Calculus: Abstraction

The root of calculus is how mathematics solves problems across disciplines by abstractions and finds the secret analogies that tie these problems together across the fields. In calculus in particular we start by examining the limit, what happens on a limit. For example in Zeno’s Paradox, presumably a man can never finish walking a step because he has to complete first the first half, then half of the remaining and so forth. So he has infinite tasks and so it seems he can never get done. But in fact calculus tells us in the limit, the infinite series has a finite sum and the task can be completed, a seemingly insurmountable task can be completed in a finite amount of time because the individual components of the task get smaller and thus easier. Calculus moves on to tell us about derivatives which investigate the rate of change and integrals which calculate areas under curves.

Converting differentials with changes of variable is a frequently used method using the chain rule of differentiation which tells us functions have derivatives equal to the derivatives of these functions within functions multiplied together. The essence of calculus though is that it tells us what to ignore. Some things will fade in the limit compared to other factors and we can ignore what is going to go away or be dominated in the limit. For instance, if you are constantly called upon to certify your credentials, you may have a Herculean task in front of you as there is no end to what can be justified or reasoned away to certify your credentials. Fortunately, we can ignore this process of certification because it is dominated by other indicators such as the social status that one has depending on one’s job or prior achievements.

It is only dominated in the limit as time goes on because one’s career grows faster than one’s ability to boast and justify this boasting in a credential certification process as time goes on. So calculus is the study of abstraction including functions and their linearizations. For example we can linearize a function using derivatives and tangent lines and represent that function much more easily than all the complexity in the function before. How does this relate to stories? I focus on stories because in an economic journal, stories come to the forefront when people use them in substitution for quantitative reasoning. Stories are often used as models to describe a scenario by storytellers who assign you roles and then they say: it’s fiction but people write about it so it might be real or who would read it?

Calculus flat out proves this reasoning wrong: a story is no model because in the limits, many stories will resemble what is in front of you and all of them will eventually break down except for what is truly going on. What is fiction is carefully constructed not because it is real but because it is fake. Fiction is a simulation of what otherwise could not occur in the real world. And if you have a desire to live your life following models in simulation then go ahead and believe fiction until you run out of fictional ideas. In short, if you desire abstraction to guide your life, you should be turning to calculus not stories. Because the reasoning of calculus will hold in the limits while stories can only rationalize what has already occurred and will always be a step behind what happens in the limits which require the storyteller to be one step ahead and predict what will happen in the limits before he gets there.

Such a storyteller we often call a fortune teller and that sort of person is usually given very little credibility as his way of predicting what happens in the limits is often gauged from the person he is interviewing. It is in short a fixed match. It is a human tendency to believe stories and to learn from them such as the ones in religious texts but in truth, a story cannot be judged by its own merits but only on whether it survives in the limit: whether the story can be abstracted, whether the story enters the realm of culture and civilization through passing through limits, and that is the test of a classic. The next time you see a situation unfolding in your life similar to stories, for example if I feel like Caesar, I will know it is not because fiction is real but because fiction is fake that I perceive this.

In short, many stories are crowding around me and in the limit one of these stories will dominate and the rest I can ignore. In short calculus allows for one story as the abstraction allows us to conjoin worlds, compare their significance, and avoid switching world views to account for all the different stories. The one story which seems quite evident to me now is the Second World War out in Chicago where Chicago is America, the Episcopal Church is New England, and the Catholic Church is Free France. We also have the Clinton campaign as Nationalist China. They are facing imperialists such as for example the real United Kingdom playing as Japan on the Clinton campaign, and the imperialists are friendly with more fascist types from the German tradition which have reach into the United States through the right wing in America.

If I didn’t outline this, this story may never have happened except in a rough approximate manner. But the abstraction in calculus let me see past the minor stories in Chicago such as for example the real Japanese angle. Real Japan being a USA ally would probably side with Clinton China. Have they? It doesn’t matter real Japan, though they can deploy first well before Americans in China like how Japanese communists went to fight against Japanese imperialists in real history, are too small compared to American and Nationalist Clinton China forces and thus will be dominated by other forces in the limit. There is no right answer except that it is irrelevant. What about all the cultural significance of real Japan becoming politically potent again in the United States? It is already won: real Japan proved Asians can do this too, write stories without copying them by using math not creativity to write stories.

So if you want to be two people, make sure all but one disappears in the limit or your model won’t work as physically you are one person. My Japanese disappears in the limit and I remain American. And for the China Clinton side, they were reluctant to give up on what the real Japanese demanded which was a friend if the real Japanese became a friend and did as promised, but after they gave her up, we found the story could move on again and reach the limits which tells us what is relevant and what can be ignored: both the China Clinton friend who is a girl and the real Japanese are staying in China to fight for the Clinton Chinese. This is to save the good name of Japan as the British imperialists are using Japan’s former position to conquer Clinton China. I even turned over the American stuff to my best friend from Texas who is Franz Liszt Wolverine Tel Aviv as if I want to be what is dominated in the limit, the Japanese, so I can stay with let’s say the Clinton China girl who is a friend, I have to discard what would have made me ignore her in the end: I discarded my face, the yellow one which requires me to be American at all times with proof available at all times.

They say Asians only care about shame and Westerners only about guilt. There is no shame in playing against me if you lost honorably I say to the China Clinton girl who is a friend. For guilt I will have to read the catechism. Obviously if you live in a big city around China Clinton crowd you’ll be friends with them, but if you are like me living in a small town, you will be American, kingdom or empire it doesn’t matter, and look at the China Clinton crowd skeptically with all the problems they’ve had with the law. I’ve had my problems with the law but they were resolved philosophically. No, all I regret is what I just lost which was my innocence as I realized it was because I couldn’t give up my American that in the limit, I kept acting like the global arrogance. We will get you paper tigers next time and an Axis of Hegemony too. For purple mountain majesties….

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