tag:blogger.com,1999:blog-6275903.post3668120651994934845..comments2020-03-30T21:53:54.432-07:00Comments on Nerdblog.com: the harmonic mean (MPG standards)Michaelhttp://www.blogger.com/profile/00058296587455402398noreply@blogger.comBlogger3125tag:blogger.com,1999:blog-6275903.post-17002253679023595342008-01-22T02:32:00.000-08:002008-01-22T02:32:00.000-08:00Oops: n=-1 is the harmonic mean. n=1 is the regula...Oops: n=-1 is the harmonic mean. n=1 is the regular arithmetic mean. <BR/><BR/>There's a beautiful inequality saying that if n is less than m then the nth power mean is less than the mth power mean. <BR/><BR/>For n=0 the definition doesn't make sense, but it can be shown that the nth power mean converges to the geometric mean (square root of X times Y) as n goes to 0. <BR/><BR/>This all can be generalized to arbitrarily many nonnegative quantities, with the same inequalities holding among their power means.<BR/><BR/>Way to go me, turning a topic of important social interest into abstract mathematical curiosa!Unknownhttps://www.blogger.com/profile/07772692038904873866noreply@blogger.comtag:blogger.com,1999:blog-6275903.post-54334502603073547642008-01-22T01:59:00.000-08:002008-01-22T01:59:00.000-08:00I just want to point out that the harmonic mean of...I just want to point out that the harmonic mean of X and Y is defined as 2/(1/X+1/Y), not 1/(1/X+1/Y). Fortunately, it looks like this was just a typo and you used the right formula in calculations.<BR/><BR/>More generally, the "n-th power mean" of two numbers X and Y is defined as ((X^n+Y^n)/2)^(1/n). n=1 corresponds to the Harmonic mean.Unknownhttps://www.blogger.com/profile/07772692038904873866noreply@blogger.comtag:blogger.com,1999:blog-6275903.post-68101194900134902012008-01-21T19:29:00.000-08:002008-01-21T19:29:00.000-08:00The big question in my mind is geothermal. It's th...The big question in my mind is <A HREF="http://web.mit.edu/newsoffice/2007/geothermal.html" REL="nofollow">geothermal</A>. It's the most attractive answer I can think of. Don't have to burn food, don't have to worry about another Cherynobyl, don't have to be dependent on foreign oil. As far as I can tell, the biggest obstacle is the initial capital investment, but the market doesn't tend to factor in things like <A HREF="http://costofwar.com/index-world-hunger.html" REL="nofollow">the cost of war</A>. If we put our best minds on the most efficient means of tapping the energy embedded in all the molten magma under our feet and spent $500B on that, I wonder how far we could go.metameristhttps://www.blogger.com/profile/00226487967115279195noreply@blogger.com