on maths

 a

You're articulating a compelling counterpoint to Wigner's famous idea of the “unreasonable effectiveness of mathematics in the natural sciences.” Your argument reframes this apparent mystery as a form of selection bias—a survivorship effect. We marvel at math’s power because we only retain and develop the parts that turn out to be effective. Here's a more formal unpacking and elaboration of your point:

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Selection Bias in Mathematical Development

1. Mathematics as an Evolved Tool:

   • Much like technology or biological traits, mathematical concepts evolve. Only those that prove fruitful—either internally (coherence, elegance) or externally (applicability, predictive power)—survive.

   • Whole branches of math that once seemed promising but turned out to be sterile or inconsistent are abandoned, forgotten, or remain as curiosities.

2. Survivorship Bias in Hindsight:

   • We look at calculus, linear algebra, group theory, and probability and marvel at their applicability—from physics to economics to genetics.

   • But this perspective ignores the uncounted mathematical frameworks that never found purchase in the natural sciences or failed to cohere logically.

3. Mathematics Is Shaped by the Physical World:

   • A lot of mathematics didn’t emerge from pure abstraction, but in response to problems in the real world: motion (calculus), symmetry (group theory), counting (number theory), and space (geometry).

   • So it's less surprising they turn out to be effective—they were shaped by the very problems they are now used to solve.

4. Anthropic Reasoning in Science and Math:

   • We're intelligent agents in a universe where some parts of mathematics work astonishingly well—perhaps because we could not evolve or survive in a universe where no such patterns existed.

   • This creates a kind of anthropic filter: only beings in math-friendly universes can reflect on the effectiveness of mathematics.

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Examples of Abandoned or Niche Math:

• Non-Associative Arithmetics: Rarely used outside of exotic contexts (e.g., octonions in theoretical physics).

• Inconsistent or Non-Euclidean Geometries: Most are logically consistent but don’t map easily to our physical reality—yet some (like Riemannian geometry) found use in general relativity.

• Pre-Cantorian Theories of Infinity: Failed to offer a stable foundation for mathematics, supplanted by set theory.

• Obscure Algebraic Systems: Many exotic algebraic structures exist but never gained traction because they didn’t lead to useful generalizations or applications.

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Conclusion:

The effectiveness of mathematics may feel uncanny, but it's not mystical. It's the result of:

• Human tendency to refine and preserve only the useful.

• Historical shaping of math by physical problems.

• Cognitive biases like hindsight and survivorship.

What appears as “unreasonable” might simply be “filtered.” The marvel is not that math works so well, but that we are so good at sculpting and selecting the math that does.

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Would you like to turn this into a formal essay or a short article?