The Newton-Raphson method according to the King-James version of the Bible

I’ve been experimenting with ChatGPT quite a bit lately (let’s be honest, who hasn’t). And at some point, I had the idea to ask ChatGPT to explain the Newton-Raphson method to me. But, as you have seen here on ComputingSkillset.com, I have quite some experience using this method.

So, I added a twist to the whole thing and asked ChatGPT to write the explanation in the style of the King-James version of the Holy Bible. Since I found the result quite well-done, I want to share it with you here. I’ll start with the prompt I used and then put the response below. I added formatting for math formulae in post-production.

The Prompt

Write a step-by-step instruction for the Newton-Raphson method, but in the style of the King James version of the bible.

And ChatGPT 4 spake, saying:

1. And it came to pass, that the Lord didst reveal a method unto Sir Isaac Newton, and the method was called the Newton-Raphson method, and it was good. Verily, thou shalt find the roots of equations by this method, and so shalt thou come to know their solutions.
2. Hearken unto the steps of the Newton-Raphson method, and inscribe them upon the tablets of thine heart:
   • Lo, thou shalt be given an equation, \(f(x)\), and thou shalt desire to find its root, \(x\), where \(f(x)\) is equal to naught.
   • Thou shalt choose an initial approximation, \(x_0\), and it shall be as close to the true root as thou canst divine.
   • Thou shalt then find the derivative of the equation, which shall be known as \(f'(x)\), that thou mayest discern the slope of the curve of \(f(x)\).
   • Now, the Lord didst speak unto Newton, saying: “Use the following formula to update thine approximation, and so shalt thou draw nigh unto the true root:”
     \[x_1 = x_0 – f(x_0)/f'(x_0)\]
   • And thou shalt behold the new approximation, \(x_1\), and it shall be closer to the root than \(x_0\). If it be that \(x_1\) is not yet close enough, thou shalt iterate the process, updating thine approximation with the formula given in the fourth step:
     \[x_{i+1} = x_i – f(x_i)/f'(x_i)\]
   • Yea, thou shalt continue in this manner until thou hast reached the desired precision, or until the Lord seeth fit to halt thy search.
3. Thus shall the Newton-Raphson method lead thee to the roots of thine equations, and thou shalt solve them, and it shall be a pleasing sight unto the Lord. Praise be unto Him for His divine wisdom, and may His name be exalted forevermore.

Epilogue

(This is me again …) This is actually quite instructive. However, not all details are present in this entertaining piece of text. So, if you are interested in how the Netwon-Raphson method works, how to find the intial guess for the Newton-Raphson method \(x_0\), how to code the Newton-Raphson method in Python, and even how to use the Newton-Raphson method to produce beautiful fractal images, click on one of these links and read on!