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	<title>dispersion &#8211; Science</title>
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	<title>dispersion &#8211; Science</title>
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		<title>Optical Rotation Gets a Reality Check: Why Methanol Can Mislead Natural Product Chemists</title>
		<link>https://scienmag.com/optical-rotation-gets-a-reality-check-why-methanol-can-mislead-natural-product-chemists/</link>
		
		<dc:creator><![CDATA[]]></dc:creator>
		<pubDate>Fri, 16 Oct 2026 14:37:32 +0000</pubDate>
				<category><![CDATA[Science News]]></category>
		<category><![CDATA[absolute configuration of secondary metabolites]]></category>
		<category><![CDATA[challenges in stereochemical assignment]]></category>
		<category><![CDATA[chiral molecule optical rotation]]></category>
		<category><![CDATA[chiroptical properties in natural products]]></category>
		<category><![CDATA[chiroptical spectroscopy]]></category>
		<category><![CDATA[dispersion]]></category>
		<category><![CDATA[furofuran]]></category>
		<category><![CDATA[furofuran lignans structural analysis]]></category>
		<category><![CDATA[influence of methanol on optical rotation measurements]]></category>
		<category><![CDATA[lignans]]></category>
		<category><![CDATA[natural product chemists]]></category>
		<category><![CDATA[natural products]]></category>
		<category><![CDATA[optical]]></category>
		<category><![CDATA[optical rotatory dispersion]]></category>
		<category><![CDATA[pitfalls]]></category>
		<category><![CDATA[plant secondary metabolites optical properties]]></category>
		<category><![CDATA[potential]]></category>
		<category><![CDATA[rotatory]]></category>
		<category><![CDATA[Scientific Research]]></category>
		<category><![CDATA[solvent effects]]></category>
		<category><![CDATA[solvent effects on optical rotation]]></category>
		<category><![CDATA[stereochemistry]]></category>
		<category><![CDATA[stereochemistry determination]]></category>
		<category><![CDATA[wavelength-dependent optical rotation]]></category>
		<guid isPermaLink="false">https://scienmag.com/?p=285974</guid>

					<description><![CDATA[A systematic study of furofuran lignans shows that optical rotatory dispersion can reliably assign absolute configurations, but only if the solvent is chosen carefully.]]></description>
										<content:encoded><![CDATA[<p>Every chiral molecule interacts with light in a characteristic way. When a beam of left- and right-circularly polarized light passes through a solution of a non-racemic chiral compound, the two components are refracted to different degrees, rotating the plane of polarized light. This optical rotation has been measured by natural product chemists for more than a century, and it remains the single most frequently reported chiroptical property in the literature. Yet a new study published in Frontiers in Natural Products demonstrates that this seemingly simple number can betray chemists when the solvent is wrong, and that a more rigorous wavelength-dependent approach, optical rotatory dispersion, offers a safer path to one of the field&#8217;s most stubborn problems: assigning the absolute configuration of chiral secondary metabolites.</p>
<p>The research, led by Eric Y. Lee, Victor M. S. Sousa, Isabele R. Nascimento, and Joao M. Batista Jr. at the Federal University of São Paulo and São Paulo State University, focused on furofuran lignans, a widespread subclass of plant secondary metabolites built from the central-carbon fusion of two phenylpropanoid units. These molecules share the 2,6-diaryl-3,7-dioxabicyclo[3.3.0]octane skeleton and exhibit a range of biological activities, including antioxidant, anti-inflammatory, cytotoxic, and antimicrobial effects. Although their relative configurations can be determined efficiently by nuclear magnetic resonance spectroscopy, their absolute configurations have often been assigned in the literature through empirical comparisons of optical rotation values with those of structurally related molecules, a practice the authors describe as risky.</p>
<p>The problem with empirical comparison is fundamental. Optical rotation is simply a signed number that carries no structural information by itself. It is sensitive to solvent, concentration, path length, and temperature, and slight structural changes between related molecules can completely invert the sign of rotation. The only acceptable empirical protocol involves comparing the two enantiomers of the same molecule under identical conditions, and even then the assignment is warranted only if one enantiomer&#8217;s absolute stereochemistry has been secured by independent methods. The golden standard, single-crystal X-ray crystallography, is restricted to high-quality crystals in the solid state, while NMR is intrinsically achiral in isotropic media and requires chiral auxiliaries to differentiate enantiomers.</p>
<p>To overcome these limitations, the team turned to optical rotatory dispersion, the wavelength-dependent version of optical rotation. Instead of recording a single value at the sodium D line of 589 nanometers, they measured specific rotations at six wavelengths: 589, 578, 546, 436, 405, and 365 nanometers. This produces a dispersion curve in the non-resonant region, which can then be compared with density functional theory simulations at the B3LYP/PCM/6-311G++(d,p) level of theory. The comparison of an entire curve rather than a single point provides a far more reliable basis for assigning absolute configuration.</p>
<p>The six lignans studied were isolated from Aristolochia species, including A. gigantea, A. pubescens, A. warmingii, and A. galeata, and their enantiomeric purities had been established previously by chiral HPLC. The researchers measured ORD in three solvents: acetonitrile, chloroform, and methanol. These solvents differ in polarity and hydrogen-bonding capability, properties that can affect molecular conformations, intermolecular interactions, and electronic transitions, all of which influence optical rotation.</p>
<p>The results were striking. For five of the six compounds, the absolute configurations could be unambiguously assigned by comparing experimental and calculated dispersion curves. The dextrorotatory compounds 1, 2, and 3 were assigned as (7S,8R,7′S,8′R), compound 5 as (7S,8R,7′R,8′R), and the levorotatory compounds 4 and 6 as (7R,8S,7′S,8′S). Chloroform emerged as the solvent of choice, providing better dispersion properties, less variation across wavelengths, and improved reproducibility, likely due to lower saturation of the photomultiplier tube detector and smaller conformational perturbation from the less polar medium.</p>
<p>But one compound defied the protocol. Sesamin, measured in methanol, produced calculated dispersion curves that led to the wrong absolute configuration assignment. The theoretical curve for the (7R,8S,7′R,8′S) configuration remained positive in methanol, in contrast to the results in acetonitrile and chloroform and to literature values. When the researchers assigned equal weights to the identified conformers instead of Boltzmann averaging, the curve adopted a negative trend, suggesting problems with the conformational ensemble selection, either from inaccurate geometries or incorrect energy estimations caused by the solvent.</p>
<p>To investigate this anomaly, the team employed molecular dynamics simulations followed by quantum mechanics/molecular mechanics calculations. A cubic box of 50 by 50 by 50 angstroms was filled with a single lignan molecule and 1,600 methanol molecules, and simulations ran for 20 nanoseconds at 300 kelvin and 1 bar. Snapshots taken every 50 picoseconds were subjected to geometry optimization using the two-layer ONIOM method, keeping only solvent molecules within 7 to 8 angstroms of the lignan. Despite this more realistic approach, the theoretical ORD values remained largely positive for the incorrect configuration. The researchers then tested micro-solvation, explicitly including one to four methanol molecules positioned to favor hydrogen-bond interactions with the oxygen atoms of the methylenedioxy and furofuran groups. Even though important structural changes from twisted to flat furofuran moieties were observed, the specific rotation values remained largely positive. The dominant structural factor for sign inversion appeared to be the relative orientation of the dipole moments of the identical aromatic rings, an orientation that seemed to be overestimated when geometry optimizations were performed with implicit solvation.</p>
<p>The findings carry implications far beyond furofuran lignans. Methanol is one of the most common solvents in natural product chemistry, and the authors recommend using it with caution for optical rotation measurements of this class of compounds, especially when absolute configuration assignments are intended. Chloroform is the preferable choice for ORD, as it leads to higher intensities, lower intermolecular interactions, and improved reproducibility. If solubility is an issue, acetonitrile is recommended. The authors also suggest obtaining optical rotation in different solvents for more reliable assignments. Given that empirical comparisons of specific rotation for structurally related molecules remain a common practice in natural product stereochemistry, these results are far-reaching, reinforcing that the solvent environment is not a passive backdrop but an active participant in the chiroptical properties of chiral molecules.</p>
<p><strong>Subject of Research:</strong> Chemistry</p>
<p><strong>Article Title:</strong> Stereochemistry of furofuran lignans from optical rotatory dispersion: potential and pitfalls</p>
<p><strong>Article References:</strong> Stereochemistry of furofuran lignans from optical rotatory dispersion: potential and pitfalls. (n.d.). <a href="https://doi.org/10.3389/fntpr.2026.1916076" rel="noopener noreferrer">https://doi.org/10.3389/fntpr.2026.1916076</a></p>
<p><strong>Image Credits:</strong> AI Generated</p>
<p><strong>DOI:</strong> <a href="https://doi.org/10.3389/fntpr.2026.1916076" rel="noopener noreferrer">10.3389/fntpr.2026.1916076</a></p>
<p><strong>Keywords:</strong> stereochemistry, natural products, chiroptical spectroscopy, lignans, solvent effects, furofuran, optical, rotatory, dispersion, potential, pitfalls, scientific research</p>
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		<post-id xmlns="com-wordpress:feed-additions:1">285974</post-id>	</item>
		<item>
		<title>Where Zero-Dose Children Live: Geography Tops Wealth and Education in Vaccine Gaps</title>
		<link>https://scienmag.com/where-zero-dose-children-live-geography-tops-wealth-and-education-in-vaccine-gaps/</link>
		
		<dc:creator><![CDATA[Courtney Benton]]></dc:creator>
		<pubDate>Thu, 15 Oct 2026 07:53:02 +0000</pubDate>
				<category><![CDATA[Science Education]]></category>
		<category><![CDATA[Comparison]]></category>
		<category><![CDATA[cross-country vaccine analysis]]></category>
		<category><![CDATA[dispersion]]></category>
		<category><![CDATA[global immunization gaps]]></category>
		<category><![CDATA[health disparities by wealth]]></category>
		<category><![CDATA[health equity]]></category>
		<category><![CDATA[immunization]]></category>
		<category><![CDATA[maternal education impact on vaccination]]></category>
		<category><![CDATA[Multidimensional]]></category>
		<category><![CDATA[public health equity]]></category>
		<category><![CDATA[Regional]]></category>
		<category><![CDATA[regional differences in vaccine coverage]]></category>
		<category><![CDATA[rural versus urban health access]]></category>
		<category><![CDATA[socio-economic factors in immunization]]></category>
		<category><![CDATA[Subnational]]></category>
		<category><![CDATA[subnational regions]]></category>
		<category><![CDATA[vaccination]]></category>
		<category><![CDATA[vaccination coverage disparities]]></category>
		<category><![CDATA[vaccination inequality]]></category>
		<category><![CDATA[vaccine inequality]]></category>
		<category><![CDATA[WHO health inequality data]]></category>
		<category><![CDATA[zero-dose]]></category>
		<category><![CDATA[zero-dose children]]></category>
		<guid isPermaLink="false">https://scienmag.com/?p=273111</guid>

					<description><![CDATA[A sweeping analysis of 339 surveys finds subnational region is most often the largest dimension of zero-dose inequality, but classifications are often uncertain and unstable over time.]]></description>
										<content:encoded><![CDATA[<p>Some of the world&#8217;s most consequential public health questions hide inside a deceptively simple statistic: which children have never received a single dose of routine vaccines. These zero-dose children, concentrated overwhelmingly in disadvantaged populations, are the central target of the global immunization agenda, and governments and donors have long debated where the deepest pockets of disadvantage actually lie. Is inequality in zero-dose prevalence driven mainly by household wealth, by how far mothers went in school, by the rural–urban divide, or by the region of the country a child happens to be born in? A new analysis published in the International Journal for Equity in Health offers the most systematic answer yet, and its conclusion is more nuanced than any single label can capture.</p>
<p>Han Qiu of Beijing University of Chinese Medicine and Yue Zhong of Wuhan University assembled an unusually large evidence base: 339 eligible country–year surveys from 86 countries, conducted between 1993 and 2023 and drawn from the WHO Health Inequality Data Repository. For each survey, they measured inequality in zero-dose prevalence along four stratifiers—household wealth, maternal education, place of residence, and subnational region. The technical challenge they confronted is one that has plagued cross-country comparisons for years. These stratifiers do not divide a population into comparable pieces. Wealth quintiles split households into five groups, education categories may number three or four, urban and rural residence yields two, while subnational regions can range from a handful to dozens of administrative units with wildly different population sizes. Comparing inequality measures across stratifiers with different group counts and group populations risks rewarding whichever dimension happens to be sliced most finely.</p>
<p>To level the playing field, the researchers used a single descriptive statistic for all four stratifiers: the population-weighted between-group standard deviation of subgroup-specific zero-dose prevalence. In plain terms, this measure captures how widely zero-dose prevalence scatters across the constituent groups of a given stratifier, weighted by how many children live in each group. A large between-group standard deviation means some groups carry far higher zero-dose prevalence than others along that dimension. For each survey, the stratifier with the largest value was classified as the leading observed inequality dimension. The approach deliberately treats the comparison as descriptive rather than causal, a distinction that turns out to matter enormously for how the results should be used.</p>
<p>The headline finding is that geography dominates more often than any other dimension. Subnational region was the leading observed inequality dimension in 209 of the 339 surveys, or 61.7 percent. Household wealth led in 67 surveys (19.8 percent), maternal education in 61 (18.0 percent), and place of residence in just 2 (0.6 percent). The urban–rural divide, long a staple of health equity discourse, was almost never the largest observed source of zero-dose inequality once it competed on equal footing with the other stratifiers. Regional dispersion, in other words, is where the deepest between-group gaps in unvaccinated children are most frequently found.</p>
<p>But the study&#8217;s most important contribution may be its refusal to stop at that headline. The authors recognized that identifying a leading dimension from survey data is itself a statistical act subject to sampling error. Subgroup prevalence estimates come with standard errors, and when two stratifiers produce similar between-group standard deviations, the ranking between them may be little more than noise. To quantify this fragility, they ran 5,000 parametric simulations for each survey, resampling from the reported subgroup standard errors and recording how often each stratifier emerged as the leading dimension. A survey was considered to have an uncertain classification if the maximum simulated probability of any single leading dimension fell below 0.80.</p>
<p>The results of that uncertainty analysis are sobering. Only 145 surveys, or 42.8 percent, had a maximum simulated leading-dimension probability of at least 0.80. In well over half of the surveys, the identity of the leading inequality dimension could not be stated with reasonable confidence. This does not mean the underlying data are poor; it means that when multiple dimensions of disadvantage overlap—as wealth, education, and geography so often do—the survey sample sizes available for subgroup estimates are often insufficient to declare a clear winner. The authors&#8217; framing is careful: the numerically largest dimension does not necessarily represent the most appropriate intervention target, and a leading-dimension label should never be mistaken for a causal mechanism.</p>
<p>The team stress-tested their conclusions from every direction. Across six alternative inequality measures, the proportion of region-led surveys ranged from 50.1 percent to 70.5 percent, confirming that the regional pattern is not an artifact of one particular statistic. When countries were weighted equally rather than by survey count, the regional share remained similar at 62.5 percent (95 percent CI, 54.9–70.1). When only the most recent survey from each country was retained, the share rose modestly to 68.6 percent (95 percent CI, 59.3–77.9). Adding child sex and, where available, maternal age as additional stratifiers did not change the original classifications. One sensitivity finding deserves particular attention: regional dispersion was positively associated with the number of reported subnational regions, with a Spearman correlation of 0.355 (p &lt; 0.001). Countries that carve themselves into more administrative units tend to show larger between-region dispersion, a reminder that the regional stratifier is partly a function of how a country chooses to draw its internal boundaries.</p>
<p>Stability over time proved equally elusive. Among the 66 countries with repeated surveys, 37—56.1 percent—changed their leading dimension at least once between survey rounds. A country whose zero-dose inequality appeared wealth-driven in one decade might appear region-driven in the next, not necessarily because the underlying social structure transformed, but because sampling variation, changing administrative boundaries, and shifting demographic patterns all conspire to move the ranking. The practical implication is direct: any single-snapshot assessment of where disadvantage is concentrated should be treated as provisional, and repeated multidimensional assessment is needed to track where zero-dose children actually cluster as circumstances evolve.</p>
<p>The authors conclude that subnational region should be interpreted as a composite spatial stratifier rather than an independent causal mechanism. Regions bundle together everything that varies across a country&#8217;s territory—local health system capacity, road access, conflict, climate, cultural practices, local wealth and education levels—so a large between-region dispersion signals that disadvantage is spatially clustered without specifying which ingredient drives it. For immunization programs, this cuts both ways. Region-led inequality suggests that geographically targeted outreach, subnational microplanning, and region-specific supply chains could reach many zero-dose children efficiently. Yet because the classification was uncertain in most surveys and unstable in half of countries with repeated data, programs should avoid anchoring their entire strategy to whichever dimension happened to top a single survey&#8217;s ranking.</p>
<p>For a global health community racing to reach the children the routine system has missed, the study offers both a map and a warning. The map points to geography: in roughly six in ten surveys across 86 countries and three decades, the widest gaps in zero-dose prevalence fall along regional lines, dwarfing the familiar wealth and education gradients and rendering the rural–urban binary nearly irrelevant as a leading dimension. The warning is about certainty: in most surveys the leading dimension could not be identified with confidence, and in most countries with longitudinal data it changed over time. Zero-dose disadvantage is real, measurable, and most often spatially concentrated—but pinning it to a single permanent label, the analysis makes clear, is a luxury the data rarely afford. The path forward the authors describe is neither glamorous nor simple: keep measuring, keep comparing dimensions, and keep revising the picture of where the unvaccinated live as new evidence arrives.</p>
<p><strong>Subject of Research:</strong> Zero-dose vaccination inequality across 339 surveys in 86 countries</p>
<p><strong>Article Title:</strong> Subnational regional dispersion in zero-dose vaccination: a multidimensional comparison across 339 country–year surveys</p>
<p><strong>Article References:</strong> Subnational regional dispersion in zero-dose vaccination: a multidimensional comparison across 339 country–year surveys. (n.d.). <a href="https://doi.org/10.1186/s12939-026-03064-x" rel="noopener noreferrer">https://doi.org/10.1186/s12939-026-03064-x</a></p>
<p><strong>Image Credits:</strong> AI Generated</p>
<p><strong>DOI:</strong> <a href="https://doi.org/10.1186/s12939-026-03064-x" rel="noopener noreferrer">10.1186/s12939-026-03064-x</a></p>
<p><strong>Keywords:</strong> zero-dose children, vaccination inequality, subnational regions, health equity, immunization, Subnational, regional, dispersion, zero-dose, vaccination, multidimensional, comparison</p>
]]></content:encoded>
					
		
		
		<post-id xmlns="com-wordpress:feed-additions:1">273111</post-id>	</item>
		<item>
		<title>Your Brain Really Does Average Numbers, New Study Finds</title>
		<link>https://scienmag.com/your-brain-really-does-average-numbers-new-study-finds/</link>
		
		<dc:creator><![CDATA[Cassandra Pierce]]></dc:creator>
		<pubDate>Tue, 13 Oct 2026 18:57:59 +0000</pubDate>
				<category><![CDATA[Psychology & Psychiatry]]></category>
		<category><![CDATA[averaging numbers]]></category>
		<category><![CDATA[cognitive mechanisms of averaging]]></category>
		<category><![CDATA[criterion judgment]]></category>
		<category><![CDATA[decision-making]]></category>
		<category><![CDATA[dispersion]]></category>
		<category><![CDATA[distance effect]]></category>
		<category><![CDATA[ensemble averaging]]></category>
		<category><![CDATA[ensemble perception]]></category>
		<category><![CDATA[experimental psychology of numerical processing]]></category>
		<category><![CDATA[heuristic strategies in number judgment]]></category>
		<category><![CDATA[heuristics]]></category>
		<category><![CDATA[human numerical cognition]]></category>
		<category><![CDATA[judgment of group averages]]></category>
		<category><![CDATA[mean calculation in cognition]]></category>
		<category><![CDATA[mental number line]]></category>
		<category><![CDATA[neural basis of numerical averaging]]></category>
		<category><![CDATA[numerical cognition]]></category>
		<category><![CDATA[perceptual vs. computational strategies]]></category>
		<category><![CDATA[psychophysics]]></category>
		<category><![CDATA[statistical computation in the brain]]></category>
		<category><![CDATA[summary statistics]]></category>
		<category><![CDATA[symbolic numbers]]></category>
		<category><![CDATA[visual ensemble perception]]></category>
		<guid isPermaLink="false">https://scienmag.com/?p=268771</guid>

					<description><![CDATA[A new pair of experiments shows that people genuinely compute the average of symbolic digit arrays, with mean distance from a criterion predicting performance better than heuristic shortcuts.]]></description>
										<content:encoded><![CDATA[<p>Glance at a handful of numbers scattered across a screen and, within a fraction of a second, your mind seems to deliver a verdict about their average. For decades, psychologists have debated whether that verdict reflects genuine statistical computation or a clever shortcut. Now a new study published in the journal Attention, Perception, &amp; Psychophysics provides some of the strongest evidence yet that the human mind can truly compute the mean of a set of symbolic numbers, and that heuristic strategies play only a supporting role. The research, conducted by Daniel Fitousi and Hadar Srulovich of Ariel University, used an elegant experimental design that pits the arithmetic mean against rival strategies in a direct contest, and the mean won decisively.</p>
<p>The question matters because ensemble perception, the ability to extract summary statistics from groups of objects, has been documented extensively for visual properties such as size, orientation, color, facial emotion, and rough numerosity. When people view a crowd of faces, they can rapidly judge the average emotional expression; when they see a field of textured lines, they can sense the mean orientation. These findings suggested that the visual system computes averages much as a statistician would. But when the items are symbolic numerals, such as the Arabic digits 2, 4, 7, and 9, the story becomes murkier. Observers might genuinely integrate the magnitudes of all four digits, or they might rely on shortcuts, such as attending only to the most extreme digit, or counting how many digits fall above versus below some reference value.</p>
<p>Distinguishing genuine averaging from heuristic shortcuts is notoriously difficult, because both strategies often produce similar patterns of behavior. If a set of numbers has a mean well above five, then typically most of its digits are also above five, and its largest digit is likely far above five as well. A participant who answers correctly could be doing full integration or could be exploiting any of these correlated cues. Fitousi and Srulovich solved this problem with a criterion-based design in which participants viewed a two-by-two array of four Arabic digits and had to decide, under time pressure, whether the arithmetic mean of the set was smaller or larger than five. The key insight is that a true mean-based mechanism makes a precise prediction: performance should depend on the distance between the set mean and the criterion of five. The closer the mean sits to five, the harder the judgment should be, producing slower responses and more errors. This is the classic distance effect known from single-number comparison research dating back to the landmark 1967 study by Moyer and Landauer, who showed that comparing numbers takes longer when the numbers are numerically close.</p>
<p>In their first experiment, with forty participants, the researchers found exactly that signature. Accuracy and response time showed a robust ensemble-distance effect: decisions were slowest and least accurate when the set mean was closest to five, and performance improved monotonically as the mean moved farther from the criterion. Crucially, the authors went beyond the aggregate pattern and conducted item-level model comparisons, asking which statistical property of each individual digit array best predicted the participant&#8217;s behavior on that trial. The mean distance outperformed prominent heuristic alternatives based on the most extreme digit in the array or on the majority of digits lying above versus below the criterion. In other words, what best explained the data was not any single salient element or a simple tally, but the computed average of the whole set.</p>
<p>The first experiment also uncovered a second, independent influence on performance: the dispersion of the digits within the set. When the four numbers were widely spread out, judgments were impaired even after accounting for the distance of the mean from the criterion. This dispersion effect is theoretically interesting because a perfect averaging mechanism that simply pools four magnitudes might be expected to be indifferent to how spread out those magnitudes are. The finding suggests that internal representations of numerical magnitude are noisy, and that this noise accumulates when items vary widely, degrading the precision of the pooled estimate. Similar effects of heterogeneity have been reported in ensemble perception for visual properties, and their appearance here with symbolic numbers hints at a common architecture for statistical summary computation across perceptual and symbolic domains.</p>
<p>Yet the strongest objections to ensemble averaging have always come from the possibility that correlated cues are doing the work. The second experiment was designed as a diagnostic test that would break those correlations. The researchers constructed stimulus regimes in which the heuristic cues became uninformative or actively misleading, while carefully matching the mean distance and the dispersion of the sets across regimes. In one regime, the majority cue was tied, meaning that an equal number of digits fell above and below the criterion, so counting digits could not help. In another regime, the extreme-item cue conflicted with the correct answer, meaning that the most extreme digit in the array pointed toward the wrong response. If participants were relying on heuristics, their performance should have collapsed or flipped in these critical regimes.</p>
<p>It did not. Across regimes, the model comparisons again favored mean distance as the best predictor of both accuracy and response time. The distance effect persisted when majority information carried no diagnostic value whatsoever, and it persisted when the most extreme digit favored the incorrect response. Participants continued to judge the sets according to their true averages, even when every available shortcut pointed elsewhere. This pattern is precisely what a genuine mean-based integration mechanism would produce, and it is difficult to reconcile with accounts in which averaging-like behavior is an illusion created by cue redundancy. The authors conclude that the results support real mean-based integration of symbolic magnitudes, while showing that heuristic strategies have only a secondary role, one that becomes apparent mainly under increased uncertainty.</p>
<p>The findings carry weight for several ongoing debates in cognitive science. First, they extend ensemble perception into the domain of abstract symbols, suggesting that the machinery for statistical summarization is not limited to low-level visual features but can operate on semantic, culturally learned magnitudes. This connects the ensemble literature to the numerical cognition literature, including the influential idea of a mental number line and the parietal circuits that represent numerical magnitude in a roughly continuous, analog format. If digits are converted to analog magnitudes and then pooled, ensemble averaging of numerals may share a perceptual-like population-coding mechanism with the averaging of dots, orientations, and faces, a possibility that previous theoretical work on approximate numerical averaging has explored.</p>
<p>Second, the study speaks to the long-running tension between heuristic and exhaustive processing in judgment and decision making. Since Tversky and Kahneman&#8217;s classic work on heuristics and biases, researchers have documented countless cases in which people substitute easy questions for hard ones. The new results show that this tendency is not absolute. When the task structure makes the summary statistic the only reliable guide, the mind appears capable of deploying genuine integration, at least for small sets of four items presented simultaneously. Heuristics, on this view, are not the default everywhere; they emerge as competitors chiefly when the diagnostic value of the true statistic is degraded or when uncertainty rises.</p>
<p>Finally, the work has practical resonance. Averaging lies at the heart of numerical literacy, from estimating a grocery bill to interpreting medical risk statistics, and prior research has linked competence with numerical integration to broader mathematics achievement. Understanding that adults can compute set means rapidly and automatically, and that their precision depends on the distance of the mean from a criterion and on the spread of the items, may inform models of how people extract statistical information from displays, dashboards, and data visualizations. The study also leaves open questions that future research can pursue: whether the same mechanisms hold for larger sets, for sequentially presented numbers, for fractions and decimals, and for children whose numerical representations are still developing. Data and stimuli from the study are publicly available, and the criterion-based paradigm it introduces offers a template for testing ensemble computation in any domain where summary statistics compete with salient single items for control of behavior.</p>
<p><strong>Subject of Research:</strong> Ensemble averaging of symbolic numbers and the role of heuristic shortcuts in numerical summary judgments</p>
<p><strong>Article Title:</strong> Ensemble averaging of symbolic numbers: Criterion mean judgments beat heuristics</p>
<p><strong>Article References:</strong> Fitousi, D., &amp; Srulovich, H. (2026). Ensemble averaging of symbolic numbers: Criterion mean judgments beat heuristics. <em>Attention, Perception, &amp;amp; Psychophysics, 88</em>(7), Article 204. <a href="https://doi.org/10.3758/s13414-026-03338-0" rel="noopener noreferrer">https://doi.org/10.3758/s13414-026-03338-0</a></p>
<p><strong>Image Credits:</strong> AI Generated</p>
<p><strong>DOI:</strong> <a href="https://doi.org/10.3758/s13414-026-03338-0" rel="noopener noreferrer">10.3758/s13414-026-03338-0</a></p>
<p><strong>Keywords:</strong> numerical cognition, ensemble perception, ensemble averaging, distance effect, heuristics, symbolic numbers, decision making, mental number line, summary statistics, psychophysics, criterion judgment, dispersion</p>
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		<post-id xmlns="com-wordpress:feed-additions:1">268771</post-id>	</item>
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		<title>Groundwater &#8216;Ages&#8217; Hide a Factor of 60 — And That Error Could Finally Reveal How Water Really Moves Underground</title>
		<link>https://scienmag.com/groundwater-ages-hide-a-factor-of-60-and-that-error-could-finally-reveal-how-water-really-moves-underground/</link>
		
		<dc:creator><![CDATA[Violet Maxwell]]></dc:creator>
		<pubDate>Sat, 12 Sep 2026 21:55:48 +0000</pubDate>
				<category><![CDATA[Earth Science]]></category>
		<category><![CDATA[advances in understanding groundwater flow dynamics]]></category>
		<category><![CDATA[advection]]></category>
		<category><![CDATA[advective travel time versus tracer age]]></category>
		<category><![CDATA[aquifer water movement]]></category>
		<category><![CDATA[argon-39]]></category>
		<category><![CDATA[dispersion]]></category>
		<category><![CDATA[environmental tracers]]></category>
		<category><![CDATA[environmental tracers in hydrogeology]]></category>
		<category><![CDATA[groundwater]]></category>
		<category><![CDATA[groundwater age measurement inaccuracies]]></category>
		<category><![CDATA[groundwater mixing and dispersion]]></category>
		<category><![CDATA[helium-4]]></category>
		<category><![CDATA[hydrogeology]]></category>
		<category><![CDATA[hydrogeology textbook assumptions]]></category>
		<category><![CDATA[implications for subsurface hydrology]]></category>
		<category><![CDATA[krypton-81]]></category>
		<category><![CDATA[limitations of radiocarbon and tritium dating]]></category>
		<category><![CDATA[longitudinal dispersion in groundwater]]></category>
		<category><![CDATA[Mean Residence Time]]></category>
		<category><![CDATA[new methods for measuring underground water flow]]></category>
		<category><![CDATA[paleoclimate]]></category>
		<category><![CDATA[Peclet number]]></category>
		<category><![CDATA[radiocarbon dating]]></category>
		<category><![CDATA[significance of groundwater age discrepancies]]></category>
		<guid isPermaLink="false">https://scienmag.com/?p=199004</guid>

					<description><![CDATA[A new theoretical study shows that dispersion can make tracer-based groundwater ages differ from true travel times by up to a factor of sixty, opening a novel way to measure Peclet numbers at large scales.]]></description>
										<content:encoded><![CDATA[<p>Beneath the surface of nearly every hydrogeology textbook sits an assumption so widely repeated that most researchers no longer question it: that the age of a groundwater sample, calculated from an environmental tracer such as radiocarbon or tritium, tells us how fast the water has travelled through the aquifer. A new theoretical study published in Hydrogeology Journal by Axel Suckow of CSIRO Environment in Australia dismantles that assumption with striking precision. The work shows that for realistic amounts of underground mixing, the difference between the age a tracer reports and the true advective travel time of the water can reach a factor of sixty. Far from being an inconvenient error, however, that discrepancy turns out to be a gift: it offers, for the first time, a practical way to measure one of the most elusive parameters in all of subsurface science — longitudinal dispersion — at scales of centuries to hundreds of millennia.</p>
<p>The confusion stems from the fact that &#8216;groundwater age&#8217; is not one quantity but three. The first is the Peak Age, sometimes called the piston-flow or advective age, which describes how long it takes the centre of a concentration front — the peak of a tracer pulse — to travel a given distance. The second is the Mean Residence Time, the average age of all the water molecules in a sample, equivalent to the centre of mass of the age distribution. The third is the Tracer Age, the number actually calculated from a measured tracer concentration using standard formulas such as the conventional radiocarbon age or the tritium–helium age. In a perfectly ordered, dispersion-free aquifer these three values coincide. In the real world, where groundwater always undergoes at least some dispersive mixing, they diverge — sometimes dramatically.</p>
<p>Suckow&#8217;s analysis rests on the one-dimensional advection–dispersion equation, the workhorse model of solute transport, in which the balance between advective flow and dispersive spreading is captured by a single dimensionless quantity: the Peclet number. A high Peclet number means advection dominates and the water moves like a piston; a low Peclet number means dispersion smears everything extensively. Drawing on the classic field-data review by Gelhar and colleagues, the study notes that Peclet numbers observed in aquifers span an enormous range, from about 0.1 to 1000, with a best estimate near 10. When Suckow computed tracer output concentrations across that range, the consequences were sobering. For a Peclet number of 0.1, the Mean Residence Time exceeds the Peak Age by a factor of sixty; even at a Peclet number of 1, the gap is still a factor of six.</p>
<p>The behaviour of individual tracers adds further layers of complexity. For radioactive tracers with a constant atmospheric input — a reasonable approximation for argon-39, carbon-14 and krypton-81 — the calculated Tracer Age starts out equal to the Mean Residence Time and only gradually approaches the Peak Age as the water ages toward the tracer&#8217;s detection limit. For helium-4, a stable isotope produced underground at a roughly constant rate by the decay of uranium and thorium, the situation is different again: because helium mixes linearly rather than exponentially, its Tracer Age always reflects the Mean Residence Time and never the advective velocity. The practical result is that a single water sample, measured with a suite of modern tracers, will yield systematically different ages that increase in the order of tracer half-life: tritium, then argon-39, then carbon-14, then krypton-81, then helium-4.</p>
<p>Some of these discrepancies are large enough to rewrite interpretations of published datasets. The study highlights that reported contradictions between carbon-14 ages and helium-4 ages in major aquifers — differences previously explained by invoking a mysterious &#8216;crustal flux&#8217; of helium rising from deep strata — may simply reflect low Peclet numbers. In the Great Artesian Basin of Australia, Torgersen and Clarke reported in 1985 that helium-based ages exceeded hydrologic age estimates by a factor of seventy-four, remarkably close to the factor of sixty that pure dispersion produces at a Peclet number of 0.1. Suckow is careful not to dismiss crustal degassing as a real phenomenon, but points out that such an external flux could only be quantified once the Peclet number is known — and under low-Peclet conditions the inferred flux would be substantially smaller than previously claimed.</p>
<p>The timing of this theoretical advance is no accident. For decades, the tracers needed to test these ideas simultaneously simply could not be measured on the same sample. That changed with the advent of Atom Trap Trace Analysis, or ATTA, a laser-based technique developed for krypton-81 and argon-39 that has turned isotopes once considered unmeasurable into routine tools. Before ATTA, only around 300 argon-39 groundwater measurements existed worldwide; today the two ATTA laboratories, in Hefei, China and Heidelberg, Germany, each process on the order of a hundred samples per year. Combined with the established workhorses tritium–helium, radiocarbon and chlorine-36, and supplemented by new stable noble-gas methods, researchers can now assemble continuous groundwater dating records spanning from a few decades to more than a million years — precisely the range needed to exploit Suckow&#8217;s framework.</p>
<p>The practical payoff is a new method for determining Peclet numbers on time scales of centuries to many millennia, something field tracer tests and contaminant plume studies — typically confined to transport distances of tens to hundreds of metres — have never been able to deliver. The logic is elegant: because each tracer&#8217;s age responds differently to dispersion depending on its half-life, the spread of Tracer Ages measured along a flow path encodes the Peclet number itself. For Peclet numbers below about 2, the differences between tracers become large and systematic; above 2, all tracers converge on the same age. By fitting the advection–dispersion equation directly to multi-tracer data from a series of wells, both the advective velocity and the Peclet number can be recovered simultaneously. Suckow demonstrates the approach on two published datasets — the Guarani aquifer in South America and the western Great Artesian Basin in Australia — deriving Peclet numbers of roughly 0.2 and 0.1, and correspondingly higher flow velocities than the original studies had estimated, a result with direct consequences for groundwater resource management in arid regions.</p>
<p>The findings also cast new light on palaeoclimate records preserved in groundwater. Noble-gas palaeotemperatures dissolved in recharging water have long been used to reconstruct past climates, and multiple studies report that land temperatures during the Last Glacial Maximum were about six degrees Celsius cooler than today. But dispersion acts as a low-pass filter on any signal carried by groundwater. Suckow&#8217;s calculations show that at Peclet numbers of 10 or less, temporal variations in the palaeotemperature record are progressively ironed out, and the reconstructed glacial cooling becomes biased warm — by nearly a degree at a Peclet number of 10, and potentially by several degrees at lower values. The widespread six-degree figure, in other words, may partly be an artefact of dispersive smoothing, and the true Last Glacial Maximum cooling on land could have been colder than commonly stated. The study also suggests that groundwater realistically preserves climate signals only up to about 100,000 years, even under favourable transport conditions.</p>
<p>For practitioners, the message is a call to methodological reform. Tracer Ages, the study concludes, should only be interpreted as advective or piston-flow ages when the Peclet number is known to exceed 2 — a condition rarely demonstrated in historical studies. Tritium–helium ages deserve particular caution: for all realistic dispersive conditions with Peclet numbers below 10, they do not represent the movement of a concentration front, as generally assumed, but instead follow or exceed the Mean Residence Time before levelling off with distance. The strongest recommendation is to measure as many tracers with different time scales as possible on every sample along a flow path, since no single tracer can disentangle velocity from dispersion. In an era when aquifers supply drinking water to billions and host critical infrastructure from nuclear waste repositories to carbon storage sites, knowing how water — and whatever it carries — actually moves underground has never mattered more. What was once dismissed as pedantic quibbling over definitions now looks like the key to one of hydrogeology&#8217;s oldest unsolved problems.</p>
<p><strong>Subject of Research:</strong> The effect of dispersion on tracer-derived groundwater ages and its use for deriving Peclet numbers in large-scale groundwater transport</p>
<p><strong>Article Title:</strong> The effect of dispersion on the “age” of groundwater calculated from environmental tracers allows a novel way to derive Peclet numbers for large-scale groundwater transport</p>
<p><strong>Article References:</strong> Suckow, A. (2026). The effect of dispersion on the “age” of groundwater calculated from environmental tracers allows a novel way to derive Peclet numbers for large-scale groundwater transport. <em>Hydrogeology Journal</em>. <a href="https://doi.org/10.1007/s10040-026-03156-6" rel="noopener noreferrer">https://doi.org/10.1007/s10040-026-03156-6</a></p>
<p><strong>Image Credits:</strong> AI Generated</p>
<p><strong>DOI:</strong> <a href="https://doi.org/10.1007/s10040-026-03156-6" rel="noopener noreferrer">10.1007/s10040-026-03156-6</a></p>
<p><strong>Keywords:</strong> groundwater, environmental tracers, dispersion, Peclet number, hydrogeology, radiocarbon dating, krypton-81, argon-39, helium-4, advection, Mean Residence Time, paleoclimate</p>
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