Crowds

This post is being salvaged from December - it was written about the time I was wrapping up my Christmas shopping.

I'm sure there must be some mathematical expression for determining the aggravation level associated with interacting with a large crowd of people. For example, a small crowd of people (let's say the folks at the gym at 2am) is not very frustrating. A large crowd of people (read: the mall this whole week) is very, VERY frustrating. But it's not linear; it's exponential. Assume the following:

• Let x = size of location in square feet
• Let c = the current individual
• Let b = number of people in the crowd
• Let n = time spent in said crowd (b)
• Let a = level of agitation

So, c(a) = b^n/x.

The gym at my apartment complex, which is about 300 sq. ft., has an average of three people in it (that's a guess - it's normally pretty empty), and I normally spend about a half-hour, when I go. That would work out to c(a) = 3 X 30 / 300, or c(a) = .3. That's pretty low.

Now, let's take the mall (remember - I'm pulling these numbers completely out of my, uh, brain).

I'm guessing that the mall is about 300,000 sq ft, which is based on a phone call to the personnel at the mall information desk. This may be a bit on the small side, but this is an example. I'll try to find better information later.

Anyway, so let's call the mall 300,000 sq ft. And let's assume that, during the week before Christmas, you have approximately 2500 people in the mall at any given time. I think this number is small as well. Let's also assume that, if you're a normal shopper, and spend some time browsing, looking for the perfect item, you'll spend about 2.5 hours in the mall (including dealing with parking), which is 150 minutes. So here's my equation: c(a) = 2500 X 150 / 300,000 so c(a) = 1.25. This is about 4 times higher than my gym example. I'll get to work on my Nobel acceptance speech.