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“Endless Forms Most Beautiful and Most Wonderful”: Ruliobiology and the Theoretical Foundations of Biological Form

Stephen Wolfram · 23 Oct 2026

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Every claim below was made in this piece, quoted word for word and numbered in the order the piece makes them, so you can read it there rather than take our word for it. The sentence above each quote is our reading of the claim, not their wording. Each quote was checked against a stored copy of the page at build time; where the two differ, the quote is the fact.

  1. Our reading

    Biology's endless forms arise inevitably from adaptive evolution interacting with computational irreducibility, not from natural selection alone.

    Their wordsthere is a certain theoretically-derivable inevitability to the generation of "endless forms most beautiful and most wonderful". One of the ingredients that's needed is indeed Darwin's idea of natural selection

  2. Our reading

    Biology has computational irreducibility at its core, so biological phenomena depend inevitably on history.

    Their wordsRuliobiology-and, I believe, biology-have computational irreducibility at their core. So, for example, whereas in physics one can discuss a phenomenon just as something happening "here and now", in ruliobiology-and biology-there is an inevitable dependence on history

  3. Our reading

    Exotic biological forms can arise without an exotic environment or fitness function, as side effects of computational irreducibility.

    Their wordsexotic forms can actually arise-albeit rarely-without an exotic fitness function, in effect just as examples of "surprises" that can inevitably be created by computational irreducibility.

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