There is only one way to find out (for an engineer). Derive the equation for the system and see if there is a maximum. Pretty easy, except that we are dealing with humans, not atoms, so there will have to be some approximation. So, simplifying it down, I propose the Connection Index (CI).
Connection Index = number of connections * average quality of each connection
I also propose that each of us desires to maximize our CI. Since the equation is straightforward, maximization of CI involves increasing the number of connections and/or their quality. It gets complicated when we consider that one of those factors is easy to both influence and measure, while the other is not.
As a result of man's aversion to complexity, we are therefore drawn to the simple factor: number of connections. We know that a single connection makes us feel good, so we strive to increase the number of connections, knowing that more connections leads to greater CI (assuming constant quality). Since we are ignoring quality because it is too complex, we might as well assume it is constant. So we have more Twitter followers, more Facebook friends, and more LinkedIn connections, each one linearly increasing our CI...right?
Clearly, this logic breaks down. A short pause is all it takes to realize that my 350th friend on Facebook does not have the same quality of connection that I do with my wife (at least, they better not). So if the average quality of each connection is not the same, our assumption of constant average quality may not be as valid as we would like to think.
Imagine, for example that you have one connection with your soul mate. Your best friend in the entire world. One connection times a very high average quality equals a high CI. Now add another connection of an old classmate whom you have not seen in 15 years (a common Facebook occurrence). Very little connection quality, dragging the average quality of connections down significantly. But the number doubled, so the overall CI likely went up a bit, since the connection with your soul mate is unaffected by this new Facebook friend. So far, so good...Facebook has increased our CI.
Continue the thought experiment for a while, now. More and more people friend you on Facebook. One introduces you to Twitter and mentions LinkedIn. MySpace looks interesting, as does Tumblr. Google throws in Wave and Buzz. Connections (and the platforms that facilitate them) are multiplying rapidly. Which is good, since more connections leads to greater CI...right?
This is where it gets sticky. All those connections are clamoring for time and attention. On Facebook, your spouse gets equal screen time with your college roommates who compete with your clients on LinkedIn. Simply having a connection requires something of you, and that something has to come from somewhere. That somewhere will eventually be from the time and attention spent on your soul mate, that first and strongest connection. At first, that is no big deal. But soon, a loss of time will lead to a loss of quality in that connection, and CI begins to drop.
By this reasoning, at some point, additional connections begin to reduce the average quality more than can be compensated by the added connection. CI starts dropping, and will continue to drop with more connections, likely accelerating as we try to compensate for the negative feeling of a lower CI with a greater number of connections. (Remember our focus on the easy part of the equation? Plus, it worked up until now, right?)
So where does that leave us? In an ever downward spiral of reaching for something that is fleeing from us faster than we can pursue it. Once CI begins to drop, the only way to stop the bleeding is to defy instinct and stop. Don't add more friends, don't join another network, just stop.
Then focus on the other half of the equation. Rather than increasing numbers, increase the quality. Spend more time with your spouse, face-to-face with friends. Invest in the connections you have, and maybe even cut off some of those that are wasting your time.
The index is what matters. Stop stressing quantity and make the quality happen.
