The part of the primate visual cortex responsible for the recognition of objects is parcelled into about a dozen areas organized somewhat hierarchically (the region is called the ventral stream). Why are there approximately this many hierarchical levels? Here I put forth a generic information-processing hierarchical model, and show how the total number of neurons required depends on the number of hierarchical levels and on the complexity of visual objects that must be recognized. Because the recognition of written words appears to occur in a similar part of inferotemporal cortex as other visual objects, the complexity of written words may be similar to that of other visual objects for humans; for this reason, I measure the complexity of written words, and use it as an approximate estimate of the complexity more generally of visual objects. I then show that the information-processing hierarchy that accommodates visual objects of that complexity possesses the minimum number of neurons when the number of hierarchical levels is approximately 15.