3 ms·
Darwin 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 infin
by xamuel 8y ago
Darwin 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