We uncover how river networks are not random but self-organizing, guided by scale-invariant math. We'll explore Hack's Law and Horton’s laws, the bifurcation ratio, and how fractal geometry defines the network's complexity, while stream power explains how rivers carve their channels. We'll also discuss the surprising log-normal width of headwater streams around 32 cm, the restoration implications, and even how these rules might apply to river-like patterns on Mars and Titan. Note: This...
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We uncover how river networks are not random but self-organizing, guided by scale-invariant math. We'll explore Hack's Law and Horton’s laws, the bifurcation ratio, and how fractal geometry defines the network's complexity, while stream power explains how rivers carve their channels. We'll also discuss the surprising log-normal width of headwater streams around 32 cm, the restoration implications, and even how these rules might apply to river-like patterns on Mars and Titan. Note: This...
The 32-Bar Blueprint: How AABA Makes Great Songs Feel Effortless
Intellectually Curious
4 minutes
1 week ago
The 32-Bar Blueprint: How AABA Makes Great Songs Feel Effortless
A rigorous yet intimate tour of the 32‑bar song form (AABA) that underpins countless classics. We break down the four eight‑bar sections—three A sections with the same hook, a contrasting B bridge, and a triumphant return—and show how this tight structure creates emotional payoff. From Gershwin’s I Got Rhythm to early rock ’n’ roll and even Doctor Who themes, we trace how constraint breeds creativity, explain the old chorus/refrain terminology, and illuminate why composers keep returning to t...
Intellectually Curious
We uncover how river networks are not random but self-organizing, guided by scale-invariant math. We'll explore Hack's Law and Horton’s laws, the bifurcation ratio, and how fractal geometry defines the network's complexity, while stream power explains how rivers carve their channels. We'll also discuss the surprising log-normal width of headwater streams around 32 cm, the restoration implications, and even how these rules might apply to river-like patterns on Mars and Titan. Note: This...
