# Social network nitpicking

Dave point out that some stuff going on at LinkedIn which led him to mention this Business 2.0 article.

No, I don’t want to talk about Sundays at the Mountain View Starbucks—I guess I used to go to the other Starbucks—I just want to nitpick two things I read in the article.

[My two nitpicks after the jump.]

The first mistake is because LinkedIn has sustained exponential growth it is a “tipping point.” No, it isn’t. In fact, “Tipping point” is not a “tipping point” because exponential growth is linear! Huh?

Look, viral growth is a first order linear differential equation (if you continuize the difference equation). The solutions to this equation are exponentials: ekt. If you have exponential growth it means your constant is greater than zero (this means each user is bringing in more than one other user within your “time step”). When you do something to move that constant from less than one to greater than one you’ve reached a tipping point but when you are at exponential growth, you haven’t reached a tipping point.

The fact that this is exponential makes people think you are “going non-linear” and thus at a “tipping point.” But you aren’t, you’re just linear because a positive feedback loop is creating growth.

When people forget that this is just a model, they extrapolate the growth to singularity because they are an idiots who has forgotten the underlying reality that they are just modelling and not simulating. I can’t tell you how many times shit like this pissed me off.

Now because Malcolm Gladwell doesn’t know basic applied mathematics and most of the people in the Valley seem to have forgotten it, they throw around terms like “tipping point” and “non-linearities” like they are candy and make a simple, yet complex thing very complicated, yet simplistic.

Please, use the brains God gave you and think critically. I’m dying over here. (Don’t believe me? Please buy the linked book and at least I’ll get some associate dollars for your circle jerk.)

### Reid’s Law

According to the sidebar, this is apparently that the usefulness of a business network grows exponentially as its ranks expand.

Really? I thought that is called Melcalfe’s Law. (Since none of you obviously click on my too useful links in old blog entries.) And again, it isn’t exponential. The usefulness according to your chart is growing linearly as the ranks expand exponentially! The real usefulness appears to be somewhere as n log n.

Really, what do they teach you people in business school?

Too much for the poor author? Then can he please stop bandying around terms like exponential and calling things “Reid’s Law”?

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