# Where does "on the wrong side of square law" come from?

June 28, 2012 8:09 AM Subscribe

Where does this phrase come from? "On the wrong side of square law" is a science aphorism for a situation in which efforts must be increased at an exponential rate to achieve only modest returns. Does it have a specific origin or source?

I've not heard this phrase before, but I would imagine it is because a power law distribution with exponent between -1 and -2 has a finite mean and an infinite variance. That means the average value is finite, but the average squared value is infinite.

That makes life very difficult experimentally or in simulations. You're studying something (say how long it takes for your system to go from X to Y, whatever those are), and you want to figure you the average time. A finite average time exists if your exponent is between -1 and -2, but since the variance is infinite you're guaranteed to measure some very large values. Your experimental values will fluctuate

That's my guess anyway. I'm always dealing with finite mean and variance distributions, so my life is easy.

posted by bessel functions seem unnecessarily complicated at 8:26 AM on June 28, 2012

That makes life very difficult experimentally or in simulations. You're studying something (say how long it takes for your system to go from X to Y, whatever those are), and you want to figure you the average time. A finite average time exists if your exponent is between -1 and -2, but since the variance is infinite you're guaranteed to measure some very large values. Your experimental values will fluctuate

*wildly*because of the diverging variance. Because you're only going to do a bit of sampling (i.e. you won't do your experiment millions of times), those large values will throw off your estimate of the average.That's my guess anyway. I'm always dealing with finite mean and variance distributions, so my life is easy.

posted by bessel functions seem unnecessarily complicated at 8:26 AM on June 28, 2012

The only reference to that phrase that google coughs up is the original mention by Fred Pollack, Intel Fellow and Director of Microprocessor Research Labs, in 2000, and references thereto. It appears he's referring to the exponential growth of computing power predicted by Moore's Law, and how, based on the diminishing returns of making smaller and smaller transistors on processing chips, they were failing to keep up with the "Square law," that is, the exponential increase, in computing power.

posted by Sunburnt at 8:47 AM on June 28, 2012

posted by Sunburnt at 8:47 AM on June 28, 2012

The correct phrase is "on the wrong side of

posted by beagle at 8:50 AM on June 28, 2012

*square law". Sunburnt's citation can be viewed here. Pollack in 2000 does appear to be the originator of the phrase.***a**posted by beagle at 8:50 AM on June 28, 2012

This paper says that Pollack first said it in 1999 "in his keynote at MICRO-32." Pollack's presentation at MICRO-32. MICRO-32 took place November, 1999.

posted by beagle at 9:02 AM on June 28, 2012

posted by beagle at 9:02 AM on June 28, 2012

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posted by laconic skeuomorph at 8:17 AM on June 28, 2012 [2 favorites]