Schizophrenia
http://www.mayoclinic.org/diseases-conditions/schizophrenia/home/ovc-20253194
Although the play doesn't give a strict diagnosis, we know Alan believes that horses speak to him, and that he sees things that others don't see. It might enhance classroom discussion if you take some time to consider him from a clinical perspective. Schizophrenia and Bipolar Disorder are two diagnoses that might suit Alan. The Mayo Clinic provides excellent, free overviews of both.
Bipolar Disorder
http://www.mayoclinic.org/diseases-conditions/bipolar-disorder/home/ovc-20307967
Although the play doesn't give a strict diagnosis, we know Alan believes that horses speak to him, and that...