# Fundamental Algebra, Synthetic and Analytic Geometry and Combinatorics

In geometry, we speak of synthetic geometry when we use Euclidean methods without superimposing axes onto the planes and analytic geometry when we do. Interestingly in psychiatry, we hear lawyers and particularly judges sometimes speak disparagingly about antipsychotic medications, calling them generators of synthetic sanity. What does that mean? It means the sanity is not analytic. There are no axes that can be imposed through the sanity that is created by antipsychotics. In short, someone who is sane by virtue of taking antipsychotics is in control of his actions but not necessarily in control of his mind as no dimensions can be drawn through his mind and defined as a spectrum of sanity. Analytic sanity on the other hand would have axes that can be superimposed onto the mind and could be respected by the legal profession. Someone who is analytically sane is in charge of his actions and his mind. Someone who is synthetically sane may only be in charge of his mind and not his actions. Take someone who is confused and commits a crime by breaking a law. That is no excuse. That may even be criminal insanity. But take someone who is no longer in control of his mind or his actions and seems to be breaking laws but really is just out of control and is sick and needs help. The only difference is whether that person can analyze his actions and explain them to others. If he can’t, these two scenarios look exactly the same to outsiders. The best example I will give is if influential officials are suddenly cracked down upon for bribery by police much like that which occurs in the People’s Republic of China routinely. Is it the police that are out of control? No, the laws make the penalties extremely high and executions are not uncommon. What is wrong is the official turned to bribery. Is that insanity? No it is crime. The protest of legal defense is that the entire case resulted from insanity because it was insanity that led to receiving a bribe in the first place. So confusion caused by insanity led to the breaking of the law. Yet the argument I ultimately would make is that I broke no laws in this hypothetical scenario. Because taking a bribe requires a conscious desire to break the law. I have thus illustrated what analytic sanity is capable of doing while synthetic sanity capable may only be able to argue that one thought someone was something else or that there was magic involved or that someone had to impart a lesson but these are all interpretations many of which show religiosity. Analytic geometry rose hundreds of years after synthetic geometry and I’d imagine analytic sanity took a long time to arise after synthetic sanity to explain the same things in the past but in a logical scientific fashion instead of one that overly appealed to religion and superstition.

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