A correlation dimension analysis of people's visual experiential streams captured by a smartphone shows that visual experience is two-scaled with a smaller dimension at shorter length scales than at longer length scales. The bend between the two scales is a phase transition point where the lower scale primarily captures relationships within the same context and the higher dimensional scale captures relationships between different contexts. The dimensionality estimates are confirmed using Takens' delay embedding procedure on the image stream, while the randomly permuted stream is shown to be space-filling thereby establishing that the two-scaled structure is a consequence of the dynamics. We note that the structure of visual experience closely resembles the structure of another domain of experience: natural language discourse. The emergence of an identical structure across different domains of human experience suggests that the two-scaled geometry reflects a general organizational principle.