Comment on A.-L. Barabasi, Nature 435 207-211 (2005)

The purpose of this communication is twofold. First, it clarifies the origin of the power law obtained in the computer simulations presented in A.-L. Barabasi, Nature 435 207-211 (2005) as well as presenting a statistically more sound analysis of the experimental email data used in that paper and in [4]. The second purpose is to clarify the origin of the the suggestion of power law probability distribution for the response times of humans presented with a piece of new information either as a news event or through the reception of an email. In a letter in Nature published May 2005 [1], A.-L. Barabasi presents results from an email experiment[2], which suggest that the time lag τ between the reception of an email and the following reply for an individual follows a power law probability distribution P (τ) ∼ τ −1 , (1) when averaged over time. Only a single example(user) is shown and the claimed scaling region is extremely limited. At the conference " Frontier Science 2003-A Non-Linear World: The Real World " in Pavia, Italy, Sept. 2003, where A.-L. Barabasi also was present and more than one year prior to the submission of [1] to Nature, I showed with high statistical significance, i.e., much higher than that of [1], using the same data set of [2], that when averaged over both time and population the time lag τ follows a power law probability distribution P (τ) ∼ (τ + c) −1 , (2) where the reason behind the constant c is simply that the computer time lag measured is not the true response time 1. The prime reason for the " shift " c is that most people do not down-load and/or read new e-mail messages instantaneously. Not only is the statistical significance substantially higher compared with [1] because of the population averaging, but also because the cumulative distribution of measurements were used thus filtering out much of the high-frequency (Integration effectively result in a low-pass filtering). The deviation between the data and the logarithmic fit for long times can be attributed to to limitations in peoples ability to answer a large number of email, i.e., a finite size effect due to a limited amount of time and 1 A quite crude approximation is made here as the time-lag c is taken to be the same for all individuals. This explains the small deviation between the data and the …