Nuclear Email

This morning I received an email from a friend with a video clip about a tame Canadian goose who has made friends with a man and his dog. The video has some amazing sections showing the goose flying along side a speeding motorboat, so close that the man can reach out and touch it. My friend knew I would enjoy this video, and so he passed it along to me.

Another friend had done the same thing, with the same video, just a couple of days before. That sort of thing has happened to me many times; sometimes I’ve received the same joke, photos, sound clip, or video dozens of times. What’s going on here?

As I was trying to word a response to my friend, trying to find a way to say “Thanks! But I’ve already seen this…” I got to pondering this phenomenon. Why does this happen so often? And why are the contents of these emails quite often genuinely entertaining or interesting (or both!)?

So I started with my own behavior. When I get one of these emails, what do I do? Sometimes I post it on my blog, where it will be seen (and often passed along) by somewhere between a few dozen and a few hundred people (the number of people reading my blog varies tremendously from day-to-day). Sometimes I forward the email, and when I do, I usually forward it to 10 or 12 people I think might enjoy it. The majority of these emails I read, enjoy, and delete. I would guess that I delete 80% or so of them. But the 20% that I don’t delete get seen by something like 20 people (averaging between the blog and the forwarded emails). So…if 20% of the emails I receive are seen by 20 people each, that means that on average, every email I receive is then seen by 4 other people.

Am I typical? I don’t know. But just to be conservative, let’s say my behavior is double the average person’s forwarding behavior. If that were true, that means that every email sent out is see by 2 additional people, on average. This process is self-selective on the quality of the email’s contents, too — because of course the more entertaining or interesting contents will be forwarded more often…

Now lets see what this implies. Imagine that you created a short video of the earthworm you laboriously trained to do backflips on verbal command. This is something most people would consider both interesting and entertaining. Now you send this video to your two friends — and three people will have seen it. If, on average, they send it to two people, that means four more — a total of seven — will have seen it. If those four now each send it to two people, then eight more — fifteen in total will have seen it. And so on. We can reduce this to a simple formula: V = A^G - 1, where V is the number of people who have viewed the email, A is the average number of unique new viewers that each viewer sends it on to, and G is the number of “generations” including the original sender. So…if A = 2 and G = 10 (meaning that the email has been forwarded 10 times) then V = 2^10-1 = 1023 people will have seen it. But if G = 20, then A = 2^20-1 = 1,048,575 people will have seen it — and twice that many on the very next generation! How long does it take for an email to be forwarded 20 times? I would guess just five or six days, maybe ten at the most. And if this went on for 33 generations — then every single person on the planet will have seen the email!

The analysis above is not rigorous by any means. For starters, it’s almost certain that A varies from generation to generation, especially in the early generations. But it does illustrate just how quickly one of this email can propagate. It also shows just how likely it is that multiple people would send it to you at nearly the same time — if a million people have seen an email, what’s the chances that you know two of them? Or if 100 million people have seen an email? Pretty good, I think…

In fact, the process reminds me of another phenomenon of quick propagation: a self-sustaining nuclear reaction, as you’d find in a nuclear bomb. In these reactions, each decaying atom throws out two (or more) high-energy particles — each of which can then cause another atom to split and decay. The nuclear reaction proceeds much faster than email, as the energetic particles are moving at near the speed of light, and they only have to move an inch or two at most. But the underlying math is very similar…

Email and nuclear weapons are related!