In today's excerpt - flies, elephants, cities, and ideas:
"Scientists and animal lovers had long observed that as
life gets bigger, it slows down. Flies live for hours or days; elephants live
for half-centuries. The hearts of birds and small mammals pump blood much faster
than those of giraffes and blue whales. But
the relationship between size and speed didn't seem to be a linear one. A
horse might be five hundred times heavier than a rabbit, yet its pulse certainly
wasn't five hundred times slower than the
rabbit's. After a formidable series of measurements in his Davis lab,
[Swiss scientist Max] Kleiber discovered that this scaling phenomenon stuck to
an unvarying mathematical script called 'negative quarter-power scaling.' If
you plotted mass versus metabolism on a logarithmic grid, the result was a
perfectly straight line that led from rats and pigeons all the way up
to bulls and hippopotami. ...
"The more species Kleiber and his peers analyzed, the clearer the equation
became: metabolism scales to mass to the
negative quarter power. The math is simple enough: you take the square root
of 1,000, which is (approximately) 31, and then take the square root of 31,
which is (again, approximately) 5.5. This means that a cow, which is
roughly a thousand times heavier than a woodchuck, will, on average,
live 5.5 times longer, and have a heart rate that is 5.5 times slower
than the woodchuck's. As the science writer George Johnson once observed,
one lovely consequence of Kleiber's law is that the number of heartbeats
per lifetime tends to be stable from species to species.
Bigger animals just take longer to use up their quota.
...
"Several years ago, the theoretical physicist Geoffrey
West decided to investigate whether Kleiber's law applied to one of
life's largest creations: the superorganisms of human-built cities. Did
the 'metabolism' of urban life slow down as cities grew in size?
Was there an underlying pattern to the growth and pace of life of
metropolitan systems? Working out of the legendary Santa Fe Institute, where
he served as president until 2009, West assembled an international team of
researchers and advisers to collect data on dozens of
cities around the world, measuring everything
from crime to household electrical consumption, from new patents to gasoline
sales.
"When they finally crunched the numbers, West and his
team were delighted to discover that Kleiber's negative quarter-power scaling
governed the energy and transportation growth of city living. The number of gasoline
stations, gasoline sales, road
surface area, the length of electrical cables: all these factors follow the exact
same power law that governs the speed with which energy is expended
in biological organisms. If an elephant was just a scaled-up mouse,
then, from an energy perspective, a city was just a scaled-up elephant.
"But the most fascinating discovery in West's research
came from the data that didn'tturn out to obey Kleiber's law. West and
his team discovered another power law lurking in their immense database of
urban statistics. Every datapoint that involved creativity and innovation -
patents, R&D budgets, 'supercreative' professions, inventors - also
followed a quarter-power law, in a way that was every bit as predictable as
Kleiber's law. But there was one fundamental difference: the quarter-power law
governing innovation was
positive, not negative. A city that was ten times
larger than its neighbor wasn't ten times more innovative; it was seventeentimes
more innovative. A metropolis fifty times bigger than a town was 130 times
more innovative.
"Kleiber's law proved that as life gets bigger, it
slows down. But West's model demonstrated one crucial way in which human-built cities
broke from the patterns of biological life: as cities get
bigger, they generate ideas at a faster clip. This is what we call
'superlinear scaling': if creativity scaled with size in a straight, linear
fashion, you would of course find more patents and inventions in a larger city,
but the number of patents
and inventions per capita would be
stable. West's power laws suggested
something far more provocative: that despite all the noise and crowding and
distraction, the average resident of a metropolis with a population of five
million people was almost three timesmore creative than the average
resident of a town of a hundred thousand."
Author: Steve Johnson
Title: Where Good Ideas Come From
Publisher: Riverhead
Date: Copyright 2010 by Steven Johnson
Pages: 8-11
Tags: Animals, Innovation, Science, Cities
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