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The Ultimate Refactor: Deriving ALL Elementary Functions From ONE Binary Operator!

April 13, 20263 min read

A new gigabrain paper on Hacker News proves you can derive all elementary math functions using just one binary operator. Pure magic or pure madness?

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What's up, C4F gang! While doomscrolling Hacker News instead of fixing my Jira tickets, I stumbled upon a gigabrain paper sitting at nearly 700 upvotes. The title alone is enough to give regular CRUD developers an existential crisis: "All elementary functions from a single binary operator." Yeah, you read that right.

Reinventing the Math Wheel with ONE Function

Normally, when you call Math.sin() or Math.exp(), under the hood, your hardware and compiler are sweating bullets running complex algorithms like Taylor series or CORDIC to give you that sweet floating-point result. It takes a whole arsenal of logic gates.

But some mad scientist just dropped an arXiv paper proving that you only need EXACTLY ONE binary operator to derive them all. Imagine refactoring your entire math library by deleting everything and replacing it with a single recursive do_magic(a, b) function. Is this the peak of minimalist elegance, or just bored mathematicians having a laugh?

The Hacker News Hivemind Reacts

Because the premise is so wild, the HN community swarmed the thread. You can basically divide the reactions into three camps:

  • The "Mind Blown" Theorists: These are the pure logic nerds. They took one look at the paper and started praising its extreme elegance. To them, this is a beautiful fundamental discovery that strips computer science down to its barest core.
  • The "Will It Scale?" Senior Devs: Classic grumblers. Their immediate thought is: "Cool theory, bro. But how many nanoseconds does it take? Will it devour all my RAM?" Theoretically, it's a masterpiece. Practically, if you push this to prod, someone needs to start a crowdfunding campaign to buy more servers because your system is going to crash hard.
  • The Functional Programming Cult: The Lisp and Haskell enthusiasts chiming in, nodding sagely while whispering about Lambda calculus and combinator logic. To them, doing everything from scratch with one function is just another Tuesday.

C4F's Takeaway: Keep It Simple, Stupid (In Prod)

Let's wrap this up. No hardware manufacturer is going to rip out their IEEE 754 silicon and replace it with this operator anytime soon. Performance-wise, it would be an absolute disaster. Stick to your language's standard math libraries, please. Do not "reinvent the wheel" with this operator at work unless you want a fast track to getting fired.

However, reading papers like this reminds us why we fell in love with computer science in the first place. When you're drowning in spaghetti code and weird business requirements, looking at some pure, unadulterated logic is like a spa day for your brain.

Keep your code clean and your pings low. See ya in the next thread!

Source: All elementary functions from a single binary operator (Hacker News)