Category Math

Not Such A Good Deal

As of this writing, the Ronald Reagan Memorial National Debt stands at eight trillion, ninety-five billion, nine hundred forty-four million, eight hundred ninety-two thousand, three hundred seventy-one dollars and forty-eight cents. That’s a stack of $100 bills 549 miles high ([1]). The Hubble Space Telescope orbits about 375 miles above Earth.

In fiscal 2005, the US government made $2.053 trillion, and spent $352 billion paying interest on the debt. This is just the minimum payment to keep the debt from growing even more.

In other words, for every dollar that the US government receives in taxes, 17 cents gets taken off the top right off the bat to pay interest on the debt. For every one of your tax dollars, the government can only spend 83 cents on defense, homeland security, urban development, law enforcement, Medicare/Medicaid, research, and everything else the government does.

We Americans love a good bargain. I don’t think paying $1.20 for a dollar’s worth of defense is a good deal.

Drunken Walks 2: Neutral Drift Boogaloo

In our last episode, our heroes saw that just by taking lots of steps in random directions, you could wind up arbitrarily far from where you started. This time, we’ll take a look at what it means for population genetics and evolution.

As we’ve all learned, evolution is “allele frequency change in a population over generations”. And the way we all visualize this, I think, is to think of a population in which one member has a slight advantage over the others, such as sharper teeth, better resistance to poison, slightly more efficient camouflage, etc. As generations pass, a greater and greater percentage of the population has this advantageous trait, until eventually it’s the norm. Either that, or detrimental traits get removed from the gene pool.

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Drunken Walks (But Not the Pubcrawl Variety)

Imagine a drunk standing in the middle of a field. Every time he tries to walk a step, he winds up staggering in a random direction: north, south, east, or west. How long will it take him to get to the edge of the field?

We can look at it intuitively, and say that he’s as likely to stagger north as south, as likely to go east as west. So after 100 steps, he will most likely have made 25 steps north and 25 steps south, which cancel out; and 25 steps east and 25 west, which also cancel out. So he’ll just keep staggering around his spot in the middle of the field until he sobers up.
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