The Newton-Raphson method, narrated in the style of a Film Noir Voiceover

You may have seen my post on the Newton-Raphson methodOpens in a new tab. in the style of the King-James version of the Bible. Since that turned out very well, I asked ChatGPTOpens in a new tab. to explain the method again to me, but this time in the style of a Film NoirOpens in a new tab. Voiceover. Here is the result. Enjoy!

The prompt

Write a step-by-step instruction for the Newton-Raphson method, but in the style of a Film Noir Voiceover: A hard-boiled detective narrates his way through the method like he’s solving a complex crime.

And the result

The night was darker than a blackboard in a power outage, and I was alone in my office, the only sound the steady tap of rain on the window. I had a problem to solve – an equation that needed roots, and the only friend I had in this lonely task was an old ally: the Newton-Raphson method.

  1. The Set-Up: It started simple enough, see. I had this equation, \(f(x)\), its heart beating with unknown roots. It was a mystery wrapped in an enigma, tucked inside a numerical riddle.
  2. The First Lead: I needed a place to start, an initial guess, \(x_0\). Some number that looked like it might be cozying up to the true root. It wasn’t perfect, but nothing in this world is.
  3. The Insider Tip: Next, I needed the inside scoop – the derivative of the equation, \(f'(x)\). That’s the way the curve was leaning, see. It was like the whispers of a double-crosser, always pointing to where the action was.
  4. The Stakeout: Then I used the formula that’s as old as the method itself. It’s seen more equations than a university math book. It goes like this:
    \[x_1 = x_0 – f(x_0)/f'(x_0)\]
    My new approximation, \(x_1\), it was a step closer to the truth, closer to the root than my initial guess, \(x_0\).
  5. The Chase: But one step wasn’t enough. I needed to follow this trail to the end. So I repeated the formula, turning the pages of the mystery:
    \[x_{i+1} = x_i – f(x_i)/f'(x_i)\]
  6. The Showdown: I kept at it, iteration after iteration, until the answers started making sense, until the root was as clear as the guilt in a crook’s eyes. I kept going until I couldn’t get any closer to the truth.

And that, my friend, is how the Newton-Raphson method and I cracked the case wide open. It’s a tough job, but in this city of numbers and equations, it’s the only job I know.

More Newton-Raphson Style Variations

If you like this sort of thing, i.e., fun versions of scientific explanations, then you might be interested to read one of the following as well. At least, once you are through them all, you should be able to explain the Newton-Raphson method to absolutely anybody


I am a nerd and trained in theoretical physics (with a PhD and everything ...). My interests are life as a human being and how computing can teach us valuable things about that as well as about nature in general. Read more about me.

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