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Philosophy · 05 of 06

majjhimā paṭipadā

The Middle Way.

Neither greed nor fear.

ISutra

“But when your harp’s strings were tuned neither too tight nor too slack, but fixed at an even tension, was it resonant and playable?”

“In the same way, Soṇa, when energy is too forceful it leads to restlessness. When energy is too slack it leads to laziness.

— AN 6.55:6.1, 7.1 · With Soṇa · Numbered Discourses (Aṅguttara Nikāya)

Translated by Bhikkhu Sujato (CC0), as published on SuttaCentral 11 Nov 2026

Avoiding these two extremes, the Realized One understood the middle way of practice, which gives vision and knowledge, and leads to peace, direct knowledge, awakening, and extinguishment.

— SN 56.11:2.4 · Rolling Forth the Wheel of Dhamma · Linked Discourses (Saṃyutta Nikāya)

Translated by Bhikkhu Sujato (CC0), as published on SuttaCentral 11 Nov 2026

IIPrinciple

Moderate size. Moderate models.

Position size is tuned like a string: too slack and the edge is wasted, too tight and one bad stretch snaps it. We size below the growth-optimal point, on purpose.

Models get the same discipline — simple enough to trust, rich enough to matter. Too simple underfits; too complex memorises the past.

IIIProof

g(f) = μf − ½σ²f²  ·  f* = μ / σ²  ·  g(2f*) = 0
Proof · neither greed nor fearIllustrative
fearmiddle waygreed−10g*½ f* · 75% growth, ¼ variancef* · maximum growth2 f* · zero growth, 4× the variance00.5 f*1 f*1.5 f*2 f*position size · g(f) = μf − ½σ²f²
Expected log-growth of capital against position size, in units of the Kelly fraction f* = μ/σ². Fear — sizing near zero — leaves growth unused. Greed — beyond f* — buys more variance for less growth, and at 2f* grows nothing at all. Half of f* keeps three quarters of the growth for a quarter of the variance. The same curve governs models: too simple underfits, too complex overfits. Exact arithmetic, not data.