In the movie A Beautiful Mind how could Nash tell the difference between real or imagined people?

In the movie "A Beautiful Mind," John Nash suffered from schizophrenia. Throughout the beginning of the movie, various odd occurrences took place, and the viewer was not aware that Nash suffered from schizophrenia. He believed he was followed by the police and repeatedly had invisible friends. He realized the man and the little girl were not real when he noticed they were not aging. Despite his schizophrenia, Nash continued on to be a brilliant mathematician at Princeton University.

Schizophrenia is an often misunderstood disease, and an illness people like to portray in colloquialism. Schizophrenia is marked by a combination of several factors, all of which must be present to have some qualify as a schizophrenic. First, the person may suffer from delusions, which may include someone thinking they are being harassed. However, this should not be confused with a normal person believing they are being harassed when they actually are. In this society, that does occur. In Nash's case, he thought he was being harassed for secret information he contained in his arm. That is not a thought process an average person would believe. Believing one is being harassed does not make that person schizophrenic.

Second, the schizophrenic suffers from hallucinations.  That is, they see things that are not there. In the case of Nash, he hallucinated friends and acquaintances. That is not the same as if in reality someone says they know someone who someone else says they don't. That is not a hallucination. The person is stating they know a real person, and others disagree with them. This can be either proven or disproven. Nonetheless, the individual does exist and some sort of relationship may exist between the two individuals. In the case of Nash, the man and the little girl did not.

Disorganized thinking and speech is another characteristic. This is not the same as someone who may ramble in sentences or say things out of the blue. Their thinking simply does follow. For example, they may say something like, "orange yellow blue sky has black olives." Or, perhaps, the person will be giving a talk and the sentences in no way link together. 

Schizophrenics also have abnormal motor behavior. This is ongoing and not simply someone acting agitated. For example, an individual may have agitated behavior in their home, walking fast because they are upset, or in a hurry. Someone may swing their foot out of habit while watching television. However, this is not abnormal motor behavior. Hypearctivity is severe. Individuals would be unable to sit still and concentrate. 

A person with schizophrenia also speaks without appropriate inflection, with monotone, and might not display emotions such as anger or even happiness. The person may not be able to carry out normal social activities. The schizophrenic may not be able to talk to others and may not take care of personal hygiene for days on end. 

In order for someone to be considered schizophrenic, these behaviors would be exaggerated in nature and not simply mild personal idiosyncracies. For example, someone stating another is harassing them, is not schizophrenic...when in fact the person or group of people may be harassing them.