### Vic Sergey Google and the logarithmic derivative

Posted by Francesco Gadaleta on May 4, 2012

Back in 2011, Vic Gundotra and Sergey Brin appeared at the Web 2.0 Summit and talked about Google, more specifically Google+. You can view the video of that interview on Youtube or below At the time, Google+ was—and still is at the time of writing—one of the most innovative social networks on earth and the first social network platform without users (oo). It’s even kind of weird to call it social.

One thing I am amazed by is the way managers and presidents like Vic can make sad statements and still look cool, making people believe that the product is actually quite amazing. They claim that the 40 million users per month figure was a well-above their expectation without putting it in context. It is indeed a large number of users, which any company would love to have in one month. Unfortunately, Vic and Sergey are not considering the logarithmic derivative. Or rather, they are choosing not to discuss it.

Let me describe it in piggy terms. Let the growth of new subscribers to Google+ be, as they claim, $g'(x)=+40mln$ per month. But if we assume that the initial number of available users subscribing to the new service is represented by $g(x)$, that the relative rate of growth should be computed according to the logarithmic derivative given by $\frac{g'(x)}{g(x)}$ and that $g(x)$ is actually a very large number, there’s absolutely nothing to be proud of. An increase of 40 million customers for a company with, let’s say, 100 million customers has a relative growth rate of 40%

But the relative growth rate for a company with 1 billion, such as Google, would be about 4%.

Now Vic, are you still impressed? (oo)

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