Thursday, July 10, 2008
Silence and the Power Law
Forgive the silence. This is not because I got drunk with Nige last night. I was not drinking though I managed, nonetheless, to hold my end up on another night of magic. Rather it is because I have been working too hard, in particular I am attempting to understand power law. Wikipedia does little to lighten the darkness. I think I am there but would be grateful if any of you bright sparks could do it in a couple of sentences. I can do relativity in seven words - action at a distance happens in time - but this has so far defeated me.
Subscribe to:
Post Comments (Atom)
A blog about, among other things, imaginary ideas - What ifs? and Imagine thats. What if photographs looked nothing like what we see with our eyes? Imagine that the Berlin Wall had never come down. What if we were the punchline of an interminable joke? All contributions welcome.
well, yes, it appears that the little graph, top right, represents levels of happiness over understanding. as you leave the green region you begin to abandon all hope of sustained sanity. hope that helps.
ReplyDeleteI thought power law was like the 80:20 rule - "Extreme and rare events have a greater than expected impact" as the econophysics blog has it - but perhaps that's a misunderstanding of power law. The article on Wikipedia is far too forbidding for me.
ReplyDeleteExtreme events have a disproportionate impact? It's like that saying: war is long periods of boredom punctuated by brief moments of terror. Or like the monsoon - 90 per cent of the rain falls in 10 per cent of the year, etc. Actually we had that yesterday. Oh well, dunno. Sounds an interesting subject though. The 80:20 rule comparison doesn't make it clear enough that the pattern is unpredictable, too.
Sh*t happens. Disproportionately. At times.
ReplyDeleteI've always known these as polynomial functions -- a class of descriptive mathematical equations. Now they've apparently become "Power Laws". The human impulse to change descriptions of natural phenomena into deterministic "natural laws" is seemingly irresistable. Something religion and science have in common.
ReplyDeletePower law distributions have such a fat tail that they don't have either a mean value, or a width. They are also scale-invariant, which means that the relative frequency of events or objects of magnitude 100 and magnitude 10, is the same as the relative frequency of events or objects of magnitude 10000000 and magnitude 1000000. Extreme events or objects are described by the same distribution as events or objects of small magnitude.
ReplyDeleteIf the music on a vinyl LP were scale-free over its entire frequency range, then the melody would sound exactly the same whatever speed you played it at.
Nicholas Nassim Taleb does a good job of describing power law phenomena in the Black Swan. It describes variables whose distribution is more weighted toward the exremes than a normal, or Gaussian, distribution. Basically its the anti-bell curve.
ReplyDeleteChrist, it was written by the same fellow who did the Lisbon treaties. Would that I had Randy a few weeks ago he seems to have a gift.
ReplyDelete