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Why I didn’t answer your email

In a recent Nature article, Albert-Lászlo Barabási and João Gama Oliveira, have found the perfect excuse for lazy people not answering some emails in their inbox: they analyzed the time response of emails and found that they follow a power law probability distribution of the form P(t) = 1/t. In particular this implies that not even the mean response time is finite. Hey! why should you then expect me to answer your emails within my lifetime period! The usual buzz after the publication in Nature reach other scientific and non-scientific publications.

Unfortunately for lazy people like me, Barabási and Oliveira analysis of the data is wrong and the power law observed is an artifact of a bad analysis of the data, which is immensely better described by a log-normal distribution as shown in a recent comment by Stouffer, Malmgrem and Amaral also submitted to Nature. The inconsistency of Barabási’s analysis is shown in different ways, but their main points are:

  1. In the data considered by Barabási and Oliveira, the most frequent time interval between emails for some specific users is smaller than a second. This means that some people answer more than 60 emails per minute. Wow! that is fast and, unfortunately unrealistic.
  2. If P(t) is a power-law with exponent -1, when plotting the P(s) where s = ln(t) we should observe a uniform probability distribution (P(s) = const.). However, Stouffer et al. found that it is far from uniform and it looks more like a Gaussian (which correspond to assume that P(t) is a log-normal distribution).
  3. Stouffer et al. use Bayesian model selection analysis to find that the log-normal distribution is the one describing the data with probability one.

Moreover, the authors do also criticized the model proposed by Barabási and Oliveira to explain the data. Some other people comment on this flawed analysis of Barabási and Oliveira in their blogs.

Finally, it is interesting to find in the comment by Stouffer et al. the following sentence:

Barabási analyzed the email communication patterns of a subset of users [2] in a database containing the email usage records of 3188 individuals using a university e-mail server over an 83-day period [3]. Upon examining the same data, we find a number of significant deficiencies in his analysis. These deficiencies were communicated to Barabási well in advance of publication [4].

If Barabási and Oliveira were right, they should not expect an answer to this communication in finite time!



Professor at Universidad Carlos III de Madrid and MIT Medialab. Working on Complex Systems, Social Networks and Urban Science.