The Internet is a world-wide communication network, whose optimization depends on the knowledge of the statistical characterization of the aggregated traffic flow. Internet traffic is dependent on a number off actors, including communication protocols, network topology, and human behavior. Using a recently proposed segmentation algorithm, we find a surprising analogy between the nonstationarity and the correlations in the communication dynamics in the Internet and in another communication network of great interest: the autonomic nervous system (ANS). The ANS controls involuntary muscle motion, secreting glands, and the heart, hence, we surmise that the time interval between successive heartbeats-an easily measured physiological signal-provides a probe of the communication dynamics for the ANS. We find quantitative similarities between the statistical properties of i) healthy heart rate variability and non-congested Internet traffic, and ii) diseased heart rate variability and congested Internet traffic. Our findings suggest that the understanding of the mechanisms underlying the "human-made" Internet could help to understand the "natural" network that controls the heart.