## Friday, September 10, 2010

### Bounding Beck

Sarah Palin said there were “hundreds and hundreds of thousands of people.”  Glenn Beck put the estimate at 500,000 people.  Congresswoman Michelle Bachmann stated that she wouldn’t let anyone tell her there were less than 1 million people.  AirPhotosLive.com estimated only 87,000 people based on aerial pictures it took.  How many people were at the Glenn Beck rally?

As you can see from the photos on AirPhotosLive.com, most of the people assembled along the Lincoln Memorial Reflecting Pool.  According to Wikipedia, the pool is approximately 618 m long by 51 m wide.  Judging from the photos, attendees seem to cover an area between 3 and 4 reflecting pools wide, or roughly between 150 m and 200 m.  Multiplying by the reflecting pool length, this means the total area taken up by the attendees is between 92,700 m2 and 125,000 m2.  To be sure we’re not forgetting anyone, we’ll count the attendees that spilled over near the Washington monument and those that got a front row seat.   This looks like no more than 20% of the total number of people, so we’ll say they cover a total area of at least 90,000 mand at most 150,000 m2

Looking at the aerial photo, there’s a whole lot of green grass you can see between people.  This makes sense since most people don’t like to be squished and you need some extra room so that people can move around.  Each person needs at least 1.0 m2 of space to feel comfortable.  Judging from the sparse parts of the crowd, there’s appears to be no more than 10 m2 of space between people on average.  The average density certainly lies between these two extremes.  From these densities, we can use the equation

number of people = (density of people) × (area)

to compute an upper bound,

number of people = (1.0 person per m2) × (150,000 m2)
= 150,000 people

and lower bound,

number of people = (0.1 people per m2) × (90,000 m2)
9,000 people.

As you can see, the “87,000 people” estimate from AirPhotosLive lies right in the middle of the two extremes.  It is certainly a reasonable estimate, and it brings up an important point.  One way to test the accuracy of your estimate is using upper and lower bounds.  By using the largest and smallest realistic numbers in your estimation, you can put a cap on what the actual number must be.  We know there’s certainly more than our lower bound of 9,000 people and certainly less that our upper bound of 150,000 people.

By using upper and lower bounds, we also see that our politicians and pundits are either lying or possess a certain degree of innumeracy. Of these two options, I sincerely hope it’s lying.  I’ve grown accustomed to politicians bending the truth, but I’m absolutely terrified by the thought that people who have gained this much influence can’t do middle school math. This does beg one to ask, “Why even bother lying about numbers like this?”  For one, false claims like this are easy to debunk even with mediocre math skills.  In addition, 87,000 people at a rally is nothing to sneeze at, so why exaggerate?

Finally, I should note that I had some hesitation when writing this post.  This is not intended to be a political blog, and I’m not here to spout my personal beliefs.  The fact is that no matter what side of the political spectrum they’re on, rally organizers tend to exaggerate numbers to make it seem like they’re more popular than they really are, and it’s our duty as rationally thinking citizens to call them on it.