Taylor Series Sanctification
In Christian theology, there is an important distinction between the doctrines of justification and sanctification. Briefly stated, justification is God’s forensic declaration that a Christian is righteous. That is to say, when God looks at the Christian, rather than seeing that individual’s own “righteousness”, God sees the imputed righteousness of Christ. Reflecting on justification often raises the question “Well, if Christians are considered righteous, then, why don’t they act like it?!” This then leads to the doctrine of sanctification. Briefly stated, sanctification is the process by which the Christian is conformed to the image of Christ and begins to imitate Christ. In other words, sanctification is the process by which the Christian is shaped into being righteous.
Conflation of these two can lead to some dangerous theology. On the one hand, one could collapse everything into sanctification and state that unless one acts perfectly, then one is not saved/justified; this is called works-righteousness and is often associated with legalism. On the other hand, one could collapse everything into justification and state that at the moment of repentance, one is more or less free to do what they want; this is equally as bad as the previous error.
Are there any parallels to this process?
Sanctification is often compared to pottery making pointing to verses like Ephesians 2:10 (Christians are the workmanship of God), Romans 9:21 (the potter is sovereign to create vessels for honourable use and dishonourable use) and many, many others. I think that another parallel can be made with mathematical approximation formulas; specifically the Taylor Series (and related Maclaurin Series). The Taylor Series can be used to approximate any function about a point in the form
f(a) + f'(a)(x-a) + [f”(a)/2!](x-a)^2 + [f”(a)/3!](x-a)^3…
Essentially, you stick a line on a point of the graph you want to approximate and then progressively get closer to the picture with each successive iteration. Now, suppose that the original function is Christ and it becomes fairly easy to see the parallel. The life of the Christian is to become a power series representation of Christ while on Earth. In other words, as the approximation line conforms to the image of the original function, Christians also conform to the image of Christ.
There are problems with this analogy as there are problems with all analogies. For example, the process of sanctification is a more involved, multifaceted process whereas the Taylor Series involves discrete succession of individual components. While sanctification is a continual, ongoing process, a Taylor Series approximation occurs in individual segments.