On the ubiquity of power law behavior
The signature of power law behavior (short things are more probable than long ones in a predictable way) is often used as a benchmark (for instance, of a system poised at criticality).
In that pursuit, many remind us that we need to be mindful that all sorts of (not very remarkable). things can have that signature. One of the most colorful illustrations I've read is this one here:
Some Effects of Intermittent Silence
George A. Miller
1957
Imagine that a monkey hits the keys of a typewriter at random, subject only to these constraints: (1) he must hit the space bar with a probability of p() and all the other keys with a probability of p(L) = 1 - P() and (2) he must never hit the space bar twice.
Word length will fall off with power law behavior.
https://doi.org/10.2307/1419346
Nicole Rust /
npub1cu…0zuw2
2024-03-01 13:24:47
Author Public Key
npub1cud99prgj4etl597aaxthxenrcjmfxl92dgj8snf9a9p8ctupfyq80zuw2Published at
2024-03-01 13:24:47Event JSON
{
"id": "a93f3d5a55ba6be131a572d79510c1a538fcbd84095e10646e9140bb884bf91d",
"pubkey": "c71a5284689572bfd0beef4cbb9b331e25b49be5535123c2692f4a13e17c0a48",
"created_at": 1709299487,
"kind": 1,
"tags": [
[
"proxy",
"https://neuromatch.social/users/NicoleCRust/statuses/112020651237039745",
"activitypub"
]
],
"content": "On the ubiquity of power law behavior\n\nThe signature of power law behavior (short things are more probable than long ones in a predictable way) is often used as a benchmark (for instance, of a system poised at criticality).\n\nIn that pursuit, many remind us that we need to be mindful that all sorts of (not very remarkable). things can have that signature. One of the most colorful illustrations I've read is this one here:\n\nSome Effects of Intermittent Silence\nGeorge A. Miller\n1957\n\nImagine that a monkey hits the keys of a typewriter at random, subject only to these constraints: (1) he must hit the space bar with a probability of p() and all the other keys with a probability of p(L) = 1 - P() and (2) he must never hit the space bar twice.\n\nWord length will fall off with power law behavior.\n\nhttps://doi.org/10.2307/1419346",
"sig": "8b57a9aa058b8fc7b6263097fdcdd0fad7331f0bf723b14330e59ff3e709789dfcc31103ef7a58e4f703004bd90694baf655caaa09b81ac08a3248333d7bee1a"
}