Examining The Mathematics Of Text Messaging And Its Affect On Human Behavior

In an attempt to help wireless service providers better manage their networks and resources, researchers have analyzed the mathematics behind SMS usage and its affects on human behavior.  What’s been found is that human communication patterns, particularly in the form of text messages, appear to follow a pattern that’s a fusion of two mathematical models.

In a paper published in PNAS on Monday, researchers analyzed a large set of text messages from service providers and found most users trade over 90 percent of their messages in bursts with only one other person, followed by an exponential drop into silence.  Text message sets often start off with a burst, and the time between messages are short and follow a “power-law distribution,” meaning there are a lot of text messages with short intervals between them.

In addition, outside of an initial two- to twenty-minute window, the time between messages fall dramatically.  There are fewer, longer intervals between messages, and the tail can extend up to five or six hours past the initial burst as the intervals continue to grow longer and the texts less frequent.  Here’s where things get interesting; researchers tried to reverse engineer the power law/exponential distributions of these text message conversations to better grasp why conversations happen this way.

What they found is that graphs could be reproduced if they assumed that two people were talking about a topic both could contribute to.  A conversation would start when there was a  topic of discussion that required the action of both people, and one conversant brought it up with the other — for instance, two people in a relationship deciding what to eat for dinner.  The initial text message puts the “task” on both conversants’ “to-do lists” so-to-speak.

Researchers next assigned a probability that the recipient of the first message would care about the task and respond.  A 100 percent chance of caring would result in endless text messages back and forth, while likewise, a zero percent probability never produces a response.  Using this model, the size of the text message bursts were tunable by this response probability.  The larger the burst, the higher priority the task for both parties, with all exchanges of a priority between 100 and zero eventually tapering off.

While it all sounds complicated, it actually provides some insight into how we all utilize text messaging on a daily basis.  For example, the research may explain why most texters overwhelmingly favor one texting partner.  The two may happen to share a large number of high-priority “tasks.”  Even the best of friends run out of chatting steam regularly (a few times a day, according to the records) but, because they have so many conversations, the texting still manages to occupy a lot of each others’ time.

Coming back to the reasoning behind such research, the authors speculate that this burst-and-taper pattern of text messaging also applies to other information ecosystems like email and trading, and that service providers could potentially allocate their bandwidth management or phone line availability based on this pattern.