Skip to content
Science Journaling Club

Volume 1, Issue 2December 2024

Winter 2025

Things spreading through a lattice, a network, a coastline and a forest, next to the solid iron ball two thousand kilometres beneath our feet and a compound built from 0.3 milligrams of an element that was decaying while chemists worked with it.

This issueSJC 1.2
Published
December 2024
Articles
8
Research
5
Field notes
3
With code
7

Contents

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

  1. ResearchReplication

    Measuring a Universal Constant on a Laptop: The Site Percolation Threshold

    Fill the cells of a square grid at random. Each cell is occupied with probability pp, independently. Below a certain density the cells form scattered islands. Above it, one cluster reaches from top edge to bottom. That density, on an infinite grid, is the site percolation threshold. The square lattice has no closed form for it, so the constant has to be measured. We measured it. Our experiment is a computation, and nothing was observed in the physical world: a club program ran 114,520 Newman-Ziff union-find sweeps on lattices from L=16L = 16 to L=1024L = 1024, in 526.5 seconds of wall clock, seeded from 20251215. Extrapolate the half-crossing point p∗(L)p^*(L) to infinite size with the exact two-dimensional exponent 1/ν=3/41/\nu = 3/4, and the intercept comes out at pc=0.5928171±0.0001110p_c = 0.5928171 \pm 0.0001110, the error bar bootstrapped from the sweeps themselves. The accepted value is 0.59274605. We sit +0.0000710 above it. Call that +0.64 of our own error bars. The disagreement first appears in the fifth decimal place, and three checks stand behind the number. The union-find matched a separate flood fill on 11,400 random configurations, with zero mismatches, and the pipeline reproduced the exact crossing polynomial of the 3×3 and 4×4 lattices to within 0.5 standard errors at every point tested. And the crossing probability at the accepted threshold settled onto a size-independent 1/2, as conformal field theory says it must, moving from 6.60 standard errors high at L=16L = 16 to 0.08 at L=256L = 256. The fractal dimension of the largest cluster came out at 1.8823 against the exact 91/48 = 1.8958, a shortfall we keep and explain rather than fit away. Including our smallest lattice moves the answer to 0.5930250, 2.92 error bars out, and that single modelling choice is the largest one in the study.

    Winter 2025Read 25 minSections 12

  2. ResearchOriginal Research

    The Same Disease on Four Different Networks

    Give four populations the same disease and the same average number of contacts each, then change nothing but the shape of the contact network. Nobody was infected, contacted or observed. The computation is the experiment. It ran on a school laptop, and a rerun finishes in minutes. We simulated stochastic SIR epidemics on four graphs of 10,000 nodes with mean degree fixed at 6, a triangular lattice, an Erdős-Rényi random graph, a Watts-Strogatz small world and a Barabási-Albert scale-free network, at 600 runs per configuration across fourteen transmission rates, plus refinement, validation and convergence sweeps, 80,700 simulated epidemics in all. At a matched transmissibility of T = 0.50 the four networks agreed on the final attack fraction to within a factor of 1.06 and disagreed about everything else: peak prevalence ranged from 0.0602 on the lattice to 0.4406 on the scale-free network, a factor of 7.32, and time to peak ran from 12.8 steps to 136.6, a factor of 10.69. Measured epidemic thresholds spanned a factor of 5.14, from Tc = 0.0728 on the scale-free network to 0.3741 on the small world, against a well-mixed prediction of 0.1667 for all four. The random graph landed on the Molloy-Reed value 0.1665 to within 0.0014; the lattice and the small world sat 1.76 and 1.89 times above it. Validation: the mass-action limit reproduced the Kermack-McKendrick final size equation to within 0.0074 at every R0 above 1.25 and to 0.0011 above 1.5, and a constant-infectious-period lattice recovered the exactly known triangular bond percolation threshold 2 sin(π/18) = 0.34730 as 0.33068 ± 0.00875, 1.90 standard errors low, with finite-size scaling across L = 40 to 140 showing the gap closing as L−3/4 exactly as percolation requires. Seed 20251215.

    Winter 2025Read 28 minSections 12

  3. ResearchOriginal Research

    When Most People Infect Nobody: What Overdispersion Does to an Outbreak

    An outbreak's average reproduction number, RR, does not say how that transmission is shared out. We fixed R=2.5R = 2.5 and swept the negative binomial dispersion parameter kk across seventeen values from 0.01 (extreme superspreading) to 10,000 (indistinguishable from Poisson, no superspreading at all), running 40,000 independent branching-process replicates per value and checking every simulated extinction probability against the exact analytic root of the offspring distribution's probability-generating function. They agreed everywhere: the largest deviation across all seventeen cells was 2.26 standard errors, and none exceeded 3. At the realistic value k=0.1k = 0.1, reported for SARS and SARS-CoV-2, a lone introduction died out on its own 86.11% ± 0.17 percentage points of the time. At k=10,000k = 10{,}000, the near-homogeneous case with the identical average, it died out only 10.51% ± 0.15 points of the time, matching the classical Poisson branching-process result (0.1074) to 3.65×10-5. Same average transmission, nine-fold difference in how often the chain simply stops. Among the cases that transmit at all when k=0.1k = 0.1, the most active 10% account for 81.9% of all onward infection. We then compared two ways of spending an identical unit of control effort, defined as an equal fractional cut to the uncontrolled mean: thinning every case's transmission uniformly, against capping only the largest gathering-driven events to hit that same mean. Across thirteen effort levels, uniform thinning produced a higher extinction probability than capping at eleven of them, by up to 5.2 percentage points (z=19.4z = 19.4) at 45% effort, reversing only at the very edge of guaranteed elimination. No person, gathering or pathogen was involved in any of it; every number above is the printed output of a program the club wrote and ran on a laptop. Master seed 20251217.

    Winter 2025Read 24 minSections 11

  4. Field notePaper Analysis

    Solving a Ten-Year Marine Murder Case: What Actually Killed Five Billion Sea Stars

    Sea star wasting disease began in 2013. It emptied the Pacific coast of North America of sunflower sea stars. Roughly 3,000 km of coast. The prime suspect for ten years was a virus. Wrong suspect. In August 2025 a team led by Melanie Prentice named the killer: Vibrio pectenicida strain FHCF-3, cultured from the coelomic fluid of a diseased star, able to reproduce the disease in healthy animals and recoverable from them afterwards [1]. The evidence is a plain walk through Koch's postulates, done in flowing seawater. This field note reconstructs the case. It follows the filtration step that quietly killed the virus hypothesis, and then goes further than the paper does. We built a deliberately simple three-species model of a kelp reef, our arithmetic and not theirs, and it says that a 96.2% loss of sea stars flips the modelled forest into an urchin barren within 2.7 years. Putting the kelp back inside forty years costs more still. 55% more sea stars than were there before the outbreak. A second club model walks an epidemic down a coastline at 8.22 km per day. It returns a reproduction number of 1.57. That number is too small to explain the mortality anyone observed. We take the mismatch seriously. The strongest published objection to the bacterial result gets its own section.

    Disease EcologyRead 34 minSections 12

  5. ResearchOriginal Research

    Why Small Fires Are Common and Big Fires Are Not Rare Enough

    Trees grow at random, lightning falls at random, and whatever connected patch the bolt lands in burns. Those two rules make the Drossel-Schwabl forest fire model, which the literature quotes everywhere as a clean case of self-organised criticality, complete with a power-law distribution of fire sizes. We tested the claim rather than repeating it. The club wrote the model and ran it on a laptop, and since no forest was observed and no fire measured anywhere, the computation itself is the experiment. Across five values of θ=p/f\theta = p/f spanning two decades and three lattice sizes we recorded 416,000 fires, 120,000 of them in a main run at 512×512512 \times 512 with θ=500\theta = 500. We fitted a truncated discrete power law by maximum likelihood, after first checking the estimator on synthetic data with a known exponent, where it recovered the truth in all five tests with a largest zz of 1.61. The same synthetic data fitted the popular way, a straight line through a log-log histogram, came out 35.2% low on a known τ=1.5\tau = 1.5, which is the sort of error nobody notices when the true answer is unknown. On the fire data, the main-run exponent over s∈[4,500]s \in [4, 500] is τ=1.1269±0.0025\tau = 1.1269 \pm 0.0025 (moving-block bootstrap), close to the 1.151.15 the pre-2002 literature reports. The power law is nonetheless rejected: the Kolmogorov-Smirnov distance of 0.00824 gives p<0.005p < 0.005 over that window, and over the full range the distance is 26× the 95th percentile of what the fitted law itself produces. The exponent is not a constant of the model either, which is the part that unsettled us. It climbs from 1.0394 at θ=50\theta = 50 to 1.1741 at θ=5000\theta = 5000, a drift of +0.069 per decade, with χ2=466.3\chi^2 = 466.3 on 4 degrees of freedom against a constant. Two things did land: the steady-state identity ⟨s⟩=θ(1−ρ)/ρ\langle s \rangle = \theta(1-\rho)/\rho held to 0.14%, and our tree density at θ=125\theta = 125, 0.38073, sits 0.9 standard errors from Grassberger's tabulated 0.379837. Our lattices are three to four orders of magnitude smaller in area than the ones that reopened the criticality argument, so we can measure the drift and cannot settle where it stops. Seed 20251124.

    Winter 2025Read 32 minSections 12

  6. ResearchOriginal Research

    Can You Tell a System Is About to Tip Before It Does

    A system approaching a fold bifurcation recovers from disturbance more and more slowly, and that slowing is supposed to be readable in ordinary noisy measurements before anything visible happens. The club has no laboratory, so we tested the claim by simulation, which is in any case the only place where the control can be run. In 38,600 simulated trajectories of a cusp normal form driven slowly toward its fold under process and observation noise, the signal is unmistakably there: mean lag-1 autocorrelation climbs from 0.331 to 0.691 and variance triples, both far outside their standard errors, and both match the analytic Ornstein-Uhlenbeck prediction once the known bias of a 100-sample detrended window (0.8722, measured separately on a stationary control) is divided out, with a corrected ratio of 1.002 at the start of the run. The measured recovery rate lands 0.24% from κ=3x∗2−1\kappa = 3x^{*2}-1 and 0.76% from the exact value for the Euler scheme we actually integrated, which brackets the fit between the two predictions. Usefulness is another matter. A textbook one-sided Mann-Kendall trend test at nominal α=0.05\alpha = 0.05, run on overlapping sliding windows the way it usually is, fires on 30.17% ± 0.84% of controls that are not approaching anything, 30 standard errors from nominal. Removing the window overlap restores the nominal rate (5.20% ± 0.41%). The remaining problem does not go away. A control driven at the same rate that stops 10% short of the fold triggers a calibrated 5% detector on 20.53% of runs against 21.07% power on runs that genuinely tip, an AUC of 0.502. Across ten configurations spanning noise, driving speed, window length and observation noise, the mean gap between detection power and the near-miss alarm rate is 0.0127. The indicator measures how close a system is to a threshold. It says nothing about whether the system will cross it. Seed 20251217.

    Winter 2025Read 33 minSections 12

  7. Field notePaper Analysis

    The Iron Ball at the Center of the Earth Keeps Changing Its Skin

    Nobody has ever touched Earth's inner core, and nobody ever will. Every fact we own about it arrives secondhand, carried the last 5,150 kilometres by a seismic wave. In February 2025, a team led by John Vidale re-examined a dataset built for a different purpose — 121 repeating earthquakes near Antarctica's South Sandwich Islands, recorded between 1991 and 2023 by two seismic arrays in the far north — and asked a narrower question than usual: when the inner core's own drifting rotation brings it back to a position it already occupied years earlier, do the two recordings match [1]? At one array, Yellowknife (YKA), whose waves graze the inner core's outer few hundred kilometres, some pairs recorded between 2004 and 2008 did not match. At the other, Eielson (ILAR), whose waves bottom out deep near the centre, the same pairs matched fine [1]. The clean explanation is that whatever changed did not change everywhere — it changed near the boundary, on a timescale of a few years, while the deep interior stayed put. We rebuild the geometry that makes this comparison possible, work out why a solid iron sphere is not supposed to do this, and then do the club's own arithmetic: the inner core is about 35% the volume of the Moon, and the thin, structurally softer "mushy" layer that a separate 2017 study found elsewhere on the same boundary is only about 0.3–0.7% of the inner core's radius — a few kilometres of restless skin wrapped around twelve hundred kilometres of otherwise very patient iron.

    GeophysicsRead 23 minSections 13

  8. Field notePaper Analysis

    The Sandwich Compound That Raced Its Own Half-Life

    In February 2025 a team working across Lawrence Berkeley National Laboratory and Oak Ridge reported the first structurally confirmed carbon-berkelium bond: a metallocene, an ion clamped between two flat carbon rings like the meat in a sandwich, built around the intensely radioactive, synthetic element berkelium [1]. What makes this remarkable is less the molecule than the material it is made of. The whole synthesis ran on 0.3 milligrams of berkelium-249, an isotope with a half-life of roughly 327 days [2] that the world produces in batches of about 13 milligrams every couple of years [9], and by the researchers' own account, the 0.3 mg they had on hand already came mixed with 0.2 mg of californium-249 — the isotope's own decay product — before the reaction even started [9]. This note is about three things: what a "sandwich compound" structurally is, why doing wet chemistry on a sample that is actively transmuting into a different element counts as an extraordinary experimental feat, and what it means that the resulting berkelium-carbon bond turned out to hold onto real covalent character deep into a part of the periodic table where chemists mostly expected ionic, lanthanide-like behaviour. Along the way we run our own numbers: from the reported 0.3 mg/0.2 mg berkelium/californium mixture and the published half-life, we back out roughly how long the isotope had been sitting since it was last purified, and we hold 0.3 milligrams up against a few things you can picture without a periodic table.

    Actinide ChemistryRead 19 minSections 12