à propos of nothing, earlier conversation with @berglar recalled my experience writing what i would characterize as "dense hypermedia", where all digressions/parentheticals were given their own page.
the number of drafts increased ~quadratically to the actual intended product.
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this made me think of how random walks are √n steps from the origin on average, and kinda had a miniature holy-shit moment
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a complete graph has (n²-n)/2 edges for n nodes, so it's not quite the square, but it's proportional (take away the /2 for directed graphs)
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dorian taylor Retweeted Anuraj R.
anyway thinking about this from hamming's book, and…https://twitter.com/anurajenp/status/1350459769904099330 …
dorian taylor added,
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…if concepts are nodes and analogical relations between concepts are edges, then you'd have a complete graph if all concepts related to all other concepts in a meaningful way…
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…the complete scenario may not happen but consider a digression or parenthetical is a set of remarks on a concept in the context of all the other concepts you're writing about
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anyway tl;dr the task in front of you could very well be proportional to x² of what you think it is instead of a·x
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dorian taylor Retweeted Venkatesh Rao
also
@vgr has coincidentally been thinking about this too:https://twitter.com/vgr/status/1350259689599107072 …dorian taylor added,
Venkatesh Rao @vgrHad a thought that sqrt(n) to n^2 via n is a vastly more important phenomenon than 0 to 1. sqrt(n) = random walk n = muddling through (filtered random walk) n^2 = network effect This is what things like product-market fit really are. https://twitter.com/vgr/status/1350190715867865088 …Show this thread1 reply 0 retweets 2 likesShow this thread -
Replying to @doriantaylor
Venkatesh Rao Retweeted Venkatesh Rao
Venkatesh Rao added,
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Replying to @vgr
i feel like there is some graph theory/combinatorics that explains this that i am ignorant about
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Possibly this. It’s how I’ve always connected graph growth to compound interest. Network effects are the compound interest effects of preferential attachment dynamics. For an individual, just building on your own past work. https://en.wikipedia.org/wiki/Preferential_attachment …
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Replying to @vgr
now thinking out what the topological connection is, like activity on the surface of a sphere
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Replying to @doriantaylor
Fractals. Fractal equations are compound-interest-like.
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