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.

Another area that is interesting and pertains to this topic is combinatorics which can arise out of card games that involve coincidences as we investigate how often each coincidence can arise out of all the possible events that could arise to determine if the coincidence truly was remarkable. In doing this type of mathematics we frequently partition the real number space. I’m going to avoid getting into the mathematical calculations as it is unnecessary for our scope here but rather say that a coincidence is by its nature unremarkable, it is only the counting of coincidences that makes them remarkable. In the same way, it is counting not stories that make remarkable works. It does not have to be fungible things that are counted. Partitioning spaces to solve problems is like how the office works: each person works on a specific task and a linear mapping results that often clarifies procedures. Where it gets interesting is when all this is applied to Dali’s surrealism: a mathematician who taught me back in college was fond of Dali’s paintings and had a poster up. He would always say analysis was his nemesis but he liked algebra. The fundamental theorem of algebra talks about how polynomials raised to certain powers have a certain number of rational roots. But what does all this mean? Algebra is the mending of broken parts by its definition. What I think the fundamental theorem of algebra largely means is it all used to make sense before it was all broken as whatever power it was raised to, that’s how many roots there are, but I don’t think anyone can mend everything, so instead of worrying about who makes the most money, just try to do well for yourself maybe, or better put, doesn’t it bother you that there’s always two narratives? What happens and an interpretation? So why not live in the moment and let a clock just be a Merry-Go-Around like in J.D. Salinger’s “Catcher in the Rye” which has its ultimate lesson I think that it is okay to go crazy, as long as you know crazy is different for each person you interact with as we are all different and crazy isn’t really an attribute of a person so much as a count of his works, and when the count is negative we say he is crazy as he is slipping: a story can’t be crazy on its own, numbers can be crazy, a business that runs into the ground is crazy, so I suppose a story can only be crazy if it also makes businesses run into the ground, and that story would be a love story between People’s Republic of China and Dr. Bethune of Canada a doctor who treated Chairman Mao. I wrote that story. The Canadian doctor treated the granddaughter of Chairman Mao, since Canada is the same age as the grandkids of China, and after I wrote it, I wondered why I did it: the fundamental theorem of algebra seemed to have required me to mend my broken parts in a way that made it all make sense in the past. But my past now mended seems absolutely not myself. And that is the final lesson of surrealism; be careful what you wish for as when you find the explanation you may realize you are in the wrong. The story was Smallville. Lana went with Lex Luthor who became Prime Minister. We had grown up in small towns near each other together in Canada as an American in my case or Chinese in her case. But she was destined for America she knew because China is normal country and its citizens move all over the world. I think Lana wised up later but she is still laced with Kryptonite probably which wipes out Superman. Kryptonite is based on the whole Canadian multiculturalism concept which can be incompatible with American motherhood and apple pie. Canada says it is like a mosaic while America is like a melting pot. Occasionally Lana sends greetings through her old job and corporate network I like to think. But honestly you see how stories are weak in explanatory power and you need mathematics to bring you to the truth and then you tell the narrative. Or you put the cart before the horse. Someone who doesn’t know mathematics needs to put hand over hand and twiddle thumbs until someone can help them or alternatively, get a strong gal and Guinness.


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