tag:blogger.com,1999:blog-6555947.post109597736313046590..comments2014-01-12T10:46:48.153-07:00Comments on The Geomblog: Geometric ProbabilitySuresh Venkatasubramaniannoreply@blogger.comBlogger2125tag:blogger.com,1999:blog-6555947.post-1096052042135369272004-09-24T12:54:00.000-06:002004-09-24T12:54:00.000-06:00Ok. I looked at the paper more carefully after my...Ok. I looked at the paper more carefully after my morning caffinated rage wore off. While I think the result is nice, the abuse of the term "uniformly chosen at random" raised my expectations and lead me to disappointment when I saw what the model really was. Further, my criticism of the figure was unfounded.<br /><br />It would be far cooler if the model had allowed more slopes and intercepts. Off the cuff again, say the lines in L are formed by taking the "inverse dual" of n points sampled from [-1,1]^2 That is map a point P=(x,y) to the line TP = {(u,v): v = 1/x *u + 1/y}. If the O(1) expectation holds there, that would be surprising.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-6555947.post-1096041225552833012004-09-24T09:53:00.000-06:002004-09-24T09:53:00.000-06:00I did not read the paper carefully but offhand, th...I did not read the paper carefully but offhand, the definition of "uniformly distributed lines" given Golin, Langerman and Steiger seems highly suspicious. Their definition is to take the dual of n uniformly distributed points in the unit square. But since the x coordinate of a point corresponds to the slope of the dual line, this means negatively sloped lines are not represented. This makes me wonder if their figure is accurate. First, it has lines with negative slope. Further, it has lines with slope greater than one!<br /><br />Are you sure this result is worth mentioning, let alone blogging about, or deemable as "surprising"? It seems like a piece of junk.Anonymousnoreply@blogger.com