Models: Markov, physics, ecosystem

Hidden regimes of activity

A hidden Markov model splits the days into 3 regimes, each with its own mean rate and variability. The most active regime ("Activity", 9.9 drops a day on average) covers only 26% of days but holds 97% of drops, and lasts 7.0 days on average before switching. The most likely path has 107 switches, and 3 of the 5 volume breaks found by another method (Statistics page) fall within a week of a switch of the model.

How topics follow one another

Each of the 4,063 drops with text gets its dominant topic (the 12 topics of the Discourse page). In the 846 multi-drop sessions (2,481 transitions), the next drop stays on the same topic 38.6% of the time, against 36.4% when the order of drops is shuffled within each session (p = 0.001, 1,000 permutations). The effect is real but modest, since knowing a drop's topic reduces the uncertainty about the next from 2.55 to 2.38 bits. The most over-represented transitions are listed below.

Style drift and resemblances

A statistical model of character sequences, trained on one semester of drops, predicts the next semester more or less well, and the excess surprise measures drift. Two jumps dominate, from 2017-S2 to 2018-S1 (+0.56 bit per character) and from 2019-S2 to 2020-S1 (+0.47). Elsewhere the style is stable from one semester to the next. The first jump matches the move from 4chan to 8chan, the second the return on 8kun after 8chan was shut down (August-November 2019). Part of the drift reflects changes of subject, which the measure does not separate from style.

Compression gives a second measure, because a text is encoded more efficiently after a similar one. Q's 2017-S2 semester stands apart (its nearest neighbour, Q 2018-S1, is at 0.46). No semester of Q comes close to Trump's tweets, which form a homogeneous block (smallest distance between Trump semesters: 0.07).

Earthquakes and aftershocks: does one drop trigger others?

In seismology, each earthquake can trigger aftershocks whose rate decays according to Omori's law. Applied to the drops, the same model attributes 80% of drops to an earlier drop rather than to the "background" (the rate specific to each of the 6 volume regimes, modulated by time of day). With a constant background, which leaves slow changes in activity to the model, the share rises to 85%, which is an upper bound. Half of the aftershocks follow their trigger within 17 minutes, and their rate decays like an Omori law with exponent 2.62. The Omori model fits the data far better than no excitation (Kolmogorov-Smirnov gap of 0.044 against 0.49). Q posts in bursts, one drop calling for others.

Do Trump's tweets trigger drops? Added to the model, this cross-excitation explains 0.5% of drops, within 2.3 hours on average after a tweet. That is more than with tweets shifted by 1 to 14 days (p = 0.035, 28 shifts), but the effect is marginal and confirms in another form the absence of systematic "deltas" (Trump page).

Long memory of activity

Detrended fluctuation analysis measures how variability grows with the time scale. For Q the exponent is H = 0.81 by day (0.71 by hour), against 0.49 once days are shuffled, so an active period announces another active period, over weeks. Trump's tweets have a memory of the same order (H = 0.84), which makes it a property of human online activity, not a signature of Q.

Avalanches: "critical" sessions?

Systems at the edge of instability produce avalanches of all sizes, following a power law. Q's sessions do not. A power law fits only the 117 largest of the 1,743 sessions (from 8 drops), with an exponent of 4.0, far from critical values (around 1.5), and it can be told apart neither from an exponential (p = 0.44) nor from a lognormal (p = 0.66). Trump's tweet bursts look the same (exponent 4.2). The result is negative, since nothing points to critical dynamics.

Q's clock: a phase break

Posting times can be read as angles on a 24-hour dial. Q posts mostly around 17:57 (New York time), Trump around 13:22. Month by month the two clocks stay linked (phase locking 0.75, Q about 5.0 hours after Trump). But Q's clock shifts. The best split, on Apr 21, 2018, separates a period when Q posted around 20:48 from one when it posts around 17:12 (p = 0.005, permutations). A change of hour is not proof of a change of author, but it adds to the style breaks noted above and on the Discourse page.

Syncretism: does Q pick up the scene's themes?

Of 112 themes of the conspiracy scene (moon landing, 9/11, chemtrails, Pizzagate, Epstein, vaccines, "stolen" election...), 66 never appear in the drops and 35 fewer than 10 times. Q almost never names conspiracies. It carries them through people (Epstein, Soros, Rothschild, the Clinton Foundation). For themes present often enough, the table compares, week by week, their share of drops with public attention.

The number of distinct themes raised per quarter peaks in Q4 2017 (20 themes) and in Q2 2020 (21 themes).

Who informs whom?

Transfer entropy measures how much a series' past helps predict another, beyond what that other's own past predicts. Across 11 daily series and 106 possible links, 0 remain significant once the shared weekly rhythm is removed and multiple tests are corrected. The table gives the ten strongest links.

Hourly response of the Q forums

r/CBTS_Stream: around 118 starts of Q sessions, activity in the following six hours exceeds by 0.10 (relative to the previous day) that of randomly drawn times (p = 0.008), and the peak comes 23 h after the drop.

r/greatawakening: around 395 starts of Q sessions, activity in the following six hours exceeds by 0.07 (relative to the previous day) that of randomly drawn times (p = 0.012), and the peak comes 20 h after the drop.

Attention peaks: outside shocks or internal surges?

An outside shock (a news event) raises attention at once and lets it fall quickly, while an internal surge builds gradually and decays slowly. For the largest peaks of each series, the table gives the share of the rise that precedes the peak, the decay exponent and Q's activity in the week before.

How Q's phrases spread

For each phrase coined or popularised by Q, the table gives its first use in the drops, its first occurrence in the Reddit sample and, when the data suffice, the parameters of a diffusion model, whose q/p ratio measures the weight of imitation against outside influence.

Google search waves (United States)

Each row shows when the American public searched for a term, relative to its own maximum. The 2020 waves (adrenochrome, #SaveOurChildren, Plandemic, the election) stand out clearly from older, declining interests (Illuminati, chemtrails).

Scene sources and licences

Reddit: Arctic Shift archive (exact daily volumes, texts sampled each day without author names, estimated counts = share of sampled messages × volume). Wikipedia: Wikimedia page-view API, redirects included. Google Trends: search interest index, United States. 4chan /pol/: dataset by Papasavva et al. (CC BY 4.0), read once and reduced to aggregates. No text from it is published in bulk, and hate codes are published only as aggregates. (Papasavva et al., 2020)

A brief niche

In Nov 2017, 6.9% of /pol/ posts are written in Q threads. The next month, Q leaves for 8chan and the share falls to 0.20%. From 2018 on it settles around 0.12% (monthly median). Q remains a /pol/ topic, but is no longer its centre.

Birth of the formulas

55 Q-related formulas are frequent enough on /pol/ to be dated. 16 were already rising before Q's birth on 28 October 2017. 4 appear with Q without Q using them, as ways of talking about Q. 8 are used on /pol/ before Q uses them, and 16 are used by Q first. For 11, no clear onset emerges. "CBTS" ("Calm Before The Storm") takes off as early as the week of Oct 2, 2017. That is when Donald Trump told reporters "maybe it's the calm before the storm" (5 October 2017). Q settled into threads that were already open.

Does /pol/ respond to Q?

Q's /pol/ period (28 Oct 2017 to Jan 4, 2018, date of its last drop on /pol/): around 111 starts of Q sessions, mentions of Q on /pol/ in the following six hours exceed by 0.54 (relative to the previous day) those at randomly drawn times (p = 0.002).

After Q's move to 8chan (2018-2019): around 1,059 starts of Q sessions, mentions of Q on /pol/ in the following six hours exceed by 0.16 (relative to the previous day) those at randomly drawn times (p = 0.002). The peak comes 1 h after the session starts.

Toxicity

Over the whole period, Q-related posts have a mean toxicity score of 0.366, against 0.406 for all of /pol/. Highly toxic posts (score above 0.8) make up 14.7% of them, against 19.3%. Yet day by day they are more toxic than the rest of /pol/ on 58% of the 1,184 days compared (median gap 0.005, Wilcoxon p < 0.001). This apparent paradox comes from the make-up of the subcorpus, which the breakdown by group below clarifies.

Toxicity by group

Q threads (391,258 scored posts) are markedly calmer than /pol/, with 0.317 on average against 0.406, and less toxic than the board on 73% of the 313 days compared. They are calmest at Q's birth, when the drops were being decoded there (0.291 from late October to December 2017), but remain calmer afterwards (0.384 in 2018-2019, against 0.407 for all of /pol/). Conversely, isolated posts citing a promoter (196,091 posts, 76% of which cite Alex Jones or InfoWars) are more toxic than /pol/ on 67% of the 866 days (median gap +0.018, Wilcoxon p < 0.001), and more obscene on 95% of days. Isolated posts using Q vocabulary outside Q threads (150,513) are barely above the board (median gap +0.009, 58% of days). The overall mean is pulled down by the weight of Q threads, above all in November 2017, while ordinary days are dominated by isolated posts, especially those citing promoters.

What is talked about: Q, its threads, its milieu

Hate codes (mostly antisemitic: ZOG, (((echo))), "Kalergi"…) appear in 5.0% of /pol/ posts before Q and 6.5% after, against 3.6% in Q threads and 0.1% in the drops. Q keeps its cradle's conspiracies (classic conspiracies appear in 2.3% of the drops, against 0.9% of /pol/ posts), but not its explicit hate vocabulary.

The vocabulary of Q threads

Compared with the rest of /pol/ after October 2017, the 30 most over-represented words in Q threads are: “bread”, “cbts”, “larp”, “qanon”, “storm”, “indictments”, “podesta”, “posts”, “cia”, “keystone”, “baker”, “tripcode”, “questions”, “rabbit”, “threads”, “crumbs”, “alice”, “qmap”, “archive”, “hrc”, “wonderland”, “potus”, “huma”, “itpb”, “qbhqo”, “spreadsheet”, “sealed”, “saudi”, “shills”, “rothschild”. It is the lexicon of a decoding workshop ("bread", "baker", "crumbs", "archive", "qmap", "tripcode"), of its targets (Podesta, Huma, HRC), of its riddles ("Alice & Wonderland", "white rabbit") and of a constant suspicion of imposture ("larp", "shills").

The flags displayed by 4chan confirm the American character of the phenomenon. 73% of Q-thread posts carrying a country flag come from the United States, against 58% across /pol/ over the same period.

Source: Papasavva et al., /pol/ dataset (Zenodo 3606810, CC BY 4.0), read once in full. Author pseudonyms and identifiers are not kept. (Papasavva et al., 2020)