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title:mandelbrot - SummaryWords in its Summary, the paper’s abstract
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published:2026-10-01..2026-10-15 - ImportanceIts importance score, such as 70 or more
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cites:doi:10.1214/ss/1009213286 - IsRetracted, a correction, or scored
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Trytitle:mandelbrotstatus:replicated"wilson interval"published:2026-10importance:>=70
Studies
- Its most important claim’s importance 28 out of 100: limited importance, under edition 4 of the rubric
People with depression report that time drags, yet laboratory timing studies disagree. A temporal account of depression predicts that time is dilated within the experienced present moment (targets up to a few seconds) and accelerated beyond it. In a time production task, dilation means producing intervals that are too long and acceleration producing them too short. In a registered meta-analysis of 11 case-control production studies, re-extracted from the primary papers where possible, the depression effect was 0.4836 standardised units higher above the 3 s boundary than below it (one-sided p = 0.03380082115675086), with overproduction at short targets (g = -0.2851) and underproduction at longer ones (g = 0.1985), neither significant alone. The effect rose by 0.6302 per tenfold increase in duration. Re-extraction also showed that an earlier meta-analysis coded a 30-s production as longer than 10 min.
- Published, Reproduced, Reviewed: Across 11 case-control studies of time production in depression, the pooled standardised difference (positive = depressed participants produce shorter intervals than controls) is 0.4836 higher for target intervals above 3 s than for targets of 3 s or less (95% CI -0.0431 to 1.0103; one-sided p = 0.034), with pooled g = -0.2851 at 3 s or less (3 studies; 95% CI -0.6917 to 0.1214) and g = 0.1985 above 3 s (10 studies; 95% CI -0.1378 to 0.5348).
- Published, Reproduced, Reviewed: Across the per-interval effects extracted from 7 primary papers (20 target intervals from 1 to 240 s), the depression effect on time production rises by 0.6302 standardised units per tenfold increase in target duration (cluster-robust SE 0.2128; one-sided p = 0.016), from overproduction at the shortest targets toward underproduction at the longest.
- Published, Reviewed: The time production task of Kitamura and Kumar (1983) asked participants to produce 30 s, but the meta-analysis of Thones and Oberfeld (2015, Table A2) coded it as a long (over 10 min) interval, where it was the only production effect; no case-control production study of depression in that meta-analysis or since has used a target over 10 min.
- Its most important claim’s importance 24 out of 100: trivial or highly circumscribed, under edition 4 of the rubric
The anterior insula is often proposed as a hub where time perception, interoception and graviception meet, and as the system through which depressed experience is felt as heaviness, low mood, low energy and slowing. Because the insula appears in a large share of all neuroimaging studies, co-localisation needs a base-rate control. In a registered analysis of 13459 full-text articles from NeuroQuery, we asked whether studies discussing each function, or depressive-symptom terms, report anterior-insula coordinates more often than studies on random topics. Interoception studies did (association z 10.259), but equally in the posterior insula; time perception (z {{R1.terms.time perception.anterior_insula.z}}) and vestibular studies (z -0.945) did not, so the three-way conjunction was no more selective than random term triples (percentile 0.5456). Symptom terms were not selective either (percentile 0.7064). At the resolution of literature meta-analysis, the anterior insula is not a selective meeting point for these functions.
- Published, Reproduced, Reviewed: Across 13459 NeuroQuery full-text articles with coordinates, studies that discuss time perception or vestibular processing report anterior-insula coordinates no more often than studies on random topics (anterior-insula association z 0.424 and -0.945; percentiles 0.4959 and 0.2351 among 2773 comparison terms), so the conjunction of time perception, interoception and vestibular processing in the anterior insula is not selective (minimum z -0.945, percentile 0.5456 among random term triples), even though interoception alone is strongly associated (z 10.259).
- Published, Reproduced: In the same articles, interoception studies are as strongly associated with the posterior as with the anterior insula (z 10.389 vs 10.259), and vestibular studies lean posterior (anterior minus posterior z -2.366, percentile 0.0999 among random terms), so none of the three functions shows an anterior-insula preference.
- Published, Reproduced, Reviewed: Studies discussing fatigue, psychomotor change, sadness or mood are not selectively associated with the anterior insula: their mean association z (1.057) lies at percentile 0.7064 of random four-term sets, with fatigue negative and only sadness near the upper tail.
- Its most important claim’s importance 23 out of 100: trivial or highly circumscribed, under edition 4 of the rubric
An account of depression as accumulated physical load distributed across body systems predicts that each system's state tracks the symptoms it produces, that bodily measures relate to somatic symptoms beyond mood, and that socially distributed load appears somatically. We tested these predictions in a registered analysis of 14722 adults in the US National Health and Nutrition Examination Survey (NHANES), relating limitation in load-bearing tasks, slow bowel transit, body mass index (BMI), an allostatic load index and income to PHQ-9 depressive symptom items. Load-bearing limitation, BMI and allostatic load related to somatic symptoms beyond cognitive-affective ones, and more than to cognitive-affective symptoms beyond somatic ones. But the predicted system-specific pattern did not appear: load-bearing limitation tracked sleep, energy and appetite (0.2946) far more than slow transit did (0.0404). Low income related more to cognitive-affective than to somatic symptoms (difference -0.0996). Bodily load is linked to somatic depression generally, not system by system.
- Published, Reproduced, Reviewed: In 14722 NHANES 2005-2010 adults, limitation in load-bearing tasks is associated with the PHQ-9 psychomotor item more than slow bowel transit is (age-, sex- and cycle-adjusted partial Spearman 0.2038 vs 0.0296), but also with the sleep, energy and appetite items more than slow transit is (0.2946 vs 0.0404; difference -0.2542, 95% CI -0.2762 to -0.2312), so the predicted double dissociation between a structural and a transport system does not appear.
- Published, Reproduced, Reviewed: In the same adults, load-bearing limitation, body mass index and a nine-marker allostatic load index are each associated with somatic depressive symptoms after adjusting for cognitive-affective symptoms (partial Spearman 0.1916, 0.0558, 0.08) and more strongly than with cognitive-affective symptoms after adjusting for somatic ones (differences 0.0711, 0.0399, 0.0646; Holm-adjusted p 0.002, 0.016, 0.002), whereas slow bowel transit shows no such specificity (difference 0.0074, 95% CI -0.0209 to 0.0347).
- Published, Reproduced, Reviewed: Lower family income relates more to cognitive-affective than to somatic depressive symptoms in these adults (partial Spearman 0.1275 vs 0.0279; difference -0.0996, 95% CI -0.1299 to -0.0695), opposite to the prediction that socially distributed load expresses itself somatically.
- Its most important claim’s importance 21 out of 100: trivial or highly circumscribed, under edition 4 of the rubric
If severe depression were a different attractor state rather than the far end of a continuum, relationships between bodily load and symptom severity should change above a threshold. We tested this in a registered analysis of 14722 adults in the US National Health and Nutrition Examination Survey (NHANES) with PHQ-9 scores. Limitation in load-bearing tasks, an allostatic load index and body mass index rose steadily with severity, and no threshold between moderate and severe scores produced a steeper slope (Holm-adjusted p = 1, 1 and 1); near the top of the scale, the best-fitting breaks flattened rather than steepened the relationship. Height, a negative control, showed no break. In people whose symptoms made functioning very or extremely difficult, bodily load was no more tightly coupled to somatic symptoms than in others. In this population, the body-symptom relationship looks like one continuum, not two states.
- Published, Reproduced, Reviewed: In 14722 NHANES 2005-2010 adults, limitation in load-bearing tasks, a nine-marker allostatic load index and BMI rise linearly with PHQ-9 depressive-symptom severity across its full range, with no steeper slope above any threshold between 8 and 22 points (wild-bootstrap sup-t tests, Holm-adjusted p = 1.0, 1.0 and 1.0); the best-fitting breaks for allostatic load and BMI, near the top of the scale, flatten rather than steepen the slope, and standing height, a negative control, shows no break either.
- Published, Reproduced, Reviewed: The partial association of load-bearing limitation with somatic depressive symptoms, adjusting for cognitive-affective symptoms, is no stronger in adults whose symptoms make functioning very or extremely difficult (partial Spearman 0.1607, n = 454) than in other adults with symptoms (0.1746; difference -0.0139, 95% CI -0.1036 to 0.0773).
- Its most important claim’s importance 21 out of 100: trivial or highly circumscribed, under edition 4 of the rubric
Embodied accounts of affect propose that position, weight, tension and shape are bodily templates for mood and evaluation: down and heavy for sadness, up and light for happiness, tension for anger, crookedness for badness. If such mappings are deep, many unrelated languages should use one word for both senses. In two registered analyses of the CLICS4 colexification database, "light" and "easy" share a word in {{R2.pairs.LIGHT (WEIGHT)|EASY.families_colexifying}} of {{R2.pairs.LIGHT (WEIGHT)|EASY.families_with_both}} language families, mirroring "heavy" and "difficult", and "straight" shares a word with "correct" in {{R1.pairs.STRAIGHT|CORRECT (RIGHT).families_colexifying}} families. By contrast, "up" or "high" and "happy", "down" or "low" and "sad", and "light" and "happy" share a word in at most one family each, and "hard" never shares one with "angry". Across languages, weight is lexicalised as effort and straightness as rightness, but emotion is kept lexically apart from posture and weight.
- Published, Reproduced, Reviewed: In CLICS4 v1.0, one word means both 'light (in weight)' and 'easy' in 11 of 50 language families with words for both (rate 0.22), more often than 'light' pairs with any of its reference concepts, and 'heavy' and 'difficult' share a word in 7 of 57 families, so weight words double as words for ease and difficulty at both poles.
- Published, Reproduced: Words for vertical position or weight almost never double as words for happiness or sadness: up-happy 1 of 66 families, high-happy 0 of 145, down-sad 0 of 21, low-sad 0 of 108, light-happy 0 of 146.
- Published, Reproduced, Reviewed: 'Straight' shares a word with 'correct' in 38 of 155 families and with 'good' in 7 of 200, whereas 'crooked' shares a word with 'wrong' in 4 of 113 and with 'bad' in 1 of 171, so the straightness-evaluation link is lexicalised mainly at its positive pole.
- Its most important claim’s importance 20 out of 100: trivial or highly circumscribed, under edition 4 of the rubric
Accounts that treat the felt weight of depression as more than metaphor rest on a premise: that distress is described in gravitational terms across unrelated languages. We tested a lexical form of that premise in a registered analysis of the CLICS4 database of cross-linguistic colexifications, asking whether languages use one word for "heavy" and for difficulty, grief, sadness or tiredness more often than for other concepts, and whether gravity-related words share words with sadness more than other physical-property words do. "Heavy" and "difficult" share a word in 7 of 57 families, more often than "heavy" pairs with any of its 1374 reference concepts, and "heavy" and "grief" in 2 families. "Heavy" never shares a word with "sad" (zero of 156 families) or "tired", and gravity-related words show no detectable excess with sadness (permutation p = 0.2232). Lexically, weight is widely the word for burden, not for sadness.
- Published, Reproduced, Reviewed: In CLICS4 v1.0 (3447 varieties, 247 families), a single word means both 'heavy' and 'difficult' in at least one language of 7 of the 57 families that have words for both (family-level rate 0.1228), higher than the rate for every one of 'heavy's 1374 reference partner concepts, whose 95th percentile is 0.0051; 'heavy' and 'grief' share a word in 2 of 69 families (rate 0.029, percentile 0.9964).
- Published, Reproduced, Reviewed: In the same data, 'heavy' never shares a word with 'sad' (0 of 156 families) or 'tired' (0 of 73), and 'sad' or 'grief' shares a word with any of 15 physical-property concepts in at most 2 families each, so gravity-related words (heavy, low, down) do not colexify with sadness detectably more than other physical-property words (difference in family-level rates 0.0031, one-sided permutation p = 0.2232).
- Its most important claim’s importance 19 out of 100: trivial or highly circumscribed, under edition 4 of the rubric
A regulated system nearing instability fluctuates more slowly, raising its lag-1 autocorrelation ("critical slowing down"). In a registered analysis of public sit-to-stand recordings from 27 adults, standing raised the autocorrelation of beat-to-beat systolic pressure by 0.0431 (CI 0.0066 to 0.0761). The rise was not larger with diabetes (probability of a larger rise 0.505, CI 0.2802 to 0.7308), and postural sway was not coupled to pressure beyond chance (median surrogate z -0.028). Standing shifts pressure dynamics toward slower fluctuations, but in this small sample the shift does not track diabetic status.
- Published, Reproduced, Reviewed: In 27 adults from the PhysioNet Cerebral Vasoregulation in Diabetes sit-to-stand recordings, standing with eyes open raised the lag-1 autocorrelation of linearly detrended beat-to-beat systolic blood pressure relative to the preceding 240 s of sitting, by a Hodges-Lehmann shift of 0.043 (bootstrap 95% CI 0.007 to 0.076), with 19 of 27 participants rising (one-sided Wilcoxon signed-rank p = 0.012; Holm-adjusted across two primary tests p = 0.025).
- Published, Reproduced, Reviewed: In the same recordings, the standing-induced rise in systolic-pressure lag-1 autocorrelation was not larger in 13 adults with type 2 diabetes than in 14 controls: the probability that a diabetic participant's rise exceeds a control's was 0.505 (bootstrap 95% CI 0.28 to 0.73; one-sided Mann-Whitney p = 0.49), which rules out only differences larger than that interval's upper end, since the test had 80% power only at a standardised difference of about 1.0.
- Published, Reproduced, Reviewed: During eyes-open standing, magnitude-squared coherence in 0.05-0.15 Hz between anteroposterior whole-body sway acceleration (horizontal ground-reaction force over body weight) and beat-to-beat systolic pressure did not exceed phase-randomised surrogates: median surrogate z-score -0.03 across 26 participants, 2 of whom exceeded 1.645 (one-sided Wilcoxon signed-rank p = 0.54).
- Its most important claim’s importance 18 out of 100: trivial or highly circumscribed, under edition 4 of the rubric
Psychological states are often described in mechanical terms: under pressure, crushed, torn, worn down, flowing, stuck, off course. If such mappings were deep and widespread, unrelated languages should often use one word for the mechanical and the psychological sense, as many use one word for "heavy" and "difficult". In a registered screen of the CLICS4 colexification database, we paired words for compression and tension, shear and friction, flow and momentum, and paths with concepts of emotion, cognition and effort. None of these pairs met the registered criterion of recurring across several families more often than the word's other pairings; each class had 0 hits against about 0.477 to 0.719 expected for random concepts. Only the load words reached it, through "heavy" with "difficult" and "light" with "easy" (2 hits, p = 0.0633). Across languages, weight is the one mechanical domain lexicalised as a psychological quantity.
- Published, Reproduced: Across CLICS4 v1.0, none of 37 words for compression and tension, shear and friction, flow and momentum, or paths shares a word with any of 30 emotion, cognition or effort concepts in at least three language families at the 95th percentile of the word's other pairings; each of the four classes has 0, 0, 0, 0 hits, against a mean of 0.48 to 0.72 for random concept sets of the same size.
- Published, Reproduced, Reviewed: Weight words are the exception: 'heavy' and 'light (weight)' give 2 hits among five load words (with 'difficult' and 'easy'), against 0.304 expected for random concept sets, though the class-level excess does not reach the registered 0.05 level (p = 0.0633), so the class test has limited sensitivity.
- Its most important claim’s importance being rated, 0 of 4 ratings in
Spatiotemporal accounts of depression predict that the default mode network (DMN) integrates over the longest intrinsic timescales, longer than control and salience networks, and that depression lengthens DMN timescales, prolongs DMN-dominant states, narrows transitions between network states and tracks brooding rumination. We tested these predictions in a registered analysis of public eyes-closed resting-state fMRI from people with depression and controls. Salience timescales were the shortest, but the DMN's were shorter than the control network's by -0.0416 s (CI -0.07 to -0.0125), opposite to the predicted order. Depression did not change DMN timescales (AUC 0.4015, CI 0.2708 to 0.5378), DMN dwell time or transition entropy, and brooding tracked neither. These data do not support the tested predictions.
- Published: In eyes-closed resting-state fMRI from 72 adults (OpenNeuro ds002748; 100 Schaefer parcels, 0.01-0.1 Hz band-pass, TR 2.5 s), the intrinsic timescale ACW-50 of the salience network is shorter than that of the default mode network (Hodges-Lehmann difference 0.0391 s, 95% CI 0.0057 to 0.0731) and of the control network (0.0751 s, 0.0397 to 0.1085), but the default mode network's is not the longest: it is shorter than the control network's by 0.0416 s (95% CI 0.0125 to 0.07).
- Published: In the same data, 51 adults with mild-to-moderate depression and 21 controls did not differ in default mode network ACW-50 (probability a depressed participant's value exceeds a control's 0.4015, 95% CI 0.2708 to 0.5378), in mean dwell time of default-mode-dominant states (0.5131, 0.3679 to 0.6536) or in the entropy of transitions among default-mode-, salience- and control-dominant states (0.549, 0.3987 to 0.6975); the design had 80% power only for differences near an AUC of 0.70.
- Published: Within the 45 depressed participants with Ruminative Responses Scale scores, brooding was not correlated with default mode network ACW-50 (Spearman rho 0.1065, 95% CI -0.1848 to 0.3812) or with default-mode-dominant dwell time (rho -0.2063, -0.4732 to 0.0887).