I’ve changed one term in my “Weapons of Math Destruction” post : “value” has been altered to read “interest” throughout the post.

The original public expressions of Metcalfe’s Law expressed the theoretical potential value of a communications network as being proportional to the number of pairwise connections — growing quadratically with the number of users). Similarly for community networks being valued by the number of subgroups under Reed’s Law — growing exponentially with the number of users.

I originally used the same terminology, but I’ve found the term “interest” to be less confusing. It’s hard to reason about what “theoretical potential value” means, but I think the best way to think about is that it is simply how “interesting” a network can be.

In fact, if you look at the capital valuation of a community company such as Facebook, you see that it has grown exponentially — in time, not in users. Also, the number of users has grown exponentially in time. Why?

- To have exponential growth in users, the number of users added each month must increase exponentially. The number of users each month is a direct expression of interest, which as Reed says, is in proportion to 2 to the number of users (in the previous month).
- I’m not quite sure how to look at market valuation.
- If market valuation is simply an irrational expression of exuberance, than we should see it increase each month according to interest, just like the number of users grows. That fits the data.
- However, investors may be assigning a rational valuation based on the expected potential revenue. That also fits the data, using a sober flat rate per user (of about $100).

This revision of “value” => “interest” lets us reason separately about user growth and monetization. For example, the current fashion for monetizing social media is based on either subscriptions, virtual goods, or advertising. Each of these are based on an amount per user, not per subgroup. Thus monetized value for these will grow exponentially in time just as the number of users grow exponentially in time, but not double-exponentially.