No Such Thing as Vampires (and Other Compounding Catastrophes) - 2019-07-26

Vampires. They're great for movie thrills, preying on our childhood fears and emptying our wallets at the box office. I remember being terrified of them as a kid. But as I got older, something else started to gnaw at me: math. The compounding formula, in fact, proves quite definitively that vampires can't exist.

Think about it. One vampire bites someone, turning them into another vampire. Then those two vampires each bite someone else, creating four. That's a 100% compounding rate. So, how long would it take for just one vampire to turn all 7 billion people on Earth into bloodsuckers?

Let's do the math:


You get the picture. We're doubling the number of vampires with each generation. Mathematically, this is represented as 2 power n, where 'n' is the number of generations. To find out how many generations it takes to reach 7 billion, we need to solve for 'n' in the following equation:

2 power 34 = 8,589,934,592 ~ 8.5 billions!

Using logarithms (or a calculator with that function), we find that n is approximately 34. So, in just 34 generations (assuming each "generation" takes, say, a week), the entire planet would be overrun with vampires. This means the time needed is just 34 weeks!

The simple logic test then becomes: if you're not a vampire, then they probably don't exist. The rapid, exponential growth implied by 100% compounding would have taken over the world in no time.

This seemingly silly vampire example is a powerful illustration of how compounding works—and how it doesn't work in unrealistic scenarios. It's a useful tool for debunking nonsense, like the vampire myth.

This reminds me of another classic story: the story of the clever trickster who bankrupted a king with a chess board and grain. The cheater asked for one grain on the first square, two on the second, four on the third, and so on, doubling with each square. The king, thinking it was a small request, agreed. But little did he know, the exponential growth would soon lead to an astronomical number of grains, far exceeding the kingdom's entire supply. Just like the vampires, the rapid compounding, although seemingly small at first, quickly becomes overwhelming. It's a lesson about the power of compounding—and the importance of understanding its implications.

In conclusion: While compounding can be a powerful force for good (think long-term investing), we need to be wary of any proposition that promises exponential returns, especially those that seem too good to be true. These "opportunities," whether they involve mythical creatures or financial schemes, often rely on unrealistic assumptions and can quickly spiral out of control, ultimately leaving us empty-handed. Just as the king lost his fortune to a seemingly innocent request for grain, we too can be tricked by the allure of rapid compounding. So, always be skeptical, do the math, and remember: if it sounds too good to be true, it probably is.

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