Naked Science Forum
General Science => General Science => Topic started by: thedoc on 10/04/2015 09:06:23
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Why a certain number pops up more often than you'd expect, and how this can be used to catch crooks!
Read the article (http://www.thenakedscientists.com/HTML/index.php?id=9&tx_naksciarticle_pi1%5BshowUid%5D=417&cHash=cb69b8be63) then tell us what you think...
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I don't see an article on that page.
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There is, of course, a number on the page, or more precisely a date.
Thursday, January 1, 1970, which is quite common indeed, used as the base date for representing Unix Time (http://en.wikipedia.org/wiki/Unix_time). I would think "throughout the universe" is a bit of an exaggeration, but it may well be ubiquitous on Earth.
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There is, of course, a number on the page, or more precisely a date.
Thursday, January 1, 1970, which is quite common indeed, used as the base date for representing Unix Time (http://en.wikipedia.org/wiki/Unix_time). I would think "throughout the universe" is a bit of an exaggeration, but it may well be ubiquitous on Earth.
[;D] [8D]
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As we have ten fingers, and rarely use leading zeroes, the number 1 is likely to appear before the decimal point more often than any other, though the "anomaly" decreases with increasing numbers of significant digits.
If we only had one finger and counted in binary, the number 1 would still appear slightly more frequently than 0, and in fact it doesn't matter what base you use, 1 will always dominate.
π and e turn up with depressing regularity, but their frequency depends on whether the universe is described in SI, cgs, imperial or logarithmic units.
However given the dominance of the inverse square relationship throughout physics, the most important number in the universe is 2.
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As we have ten fingers, and rarely use leading zeroes, the number 1 is likely to appear before the decimal point more often than any other, though the "anomaly" decreases with increasing numbers of significant digits.
If we only had one finger and counted in binary, the number 1 would still appear slightly more frequently than 0, and in fact it doesn't matter what base you use, 1 will always dominate.
Yes; it occurred to me that the OP might be talking about Benford's Law (http://en.wikipedia.org/wiki/Benford%27s_law), but as the OP said 'number' rather than 'digit', I pedantically discounted it; but you're probably right...
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Benford's Law and the explanations appear to be consistent with the principle that it is not the values themselves that occur with approximately equal chance, but rather their logarithms that do. That such would be generally the case across a broad range of phenomena is not unreasonable, inasmuch as it appears to be generally true that any phenomenon that occurs in various values will tend to have a range of values that is a small multiple of or small divisor of the mean. Thus, atom's radii will range from roughly 1 to 4 or 5 times that of the hydrogen atom, but not several million times. Likewise, the radii of galaxies might typically cover a range of 1 to 10 times that of the smallest, but will not be comparable to atomic radii. Therefore, a broad collection of data pulled randomly from many fields will tend to exhibit the property that the likely interval between any two readings will be proportional to their mean, resulting in a drop in probability density per linear unit when moving to higher values. Of course, the implication of this is that the density should continue to drop as we move from values beginning with 9 to values beginning with 10; however, the addition of the extra zero changes the scale by a factor of 10, putting us back in the "1s" mode but with a ten times wider sampling width, thereby returning us to the dominance of 1s due to their covering the lowest interval in any decade.
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Benford's Law (https://en.wikipedia.org/wiki/Benford%27s_law) applies most precisely to measurements that span many orders of magnitude.
Measurements which obey Benford's Law are not dependent on the units used. For example, if you convert distances from feet to meters, all of the leading digits will change on all of the road signs. However, the results will still follow Benford's Law...