Tuning in on Noise?

xkcd-904It’s a bit off-topic for the series, but I can’t even go to Google now without being reminded of the World Cup and soccer this, soccer that. (Apologies to non-Americans who know the sport as football—but don’t get me started on football!) I have often wondered: given characteristic low score values, is soccer anything more than Poisson noise? When discussing this with colleagues, one pointed me to this XKCD comic, reproduced at right.

Any random process that produces discrete events in some time interval, with uniform probability per unit time follows a Poisson distribution. When the number of events becomes large, the distribution tends toward a Gaussian (normal) distribution.

My thesis is that soccer is an amalgam of random processes whose net effect produces rare events—those more-or-less unpredictable events spread more-or-less uniformly in time. Whether a good or bad bounce off the bar, a goal keeper who may or may not prevent a goal, a referee who may or may not see an illegal action, a pass that may or may not be intercepted, and on and on: the game is full of random, unpredictable events. So I expect soccer to behave similarly to a Poisson process and follow a Poisson distribution. By extension, I will claim that the attention devoted to the World Cup is founded on flimsy numerology and might even be called a tremendous waste of time and money.

Normally I allow comments on Do the Math for ten days after each post. I’ve tackled some controversial topics and stirred up emotional responses. Yet I predict that the outrage generated by my insinuation that watching soccer is a waste of time will absolutely dwarf the reactions to my saying that we may not be looking at a space-faring future, or that indeed we may face collapse of civilization. To the extent that this (untested) prediction is true, it would seem that soccer is more important than the fate of the world, in the eyes of many. Scary, if true. [After reconsideration, I enabled comments, but I won't have time to vet and respond with my usual level of attention.]

But getting back to soccer numerology, my question becomes: given a final score (which is taken to be the ultimate “truth” of the match) how likely is it that the victor is actually a better team?

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The Energy Trap

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Many Do the Math posts have touched on the inevitable cessation of growth and on the challenge we will face in developing a replacement energy infrastructure once our fossil fuel inheritance is spent. The focus has been on long-term physical constraints, and not on the messy details of our response in the short-term. But our reaction to a diminishing flow of fossil fuel energy in the short-term will determine whether we transition to a sustainable but technological existence or allow ourselves to collapse. One stumbling block in particular has me worried. I call it The Energy Trap.

In brief, the idea is that once we enter a decline phase in fossil fuel availability—first in petroleum—our growth-based economic system will struggle to cope with a contraction of its very lifeblood. Fuel prices will skyrocket, some individuals and exporting nations will react by hoarding, and energy scarcity will quickly become the new norm. The invisible hand of the market will slap us silly demanding a new energy infrastructure based on non-fossil solutions. But here’s the rub. The construction of that shiny new infrastructure requires not just money, but…energy. And that’s the very commodity in short supply. Will we really be willing to sacrifice additional energy in the short term—effectively steepening the decline—for a long-term energy plan? It’s a trap!

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Discovering Limits to Growth

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After inaugurating the Do the Math blog with two posts on the limits to physical and economic growth, I thought it was high time that I read the classic book The Limits to Growth describing the 1972 world computer model by MIT researchers Meadows, Meadows, Randers, and Behrens. I am deeply impressed by the work, and I am compelled to share the most salient features in this post.

To borrow a word from a comment on the Do the Math site, I’m gobsmacked by how prescient some of the statements and reflections in the book are. Leaving aside remarkably good agreement in the anticipated world population and CO2 levels thirty years out (can’t fake this), I am amazed that many of the thoughts and conclusions I have formed over the past several years are not at all new, but were in black-and-white shortly after I was born. Continue reading

Does the Logistic Shoe Fit?

U.S. total energy 1650-present (logarithmic)

This is a quick update regarding the first plot shown in the galactic scale energy post. A reader, Chris, called attention to the obvious departure from exponential growth in recent decades. The post required turning a blind eye to many practical issues (like population saturation) in order to entertain indefinite growth, serving to highlight the absurdity of the notion. But Chris goaded me into paying more attention to the departure from the exponential track in the actual data, and here are the results of a logistic approach. Continue reading