Learning Via Negativa

Aug 15, 2023

Sometimes it’s easier to describe something by what it is not rather than what it is. Learning through subtracting is called via negativa.

Nassim Nicolas Taleb explains via negativa in the context of antifragility. What is wrong is usually more robust than what is right.

Proof by contradiction. (Illustrated by toy proof) Claim: There is no largest even integer. Proof: Suppose not. Assume that k is the largest even integer. Since k is even, we can write k = 2n, where n is another integer. Pick a number larger than k, say k + 2, and write it as (2n) + 2 = 2 (n + 1). That means that k + 2 is even and larger than k.

A more classic example is proving the irrationality of√2 by contradiction (left as an exercise to the reader).

What not to do. Diet: Knowing what foods to avoid is easier than knowing which are best. Reading biographies: it’s much easier to gather knowledge of what not to do rather than correlate life choices with success.

Process of elimination. Sometimes it’s easier to progressively eliminate the worst options instead of picking the best ones. For example, choosing a mutually agreed upon dinner choice.

Prompt engineering. For hard-to-qualify tasks like prompt engineering, sometimes it’s easier to start off by carefully removing pieces of the prompt to see if the desired effect still holds.

Program minimalism. It’s often good design to remove features and complexity while the program achieves its goal. Any extraneous code or logic is a surface for bugs or slowness.

Security. Security obtained by removing parts is often more effective than offensive or prescriptive security (both digital and physical).

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