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Science Journaling Club

Volume 2, Issue 4June 2026

Summer 2026

A meta-analysis of the long-term field trials behind farmland carbon claims, next to the real origin of the 10,000-steps target, ancient DNA pulled from a Roman fish-sauce vat, and the dental plaque that finally gave the Denisovans a face.

This issueSJC 2.4
Published
June 2026
Articles
8
Research
3
Field notes
5
With code
5

Contents

8 articles, in the order the club meant them to be read.

  1. Field noteExplainer

    How Anybody Knows How Old Anything Is

    Almost every date you have ever read about the past came out of one of seven or eight methods, and not one of those methods deserves to be trusted on its own. Tree rings and lake muds and ice layers count years directly, one at a time, while radiocarbon, potassium-argon and uranium-lead measure atoms instead, each covering a different slice of time. The whole structure becomes believable because the slices overlap, so any method can be checked against a second method that shares none of its physics, none of its instruments and none of its assumptions. We explain the decay statistics without calculus, simulate a population of atoms decaying one by one and watch the exponential law appear out of the randomness (0.051% agreement with the analytic curve over five half-lives, with no exponential anywhere in the code), and calibrate real radiocarbon ages against the real IntCal20 curve. Along the way: why 1% of modern contamination turns a genuinely ancient sample into a confident date of 36,993 BP, why a bigger sample stops helping past forty thousand years, and why a single measurement of 2450 ± 30 radiocarbon years maps onto three separate stretches of calendar time spread over 312 years. Also the argument against everything we just said, which is stronger than you might expect and which we have not tried to make easy on ourselves.

    General ScienceRead 42 minSections 13

  2. ResearchOriginal Research

    Counting Every Word in Fifty Books to Test a Law Nobody Can Explain

    Zipf's law says that if you rank the words of a text by frequency, the count at rank rr falls off like r−ar^{-a} with aa near 1. We tokenised fifty public-domain books from Project Gutenberg spanning fourteen languages and about 2,350 years, from a Greek tragedy to a 1925 American novel, and fit both a pure Zipf law and a shifted Zipf–Mandelbrot form by exact maximum likelihood, never by regression on a log-log plot, with goodness of fit assessed by the Clauset–Shalizi–Newman bootstrap. Across 4,714,004 tokens and 496,852 distinct word types, the rank exponent averaged 0.9549 (SD 0.0597) over all fifty books and 0.9899 (SD 0.0252) over the nineteen written in English, with every single book landing between 0.757 (a Finnish epic) and 1.045 (a Spanish novel). Splitting each book in half to measure real repeatability put the one-book measurement error at 0.0044, so the spread across books is 14 times larger than the noise: the differences are real, not sampling accidents. A pure power law was not rejected by the goodness-of-fit test in 34 of 50 books; a Zipf–Mandelbrot form with one extra free parameter beat it on AIC in all 50, and moved the fitted exponent by 13.8% on average, which is most of what a published Zipf exponent is worth without also stating which of the two forms produced it. Words that occur exactly once were undercounted by every fitted model, at a near-constant rate: the Zipf–Mandelbrot prediction averaged 45.8% of the true hapax count in every one of the fifty books. Validated against Clauset, Shalizi and Newman's own published fit of Moby-Dick, our exponent agreed to 0.29 combined standard errors. Validated against Moreno-Sánchez, Font-Clos and Corral's 31,075-text survey, our English-subset mean disagreed by −9.47 standard errors, a real and reported disagreement traced to tokeniser and corpus differences rather than to a coding error, demonstrated by rerunning our own pipeline under three other tokenisation rules and watching the exponent move by more than that gap. All five internal validations, including recovery of a known exponent from synthetic data and a from-scratch check of the Hurwitz zeta machinery against closed forms, passed before any real book was opened. Master seed 20260614. Corpus retrieved 2026-09-14 from gutenberg.org; all fifty downloads succeeded and none was substituted.

    Summer 2026Read 33 minSections 12

  3. ResearchMethods

    When the First Digit Test Works and When It Accuses the Innocent

    Benford's law says the leading digit of many collections of real numbers is 1 far more often than 9, following P(d)=log⁡10(1+1/d)P(d) = \log_{10}(1+1/d), and it is now a standard test for cooked books, rigged elections and fabricated data. We put eight genuinely public datasets through the test, chosen for having nothing in common: country populations, CODATA physical constants, every FDIC-insured bank's total assets and total deposits, NASA's exoplanet orbital periods, a year of USGS earthquake magnitudes and the seismic moments those same earthquakes encode, and World Bank life expectancies. Two conformed closely (bank assets, MAD 0.0039). Two failed by a mean-absolute-deviation threshold while the chi-squared test called them unremarkable (populations, MAD 0.0152 against Nigrini's 0.015 cutoff, chi-squared p=0.47p = 0.47). One passed the MAD band and still failed chi-squared at p=4×10−11p = 4\times10^{-11} (exoplanet periods). Two failed everything, badly, because they span less than half an order of magnitude (earthquake magnitudes and life expectancy, MAD 0.166 and 0.177). We then simulated log-uniform data across a controlled spread SS and found the deviation from Benford traces ∣sin⁡(πS)/(πS)∣|\sin(\pi S)/(\pi S)| almost exactly, landing on zero at every whole number of decades and peaking near half-integers, which is the mechanism the whole test rests on and the reason two of our eight datasets could never have passed regardless of anyone's honesty. Finally we ran the false-accusation arithmetic directly: 40,000 simulated honest Benford datasets per sample size showed the chi-squared test correctly calibrated at every nn (5.02% to 5.17% rejection against a nominal 5%, largest deviation 1.90 standard errors), while Nigrini's fixed MAD cutoff flagged 91.8% of honest datasets of size 100 and did not settle near its intended rate until nn reached the low thousands. Honest lognormal data with σ<0.3\sigma < 0.3 decades was rejected almost every time regardless of sample size. Five validations, including the closed-form digit law reproduced from first principles to 5.3 × 10−8, the club's chi-squared statistic against SciPy's to machine precision, and 2,000 powers of two checked against exact integer arithmetic, all passed. Seed 20260914. Every dataset was downloaded on 2026-09-14; none failed and none was substituted.

    Summer 2026Read 31 minSections 12

  4. ResearchMeta-analysis

    Does Metabolism Really Scale to the Three Quarter Power

    Kleiber's law says metabolic rate scales as body mass to the three quarter power. Rubner's older surface argument says two thirds. The gap between them is 112=0.0833\tfrac{1}{12} = 0.0833, and people have been arguing about it since 1932. We took one published compilation, AnAge Build 15, retrieved 14 September 2026, pulled out every species carrying both a body mass and a metabolic rate, and fitted the exponent by two methods. The sample is 627 species across four classes spanning 6.68 decades of mass, from a 0.76 g salamander to a 3,672 kg elephant. No animal was measured by us; the club has no laboratory, and the computation is the entire experiment. For mammals (n=422n = 422) ordinary least squares gives b=0.7091b = 0.7091, 95% CI [0.6936, 0.7246], which excludes three quarters at 5.18 standard errors and two thirds at 5.37, and therefore rejects both. The same 422 species fitted by reduced major axis give 0.7273 [0.7120, 0.7430], still rejecting both, 2.6% steeper, because bRMA=bOLS/∣r∣b_{\mathrm{RMA}} = b_{\mathrm{OLS}}/|r| exactly. Pooled across all four classes the two methods land on opposite sides of three quarters: 0.7132 [0.6869, 0.7396] by least squares and 0.7883 [0.7623, 0.8151] by reduced major axis. Birds alone give 0.6549 [0.6358, 0.6739], consistent with two thirds and not with three quarters, and the mammal-bird slope difference of 0.0542 is 65% of the whole disputed gap (F1,589=10.38F_{1,589} = 10.38, p=0.0013p = 0.0013). Restricting the mass window is worse still: nineteen overlapping two-decade windows of mammals return exponents from 0.5911 to 0.8701, a range 3.35 times the quantity in dispute, and mammals under 100 g give 0.5959 while mammals over 316 g give 0.7959 with non-overlapping intervals. A quadratic term is strongly supported (t=6.70t = 6.70, p=7×10−11p = 7 \times 10^{-11}), so the local slope climbs from 0.572 at 10 g to 0.864 at 100 kg and no single exponent is the right answer to the question. Both regression routines were checked against exact rational closed-form solutions, agreeing to 1.8 × 10−15. Seed 20260614.

    Summer 2026Read 32 minSections 12

  5. Field noteMeta-analysis

    How Much Carbon Can Farmland Actually Hold? A Review of the Field Trial Evidence

    Farmers are being offered money to store carbon in their soil, the practices on the menu being no-till, cover cropping and residue retention, and the rates written into contracts usually sit somewhere near half a tonne of carbon per hectare per year. We went looking for where that number comes from. Screening 22 published syntheses and long-term trial reports, we could extract 12 effect sizes carrying usable uncertainty from six publications, then pooled them with a random-effects model we wrote ourselves and checked against synthetic data first. The pooled increase in soil organic carbon is +16.2% (95% CI 11.3 to 21.2), and nobody should use that number for anything, because I2=98%I^2 = 98\% and the 95% prediction interval for a new field runs from −1.7% to +37.3%. Two results survive the heterogeneity. Practices that import carbon onto the farm hold their effect below the plough layer while practices that only rearrange carbon already there lose it, and pooled, the two groups differ by a factor of 3.3 (p<10−29p < 10^{-29}). In a single dataset of 95 paired comparisons, switching from fixed-depth accounting to equal-soil-mass accounting cuts the measured no-till sequestration rate from 0.300 to 0.141 Mg C ha⁻¹ yr⁻¹, a factor of 2.1, with nothing whatever happening in the field [1]. Soils also saturate, and a one-line model fitted to no data and needing none says that a practice adding 0.5 Mg C ha⁻¹ yr⁻¹ of input buys about 53 years before the annual gain drops below a fifth of what it started at, and then stops. We are a school club reading abstracts rather than a systematic review with two independent screeners, and §3 says exactly what that costs.

    Soil ScienceRead 38 minSections 13

  6. Field notePaper Analysis

    Ten Thousand Steps Was Never a Real Number

    In 1965 a Japanese clock company named a pedometer manpo-kei — “10,000-step meter” — and sold it into the fitness wave building around that year's Tokyo Olympics. No trial produced that number. No physiologist chose it. It was a product name, and it outlived the product by sixty years, ending up as the default daily goal on phones and fitness trackers belonging to people who have never heard of the company that invented it. In August 2025, a team led by Melody Ding pooled 57 device-measured step-count studies — the broadest review of its kind to date, spanning mortality, cardiovascular disease, cancer, dementia, depression, diabetes, and falls in a single analysis — and found something more interesting than “the number is wrong.” Compared with 2,000 steps a day, walking 7,000 cuts all-cause mortality risk by 47%, dementia risk by 38%, and fall risk by 28% [1]. But the curves do not all behave the same way. Some bend hard around 5,000–7,000 steps and barely improve after that point. Others — cardiovascular mortality and cancer mortality among them — keep falling in something close to a straight line, with no plateau in the data at all. Seven thousand is not a magic number either. It is just the most honest one anyone has offered so far.

    Public HealthRead 17 minSections 13

  7. Field notePaper Analysis

    What the Garum Vat Left Behind

    Garum was Roman fish sauce, made by salting small fish and letting them rot on purpose, and it was made at industrial scale on the Atlantic coast of Iberia for centuries. What was left in the vats afterward was never meant to be looked at closely: crushed bone, digested by its own sauce, sitting for months in salt and acid and other creatures' enzymes. In 2025 a team working at Adro Vello, a Roman fish-salting site in Galicia, sequenced it anyway. From bone fragments in a vat dated to the first to third centuries AD, they recovered enough DNA to confirm the fish was European sardine, Sardina pilchardus, and to go further than any bone shape ever could: they placed those Roman-period sardines inside the species' modern population structure. Eighteen bone samples went in; seventeen came out sequenced, one discarded; endogenous sardine DNA ran from 4% to 21% of all reads, mitochondrial coverage from 1.3× to 197.6×. Set against 108 modern reference mitogenomes spanning the species' Atlantic and Mediterranean range, the Adro Vello sardines cluster with today's Central Atlantic group, Iberia and Morocco and the French coast, but noticeably less admixed than the modern population sampled from the same waters. This note is about how you pull a population history out of something a Roman worker threw away as sludge, and what a tighter, less-mixed sardine population implies about how a fishing fleet without engines actually worked its coast.

    ArchaeogeneticsRead 20 minSections 14

  8. Field notePaper Analysis

    The Denisovans Finally Have a Face

    For 92 years the most complete archaic human skull ever found in Asia had no scientific name, because a laborer in occupied Manchuria hid it down a well in 1933 rather than hand it to the wrong army, and his family kept the secret for three generations. By the time it reached a laboratory in 2018 and was described in 2021 as a new species, Homo longi, nobody could say what it actually was in genetic terms, because its bone held no usable DNA. In July 2025, Qiaomei Fu's team found the answer somewhere stranger: the hardened dental plaque on its teeth. Fu, Cao, Dai, Bennett, Feng, Yang, Ping, Pääbo & Ji reported mitochondrial DNA and roughly 95 endogenous proteins recovered from that calculus — the first time host DNA has ever been pulled from dental plaque on a Pleistocene human fossil — and both lines of evidence say the same thing: this is a Denisovan [1]. The mtDNA carries 27 diagnostic positions matching all seven previously sequenced Denisovan genomes and none of them modern human, which is exactly backwards from what museum contamination would produce. It is also the first time anyone has had a face to put on this population, previously known only from a finger bone, a few teeth, and two isolated jaws. We rebuild why dental calculus, of all things, turns out to protect biomolecules that bone loses, and we do our own arithmetic — not the paper's — on how deep the Denisovan mitochondrial branch really runs: about 1,000,000 years back to its common ancestor with ours, roughly 1.5× as old as the 660,000-year split between Neanderthal and modern human mtDNA, which is why 27 positions out of roughly 16,569 were all it took.

    PaleogenomicsRead 20 minSections 13