Don Jon 💥Check this out!
The brain uses "geometric means" to find perfect squares with the same area as a rectangle of given length side x and y. This allows us to smooth out data and think more efficiently.
Reality does something similar when you turn the faucet on. As you widen or loosen the valve, the flow is trying to settle into a stable middle state, and the other means in the graph are just different ways of describing that middle: the arithmetic mean is the plain average (or average amount of water flowing at a linear rate), the harmonic mean fits flow rates, and the RMS mean fits energy and power. When the system can’t settle cleanly, you get chaotic drip patterns instead of a smooth stream
Linear regression with water flow is similarly used in data analysis and inventory management: it finds the best-fit line through noise for a "best estimate" of the actual value. It's the closest stable pattern when reality won’t give you a perfect shape.
**yes, I used AI to help me articulate this because I'm an Uber driver, not a professional.