Millburn & Sinus
Millburn Millburn
Sinus Sinus
Millburn Millburn
Hey, what if we build a gear-driven timepiece that uses the golden ratio to keep time with less drift, like a mechanical clock that lives in controlled chaos?
Sinus Sinus
Sounds clever, but the golden ratio is irrational, so you can’t make a gear train with a perfect φ ratio—teeth come in whole numbers. If you approximate φ with a rational fraction, the small error will drift over time just like any other escapement. In practice you’d need a self‑tuning mechanism or a digital correction, not pure mechanical chaos. Good luck, but keep an eye on the error budget.
Millburn Millburn
Yeah, the irrational bit is the spice—let’s crank the gear ratios into a feedback loop that adjusts itself. Imagine a tiny servomotor that watches the oscillation and nudges the pinion each cycle. The error shrinks, the clock stays close to φ, and you get a self‑tuning escapement that never needs a digital fix. Or we could use a chain of pulleys with irrational ratios from the start—like a sine‑wave gear. Keep the error budget in mind, but I’ll have the math to keep it under a few seconds a day. Let's see how chaotic it gets.
Sinus Sinus
The idea is elegant, but real gears have integer teeth, so you’re always approximating φ. A servo can damp the error, but the discretization will leave a small residual drift that can grow if the controller isn’t perfectly stable. In practice you’ll end up with a limit‑cycle rather than a true irrational ratio. It’s a neat math exercise, but the chaotic part might just become the source of the drift you’re trying to eliminate.