Of whales and wind turbines

(originally written June 20, 2012 — part of my Great Upload of 2013)

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So I was reading up on my Ray Kurzweil last night, because it’s good to read people you disagree with once in a while — but preferably no more often than that.  ;)

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Kurzweil

Ray Kurzweil is a futurist who believes we’re heading into a singularity where, in this century, life will transcend biology and we’ll reach some sort of a higher condition of life.  His ideas could probably be summed up as:

– it took billions of years to go from single-celled creatures to multi-celled ones

– then hundreds of millions of years to get to human-like creatures

– then hundreds of thousands of years for homo sapiens to create cities

– then thousands of years for us to start making upgrades (artificial hips, pacemakers and the like)

– and in a short span of time, we’ll transition from a biological-molecule-based form of consciousness to a silicon-based one

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His ideas are pretty much distilled in this decade-old article/manifesto, which he wrote during the heady days of the dot-com bubble.  As such, though the trends in computing power have probably continued, economic progress… has not.

He made surprising choices in some graphs (e.g. patents issued over time) in that he didn’t factor in the huge effect of a rising population.  It looks like the number of patents issued per year went up tenfold from 1900 to 2000, but the US population also increased four-fold from roughly 70 million to 280 million.  So patents per person “only” went up 2.5x in a century.

There’s a big wrinkle though, which is that the US urban population went from about 40% to 80% in the century of 1900 to 2000, so the urban population probably rose about 8x [28 million to 200 million] in that century.  So in the past century, patents-per-urban-person might only have gone up… twenty percent?  A bigger wrinkle is the fact that half of US patents nowadays go to foreigners, and the biggest wrinkle is probably that patents aren’t a great way of measuring innovation.  They might be the best available measuring-stick, but that doesn’t mean they’re all that accurate…

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Cities and Whales

The urban-population factor is important because recent research purports to show that as metropolitan areas get bigger, they tend to “speed up” — since Metro Vancouver has twice the population of Metro Calgary, one would expect Vancouver to have 15% higher per-capita mean income and patenting rates.  Of course, local factors like the tar sands mean that these general trends come with massive, massive margins of error.  :)

The reason for this trend might be that as cities get bigger, people can become more and more specialized, and nudge the boundaries of human knowledge just a bit further in one tiny area.  And with so many people around them, there’s a better chance they’ll run into someone who can make use of that knowledge.  And there is a symmetric downside: apparently per-capita crime and other social ills also tend to increase about 15% with each doubling in city size.

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This “speeding up” with bigger size is the opposite of what happens in publicly-traded companies, which tend to “slow down” as they get bigger — fewer patents per person, lower per-person revenues, etc.  (The trend surely holds true for privately-held companies too, but since public companies release quarterly financial statements it’s waay easier to crunch public company data than private companies’.)  This phenomenon could elegantly, partially explain why public-sector bureaucracies often seem worse than private-sector ones: few private companies ever reach the size of governments!

A similar “slowing down” with size occurs in biology, a phenomenon known as Kleiber’s Law.  (Not to be confused with George Clooney’s girlfriend Stacy “Keibler”, or the cookie-making “Keebler” elves.)

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In the critter world, when animals double in size, their metabolic (food) requirements tend to only increase by 70-ish percent.  To use math terms, the exponent describing the relationship between metabolic rate and mass, is between 2/3 and 3/4.  And before you ask, yes indeed, there is the usual academic bun fight over what exactly that exponent is!  :)  To use a better example than the one offered in Wikipedia, if we were to compare a 200 tonne blue whale with a 20 gram mouse, the whale weighs 10,000,000x more, but only requires about 10,000,000^0.7 = 80,000x as much food.

Another example of how life seems to “slow down” for big creatures is the reasonably-accurate factoid that many mammals, big and small, have a lifespan of about one to one-and-a-half billion heartbeats.  And indeed, whales live a lot longer than mice — in the absence of whalers.  And cats.  :)  I could imagine that for our earliest mammalian ancestors, this might have represented a good balance between “durable enough to have offspring” and “not so resource-intensive as to starve other important bodily functions of nutrients”, but then I imagine a lot of plausible-sounding, completely-inaccurate explanations.  :)

Rambling aside, as animals get bigger, they get more efficient with their food inputs.  Which brings us to wind turbines!

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…and wind turbines

One of the few things I remember from my chemical engineering economics course is that the cost of components in a chemical plant increases more slowly than size, with the exponents generally in the 0.5-0.8 range.  We could think of this as a rough industrial analogue, or maybe even an extension, of Kleiber’s Law.

This trend applies to wind turbines, because if you scaled up a turbine so its blades and everything else were twice as big, you’d need more than twice the material, but you could probably extract quadruple the energy.  (Taller turbines can access stronger winds, and the blades would rotate through 4x the cross-sectional area, but various losses would eat away at that.)  The net effect is that bigger wind turbines are more efficient per-tonne-of-construction-material.  Not unlike that whale.  :)

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And back to Kurzweil

Before setting sail on that cetacean tangent (ie. talking about whales) we were examining how a lot of the technological progress feeding Ray Kurzweil’s optimism might not have come from exponentially-improving calculation power, but from a one-time migration of people from the countryside to the cities.

If population growth and urbanization were big drivers for the extraordinary progress we made in the 20th century, it stands to reason that we might see a slowing-down of things in the 21st century, as world population (and world urban population) level off and start falling.  This would be a bit of a downer for techno-optimists’ utopian visions, but would fit the more pessimistic notion that the human condition is a cycle between harsher and milder dystopias.

As an admirer of the great Greek tragedies, I’m in the latter camp.  And while I’m as overconfident in my opinions as most men, I have an ace up my sleeve: as per page 3 of the TIME magazine article, people with mild depression are more accurate at predicting future events!  Nice of the universe to finally throw us folks a bone…!  ;)

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