tag:blogger.com,1999:blog-37148773.post7962223452985118205..comments2024-03-27T14:50:47.345-04:00Comments on <center>Sandwalk</center>: How Many M&M's in a Jar?Larry Moranhttp://www.blogger.com/profile/05756598746605455848noreply@blogger.comBlogger3125tag:blogger.com,1999:blog-37148773.post-30453775909889404422009-07-27T23:41:17.064-04:002009-07-27T23:41:17.064-04:00It seems your ego was on full throttle and brain o...<i>It seems your ego was on full throttle and brain on standby when you typed this. So you got a good estimate to the Science paper but make no effort of even hinting that your ignorant guess would be wrong a majority of the time if you were not aware of the full picture.</i> <br /><br />I don't know WTF you are talking about. The question was how to best guess M&Ms fractional packing. I recalled a similar beans packing question. Personally, I am rather amused how close the simplest educated guess turned out to be to the high-level math (or was it science? :-)). <br /><br />As I *am* a big fan of simple models that can be understood analytically without the use of computers, I do find it gratifying that the crudest estimate seems to be almost as good as experiment. Is that a crime? <br /><br /><i>Also, since this is mathematics and may have further uses than guessing how many beans fit inside a space, precision is important.</i><br /><br />It may be. But: 1) That is not my concern here and whenever this might be important is totally outside of my expertise, and 2) my experience as a biologist suggests that the precision of *this* kind is not very important. Rather, numbers that are orders of magnitude off the real life numbers (a common place) is a real problem.DKnoreply@blogger.comtag:blogger.com,1999:blog-37148773.post-50626650140448858032009-07-27T22:28:02.331-04:002009-07-27T22:28:02.331-04:00What a poor retrospective analysis of your past DK...What a poor retrospective analysis of your past DK. It seems your ego was on full throttle and brain on standby when you typed this. So you got a good estimate to the Science paper but make no effort of even hinting that your ignorant guess would be wrong a majority of the time if you were not aware of the full picture. Also, since this is mathematics and may have further uses than guessing how many beans fit inside a space, precision is important.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-37148773.post-57348014525076017072009-07-27T21:52:49.985-04:002009-07-27T21:52:49.985-04:00That was tedious. Who is the intended audience of ...That was tedious. Who is the intended audience of this guy? <br /><br />The detail he is going about it belongs to a high school (not to mention that Cl- and Na+ should have been shown with different radii). When I was a kid, I had an almost identical "bean packing" question in math olympiad (8ths grade, IIRC). Never knew what the "correct" answer was but I remember doing it this way: take fractional volume of a sphere set inside a cube (that's pie/6), then assume that beans will pack right in the the middle between spheres and total volume. Then take off ~20% to account for an imperfect packing. <br /><br />My calculator today says it is ~ 61%. The paper in Science says it is 66% for a random M&Ms packing. <br /><br />In hindsight of what I know today, my old solution was totally clueless about symmetries (assumed tetragonal without even realizing a possibility of hexagonal). Still, goes to show: a back of the envelope calculation is good enough in most cases. <br /><br />Real life lesson: complex models are overrated.DKnoreply@blogger.com