{"id":703,"date":"2008-11-13T17:08:58","date_gmt":"2008-11-13T17:08:58","guid":{"rendered":"http:\/\/scientopia.org\/blogs\/goodmath\/2008\/11\/13\/innumeracy-and-the-u-s-supreme-court\/"},"modified":"2008-11-13T17:08:58","modified_gmt":"2008-11-13T17:08:58","slug":"innumeracy-and-the-u-s-supreme-court","status":"publish","type":"post","link":"http:\/\/www.goodmath.org\/blog\/2008\/11\/13\/innumeracy-and-the-u-s-supreme-court\/","title":{"rendered":"Innumeracy and the U. S. Supreme Court"},"content":{"rendered":"

As long time readers of this blog know, one of the things that drive me crazy – in fact, one of the things that led me to start this blog – is the rampant innumeracy of our society. The vast majority of
\nAmericans have no real knowledge or comprehension of numbers or mathematics, and what makes that even worse is that most really, truly, fundamentally don’t care<\/em>.<\/p>\n

A vivid example of that is demonstrated in a recent Supreme Court ruling in a case dealing with the use of sonar in submarine training
\nby the US navy in waters inhabited by whales.<\/p>\n

<\/p>\n

The basic idea behind the case is that environmental groups had sued to prevent the navy from doing Sonar tests and training in waters where they were likely to harm marine mammals.<\/p>\n

Before getting to the innumeracy, it’s interesting to just
\ntake a look at the basic idea of the case, and how some basic numbers fit into it.<\/p>\n

Sonar is not an innocuous technology. Many of us have intuitions
\nabout it taken from movies and television shows, where it’s just a “ping” sound. But the point of sonar is to create a sound wave in the water that is powerful enough to produce accurately measurable reflections off of bodies at great distances away. Because of the way that sound propagates, there’s an inverse square relationship between signal strength and distance. So if you’ve got a target 100 meters
\naway, you’ve first got an inverse square reduction in the strength of the signal before it even hits the target. Then part<\/em> of the
\nsignal is absorbed by the target, and part is reflected. The reflected part again diminishes by inverse square. The point here is that
\nit takes a very<\/em> powerful sound pulse to get good readings.<\/p>\n

A typical sonar pulse originates at a volume of around 235 decibels.
\nThat is loud<\/em>. That is amazingly loud. In fact, that’s louder
\nthat the loudest possible sound<\/em> in air by roughly 16 times! (I
\noriginally wrote 4 times, when it fact it’s four doublings<\/em>in volume.<\/em>)<\/p>\n

To put that into context, it’s worth looking at a couple of examples to give you a sense of how much energy we’re talking about in a sonar pulse.<\/p>\n