Monthly Archives: July 2026

What are Quarternions?

I used to think complex numbers were the end of the line. You start with counting, patch in zero and the negatives, then the fractions, then the irrationals to fill the gaps between them, and finally you throw in $i$ … Continue reading

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So, what is a vector?

In my first year of undergraduate physics, one of my professors walked into the lecture hall, placed his notes on the desk, looked around the room, and asked a question that, at first, seemed almost too easy. “What is a … Continue reading

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Deriving the Euler–Lagrange Equation for Particles, Fields, and Curved Spacetime

A good way to understand the laws of motion is not to memorize a separate equation for each situation, but to notice there is really only one trick, and every equation of motion is what falls out when you apply … Continue reading

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