#, the tilde is the home directory, the # signifies super-user rights; even if the available programs prevent the bomb from being shutdown or disabled by a nonintended way, normally no root access is given for users of linux devices during normal usage; and disarming the bomb with official rules is normal usage of a bomb; a root prompt should not be necessary, if the bomb software is designed and configured well; possibly the unix prompt is a simulation for entering an answer
* Bob shurely needs more than 10s to come. So the bomb will have announced that questions, which require unix knowledge will follow - or has already asked other Unix questions; perhaps after 10s without entering anything a new question comes up
* this bomb can be disarmed with "common knowledge"

Small notes:
* The screen looks to be really grayscale (esp. the inverted "TEN") - not just because of the comic; it has at least 3 colors (black, white, tar gray); it could be that the "TEN" is updated dynamically and is thus inverted
* The comic is quite black: The screen and the bomb; Randall seldomly uses solid black areas; the bomb is a gloomy topic so it is black like "tar" (pun)

Sebastian --[[Special:Contributions/178.26.121.97|178.26.121.97]] 07:24, 1 February 2013 (UTC)

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==Zeroes==
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 --[[Special:Contributions/178.26.121.97|178.26.121.97]] 08:56, 11 January 2013 (UTC)
:I warmly recommend the article {{w|harmonic series (mathematics)}}. ;-) --[[Special:Contributions/131.152.41.173|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 --[[Special:Contributions/178.26.121.97|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 [[User:St.nerol|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. - [[User:Frankie|Frankie]] ([[User talk:Frankie|talk]]) 21:37, 11 January 2013 (UTC)
:[http://en.wikipedia.org/wiki/Benford%27s_law 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)

==Volcanoes==
"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 [http://www.guardian.co.uk/science/2005/apr/14/research.science2]

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?

Talk:1159: Countdown

2013-01-11T22:34:28Z

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==Zeroes==
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 --[[Special:Contributions/178.26.121.97|178.26.121.97]] 08:56, 11 January 2013 (UTC)
:I warmly recommend the article {{w|harmonic series (mathematics)}}. ;-) --[[Special:Contributions/131.152.41.173|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 --[[Special:Contributions/178.26.121.97|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 [[User:St.nerol|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. - [[User:Frankie|Frankie]] ([[User talk:Frankie|talk]]) 21:37, 11 January 2013 (UTC)
:[http://en.wikipedia.org/wiki/Benford%27s_law|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)

==Volcanoes==
"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 [http://www.guardian.co.uk/science/2005/apr/14/research.science2]

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?

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178.26.121.97: Created page with "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 ext..."

Talk:1158: Rubber Sheet

2013-01-09T20:18:49Z

178.26.121.97:

There is no rope in black hole analogy. On the other hand ... maybe one day this becomes common analogy for explaining some method of [http://en.wikipedia.org/wiki/Faster-than-light FTL] travel ... -- [[User:Hkmaly|Hkmaly]] ([[User talk:Hkmaly|talk]]) 08:52, 9 January 2013 (UTC)

<strike>It is no rope - it is a rubber sheet seen from the side. Sebastian --[[Special:Contributions/178.26.121.97|178.26.121.97]] 14:01, 9 January 2013 (UTC)</strike>sorry, you meant the rope there ;-) Sebastian --[[Special:Contributions/178.26.121.97|178.26.121.97]] 20:18, 9 January 2013 (UTC)

Did you see the harmonics of the wave? I think there are four different ones in the third frame. Sebastian --[[Special:Contributions/178.26.121.97|178.26.121.97]] 14:01, 9 January 2013 (UTC)

- Two harmonics, two different phases of each. [[Special:Contributions/123.237.156.13|123.237.156.13]] 15:56, 9 January 2013 (UTC)

It seems to me there should be a cross-reference to [[895: Teaching Physics]] (and if I knew more about the conventions of this wiki I would be bold and add it myself... but I don't, so I won't.) --[[Special:Contributions/67.36.177.100|67.36.177.100]] 17:35, 9 January 2013 (UTC)

Talk:1158: Rubber Sheet

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Talk:1147: Evolving

2012-12-15T07:55:08Z

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Bacteria can indeed "instantly" evolve within a generation instead of waiting for its descendents. It's called horizontal gene transfer and it's the primary mechanism for the propagation of antibiotic resistance. --[[User:Prooffreader|Prooffreader]] ([[User talk:Prooffreader|talk]]) 13:07, 14 December 2012 (UTC)
:Its sentences like that which make {{w|Microbiology|Microbiologists}} my heros. [[User:DanB|DanB]] ([[User talk:DanB|talk]]) 14:25, 14 December 2012 (UTC)
Should there be a reference to Arceus (the "ultimate creator Pokémon") here? I do not mean this for making a joke; I just thought that the coincidence can be appropriate here, since the bacteria is called "Aureus". [[User:Greyson|Greyson]] ([[User talk:Greyson|talk]]) 15:48, 14 December 2012 (UTC)

The evolved form looks the same to me. --[[Special:Contributions/178.26.121.97|178.26.121.97]] 07:54, 15 December 2012 (UTC)

Talk:1147: Evolving

2012-12-15T07:54:42Z

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Bacteria can indeed "instantly" evolve within a generation instead of waiting for its descendents. It's called horizontal gene transfer and it's the primary mechanism for the propagation of antibiotic resistance. --[[User:Prooffreader|Prooffreader]] ([[User talk:Prooffreader|talk]]) 13:07, 14 December 2012 (UTC)
:Its sentences like that which make {{w|Microbiology|Microbiologists}} my heros. [[User:DanB|DanB]] ([[User talk:DanB|talk]]) 14:25, 14 December 2012 (UTC)
Should there be a reference to Arceus (the "ultimate creator Pokémon") here? I do not mean this for making a joke; I just thought that the coincidence can be appropriate here, since the bacteria is called "Aureus". [[User:Greyson|Greyson]] ([[User talk:Greyson|talk]]) 15:48, 14 December 2012 (UTC)
The evolved form looks the same to me. --[[Special:Contributions/178.26.121.97|178.26.121.97]] 07:54, 15 December 2012 (UTC)