Shape-writing (aka gesture typing or swiping) is a word-based text entry method for touchscreen keyboards. It works by landing the finger on (or close to) the first character of the desired word and then sliding over all the other character keys without lifting the finger until the last word character is reached. This generates a trajectory of swiped characters on the keyboard layout which can be translated to a meaningful word by a statistical decoder. We hypothesize that swiping carries rich information about the user, such as demographic (e.g. age or gender) and behavioral (e.g. swiping familiarity or input finger) information. To test our hypothesis, we trained several sequence classifiers using different recurrent neural network architectures to predict demographic and behavioral correlates of users from swipe trajectories. We show that our sequence classifiers are always performing better than a random classifier, therefore we conclude that cognitive and motor control mechanisms are embodied and reflected in swipe trajectories, validating thus our research hypothesis. Taken together, our results have implications for user privacy. Currently swiping is supported by all mobile vendors and has millions of users, so people may be inadvertently profiled at an unprecedented granularity. Future work should consider new ways of addressing these issues without impacting the user's swiping experience.