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For anybody else not familiar, the Knight-Darwin Law is the idea that plants do not self-fertilize exclusively (many plants have both male and female sex organs
by toasterlovin 8y ago
For anybody else not familiar, the Knight-Darwin Law is the idea that plants do not self-fertilize exclusively (many plants have both male and female sex organs). Darwin goes on at length in On The Origin of Species about the mechanisms that plants employ to avoid self fertilization.
My own take is that this makes a lot of sense. Male and female sex organs are pretty sophisticated adaptations. Features which are that complicated generally don’t evolve unless they are useful and there are easier ways for an organism to clone itself than self fertilization.
- xamuel 8y agoDarwin actually articulates a much-more-precise law (which serves as a cornerstone of his whole book). I've argued in my papers that the KDL is in fact an infinite-graph-theoretical statement (remarkable because infinite graph theory was not a mainstream "thing" until well after Darwin). Let G be the graph of all organisms (past, present and future), with an edge directed from u to v if and only if u is a biological parent of v. The spirit of the KDL is: "G does not contain any infinite directed path consisting entirely of vertices with only one parent". Or equivalently: "Every infinite directed path in G necessarily contains a vertex with two parents." For its time, the above statement is astonishingly mathematically sophisticated. If anything, Darwin is still greatly underrated.
- quotemstr 8y agoDarwin is fantastic. Not only did he bootstrap the field of evolutionary biology despite his lack of access to modern genetics, but he also wrote about it beautifully. On the Origin of Species is still a great read and a lucid explanation of a difficult subject. He's a great person to strive to emulate.
- HelloNurse 8y agoI was particularly impressed by the part about pigeons: familiar examples used to introduce new ideas.
- toasterlovin 8y agoI never thought pigeon breeding could be an interesting subject until I read Darwin.
- gowld 8y agoIt reads like you are adding the mathematical sophistication to an intuitive idea. An "an infinite directed path consisting entirely of vertices with only one parent" is simply a chain.
- xamuel 8y agoCompare König's lemma [1] ("every infinite tree contains a vertex of infinite degree or an infinite simple path"), often considered the first example of infinite graph theory. It wasn't articulated until 1927, almost half a century after Darwin's death. [1] https://en.wikipedia.org/wiki/K%C3%B6nig%27s_lemma https://en.wikipedia.org/wiki/K%C3%B6nig%27s_lemma
- jandrese 8y agoIt won't impress mathematicians until it's stated in such a way that a layperson would be completely boggled. /s