![\"markdown](\"https://i.postimg.cc/KvNwt9Qm/md-proportions.png\")
So you probably won't find this useful, but it is kind of cool…
\nThe empirical markdown cell proportions (# markdown cells / # cells) for the notebooks have this funky fractal-esque distribution:
\n
So you probably won't find this useful, but it is kind of cool…
\nThe empirical markdown cell proportions (# markdown cells / # cells) for the notebooks have this funky fractal-esque distribution:
\n
Very interesting! What are those long lines at various intervals ?
", "rawMarkdown": "Very interesting! What are those long lines at various intervals ? ", "replies": [ { "id": 1838514, "postDate": "2022-06-30T15:43:04.483Z", "rawMarkdown": "", "votes": 1, "isDeleted": true }, { "id": 1838830, "postDate": "2022-06-30T21:40:29.073Z", "content": "Hey! Apologies for the slow response, busy week! A quick comment to compliment @patrickdwyerhoops…
\nThere are three factors giving rise to this distribution:
\nThese three factors combine to highlight proportions with a small denominator, peaked at 1/2 because there are many ways of making a proportion of 1/2(= 2/4 = 3/6 = 4/8), but also with strong peaks at 1/3, 1/4, for similar reasons.
\nThe downward trend is roughly linear because (heuristically) there are about half as many ways for a notebook to have proportion 1/4 as there are to have a proportion 1/2 so the peak at 1/4 is half the height of the peak at 1/2 - those peaks lie on the line y=Mx for a fixed M~10000.
\nThis also explains the separation phenomenon between peaks - there are relatively few notebooks that are long enough to permit a denominator giving a (# md cells / # cells) proportion very near to 1/2, as highlighted by @patrickdwyerhoops.
So it's a mixture of the properties of the rational numbers, the finiteness of notebook lengths and the tendencies of coders to do less storytelling than coding ;)
", "rawMarkdown": "Hey! Apologies for the slow response, busy week! A quick comment to compliment @patrickdwyerhoops... \n\nThere are three factors giving rise to this distribution:\n\n1. For a notebook of length N there are only a finite set of possible (# md cells / # cells) (i.e. 1/N, 2/N, …, N/N).\n2. The distribution of notebook lengths N has most of its mass on relatively small positive integers.\n3. There are typically fewer markdown cells than code cells.\n\nThese three factors combine to highlight proportions with a small denominator, peaked at 1/2 because there are many ways of making a proportion of 1/2(= 2/4 = 3/6 = 4/8), but also with strong peaks at 1/3, 1/4, for similar reasons. \nThe downward trend is roughly linear because (heuristically) there are about half as many ways for a notebook to have proportion 1/4 as there are to have a proportion 1/2 so the peak at 1/4 is half the height of the peak at 1/2 - those peaks lie on the line y=Mx for a fixed M~10000.\nThis also explains the separation phenomenon between peaks - there are relatively few notebooks that are long enough to permit a denominator giving a (# md cells / # cells) proportion very near to 1/2, as highlighted by @patrickdwyerhoops.\n\nSo it's a mixture of the properties of the rational numbers, the finiteness of notebook lengths and the tendencies of coders to do less storytelling than coding ;)", "votes": 1 } ] }, { "id": 1831207, "postDate": "2022-06-24T03:28:15.783Z", "rawMarkdown": "", "isDeleted": true } ], "comments": [ { "id": 1835824, "author_name": "theDoors", "author_url": "", "post_date": "2022-06-28T05:52:26.943000", "content": "Very interesting! What are those long lines at various intervals ?
", "votes": 0, "replies": [ { "id": 1838514, "author_name": "", "author_url": "", "post_date": "2022-06-30T15:43:04.483000", "content": "", "votes": 1, "replies": [] }, { "id": 1838830, "author_name": "jagofc", "author_url": "", "post_date": "2022-06-30T21:40:29.073000", "content": "Hey! Apologies for the slow response, busy week! A quick comment to compliment @patrickdwyerhoops…
\nThere are three factors giving rise to this distribution:
\nThese three factors combine to highlight proportions with a small denominator, peaked at 1/2 because there are many ways of making a proportion of 1/2(= 2/4 = 3/6 = 4/8), but also with strong peaks at 1/3, 1/4, for similar reasons.
\nThe downward trend is roughly linear because (heuristically) there are about half as many ways for a notebook to have proportion 1/4 as there are to have a proportion 1/2 so the peak at 1/4 is half the height of the peak at 1/2 - those peaks lie on the line y=Mx for a fixed M~10000.
\nThis also explains the separation phenomenon between peaks - there are relatively few notebooks that are long enough to permit a denominator giving a (# md cells / # cells) proportion very near to 1/2, as highlighted by @patrickdwyerhoops.
So it's a mixture of the properties of the rational numbers, the finiteness of notebook lengths and the tendencies of coders to do less storytelling than coding ;)
", "votes": 1, "replies": [] } ] }, { "id": 1831207, "author_name": "", "author_url": "", "post_date": "2022-06-24T03:28:15.783000", "content": "", "votes": 0, "replies": [] } ], "raw_markdown_by_id": { "1804370": "So you probably won't find this useful, but it *is* kind of cool...\n\nThe empirical markdown cell proportions (# markdown cells / # cells) for the notebooks have this funky fractal-esque distribution:\n\n", "1835824": "Very interesting! What are those long lines at various intervals ? ", "1831207": "" } }