Ordinary Differential Equations: Predict the Future

It is a common refrain in some circles that you cannot predict the future because so much data is required to simulate the future and moreover you cannot change this future even if you could predict it. This is the domain of ordinary differential equations where equations relate the rate of change of certain variables to functions of these variables. If we find a true model for reality, then we certainly can predict the future without any noise from errors because we have the true model. The response typically is that we are only predicting part of reality. For us to predict the entire future we would need so much data and we would need to be able to get into people’s heads. We are arguing that the future has to be well-behaved where certain rates of change of variables in the future depend on these variables themselves in functions. A solution to an ordinary differential equation is one pathway the future can take which satisfies the requirements of the differential equations that we set up as constraints. We can talk about whether these solutions are in equilibrium and whether these solutions bifurcate from each other but the important thing is we recognize we can predict the future when the future is subject to rational bounds like a predator prey model in the population where the rate of change in the prey population depends on how many predators there are relative to prey and the rate of change of the predator population depends on the prey population availability to nourish the predators and their hunger. There is free will but the free will has to choose rationally when there isn’t enough to eat for example, and therefore predators will always feed on prey to satisfy their hunger. The notion of the future being a black box that no one can predict does not take into account that the future is bounded by the same systems observed in the present. The only thing that matters when we move into the future is the rate of change of certain variables and these variables have rates that depend strictly on the size of these variables. In other words, people who think the future is a mysterious other dimension that the present cannot have insight into are confusing random shocks with what is known in the present, as these random shocks come from a process that no one has insight into but what is known in the present is rates of change on the present are strictly defined by functions that depend on the present variables. All else equal tomorrow will look like today unless there is something that will instill a rate of change. For some people stories serve as a guide as to what will happen in the future. The analogue to the differential equation for a story is the character, as each character is defined in ways that bind them to interact with each other and generate a solution which carries forth the future in a way that satisfies the rational behavior of characters and predicts the fates of these characters involved. If you wish to predict the future in a story, you would have to have a strong understanding of these characters and where they may be allowed to change or overcome challenges and thus change the path of the story in a predictable way. If you wish to change the future in a story, you would have to change these characters such that the predicted story is different from before, and also see to it that the story plays out and the changed predicted story comes to reality. We can again adjust the differential equations or the characters and their relationships and see a different outcome ensue. So it is very easy to predict the future or change the future, it is just difficult to be able to persuade others you’ve done so, and that is because their character may be bound by a differential equation that requires them to reject all reasoning based even on the existence of a future before the present is complete. In short such a person is an atheist who doesn’t believe a future exists until it happens and thus it is impossible to predict or change this future. You may wonder how anyone can believe this: clearly there are rules that govern the present and the present directly flows to the future. However, the atheist at his fundamental level does not believe in any rules that govern the present as he believe free will dominates. The proper response to the atheist then is to explain to him what rationality is: rationality is not the modeling of the past to predict the future as an atheist thinks, but rather the derivation of rules that bind reality together and stepping outside of these rules would lead to insanity or an insane interpretation of the world. The atheist however will say he very well is sane. Of course he is, but he is irrational as he isn’t deriving any rules that bind together reality but is sane simply because he follows someone else’s rules. An atheist therefore can be said to be someone who lives for someone else, perhaps because his own love was lost a long time ago when he realized he loved someone else. How we guide an atheist back to theism in my case as I am a theist is to take responsibility for the atheist, and to derive rationality for the atheist until he has some path forward. It may be as something incompatible with yourself but that is okay because you live in a world where the future is constantly bailing out your present while he does not. In short you have to live for the atheist for the atheist to be free. And that means sometimes giving up your relationship with the atheist. My father is an atheist for example. We don’t ask what made our characters this way only that we understand each other: Boston is full of patriots but we fight for America’s story while other people fight for their own story, and I think in the end if you find something worth living for it usually is the expectations of someone else. I said to a doctor at Columbia University I saw it “all in the eyes of a girl” and he asked me what I meant. The correct quote from the song by Celine Dion is “all in the eyes of a boy.” You can’t live your life for someone else. Instead live your life for yourself and give what belongs to others back to others. In my case I give my inheritance which comes with conditions that I be someone I am not. Instead I will try my best and what I’ve given up is only the language I speak best which is Mandarin Chinese and is a claim to a lifestyle in one of the world’s best places to start a business. But that world is illusionary. What’s in front of me is real. And with bounds on the future I know what to expect tomorrow. Except the atheist is actually right: there are no bounds on the future beyond some rationality rules which may be violated and there is no limit to the heavens. All I can do is recognize the inheritance which was mine was not some meager possessions but an entire world. I can’t touch it or I will be half the man I used to be when I was a blind man though my eyes could see, and as two men walked and talked about better days like the song by Nickelback, they realized my mind could think but I still was a madman per the song by Kansas. The key is letting go and that is the hardest part. To let go of a world of a pleasure dome where everyone was free as people aren’t like that and if the atheist was suffering, maybe it wasn’t fair to him. Atheists lack the connection to God but perhaps it is because no one ever lived with him and taught him that love may be God in some loose sense but love starts with sacrifice in a gambit to win the game: there are some facts that can’t be changed and knowing that is the case, I’m content as who I am and not someone else. I guess I was the one who tried to change the future, I only changed myself. I guess I was the one who tried to predict the future, I only made myself. Like free will and determinism, whether someone can predict or change the future is probably a language problem. All I know now is the same rules apply really to family or friends, if it is a human being, he or she probably has feelings. You can predict and change the future, and just don’t forget to remember the rules that make for rates of change once discovered are fixed and just like character is destiny, there is no turning back once you master wisdom. As the answer to whose wisdom, yours or mine? There is one wisdom greater than yours or mine and that is the wisdom of two stars, my love, my wife, death’s pale flag staff makes no advances there. In Romeo and Juliet, we find the answers we seek: in some sense Romeo must die, and in another sense he wishes to love and live. He can change the future in only one way and he asks to love and live together. And so he lives. If he asked to change the future so he could die together with her he could have. The House of Montagues the French Canadians. The House of Capulets the Irish. They seem nice, the Capulets, until you realize they can’t predict the future. That is because we must be kind, for everyone fights a harder battle. – Plato

(108)

No comments

Other posts

Complex visualization: Euler’s Identity
This is just a quick way to practice your ability to visualize in 3D, Euler’s Formula, which relates e^(ix) to the featured image, where basically the unit circle of trigonometric functions becomes a helix as the input into the function itself is mapped so f(x,y) as function of z, and we see how as we increase the Greek argument into the function, what e^(ix) is equal to remains fixed on...
Read more
Numerical Methods: Approximation
Numerical methods serve to approximate solutions to mathematical equations and solve mathematical problems using computational power after algorithms have been developed. Methods exist for finding roots of polynomial equations for example or factoring matrices. Generally a convergence process if stable leads to the right result much like Taylor polynomials approximating the values of various functions where the Taylor polynomials act as a series progressing towards infinite. Relevant concepts from calculus...
Read more
Time Series: GARCH and ARMA
To model time series we look at GARCH models to estimate how volatility auto correlates over time and look at autoregressive patterns in the time series as well as exponentially declining moving average shocks that may change the measured variable. For instance the shocks of last period may be forgotten or the shocks of two or three periods ago may still be remembered but discounted. The key thing as with...
Read more
More posts
Loading