tag:blogger.com,1999:blog-2433841880619171855.post3306844418301894043..comments2014-04-19T12:13:28.413+01:00Comments on Pat'sBlog: Who Created the Birthday Problem, and Even One More VersionPat Ballewhttps://plus.google.com/102211537828528656806noreply@blogger.comBlogger3125tag:blogger.com,1999:blog-2433841880619171855.post-15006918341671473822011-01-15T16:38:31.923+00:002011-01-15T16:38:31.923+00:00Steven, Mia Culpa,
Hope I corrected it everywhere....Steven, Mia Culpa,<br />Hope I corrected it everywhere. About the fact that birth dates are not equally distributed, I have a graph of the day by day births in 1978. You can obviously see every weekend and major holidays in the data. Not sure if it will show here , maybe I'll put an addendum to the graph. or another short blog.Pat Bhttp://www.blogger.com/profile/15234744401613958081noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-87402676913018446222011-01-15T14:58:18.590+00:002011-01-15T14:58:18.590+00:00There are 4 pages in Crilly's book, 17 paragra...There are 4 pages in <a href="http://www.amazon.com/Mathematics-Ideas-Really-Need-ideas/dp/1847241476/ref=sr_1_1?ie=UTF8&s=books&qid=1295102471&sr=8-1" rel="nofollow">Crilly's book</a>, 17 paragraphs, the last 4 of which I retype below:<br /><br /><b><br />The birthday calculation makes the assumption that birthdays are uniformly distributed and that each birthday has an equal chance of occurring for a person selected at random. Experimental results show this is not exactly true (more are born during the summer months) but it is close enough for the solution to be applicable.<br /><br />Birthday problems are examples of occupancy problems, in which mathematicians think about placing balls in cells. In the birthday problem, the number of cells is 365 (these are identified with possible birthdays) and the balls to be be placed at random in the cells are the people. The problem can be simplified to investigate the probability of two balls falling in the same cell. For the boys-and-girls problem, the balls are of two colours.<br /><br />It is not only mathematicians who are interested in the birthday problem. Satyendra Nath Bose was attracted to Albert Einstein's theory of light based on photons. He stepped out of the traditional lines of research and considered the physical setup in terms of an occupancy problem. For him, the cells were not days of the year as in the birthday problem but energy levels of the photons. Instead of people being put into cells as in the birthday problem he distributed numbers of photons. There are many applications of occupancy problems in other sciences. In biology, for instance, the spread of epidemics can be modelled as an occupancy problem - the cells in this case are geographical areas, the balls are diseases and the problem is to figure out how the diseases are clustered.<br /><br />The world is full of amazing coincidences but only mathematics gives us the way of calculating their probability. The classical birthday problem is just the tip of the iceberg in this respect and it is a great entry into serious mathematics with important applications. <br /></b>Steven Colyerhttp://www.blogger.com/profile/10435759210177642257noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-58088651306405240102011-01-15T13:05:49.931+00:002011-01-15T13:05:49.931+00:00It's Colyer not Crolyer, but Crolyer seems mor...It's Colyer not Crolyer, but Crolyer seems more interesting; makes one wonder which ethnicity I am. :-) <br /><br />Actually, I'm not sure of the origin of my own name. Possibly the Dutch version of the English Collier? Not worried what anyone calls me, as long as they don't call me late to dinner. American Muttski is fine, and quite properly descriptive.<br /><br />In any event, my 4 high school Maths were Algebra 1, Geometry, Analytic Geometry, and Calculus. It was on the first day of our sophomore year that our Geometry teacher posed the Birthday problem. We didn't believe it! But he asked around the class of 23 and sure enough, 2 had the same date!<br /><br />He was also a fine baseball coach, but years later did prison time for being a professional football bookie (quite illegal in the USA), indeed the largest in our state! And they said Maths doesn't pay! :-)Steven Colyerhttp://www.blogger.com/profile/10435759210177642257noreply@blogger.com