Can personality traits be clustered in a meaningful way? Or, to phrase the question in laypersons' terms, are personality types distinct? We use the myPersonality Project's dataset to attempt to answer this question. This Cambridge University-based project generously provided the scores on the “Big 5” personality traits for over 3.1 million people who took their quizzes on Facebook. To answer our initial question: yes, personality types can be clustered into two separate groups, but these groups are far from distinct. Along with providing evidence for this assertion, we explore the shape of this data and what is possible to say about it.