Editing Talk:1159: Countdown
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::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]]<span title="I'm an admin. I can help.">_a</span> ([[User talk:Lcarsos|talk]]) 23:49, 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. [[User:Lcarsos|lcarsos]]<span title="I'm an admin. I can help.">_a</span> ([[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) | : 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) | ||
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"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 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] | ||
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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 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 | + | :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 prUobability 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) | :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) | :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) | 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) | ||
− | Could "the odds are in our favour" be a reference to the hunger games? | + | Could "the odds are in our favour" be a reference to the hunger games? |
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