Christometric - Differential Equation of the Journey

About 8 years ago while in grad school, I had my first attempt to describe life using mathematics. At the point, I borrowed basic notion from quantum mechanics, optimization theory and belief propagation to understand how one perceives and acquires "the truth".

Another set of equations have been cooking in my mind for a few years now. This time, it is about the Christian journey. This set of equations shapes my world view, and how I evaluate my own life as well as lives of others. This time, a simple differential equation is used.

Let x(t) be the state of being of a person. A large value of x(t) is good. In secular term, a successful person is often used to describe a person with high x(t). It is generally good that a person aims for a high x(t), but only looking at the value of x(t) is deceiving. While x(t) shows us what a person already possesses (in wealth, knowledge, relationship, etc.), it tells us nothing about intangible things like happiness and faithfulness.

So much of life is captured in , the derivative of x(t). For example, wealthy people (who have large x(t)) feel that life is horrible and may even attempt suicide because something is happening that decreases their x(t). In other words, our feeling tends to be a function of the change of x(t), that is - . A negative derivative means we are losing something.

Now, let's dive into the equation. In the following e(t) is our own effort, s(t) > 0 is effort from the evil one (Satan if you will), c(t) is life circumstances. d(t) is the distraction function which takes on value between 0 and 1. Finally, h(t) >0 is the work of the holy spirit, whom every believer possesses.



For , we use our own strength e(t) to helps ourselves grow. Clearly, we can help ourselves as much as we have the ability to do so, hence e(t) is multiplied by x(t). e(t) can be negative when we give up and takes on a lose-lose perspective. The evil one s(t) always try to do harm to us. This is a bit of technicality, but I see s(t) is a series of impulse functions with varying magnitude. This is because the evil one is not all-present, and he has to time share his effort. The effort of the evil one is also multiplicative of x(t) - the stronger we are, the stronger its effort affects us. The average power of s(t) is stronger than x(t). That is, we don't stand a chance against evil in the long run.



The term c(t) describes circumstances of life. It acts somewhat like a random variable. They are just there and they influence us. Sometimes we get lucky and have high c(t), and sometimes we are not and we have low c(t).

So far, the picture is pretty gloomy. We stand no chance against evil. How then can we grow? Do we have to wait till we get lucky and get some high c(t) for long enough time? Human effort e(t) may help, but since we are power limited, we eventually burn out. Without the holy spirit, I am afraid that's all we have. Some people in this world have gotten lucky early on in life, and they rely on their e(t) to keep growing. However, even if they become successful in such a way - life will eventually catch up, and s(t) will eventually sink the boat.

As believers, we have the disposition to good. In other words, if we look at the second derivative , we always have a positive value h(t) > 0 due to the work of the holy spirit in us. Regardless of life circumstances c(t) or evil deeds s(t), we also have an intrinsic desire to maintain a positive due to the presence of the holy spirit. If we are attuned to h(t), there is nothing in life or death that can stall us of our growth.

Nonetheless, we sometimes are distracted. The distraction function 0 <= d(t) <= 1 takes us away from the influence of holy spirit. In some sense, a person without God has d(t) = 1 for all t. However, even a believer may have d(t) near one. Frankly we get distracted a lot. And if we do want to grow, we tend to spend our energy on e(t) rather than d(t). How silly are we? e(t) has linear effect on , whereas d(t) has exponential effect. Spending energy in e(t) stands no chance against s(t); but a bit of discipline and spending our energy on d(t) will eventually lead us to victory.

The problem is that we are too impatient. Our effort has immediate effect on , whereas lowering d(t) is a slow process, and its dividend takes years to mature.

So be patient, look for long term good. Be self-controlled and disciplined. Spend our energy to set our mind on lowering d(t), so that the work of the holy spirit h(t) can be multiplied in us.