Convexity

Notes on Nassim Nicholas Taleb’s essay “Understanding is a Poor Substitute for Convexity (Antifragility)” (Edge, 2012).

Optionality: having the choice to select only the favorable results while discarding the unfavorable ones.

Convexity: a property of payoff functions where gains from positive outcomes are larger than harms from negative outcomes.

Convex payoff benefits from uncertainty and disorder.

Antifragile systems: benefit from randomness, unpredictability, and change.

How can you maximize Convexity?

Focus on setups where the potential upside is much larger than the downside.

Increase convexity by minimizing the cost of failure per trial, so failed attempts have little impact while successful attempts deliver large benefits.

1. Spend more time designing processes and/or projects where uncertainty can help — by ensuring the upside outweighs the downside, that not knowing specifics becomes an advantage. Think about Research, technology, or decision-making.
2. Always diversify trials and spread out risks. The expected gain across multiple convex exposures would reliably outperform a concentrated approach, especially in an unpredictable or high-variance environment.
3. Regular reevaluation and incremental decision traits lead to more robust, antifragile outcomes in an uncertain environment.
4. For meaningful innovation, prioritize direct experimentation and practice, then refine theory after successful outcomes have emerged.
5. For robust progress, deliberately seek and reward simple solutions; they are much more likely to yield outsized returns when exposed to uncertainty or a high-variance environment. Simple design thrives in an uncertain environment.
6. For antifragility and innovation, actively reward and catalog what fails — this is critical for learning and maximizing the value of future experimentation in opaque and complex domains.

Applications of Convexity

1. Design so failures are cheap but successes can be substantial. Use open source prototypes where bugs are are low cost but a working solution can become widely adopted.
2. In investing or job searches, apply for many positions or invest a small anounts in a range of different technologies without trying to predict which will succeed. With more trials, there is a better chance of to catch a black swan (exceptionally outsized success), rather than betting all on one approach.
3. Set up short term milestones or regular check point in projects, allowing adjustments if it’s something promising.
4. Remain open to changing direction of project as new data or breakthrough emerges even if it contracdicts the original vision.
5. Adopt a hands-on learning approach — experiment, tinker and document what works before formalizing the theory. For certification, use practice labs and red network simulation
6. Prioritize simple solutions – like automating a manual network maintenance with a basic script.
7. Keep a ‘failure list’ in technical or learning projects, recording approaches that didn’t work. This avoid repeating mistakes and narrows the search for good solutions.